BIOS: A Study of Creation (with CD-ROM)

At a constant g, the initial bifurcation occurs at g = 2.0719 for n, and at g = 2 for smaller or larger initial values. The number of iterations required to induce bifurcation also depends on the initial value, and it is larger for n than for other initial values. When g is a function of time, the g at which bifurcations emerge also depends on the initial value, but it varies even more as a function of the rate of change ofg. 35 Patel, M. and Sabelli, H. (2003). Autocorrelation And Frequency Analysis Differentiate Cardiac And Economic Bios From 1/F Noise. Kybernetes 32: 692-702.

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unchosen branches of the unifurcation in the upper and lower paths are continued by bands in the chaotic phase, as well as by intrachaotic periodicities. The four paths that originate in the unifurcation meet at g = 4.6033... The path originating in the chosen branches of the upper and lower paths meet at At = 2n, while the paths that appear to continue the unchosen branches meet at A t = 0. (4) Bios: At this point the range of At expands drastically, both positively and negatively, and generates a pattern that we call biotic. Bios appears random but it is highly organized, as it can be readily shown with phase portraits, recurrence plots, and wavelet portraits. Bios has much larger magnitude than chaos, and is highly self-correlated (Pearson's coefficient +0.99). Biotic series are aperiodic and highly sensitive to initial conditions, like chaos, but in addition, their pattern is punctuated and episodic ("complexes") rather than static and uniform, and shows novelty, defined as less recurrent than in randomized copies. This biotic pattern closely resembles the pattern of heart rate variation. (5) Bioperiodicity and divergence: As chaos, bios includes periodicities. In contrast to chaos, bios includes only period 2 and 4, and these periods are highly sensitive to initial conditions. For this reason, we call them "bioperiodicities". These periods occur when g equals an odd multiple of n; a prominent period 4 also occurs at g = 5.4. When g equals an even multiple of pi, the biotic pattern is transiently interrupted by roughly linear flights in the positive or negative direction (divergences). When g is kept constant, divergences are flights towards infinity ("infinitations"). If g changes with iteration, divergences are "shifts" from one biotic pattern to another at a different level. In the diversifying equation, divergences are transient "leaps". With return the original level, divergences also occur near other significant values of the gain, such as g = 0.5TI2 (4.9114 to 4.93903) and g = 23 (7.9983 to 8.0101). Divergences are positive or negative, according to the initial value; minor changes in g and Ag also change the direction of divergence. Plotting the differences between consecutive values reveals bifurcation trees including periodicities and chaos within the divergences (Fig. 3.7); the tree starts with a linear increase for g = 2 n (AA = 2 n), and with a bipolar period 2 for g = 4.9114 and for g = 8. Shifts and leaps become progressively smaller at larger values of the parameter.

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Fig. 3.7 Leaps in series. There are leaps with one and with two steady states, which we observe in the plots of differences between consecutive terms.

(6) Late transient equilibria: Joel Gordon36 has discovered that when these recursions are run with a wide diversity of initial values and for very large number of iterations, some trajectories enter for long time into steady states, from which eventually they exit in the usual manner. I presumed these represent trajectories that have reached a multiple of 2n. When g increases in each iteration, we observe all the above patterns in the same time series. We give the name of Won to this sequence: fixed point, bifurcation cascade including unifurcation, logistic-like chaos with prominent period 3, chaos with prominent period 4, bios and divergence. Logistic patterns reappear at various points in the bions. Similar series are generated by the diversifying equation (Fig. 3.8). The diversifying equation differs from the process equation in the following way: (a) It has no steady state, but rather there is an initial 36 Gordon, J. (2003). Using developmental trajectories to explore "bios". Society for Chaos Theory in Psychology and Life Sciences Conference, Boston, MA.

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sudden increase followed by an exponential decrease; (b) this exponential decrease continue during the bifurcation cascade and the chaotic phase; and (c) divergences are leaps, such that the time series returns to its initial level, while in the process equation there are shifts.

Fig. 3.8 A mathematical development. The diversifying equation generates a sequence of patterns as the parameter Jt increases (X axis). Different scales are used to present low amplitude chaos (left) and higher amplitude bios (right).

3.8 Biotic Irreversibility and Global Sensitivity to Initial Conditions Bios, bioperiods, and divergences show global sensitivity to initial conditions: change in range and polarity with minor changes in initial condition. Nonstationarity, irreversibility, and global sensitivity to initial conditions differentiate bios from chaos. In chaos there is only local sensitivity to initial conditions (change in trajectory but not in basin of attraction) (Fig. 3.9). Process chaos shows long term correlation between series with different initial values as contrasted to logistic chaos in which correlation decays just as observed in the case of random series. Biotic series show much faster decay of correlation than process chaos. (Fig. 3.10). Biotic trajectories, bioperiodicities and leaps are also extremely sensitive to changes in the rate of change of the gain. Irreversibility is a property of bios that can be demonstrated by changing the gain in a nonlinear fashion. If the gain first increases and then decreases, the time series evolves from an initial steady state to greater complexity and then devolves back to simpler patterns (Figs. 3.11 and 3.12). A remarkable feature of bios is revealed by these equations. If

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the series evolves up to chaos, a subsequent decrease in the gain leads back to the initial steady state. In contrast, if the series reaches the biotic regime, a subsequent decrease in gain does not lead back to the starting point. One is tempted to relate this mathematical irreversibility of bios, absent in chaos, to the irreversibility of physical processes.

Fig. 3.9 Bios and infinitation show global sensitivity to initial conditions while chaos does not. Time series (N =90000) generated by the process equation at constant gain 4.1 (chaos, top), 4.61 (bios, middle) and 2 n (infinitation, bottom). Initial values: Left = 1.000; Right = 1.001, except for chaos, in which an initial value of 5 is used to highlight the difference between locally sensitive chaos and globally sensitive bios.

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Fig. 3.11 Irreversibility in mathematical bios generated by the cosine process equation. Left: If time is reversed during chaotic phase, paths overlap significantly. Right: After reaching bios, time reversal dramatically changes path and initial value.

Fig. 3.12 "Lifeforms" generated by a process equation computed with a gain that periodically increases and decreases (sinusoidal line). If the gain surpasses the threshold for bios, there is no complete reversibility to the initial value (left). In contrast, if the time series reaches only chaos, there is reversibility (right).

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3.9 Numerical Archetypes of Opposition Pointing to numerical archetypes, 2N and TT.N appear repeatedly as significant outcomes and gains in these biotic equations. At g = 2, the time series splits into period 2; at g = 22, period 12 develops; at g = 23, there is infinitation. Period 6 (= 2*3) and period 4 are prominent during chaos, and period 2 and period 4 bioperiodicities occur multiple times during bios. The sine recursion initially converges to integer multiples of n and the cosine recursion converges to 0.5 n (or 1.5 n, 2.5 n, etc). The diversifying recursion At+i = At + sin(At *k*t) has no steady state, but instead there is an initial sudden increase followed by an exponential decrease that approaches nil for the sine recursion and at nil2 for the cosine recursion at the point of bifurcation. This association between n and exponential decay is unlikely to be the result of chance given Euler's famous equation em = -1, and e' = deVdx, defining exponential decay. Even multiples of n mark the boundaries of basins of attraction; odd multiples of n are the initial fixed points. Unifurcation occurs when At = 1.57r and 0.5TI (for the sine equation with initial values between 0 % to 2 TC), and a logistic-like development starts from each branch.. Bios emerges abruptly when the preceding gradual expansion of chaos reaches the boundaries of the basin 0 n and 2 n. As gain, n produces unifurcation; the biotic phase is punctuated by infinitations at g = 0.5n2, 2JI, 4 JI, 2Nn, and by period 2 at g = 3rt, 5n, etc. This prominence of K is understandable as it represents the ratio between linear and circular infinity. Linear and the circular order are incommensurable. W when related in a static fashion, they generate the transcendental37 ratio n. Combined as a process in a recursion, they generate n, then multiple harmonies (periods), chaos and bios. Bipolar feedback, the mathematical generator of bios, embodies these two fundamental forms of order, linear and circular, have dominated science throughout the centuries.38 A line is open; it is unidimensional infinite. A circle is closed; it is two37

A transcendental number is an irrational number that is not the solution of any single-variable polynomial equation whose coefficients are all integers. Recognizing that jt was irrational, not a ratio (logos), the Greeks called n the "alogon" (unutterable). Also the Tao could not be named. 38 Gould, S. J. (1987). Time's Arrow Time's Cycle. Harvard University Press. Cambridge, MA.

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dimensional infinite. A line is ordered, it is a simple lattice, 1 < 2 < 3 etc. A circle is an infinite group, a closed set in which each point has an inverse -its diametric opposite. Lattice and group are two of the three mother structures of mathematics (Chapter 10). These two forms have are embodied in action and information. Opposition is connected with both twoness and n. Two abstracts the pairing of opposites. Sine and cosine portray orthogonal axes that Euler later related with his magnificent formula eie = cosB + i sine in which Q is an angle, i = V-l, defining the imaginary numbers, n describes numerically the relation between diametric opposites. The circumference 2n represents an infinite number of oppositions. Action and information are the complementary opposites that co-create pattern in the process equation. The temporal order of action is a universal asymmetry, more fundamental than mechanical reversibility. It is complementary to the symmetry of information, the simplest and fundamental form of which is the complementarity of opposites. Action is linear and information is circular. Summarizing: biotic development includes numerical archetypes, starting with % (or its multiples) as an initial asymmetric steady state, 2N periods, period 6 and later on period 3 (as in the logistic equation), period 4 during the periodic, chaotic, and biotic phases, and infinitations. 3.10 Different Types of Bios There are multiple forms of bios. The process equation with delay39 A m = At + gt * sinAn (3.7) generates biotic patterns closer to those observed in heartbeat interval series than those generated by the process equation; delay is to be expected in feedback processes. Cardiac patterns are bounded, i.e. maintained within limits by homeostatic processes. Bounded biotic series can be constructed in a 39

Sabelli, H. (1999). Process theory: mathematical formulation, experimental method, and clinical and social application. Toward New Paradigm of System Science. P. Y. Rhee (ed). Seoul: Seoul National University Press, pp. 159- 201.

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number of different ways. One type of equations that we call homeostatic rely on the addition of a negative feedback term to the recursion, such as A,+i= A, + g *sin(At) - 0.01*(A,- 31*TI).

(3.8)

More interesting are bounded forms of bios generated by the coexistence of opposites by bipolar feedback such as in the homeobiotic recursion (Fig. 3.13 left) (3.9) At+i = At + sin(At.i* Jt) - cos(At_i /Jt). This recursion illustrates a process that can maintain homeostasis without negative feedback. While the biotic patterns of the heart are bounded, the biotic patterns of economic processes are unbounded and trended (Fig. 3.13 right; see also Chapter 15). These trended biotic patterns, which we call parabiotic, are generated by the asymmetric process equation40 At+1 = A, + g * (q + sinAt). (3.10) In this recursion, the gain g represents the energy of the bipolar feedback and q (which ranges between 1 and -1) provides asymmetry. The complexity of pattern increases with the intensity (energy) of the feedback gain, from steady state to periodicity to chaos to bios. Complex biotic patterns occur only when the opposite components of bipolar feedback are symmetric or slightly asymmetric. When asymmetry is introduced, patterns become simpler; intense feedback generates parabios (bios with a linear trend), as observed in many economic processes (Fig. 3.13). As the asymmetry is progressively increased, the pattern becomes increasingly linear, reaching steady state at the extreme of unipolarity (q = 1 or q = -1). Asymmetry allows the appearance of periodic and chaotic patterns at lower gain (Fig. 3.14). High asymmetry produces simple patterns even at high gain.

40

Sabelli, H. and Kauffinan, L. (1999). The process equation: formulating and testing the process theory of systems. Cybernetics and Systems 30: 261-294.

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Fig. 3.13 Comparison of homeobiotic series with heartbeat series, and parabiotic series with the time series of an economic index, the daily Dow-Jones Industrial Average.

Fig. 3.14 Asymmetric process equation: This graph illustrates the complex pattern created in the case of a low gain (g = 3.2) by changes in the informational asymmetry q. When the opposites are symmetric (q = 0), there is period 2. Adding a small asymmetry engenders greater complexity (chaos). With even greater asymmetry, the pattern reduces to steady state.

The trifurcation equation41 A, + i=A t -A t 4 + gt*sin(A t )

(3.11)

explores processes in which the significant factor is change in action AA = At - At_i (information), rather than the action At itself. For instance, 41

Sabelli, H. (1999). Process theory: mathematical formulation, experimental method, and clinical and social application. Toward New Paradigm of System Science. P. Y. Rhee (ed). Seoul: Seoul National University Press, pp. 159- 201.

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sensation (psychobiological information) is a function of a change in the intensity of the stimulus rather than of its absolute intensity. In these equations, the two initial values generate three strands that are symmetrically distributed around 0, then approach and separate in a rhythmic fashion (period 6 bios). The initial braid shows many complexities, including expansions and multifurcations (Fig. 3.15). In these equations, periodic trajectories and chaotic ones are also globally sensitive to initial conditions and to the rate of change of the gain; particularly dramatic are the differences in the number of branches in the prebiotic braid and changes in the amplitude of the biotic stage.

•

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Fig. 3.15 Trifurcation equations: Top graph shows series at low gains. Lower graph shows series at both lower and higher gains (chaos can not be distinguished on this scale).

3.11 Biotic Diffusion and the Biotic Hypothesis A fundamental property of bios is its expansion beyond the limits of the basin of attraction within which chaos remains. The expansion of chaotic trajectories has been studied by Arnold,42 Chirikov,43 Geisel and 42

Arnold, V. I. (1965). Small Denominators. I. Mappings of the Circumference onto Itself. Am. Math. Soc. Translations 2 (46): 213-284. Providence: American Mathematics Society. 43 Chirikov, B. V., Lieberman, M. A., Shepelyansky, D.L., and F. Vivaldi. (1985). A Theory of Modulational Diffusion. Physica 14D: 289-304.

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Nierwetberg,44 and others. The trajectories are similar to those generated by a stochastic process, including mean walking distance ~ t1/2. This is called deterministic diffusion,45 or deterministic Brownian motion. This diffusion displays fractal features.46 Korabel and Klages showed that the smooth nonlinear climbing sine map exhibits deterministic diffusion. They found that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the control parameter. This is an important field far from my own; I refer to their studies rather than attempting unscholarly paraphrases. Let me only point out three salient facts: (1) Bios occurs also when diffusion is limited. As exemplified by homeobiotic equations diversification (Chapter 4) occurs in excess of and even in the absence of diffusion. Heartbeat interval series, the paradigm of bios, do not diffuse; heart rate is kept within homeostatic boundaries. (2) Growth and differentiation are very different from diffusion. Diversification can exceed diffusion (Chapter 4). (3) Expansion is an essential mechanism regarding creative processes. Many creative phenomena involve expansion such as evolving species, economic development, and the universe itself. Expansion organizes chaos to generate bios. 7 This is a generic process that contributes to creative evolution (biotic hypothesis, Chapter 8). Recursions of trigonometric functions computed modulo 2n or modulo 1, such as the one-dimensional circle map48 0n+i = 0n + Q (K/27t) * (sin2rc 0n), modulo 1, and the standard map (Chirikov-TaylorGreene map) In+i = In + K * (sin9n), modulo 2n, 6n+i = 0n + In+i = In + 0n + K *(sin0n), modulo 2n, do not generate bios and related phenomena; they only produce chaos.

44

Geisel, T., and Nierwetberg, J. (1982). Onset of Diffusion and Universal Scaling in Chaotic Systems. Physical Review Letters 48: 7-10. 45 Daniel Myers a n d coworkers have developed a new deterministic diffusion model for collective violence in which h e analyses opposing forces such as provocation and repression as separately diffusion phenomena. His results show riots as a series of interdependent events, with the mass media contributing to create and sustain. Myers, D . J. (2000). The Diffusion of Collective Violence: Infectiousness, Susceptibility, and Mass Media Networks. Amer. J. Sociology 106:173-208. 46 Korabel, N . a n d Klages, R. (2002). Fractal Structure of Normal and Anomalous Diffusion in Nonlinear Nonhyperbolic Dynamical Systems. Physical Review Letters 89: 214102-1-214104. 47 Sabelli, H. (ed). (in press). Bios Data Analysis. J. Applied Systems Studies.. 48 Arnold, V. I. (1965). Small Denominators. I. Mappings of the Circumference onto Itself. Am. Math. Soc. Translations 1 (46): 213-284. Providence: American Mathematical Society.

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Fig. 3.16 Time series generated by a kinetic computation of the Chirikov system of equations xn+1 = xn + k*sin(9n), and 9n+i = 9n + xn+1. The biotic pattern is preceded by a complex periodic braid and multiple chaotic branches as observed with the trifurcating equation. Top: low gain. Bottom: high initial gain and higher rate of increase in gain. In figures, xn+1 is replaced with pt+i, k is replaced with gt, and 0n+1 is replaced with xt+i.

Fig. 3.17 Direct transition form bifurcation to bios is observed with equation At+1=At-At.1+gt*cos(At) with initial conditions A^O, and gt=0+0.00005*t.

A direct transition from a single bifurcation into bios is observed with the equation shown in Fig. 3.17 only for certain initial values.

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3.12 Logistic Development The logistic equation At+1 = A t * g * ( l - A t ) .

(3.12)

describes an important generator of natural and human processes, namely the opposition between growth and environmental depletion in closed systems. Such opposition generates differentiation. When May49 pointed this out, he launched a revolution in our understanding of creativity. Up to then, a complex outcome was assumed to require a complex generator. The creative process is a cascade of bifurcations into opposites 2, 22, 23, 2 4 ... , 2N generated by linear opposition to each action. Bifurcation starts at g = 3. These bifurcations are asymmetric.50 The cascade of bifurcations continues doubling the period until g reaches 3.5699456... (Feigenbaum point), a threshold beyond which the cascade of bifurcations ceases and chaos emerges. The American physicist Mitchell Feigenbaum51 also discovered a constant relation between the values that separate two bifurcations in the cascade, Feigenbaum's constant 4.6692..., also labeled "universality". Chaos can be observed up to g = 4 (at which point the recursion blows up). If one thinks of twoness as the numerical form of opposition, one would regard g = 22 as suggestive that we should ask ourselves how the flight to infinity is linked to opposition, rather than taking the specific value of g at which it occurs as meaningless. Likewise, we may consider the fact that the fixed point is 1/2 and bifurcation occurs when g = 3. To this traditional description of the logistic sequence, let us add the transitional phase between the periodic and the chaotic regimes in which period 2 and chaos overlap which we identify by calling it "period 2 chaos".52 Its existence is significant because it indicates that different attractors overlap. From a process perspective, the overlap of simple and complex components is an essential feature of creative processes. In 49 May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature 261: 459-467. 50 Betraying a bias towards the static, many books depict the cascade as symmetric. 51 Feigenbaum, M. (1983). Universal behavior in nonlinear systems. Physica D: 16-39. 52 Patel, M. and Sabelli, H. (2003). Autocorrelation and Frequency Analysis Differentiate Cardiac and Economic Bios From 1/F Noise. Kybernetes 32: 692-702.

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deterministic dynamics, attractors are often described as having mutually exclusive basins. In standard dynamic equations, the gain is kept constant. The process perspective leads to computing the logistic recursion with variable feedback gain (3.13) At+1=At*k*t*(l-At), a recursion already investigated by Trulla and coworkers,53 it generates a time series of increasingly more complex pattern, resembling the bifurcation diagram of the standard logistic equation, except that the steady state is replaced by an increasing trajectory that reaches the fixed point 0.5 at the point of bifurcation (Fig. 3.18 left). The logistic walk (Fig. 3.18 right) (3.14) At+1 = At + A t * g t * ( l - A t ) shows a steady state, and evolves into periodicity, chaos and blow-up at lower g. We give the name of logon to this sequence: fixed point, bifurcation cascade, and chaos with prominent period 3. Logons appear as part of the development that leads to bios (Fig. 3.19), as well as in many other equations, such as: A!=0.01, gt=300+0.005*t At+, = At+ 0.05*[gt - (At2)], Ai=l, gt=0.00005*t At+1 = At+At*gt*sin(At), A^l, gt=0.00003*t Am = A t + [gt*sin(At)*(10 - At)], Ai=l, gt=6+0.0001*t. At+1 = At+[(l/At)*gt*sin(At)],

Fig. 3.18 Logistic developments without (left) and with (right) a conserved term.

53

Trulla, L. L., Giuliani, A., Zbilut, J. P., and Webber, Jr., C. L. (1996). Recurrence Quantification Analysis of the Logistic Equation with Transients. Phys. Lett. A 223: 255-26.

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Fig. 3.19 Logistic-like At+1=At+gt*sinAt.

developments

generated

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As in the case of the process equation, computations of the logistic equation that involve delay or the difference between successive terms generate trifurcations followed by a beautiful braid. These two equations do have an initial fixed point, and converge to attractors. Some examples include: At+1 = A t + [At*gt*(l-At4)]; At+1 = gt*[l-(At-At.i)]*(At - A M ); At+1 = At-At.! + [gt^l-CArAt.O)]. 3.13 Period Three Implies Harmony: Sarkovskii's Theorem Through the study of the logistic equation, Yorke and Li,54 in the article that gave chaos its name, demonstrated that any equation consisting of a single changeable parameter that cycles among 3 stables states at one point will necessarily show periodicities of other numerical values. Actually, this theorem is part of a larger theorem advanced earlier by the Ukrainian mathematician Oleksandr Sarkovskii.55 Sarkovskii introduced the ordering: 3 < 5 < 7 < 9... infinity < 2 x 3 < 2 x 5 < 2x7... infinity < 22 x3 < . 22 x5 < 22 x7... infinity < 2 N x3 < ... 2 N x5 < 2 N x7...infinity < 2N < ... 8 < 4 < 2 < 1. If a continuous function has a periodic point of period m and m < n in the above ordering, then / also has a periodic point of period n. Thus period 3 implies all others.56 54

Yorke, J. A., and Li, T. (1975). Period Three Implies Chaos. Amer. Math. Monthly 82: 985-92. Sarkovskii, A. N. (1964). Coexistence of Cycles of a Continuous Map of a Line into Itself. Ukrain. Mat. Z. 16: 61-71 (in Russian). 56 Sarkovskii's theorem holds for discrete systems on the real line; it does not hold for two dimensional maps or for mappings of the circle to itself. 55

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Presumably, natural processes evolve in the opposite direction, from 1 to 2 to 2N and so on. The two extremes of the Sarkovskiian series, period 3 and the bifurcation cascade, occur in nature, indicating that the Sarkovskiian sequence is not "just mathematical". In Li and Yorke's metaphor, the term chaos refers to the existence of all possible periodic orbits. Given the psychological implications of harmony and chaos, it is interesting that the demonstration of an infinite number of periodicities be interpreted as chaos.57

T

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Fig. 3.20 Biotic-like development with prominent period 4 and expansion during the chaotic phase, generated by logistic-like recursions. These equations, however, do not produce bios. The recursion on the right was described by Puu58 to model economic processes. Note the similarity with the sine reiteration described in Chapter 8, except that the latter does not blow up.

There is a noteworthy association between logistic chaos and period 3. In addition to the prominent period 3, the distribution of rise and fall sequences (to be described in Chapter 4) is triadic. In contrast, the bipolar opposition that generates bios may be associated with the prominent period 4 observed in this recursion, and with a tetradic distribution of rise and fall sequences. A bipolar opposition determines a cross of opposites, a quaternity. Notwithstanding, logistic-like recursions can generate time series (Fig. 3.20) in which the initial cascade is similar to that observed with bipolar feedback. However, there is no unifurcation after the initial bifurcation and the series blows up instead of developing 57

The term chaos was even adopted by sociologists, psychiatrists and psychologists, including the Society for Chaos Theory in Psychology and the Life Sciences, which I contributed to found. In retrospect, I wish we had chosen harmony instead. 58 Puu, T. (2000). Attractors, Bifurcations and Chaos. Berlin: Springer.

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into bios. Unifurcations are noted after period 4 (Fig. 3.20). Computing time series with positive and negative initial values shows separate trajectories up to At = 0, at which point both series overlap. 3.14 Comparing Biotic and Logistic Development The logistic model undoubtedly taps fundamental natural processes, because logistic-like bifurcation cascades occur in many recursions. Bifurcation cascades are also widespread in nature, as illustrated by sequential cell division from the egg. However, the fact that so many different generators can produce bifurcation cascades and even the entire logon indicate that observing such pattern in nature does not point to a logistic generator. The logistic generator only produces chaos, and chaos does not display growth, novelty, diversification, and episodic patterns as observed with empirical creative processes. The logistic equation portrays in a simplified manner how limits to growth resulting from scarcity can generate complex, non-periodic, nonlinear oscillations. The logistic model has roots in the political speculations of1 the British economist and churchman Thomas Malthus (1798). His main thesis was that human misery is inevitable because population tends to grow geometrically while resources grow arithmetically. Revealing his particular psychology and ideology, he did not seek a solution but rather thought that misery and war were the unavoidable outcomes of divine creation. The thesis is often repeated (as original!) in our times. Malthus speculations have been extensively refuted by empirical evidence. Already in 1845, the Belgian mathematician Pierre Verhulst offered numerous reasons to assume that exponential growth would not continue indefinitely, but rather would diminish as a function of the total population. He developed the logistic equation. Contrary to elementary presentations of chaos theory, the logistic equation does not model population growth in nature, except perhaps in closed systems such as a Petri dish. Human populations, as well as the population of rats, cockroaches, and many microorganisms, grow. Many species become extinct. Others maintain a steady population. While the logistic equation population models and economic

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models resulting from scarcity and conflict, bios models processes driven by both cooperation and conflict, abundance and scarcity. In this context, opting for a logistic or a biotic model is a significant political choice. The logistic equation offers a meaningful counterpart to biotic development. Bipolar feedback is very flexible, allowing any initial value and any value or sign for the g and J parameters, and generating biotic patterns beyond chaos. In contrast, logistic development requires initial values between 0 and 1, gains between 0.45 and 4, and flights to infinity after chaos. 3.15 Bipolar Logistic Development

Fig. 3.21 Initial epochs generated by recursions of logistic and trigonometric feedback. Note two main types of pattern: logistic (asymmetric bifurcation tree, chaos) and process (unifurcation within the bifurcation tree, chaos expansion, intrachaotic period 4). Top two different bipolar logistic equations. Bottom: another bipolar logistic equation generates logistic-like development at low h (left) and the process equation-type development at high h (right). Note the significant differences in gain required to elicit bifurcation and chaos in different recursions. There are also significant differences in amplitude (vertical scale 0 to 2n).

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Can biotic trajectories be interpreted as a sequence of jumps from one basin of attraction to another? Does bipolar feedback represent the combination of positive and negative feedback? I found59 that combining bipolar feedback with either positive or negative feedback actually produces sequences of logons leading to a point attractor (Figs. 3.22 and 3.24). A continuous biotic trajectory that connect widely different values is replaced by ordered sets of patterns, each remaining within one basin of attraction. This observation answers negatively both questions. To study positive feedback, one makes change proportional to At, in addition to the bipolar feedback provided by a trigonometric function (Fig. 3.22). This recursion generates logons,60 the number of latency of which depends on nonlinearly on a number of parameters (Fig. 3.23). To study negative feedback, one can make change proportional to either -At or 1/At. Combining either type of negative feedback with bipolar feedback generates a sequence of logons. The sequence of logons generated by At+i = At + [(h-At) * k * t * sin(At)]

(3.15)

61

exponentially increases up to h. The sequence of logons generated by At+i = At + [(1/ A,) * k * t * sin(At)] (3.16) or At+1 = At + [(1/ At) * k * t * cos(At)]

(3.17)

continues indefinitely as the gain increases in the positive or negative direction depending on the sign of k and the initial value. Table 3.1 summarizes the results obtained with recursions that combine positive, 59 Sabelli, H. The Bipolar Logistic Equation and the Concept of Mathematical Development. Annual Meeting of the Society of Chaos theory in Psychology and the Life 5WeHces,_Madison, 2 0 0 1 . 60 The bipolar logistic allows any initial value. For initial values between 0 and 2n, the recursion converges to Jt, and then bifurcates repeatedly (period 2 at g = 0.633 ...; period 4 at g = 0.835...) and develops a sequence of patterns is similar to logistic development, but also including a relatively important intrachaotic period 4 as in the process equation. When g reaches 1.127..., the series becomes slightly negative and then converges towards 0 without ever reaching it. 61 If h is very large, then the initial logons actually display the pattern observed in the process equation, and bios is generated. The parameter h determines number of logons and either convergence or explosion to infinity. Higher initial values generate a sequence of logons. Initial values between even multiples of K converge to the corresponding odd multiple of n, then generate a logon and terminate by converging to the next lower odd multiple of it. Each logon is longer and narrower than the preceding one. The sequence of patterns fit by a second order polynomial. In general, the number of logons in the sequence is proportional to the initial value, but there are deviations. A large number of logons obtains for Ai = 4l7t. There are initial values (e.g. Ai = 30 n) that do not generate any pattern.

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negative and bipolar feedback. Notably, positive and negative feedbacks modify the time series generated by bipolar feedback in similar manner. A possible explanation is that both positive and negative feedbacks represent asymmetric deviations from the symmetry of the trigonometric function. Coupled bipolar logistic equations in which one has positive feedback and the other has negative feedback generate bios with any initial value. The alternation of a positive and a negative asymmetry appears to be dynamic equivalent to the continuous symmetry of pure bipolar feedback. The bipolar logistic equations show that logons can be generated by biasing bipolar feedback in either a positive or negative direction. It seems that any type of feedback asymmetry, not only scarcity, generate logistic development.

Fig. 3.22 A bipolar logistic equation with positive feedback At+1=At+ [At*k*t*sin(At)]. Note that each logon evolves within a 2TT basin. A biotic phase develops after initial logons when the initial value is high. A(t-l)=AII)*g(t)*sin(A(t)i |

I

A(t+l)=A(t)*glt)*sin(A(t))

0 Initial value pi

50 Initial value, pi

Fig. 3.23 The number of logons generated by the bipolar logistic equation is a complex function of the initial value (left). Influence of initial value on the gain at which the shift from the first to the second logon occurs.

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Mathematical Ideas: Bios and Biotic Feedback

Fig. 3.24 Sequence of logons generated by the combination of bipolar and negative feedback 1/At. Top: ascending and descending sequences of logons generated by positive (left) or negative (right) increments k of the gain, initial value > - n. Bottom: descending (left) and ascending (right) sequences of logons generated by positive increments k of the gain starting from negative values at -n. Table 3.1 Patterns generated by feedback models At+1 = At + AA, Feedback term AAt Recursion _ . . . . . _. . Positive Negative Bipolar Logistic Process Bipolar . . . . logistic I Bipolar . : . logistic IT II Bipolar , . . ITT logistic HI|

At

Pattern generated Convergence Bios 1— e initial final no yes 3or4)

1-At sin(At) . ,. .

.

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. . h-At \

, .. I/A,

|

sin(At )

7t

. ,. . sin(At)

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. ,. . sin(A,)

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y^s only if ascending or . . , , ,. j, At is large descending* only if ascending or , . , , ,. h is large descending*4 ascending no , ,. ° I | descending**

* according to initial value ** according to gain sign and initial value

Chapter 4

Bios Data Analysis

Abstract: Bios analysis is a systematic method to study creative processes empirically, through the mathematical analysis of time series. A number of new techniques are introduced, which are summarized at the head of each section. The process method1 is a system for studying creating processes based on nonlinear dynamic techniques.2 We study temporal change by recording ' Carlson-Sabelli, L., Sabelli, H. C , Hein, N., and Javaid, 3. Psychogeometry: The Dynamics of Behavior. Proc of the Internal Soc for the Systems Sciences. 1990: 769-775; Carlson-Sabelli, L, Sabelli, H. C , Patel, M., Holm, K. The Union of Opposites in Sociometry: An Empirical Application of Process Theory. J. Group Psychotherapy, Psychodrama and Sociometry 1992: 44(4): 147-171; Carlson-Sabelli, L., Sabelli, H. C , Messer, J., Patel, M., Sugerman, A., Kauffman, L., and Walthall, K. (1997). Process method: Part I. An empirical measure of novelty differentiates creative organization from static order and chaos. Proc. International Systems Society, Kwanak Press, pp 1072-1090. Carlson-Sabelli, L, Sabelli, H., Patel, M., Sugerman, A., and Kauffman, L. (1997). Process method: II. From process thinking to the empirical study of coexisting opposites. Proc. International Systems Society, Seoul, Korea, pp 976-988; Sabelli, H. (2000). Complement plots: analyzing opposites reveals Mandala-like patterns in human heartbeats. International Journal of General Systems 29: 799-830; 143. Sabelli, H. (2001). Novelty, a Measure of Creative Organization in Natural and Mathematical Time Series. Nonlinear Dynamics, Psychology, and Life Sciences. 5: 89-113; Sabelli, H. (2001). Arrangement, a measure of nonrandom complexity. Systems Analysis Modelling Simulation 42: 395-403; Sabelli, H and A. Abouzeid. (2003). Definition and Empirical Characterization of Creative Processes. Nonlinear dynamics, Psychology and the Life Sciences. 7: 35-47; Sugerman, A., and Sabelli, H. (2003). Novelty, Diversification And Nonrandom Complexity Define Creative Processes. Kybernetes 32: 829-836; Patel, M. and H. Sabelli. (2003). Autocorrelation And Frequency Analysis Differentiate Cardiac And Economic Bios From 1/F Noise. Kybernetes. 32: 692-702; Also the series Bios Data Analysis. Process Methods to Analyze Creative Processes. J .Applied Systems Studies, special issue edited by H. Sabelli. Introduction - Sabelli, H., Kauffman, L., Patel, M., Sugerman, A., Carlson-Sabelli, L., Konecki, J., Kovacevic, L., Kane, K., Abouzeid, A., Sween, J., and Shay, K. Part 1. Empirical Foundations and Medical Application Sabelli, H., Messer, J., Carlson-Sabelli, L., Patel, M., Sugerman, A., Kauffman, L., Walthall, K., and Konecki, J.. Part 2. Theoretical Foundations of the Process Method - Sabelli H.. Part 4. Flux and Action: Process Statistics - Sabelli, H., Patel, M., Sugerman, A.. Part 5. Action and Information: Repetition, Rise and Fall - Sabelli, R , Patel, M., and Venkatachalapathy, V. K.; Part 6. Opposition: The Phase Portraits in Psychology, Sociology and Economics Sabelli, H., Zarankin, S., and Carlson-

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time series and comparing them with shuffled copies. We study informed causation by examining consecutive terms in the series. We explore creativity by measuring diversity, novelty and both simple and complex components. 4.1 Designing Methods by Studying Cardiac Patterns Focusing on the development of creative thinking, it is cogent to examine the rational and general, as well as the personal and aleatory components of the development of the process method of analysis. We came to study heartbeat series as a readily quantifiable portrait of emotions, but the field had captured the interest of physicists as well as physicians. To our delight, we found that one of the leading scientists in the field, Joseph Zbilut, was in our own Rush University, and thus we added Webber and Zbilut's powerful recurrence quantification3 to our simpler analyses. The work of Claude Bernard in the 19th century, and of Cannon and Rosenblueth in the 20th, established the importance of neural regulation to maintain parameters such as heart rate within a range compatible with health. Recognizing the importance of overall heart rate has led to the use of averaging techniques in order to eliminate variations introduced

Sabelli, L. Part 7. Opposition: Trigonometric Analysis in Time Series - Sabelli, H., and Kauffman, L. Part 8. Recurrence Isometry: Measures of Novelty, Order and Nonrandom Complexity - Sabelli, H., Sugerman, A., Carlson-Sabelli, L., Kauffman, L., and Patel, M. Part 9. Embedding Plots: A tool to Measure Simplicity, Complexity and Creativity - Sabelli, H., Sugerman, A., Carlson-Sabelli, L., Patel, M., and Kauffman, L. Part 10. Process Entropy, a Multidimensional Measure of Diversity and Symmetry - Sabelli, H., Patel, M., Sugerman, A., Kovacevic, L., and Kauffman, L. Part 11. Biotic Patterns in Biological, Economic and Physical Processes - Sabelli, H., Sugerman, A., Kauffman, L., Kovacevic, L., Carlson-Sabelli, L., Patel, M., Messer, J., Konecki, J., Walthall, K., and Kane, K. 2 Abraham, F. D. (1990). A Visual Introduction to Dynamical Systems Theory for Psychology. Santa Cruz, California: Aerial Press; Guastello, S. J. (2001). Nonlinear Dynamics in Psychology. Discrete Dynamics in Nature and Society 6: 11-29; Schroeder, M. (1991). Fractals, Chaos, Power Laws. New York: W. H. Freeman; Sprott, J. C. and Rowlands, G. (1995). Chaos Data Analyzer. New York: American Institute of Physics; Thorn, R. (1975). Structural Stability and Morphogenesis. Translated by D. H. Fowler. Reading, MA: Benjamin/Cummings; Webber, Jr., C. L. and Zbilut, J.P. (1994). Dynamical Assessment of Physiological Systems and States using Recurrence Plot Strategies. Journal of Applied Physiology 76: 965-973. 3 Webber, Jr., C. L. and Zbilut, J. P. (1996). Assessing Deterministic Structures in Physiological Systems using Recurrence Plot Strategies. Bioengineering Approaches to Pulmonary Physiology and Medicine, M. Khoo (Ed). New York: Plenum Press, pp. 137-148; Zbilut, J. P. and Webber, Jr. C. L. (1992). Embeddings and delays as derived from quantification of recurrence plots. Physics Letters A, 171: 199203.

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by chance interactions. Average heart rate is the most fundamental dimension of cardiac timing, but homeostasis is not equilibrium, neural regulation is not negative feedback, and heart rate is not regular. Variation is meaningful and vital. Heart rate regularity is a predictor of imminent death in acute cardiovascular illness4 and a predictor of cardiovascular illness in normal subjects. Beat-to-beat variations are decreased in congestive heart failure, coronary artery disease (CAD), postprandial hypotension, and with factors predisposing to cardiac illness such as diabetes mellitus, bed deconditioning, and aging. This discovery has significant clinical application in adult cardiology5 and for monitoring the state of the fetus during delivery.6 Regarding cardiac variation as variability, cardiac timing has come to be described by two statistical dimensions, mean and S.D. Measures of the S.D. have shown significant decreases in depressed patients and with antidepressant treatment.7 We found lower S.D. in psychotic patients.8 Notwithstanding, the S.D. has limitations in clinical practice; for instance, the S.D. does not detect changes in many patients with CAD; the fact that a statistical difference can be demonstrated between groups of subjects is irrelevant to clinical practice. Also, as RRIs are not normally distributed, measures of statistical variability may not properly assess heart rate variation. Another possible measure of variation is power spectrum analysis. This also requires stationary data. The most important limitation of statistical variance and of power spectrum as measures of heart rate

4

Akselrod S., D. Gordon, F.A. Ubel, A.C. Barger, and RJ. Cohen. 1981. Power spectrum analysis of heart rate fluctuation: A quantitative probe of beat-to-beat cardiovascular control. Science 213: 220-222; Liebovitch et al (2002); Ivanov et al (1996); Glass and Mackey (1988); Denton T. A., Diamond, G. A., Helfant, R.H., Kahn, S. and Karageuzian, H. (1990). Fascinating rhythm: A primer on chaos theory and its application to cardiology. American Heart Journal 120: 1419-1440. 5 Malik, M. and Camm, A. J. Heart Rate Variability. Armonk, New York: Futura Publ. Co (1995). 6 Hon E. H., Lee, S. T. Electronic evaluations of the fetal heart rate patterns preceding fetal death: Further observations. Am. J. Obstet. Gynecol. 1965;87:814-26. 7 Roose, S.P. and Glassman, H. (1989). Cardiovascular effects of tricyclic antidepressants in depressed patients. Clinical Psychiatry Monograph Series,7 (2); 8 Carlson-Sabelli, L., Sabelli, H. C , Zbilut, J., Patel, M., Messer, J., Walthall, K., Tom, C , Fink, P., Sugerman, A., Zdanovics, O. How the heart informs about the brain. A process analysis of the electrocardiogram. Cybernetics and Systems'94. 2: 1031-1038, R. Trappl (Ed.), World Scientific Publ. Company, Singapore, 1994.

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variation are changes in time.9 Heart rate is nonstationary. Patterned variation may represent low-dimensional deterministic chaos,10 a hypothesis that led to the introduction of nonlinear dynamic methods. Most of these analytic techniques require stationary data (i.e. stable mean and variance). Using wavelet methods appropriate for the analysis of nonstationary series, Ivanov and co-workers11 have generated beautiful portraits that demonstrate unequivocally fractal structure, which is compatible with chaos (as well as with bios). The nonstationary of RRI series suggested to Zbilut12 and coworkers that heart rate variation represents transients resulting from the influence of many independent endogenous factors (e.g. respiration, hormones, emotions) and external interactions. These concepts led to the use of the recurrence method13 that allows one to study nonstationary series in many dimensions. Nonetheless, in these studies, the time series is often subdivided into epochs to obtain stationary subsamples, and the analysis is carried out at low embedding dimensions. Regarding heart rhythms as creative points to a different methodology.14 First, physiological functions are all integrated in the central nervous system. Thus, the many factors that influence heart rate variation -respiration, hormones, emotions, and behavioral interactions9

Dalton, K. G., Dawes, G. S. and Patrick, G. E. (1977). American Journal of Obstetrics and Gynecology 127: 414. 10 Goldberger A. L., and West, B. J. (1987). Applications of nonlinear dynamics to clinical cardiology. In Perspectives in Biological Dynamics and Theoretical Medicine. In S.H. Koslow, A.J. Mandell, M.F. Shlesinger, Annals of the New York Academy of Sciences. New York: New York Academy of Sciences. " Ivanov, P. Ch, Goldberger, A. L. and Stanley, H. E. Fractal and Multifractal Approaches in Physiology. The Science of Disasters, pp. 218 - 257 12 Zbilut, J. P. (1991). Power laws, transients, attractors and entropy: possible implications for cardiovascular dynamics. In H. Haken and H-P Koepchen (Eds), Rhythms in Physiological Systems. Berlin: Springer, pp. 139-152. 13 Eckmann, J. P. 1987. Recurrence plots of dynamical systems. Europhysics Letters 4: 973-977. Kamphorst, S. O. and Ruelle, D.; Webber, C. L. Jr. and Zbilut, J. P. 1994. Dynamical Assessment of Physiological Systems and States Using Recurrence Plot Strategies. J. Applied Physiology. 76: 965-973; (1996); Zbilut, J.P., Giuliani, A., and Webber, Jr., C.L. (1998). Recurrence Quantification Analysis and Principle Components in the Detection of Short Complex Signals. Phys. Lett. A 237: 131-135; Zbilut, J.P. and Webber, Jr., C.L. (1998). Quantification of Heart Rate Variability using Methods Derived from Nonlinear Dynamics. In Analysis and Assessment of Cardiovascular Function. G. Drzewiecki and J. K.-J. Li (Eds.). New York: Springer Verlag, pp. 324-334. 14 Sabelli, H. and Carlson-Sabelli, L. (1999). Process Methods and the Identification of Biotic Patterns of Heartbeat Variation. Proceedings of the 4th Systems Science European Congress. L. Ferrer et al. (Eds). Valencia, Spain, pp. 493-502.

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are not independent from one other. Second, seeking to reveal novel sequences leads one to interpret recurrence plots as time graphs, and to examine long series of heartbeat intervals. We thus obtain diaries of activities and emotions along with 24-hour recordings of the electrocardiogram. This shows that the apparent transients actually are episodic patterns (complexes) that are associated with ongoing activity. Third, since creative processes by definition must include both simple and complex components, one must analyze the pattern of heartbeat intervals in low and high embedding dimensions. Fourth, searching to identify creative processes leads one to search for indications of novelty, diversification and nonrandom complexity. Points 3 and 4 came to us as result of our research. When my wife Linnea entered "50", instead of "5" as the number of embeddings in which to analyze the data, she generated a beautiful recurrence plot. Not everybody admired it, so as a gentleman I thought hard how to use her discovery, and came to the systematic analysis of data in multiple embeddings (Section 4.9). Much later, we found to our surprise that the number of recurrences in cardiac data increases by randomization. It took me more than one year to realize that I had found novelty, a phenomenon that led me to the concept of creation as an organizing principle to understand natural processes. Creative phenomena of processes cannot be detected with methodologies based on assumptions that exclude them. Focusing on isolated events or permanent structures prevents the detection of changing processes. Single observations, no matter how accurate, cannot portray processes.15 Categorical distinctions prevent the observation of coexisting opposites. Transient patterns cannot be detected by selecting stationary time series or by searching for stable attractors. Data transformations (smoothing, averaging, and eliminating outliers) can tame chaotic processes and eliminate Pareto distributions. Differencing also converts complex biotic patterns into simpler chaos. Methods to detect creative processes cannot be developed based on the assumption 15

A dramatic example of the importance of time series is the work of David Gilden demonstrating that the residual fluctuations in psychological usually discarded as "unexplained variance" show 1/f pattern analyzed in terms of their time histories. (Gilden, D.L. (2001).Cognitive emissions of 1/f noise. Psychological Review, 108(1), 33-56).

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that complexity processes can be reduced to stationary and low dimensional patterns such as chaos. Likewise mechanism and determinism exclude creativity and lead to attributing novelty to random accident. What is required to study creative phenomena? First, one must study processes in time through the analysis of time series, as contrasted to the analysis of static data such as statistical distributions or isolated events. In particular, we focus on time series of discrete actions and observe them for an extended amount of time. Second, in seeking to identify deterministic causation, one must measure simple interactions. Causation cannot be demonstrated if one focuses exclusively on complex patterns or readily accepts random causation. Contrary to standard assumptions, randomness is extremely complex (e.g. it has maximal algorithmic complexity), so it is parsimonious to search for causation rather than to postulate randomness. Attention to simple causation places a focus on opposition and triads via analyses in two and three dimensions. Third, one must also measure complex components of the process rather than focus on low dimensional components. Reduction (such as analysis of complex systems into their component parts) is a most important scientific strategy, but measuring only simple processes (e.g. low dimensional attractors in physiological data) prevents the observation of creative processes. Attention to simplicity and complexity leads us to analyze data in multiple dimensions. On theoretical grounds, the methods focused on are organized in three groups that deal with action, opposition and form, and at a more abstract level, the lattice, group, and topological aspects of processes. 1) To analyze action, we develop process oriented statistical methods including measures of diversification and diffusion, asymmetry, correlation, factor analysis, and power spectrum measures. 2) To analyze the co-creating opposites, we analyze information and opposition using repetition, rise and fall measures, the phase plane of opposites, and trigonometric analysis of opposites. 3) To analyze form itself and dimensionality, we use recurrence and wavelet plots. Dimensionality is investigated with embedding plots that distinguish simple and complex components. Isometry measures recurrence and novelty. Arrangement measures nonrandom complexity.

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In addition, in order to consider possibly random flux, we also perform these measures in shuffled copies. Shuffling leaves the mean and standard deviation unchanged, but completely destroys temporal information. The methods are directed to demonstrate two facts: (a) features of novelty that differentiate creative processes (causal or stochastic) from mechanical, periodic and chaotic changes; (b) features of causation that differentiate creative developments from stochastic processes. In our work, we find three indications of causation: partial autocorrelation, consecutive recurrence and entropy, and pattern and / or correlation in the differences between consecutive terms of the series. It is puzzling that in some series we can demonstrate one without the other.16 In this manner, we develop methods that distinguish creative developments from non-creative, though complex and irregular, data. This Chapter focuses on these new methods. It does not attempt to review the ever-expanding field of time series analysis.17 The methods are developed through comparison of empirical data, deterministic models of bios, chaos and noise (called "stochastic" but including deterministic components), randomized data generated by shuffling, and the sequence of n digits that is deterministic in its generation, random in its global pattern, and prominent in recursions that generate bios. 4.1.1 Data transformation A process is characterized by its form rather than by its composition. Thus, the analysis of a process does involve decomposition into parts, but description of its morphology, employing transformations, such as differencing and embedding, that allow one to reveal multiple dimensions of information. Data description and empirical analysis must start with the original, unprocessed data in its totality. It is only after this analysis that we can select particular epochs. Likewise, transformations must be made only after analyzing the raw data. Data transformation is a powerful analytic tool, but it can also generate significant distortions. 16 For instance, in some economic data, we find consecutive recurrence and entropy but no correlation between successive differences. In CBR, we find partial autocorrelation but no consecutive recurrence. 17 Sprott, J.C. and Rowlands, G. (1995). Chaos Data Analyzer. New York: American Institute of Physics.

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Transformations such as differencing are enormously valuable in detecting certain significant components of variation, but they also eliminate others. Data transformations necessarily distort the process under consideration. When averaging techniques are used to eliminate variability, significant variation is eliminated. Differencing, detrending and standardization, used to eliminate non-stationarity and normalize the data, eliminate major features of the actual distribution, such as significant trends and diversification. These are not innocuous procedures that can be performed prior to analysis. These obvious, but not trivial, guidelines are nevertheless frequently bypassed when evaluating statistical differences between data sets, or when seeking to reveal the existence of a chaotic attractor. Data should not be purged. Currently, outliers are often eliminated prior to analysis; their inclusion is in fact deemed to invalidate statistical analysis. This assumption removes significant observations (Chapter 14). Natural processes have asymmetric distributions with fat tails (i.e. more outliers than predicted by normal distribution). Eliminating outliers is like describing intelligence without considering Einstein, music without Beethoven, painting without Leonardo, and wealth without Gates. Many of the tools of standard statistics imply assumptions that are not satisfied by real processes. For instance, it is now obvious that normality is not as common as previously regarded, so we must adopt measures of central tendency and variation that do not presume normality. But we also want to challenge the dictum that a process must be regarded as random unless proven to be patterned is unproven, and fails to suggest possible ways for investigation. Instead, the process method assumes that the identification of pattern must be tirelessly pursued unless randomness is demonstrated. But can one prove randomness with a shorter than infinite sample.18 Assuming that variation represents non-identified pattern encourages its analysis and preservation. Assuming that variation is random discourages analysis and permits the destruction of unidentified patterns by irresponsible human intervention.18 The fact that humans have five fingers might appear to many thinkers as an accident of nature. However, it may be more 18

Berry, W. (1987). Home Economics. San Francisco: North Point Press.

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interesting to observe that five-fold symmetry is common in both the animal and the plant kingdoms. Similarity can be readily dismissed as accidental. Perhaps someone could assert with certainty that a given similarity is purely coincidental. Until that can be proven, it may be prudent to consider observed similarities as, perhaps weak but certainly meaningful, empirical evidence pointing to a causal link. The link may be as remote as the homology between arm, leg, wing and fin. In recognizing that many of the techniques used to characterize chaos may not be meaningfully applied to non-stationary data, textbooks in nonlinear dynamics prescribe to render the data stationary by first differencing the time series. The assumption that data can safely be differenced without altering fundamental features is, however, dubious, and must be proven in each case. It is important to note that differencing can markedly alter the statistical parameters describing a distribution. Differencing can, in fact, erase fundamental pattern; for example, a random walk may emerge as a random series, and biotic patterns may be transformed into chaotic ones (Fig. 4.1). Thus, biological and economic processes shown to be chaotic by the analysis of differenced time series may actually be biotic. The methodological use of differencing subsequent to analysis of the raw data must be clearly distinguished from detrending prior to data analysis. 4.1.2 Creativity and stationarity, a methodological choice Most dynamic techniques require stationary data, that is to say, data with stable mean and stable variance. Studying nonstationary data may thus be rejected as neglecting necessary scientific rigor. On the other hand, actual processes include stable and evolving aspects, stationary and nonstationary epochs. For instance, heart rate changes with activity and emotions. Shall we adapt our methods to the process under study, or select what to study on the basis of the methods developed to study simpler processes? It is, of course, possible to obtain stationary data even in the case of evolving processes. It is sufficient to choose short periods of time -for instance, a few minutes in which the person rests in the case of heart rate. Also, if we choose to study twenty-four hour recordings, we may notice

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that our data is fairly stationary on the average. A person goes through many different activities during the day, but as a rule he or she will wake up at a given time, work at certain hours, eat with more or less regularly, etc. However, to study the actual performance of the heart, it is necessary to study change. Change is, of course, a sine qua non component of creative phenomena. If we exclude change, we exclude creativity.

Fig. 4.1 Time series (center) of heartbeat intervals, chaos (g = 4.1) and bios (g = 4.61) generated by the process equation, time series of differences between consecutive terms (left) and of sums of 100 consecutive terms (right).

The choice to study stationary or nonstationary processes may appear to be a technical issue. Undoubtedly, stationarity is a question of scientific import, but it has wider relevance. It determines whether or not

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we are able to find creative phenomena, and thereby determine our conclusions about nature, society, and psychology. Establishing that the apparently innocent, methodologically founded choice of stationarity actually represents an ideological bias serves to foster a thinking that is not only critical but also creative and therapeutic. The question of stationarity is more than a methodological issue. Only in the case of mathematical series is it easy or even possible to separate stationary and nonstationary processes. In the study of nature, the investigator chooses to explore stability or change, determination or creation, or any one of the two or more complementary aspects of any question. This is the supremacy of the subjective, which complements the priority of objective reality in determining scientific conclusions (Chapter 9). Differences carry information.19 The analysis of differences between consecutive terms in a time series allows one to distinguish creative processes from stochastic ones. In mathematical bios, the time series of differences results in a chaotic pattern, demonstrating that biotic processes carry chaotic information. In stochastic processes, the time series of differences is random; it does not carry information. The differentiation of biotic series generates chaotic patterns and the integration of chaotic series generates bios. Chaos and bios can therefore be readily confused. To identify any creative process requires critical analysis of data manipulation that may hinder the identification of crucial properties. Consider an apparently trivial transformation of heartbeat interval data. It is common practice to convert heartbeat intervals into "instantaneous heart rate" (the inverse of the interval) because heart rate is a concept more familiar to clinicians. However, this practice is problematic for both theoretical and practical purposes. Theoretically, one cannot define an instantaneous rate for a sequence of discrete units. Furthermore, converting intervals into a rate transforms integers into decimals and thereby introduces unavoidable computational errors. Avoiding this type of data manipulation pertains not only to cardiological data; it is relevant to data analysis in any field of investigation. 19

Bateson, G. (1979). Mind and Nature: A Necessary Unity. New York: Dutton.

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Any rational analysis of data requires a critical examination of the assumptions embodied in the methods we employ to obtain them. Consider, for instance, partition into epochs. From a static perspective, the objective of subdividing a nonstationary series into epochs is to obtain stationary samples. From the process perspective, the objective is to demonstrate and measure episodic patterning. Empirical studies cannot be used to detect patterns if the methods that are employed to collect and analyze the data are insufficient in their scope. To identify processes, one needs to study time series. In order to be able to consider creativity, one must measure complex components of the process. To reveal coexisting opposites, one must not exclude them with linear scales. A psychologist, a sociologist, or a pollster who uses linear scales, for instance, fabricates linear data by forcing linear thinking on the subjects (and on her/ himself). To identify a creative process, it is necessary to empirically measure the development of episodic patterning, novelty, diversity, and complexity. Selecting stationary epochs precludes the identification of creative processes. When focusing on stable patterns in empirical data, it has been the custom to select stationary periods; likewise, it has become standard to discard the initial 100-200 iterations generated by mathematical recursions. However, at particular gains, the pattern generated by some mathematical equations changes after a thousand or more iterations without change in the coefficient. From a process perspective, both stationary and nonstationary data should be included. In the analysis of complex processes, one needs to examine not only for a sufficient duration of time, but also in a sufficient amount of detail; sampling the process at suitably close intervals is of utmost importance. Complexity is embodied in rapid variation. Thus, obtaining only a small number of observations - or smoothing them by averaging - expresses disregard for the most essential feature of processes, namely change. There is no mathematical trick that will allow an experimenter to see the overall pattern from a short sample or complexity from smoothed data. The recording and measurement of detailed variation must be guided by considerations of significance and reliability. Computational precision should not exceed instrumental accuracy. It is well known, but worth repeating, that when precision exceeds accuracy, it introduces error.

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Creative features can thus be obscured, or erased, by selecting stationary periods, detrending, differencing, smoothing, or by any other data manipulation. In contrast, embedding does not distort biotic patterns, but transforms chaos into bios (Fig. 4.2). Notwithstanding, using detrended fluctuation analysis,20 we have found similar results with heartbeat series and mathematical bios, as contrasted to chaotic data. l i

11

1

Fig. 4.2 Time graph of a chaotic time series (left) and of a biotic time series (right) and of the time series of Euclidean norms of 1, 2,..., 50 embeddings. Euclidean norms magnify and smooth the pattern; also negative terms are made positive.

4.1.3 Time, frequency and statistical frequency Three major modes of data analysis are employed: the measure of frequency in statistical distributions, measures in the time domain, and frequency analysis. Time involves duration and order. The measurement of sequences of intervals between actions, such as between heartbeats, allows one to study temporal order and the duration of individual events; the measurement of frequency, such as heart rate, focuses on collectives, and ignores temporal order. Focusing on temporal order leads one to study data primarily on the time domain, and to consider also analyses on the frequency domain within the perspective of action. Frequency is the 20

Ivanov, P. C , Rosenblum, M. G., Peng, C.-K., Mietus, J., Havlin, S., Stanley, H. E. and Goldberger, A. L. (1996). Scaling behavior of heartbeat intervals obtained by wavelet-based timeseries analysis. Nature. 383, 323-327. 21 Gordon, D. and Sabelli, H. (1999). Biotic patterns of heart rate variation in newborn infants and thendisruption in newborns with severe congenital illness. 43rd Annual Meeting of the International Society for the Systems Sciences, Asilomar, California. Proc. 43rd Annual Meeting of the International Society for the Systems Sciences, edited by J. K. Allen, M. L. Hall and J. Wilby. Abstracts 186-187.

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inverse of time. The frequency of periodic change is the rate at which action changes from one polarity to its opposite -the interval is the duration throughout which it remains at one polarity. The time domain portrays actions. Frequency portrays information as the switch in the polarity of opposites. When we say that power is inversely proportional to frequency -the well-known 1/f pattern—we mean that power is proportional to duration (time). 4.2 Process Statistics: Diversification, Asymmetry, and 1/f Novelty Abstract: Process statistics aims at revealing patterns of action rather than establish differences between data sets in spite of irrelevant variability. Diversification (changes in variance with embedding in excess of diffusion) characterizes creative processes, differentiating them from chaos and random. Asymmetry is also found in creative processes, while chaotic series are largely symmetric become more symmetric with embedding and sample duration. Correlation measures demonstrate nonrandom causation in bios and in empirical data, distinguishing them from noise and random data. Correlation measures reveal overlaps of periodicity with chaos or bios, indicating that attractors are not mutually exclusive. Partial autocorrelation measures indicate causal processes, at variance with widespread assertions in the statistical community. Natural processes and biotic series display an inverse relation between frequency and power. Recurrence analysis distinguishes three types of 1/fpattern: deterministic (recurrent and co-recurrent), biotic (novel and co-recurrent), and (novel and not co-recurrent), suggesting a nonrandom generation of "colored noise ". Random walks are nonstationary. By necessity, creative processes are evolutionary rather than stationary. Regarding variation as meaningful change rather than meaningless variability, process statistics22 (1) analyzes time series (rather than static data); (2) measures changes in 22

Patel, M. and Sabelli, H. (2003). Autocorrelation And Frequency Analysis Differentiate Cardiac And Economic Bios From 1/F Noise. Kybernetes 32: 692-702; Sabelli, H., Patel, M., and A. Sugerman. (accepted for publication). Bios Data Analysis. Part 4. Flux and Action: Process Statistics. J. Applied Systems Studies.

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statistical parameters; (3) focuses on asymmetry and causality, the properties of directed action; (4) rejects methodological assumptions and data transformations (selection of stationary periods, detrending, and elimination of "outliers") that prevent the identification of creative processes; and (5) compares each time series with shuffled copies to differentiate temporal pattern from other types of regularities in the distribution. Process statistics seeks its roots in the natural sciences, and in the empirical analysis of concrete data. Standard statistics is based on abstract probability theory, which was originally developed in the context of the gambling mores of idle aristocrats; game theory is still prominent in contemporary research. Statistics entered science with sociology, as a search for invariance believed to be obscured by the enormous variations in the data. Standard statistics is still largely dominated by static views.23 The underlying assumption is that change is less fundamental than permanence. Significantly, standard statistics regards variation as meaningless variability and error. Similarly, variation came to be regarded as "noise" in the context of information sciences. Standard statistics takes randomness as its point of reference. Randomness is stationary. Thus statistics measures distributions. Statistical parameters are calculated for the entire set of data. To evaluate the significance of differences between data sets, analyses focus on central tendency, employ averaging techniques to overcome variability, and transform the data to eliminate nonstationarity and normalize them. Aperiodic fluctuations are regarded as random, normally distributed, and meaningless variability. These assumptions do not apply to creative processes in which variation is determined, asymmetric, and meaningful. 4.2.1 Diffusion and diversification Many natural processes are nonstationary, i.e. their mean and/or variance changes with time. This implies non-randomness.24 Creative processes 23

Kendal, M. (1973). Time Series. London: Charles Griffin. Stock prices are non-stationary processes; the value of stock can grow without bounds and it does so as a rule, because of a continuous devaluation of money -this is in fact the reason why holding stock over the long haul can as a rule produce a positive outcome. Although changes in price may appear to be random, there is a deterministic component that promotes nonstationarity.

24

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expand, as illustrated by successful biological populations, languages, customs and inventions. As described in Chapter 3, bios is related to the phenomenon of deterministic diffusion. Thus to study creative processes we must start by measuring the degree of nonstationarity in the data. In contrast, stationary epochs are often selected for analysis because the available methods can only be applied to stationary data. Stationarity is not only an objective property of the data but a subjective choice of the experimenter according to the epochs he chooses, a choice that largely depends upon his worldviews.25 Statistically, one can measure expansion by the mean squared displacement (M.S.D.), which is the average of the square of the deviations of each term in the series from the origin. In addition to this global measure, we26 have introduced a local measure of diffusion by calculating changes in M.S.D. with embedding. Global and local diffusion are frequently observed in empirical series, in mathematical bios, and in random walks. However, diffusion is not inherent in mathematical or natural bios. RRI and atmospheric temperature are bounded processes. The essential property is increase in diversity. Homeostatic processes maintain the mean of biological processes stationary; e.g., the average duration of heartbeat intervals is, on average, the same at the time of waking each day. It is thus surprising that the standard deviation (S.D.) of heartbeat interval series increases with the duration of the recording (Fig. 4.3) as discovered by Dalton.27 This observation led us to define diversification as an essential characteristic of creative processes that differentiates them from static chaos, and to develop methods for its quantification.28

25 A stationary process is one in which the statistical properties of the time series remain constant over long periods. When shorter periods are considered, even a truly stationary variable may appear nonstationary. Conversely, a process that appears to be stationary in a relatively long run may not be stationary if we consider even longer periods. 26 Sabelli, H., Patel, M . , and Sugerman, A . (accepted for publication). Bios Data Analysis. Process Methods to Analyze Creative Processes. Part 4. Flux and Action: Process Statistics. Journal of Applied Systems Studies. 27 Dalton, K. G., Dawes, G. S. and Patrick, G. E. (1977). Amer. J. Obstetrics Gynecology 127: 414. 28 Sabelli, H and Carlson-Sabelli, L. (1999). Process Methods and the Identification of Biotic Patterns o f Heartbeat Variation. Proceedings of the 4th Systems Science European Congress. Edited by L. Ferrer et al. Valencia, Spain, p p . 493-502; Sabelli, H and A . Abouzeid. (2003). Definition and Empirical Characterization of Creative Processes. Nonlinear Dynamics, Psychology and the Life Sciences 7: 35-47;

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Diversity is a measure of changes in variation among consecutive epochs.29 Diversity is low in random, periodic and chaotic data, and it is high in heartbeat interval series, random walks, and mathematical bios. Global diversification is the increase in variance with duration of the sample (100, 200,..., N) starting with the first term of the series. Diversification is observed in heartbeat intervals, electroencephalogram, respiration, vowel sounds, daily atmospheric temperature, economic prices and indexes, and many other processes. It is also observed with biotic series and statistical noise (random walks, Brownian motion, 1/f noise). In contrast, variance decreases or do not change with the duration of the sample in the case of random, periodic, chaotic series. Earthquakes recordings show, as expected, a decrease in variance with time. The increase in variance with the duration of the sample is the most intuitive measure of diversification. However, it requires long series of data, and it is highly influenced by major discontinuities. A time series can show global diversification because it evolves from one pattern to another (for instance, from rest to exercise in the case of respiration or heart rate),

Sugerman, A. and H. Sabelli. (2003). Novelty, Diversification and Nonrandom Complexity Define Creative Processes. Kybernetes 32: 829-836. 29 To measure diversity, the time series is divided into epochs (e.g. of 100 consecutive terms), and the deviation (S.D. or A.D.) is computed for each of these subsamples. We calculate changes in the S.D. in normally distributed data, and the average deviation A.D. (the average of the absolute value of the deviations of each term of the series from its mean) in the far more numerous non-normal cases. The diversity of the values obtained is computed by calculating the S.D. of these measurements divided by their mean.

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while each of these patterns is stable. Conversely, changes in heart rate may actually result in a decrease in average diversity. Measuring changes in variance with embedding provides a more convenient, robust, and revealing measure, which we call local diversification. The S.D. (or the A.D.) is computed for sets ("embeddings") of 2, 3, 5, 7, 10, 50, 75, 100 and 200 consecutive terms of the time series, starting with each term in the series. The values obtained for each embedding are averaged for the entire series, and these averages are plotted as a function of the number of embeddings. The results obtained with short (2 to 10) and long (50 to 200) reveal different properties of processes. With long embeddings (50 to 200), deviation increases with embeddings in series of heartbeat intervals, respiration, ocean water temperature, air temperature, many economic series, random walks and bios. In contrast, the S.D. or the A.D. decreases or does not change as a function of the number of embeddings in periodic, chaotic or random data (Fig. 4.4). In all cases, the presence of absence of local diversification can be demonstrated with relatively short samples (e.g. 2000 data) and it is relatively insensitive to discontinuities. We thus consider an increase in the S.D. with progressively longer embeddings as a measure of diversification. It is noteworthy that local and global diversifications, which are quite different measures of variation, provide similar results in most cases. Local diversification does not correlate with divergence as measured by the largest positive Lyapunov exponent. The results are quite different with small number of embeddings (2 to 10). The S.D. and the A.D. decrease with the number of embeddings for periodic series, instead of remaining constant, as well as in logistic and process chaos and in biotic series (natural or mathematical). These results may portray the divergence of trajectories regarded as characteristic of chaotic series, which is measured by the Lyapunov exponent and possibly by relative dispersion. West and coworkers30 measure the change in the coefficient of variation (S.D. divided by the mean) as a function of embedding, as an index of the fractal dimensions of the time series which they call relative 30 West, B. J., Hamilton, P. and West, D. J. (2000). Nonlinear Dynamics, Psychology and Life Sciences 4: 87-111.

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dispersion.31 We have observed significant relative dispersion in series that are neither chaotic nor biotic. 8 -1

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Global diversification and local diversification measure different properties of the time series; in many cases, local diversification is demonstrable while global diversification is absent. Both measures of 31

Either the S.D. or the C.V. may thus be used to measure divergence. However, they do not provide the same information for larger embeddings.

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diversification capture different aspects of innovation than relative dispersion, the Lyapunov and the Hurst exponents. Diversification differentiates creative processes from conservative processes (equilibrium, periodic or random) that maintain their initial degree of diversity, and from processes that converge to equilibrium, periodic or chaotic attractors. Chaos includes early divergence followed by convergence to a stable state, while creative processes and their biotic models display both divergence and continuing diversification. Diversification may result from simple diffusion (e.g. an expanding time series). Time series of heartbeats, bios, and random walks often (but not always) show both diversification and diffusion. Diversification without diffusion is observed in some heartbeat series and in mathematically generated homeobiotic series (bounded bios) described in Chapter 5. Figure 4.5 illustrates the increase in the S.D./M.S.D. ratio with embedding and its decrease with duration of the sample in a biotic series. Apparently, diversification, which portrays complex processes, predominates locally, while simpler diffusion predominates overall. This fits with the idea that complexity emerges locally within simpler and larger systems, the concept of global priority of the simple and local supremacy of the complex (Chapter 9). 4.2.2 Asymmetry and symmetry, co-creating complementaries Measures of skewness (Fig. 4.6) show that heartbeat intervals, economic series, meteorological data, random walks, and mathematical bios are asymmetric. In contrast, symmetry is the rule for the distribution of random and periodic series. Chaotic series are highly symmetric (process chaos and logistic chaos, g = 4) or asymmetric (logistic chaos). Note, however, that the bifurcations in the process equation and in the logistic equation are highly asymmetric. In mathematical recursions, there is a net increase in asymmetry with complexity, from periodicity to chaos and from chaos to bios (Fig. 4.7).

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Fig. 4.6 Asymmetry measured by the absolute value of statistical skewness.

Fig. 4.7 Symmetrization in logistic chaos At+1 = At * g * (1-At).

A tendency to equilibrium may be expected to reduce asymmetry. Symmetrization can be measured by quantifying its changes with duration of the sample and with embedding. We refer to this new test as dynamic skewness. Vectors of 30, 40, 50, ..., 200 terms starting with each term of the series are constructed, and their skewness is measured. The average skewness for all vectors of the same length is calculated, and plotted against the vector length (embedding). Symmetrization is

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demonstrable in chaotic series (Fig. 4.7) but it is not consistently found in biotic series, either mathematical or empirical.32

Fig. 4.8 Skewness in the process (left) and logistic (right) equations. Top: Skewness is calculated for series of 2000 terms generated by the process and the logistic equations at fixed values of the gain. Bottom: Gain changes every 200 iterations. The logistic recursion becomes asymmetric with bifurcation cascade into chaos, reaching a peak of asymmetry at the end of period 2, at which point chaos become less asymmetric. Reversed asymmetry at period 3, and practically no asymmetry at 4.

32

Dynamic skewness is positive for some (but not all) economic data. Most the biological series examined show decreases in asymmetry, indicating equilibration. We observed increasing skewness with biotic series generated by the process equation at low gain (4.61 to 4.63) and both increases and decreases with biotic series generated at higher gains and with random walks.

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4.2.3 Transitivity, correlation and causality Correlation techniques can distinguish between deterministic and stochastic creative processes.33 Distinguishing deterministic chaos from colored noise is one important problem in time series analysis; several algorithms have been proposed. Correlation analysis is a simpler method, and it also differentiates bios from chaos. Aperiodic patterns such as those observed in many creative processes can be produced deterministically or randomly. Novelty may be generated by chance (i.e. as a result of an external agency); each change is independent from all previous ones. In contrast, a truly creative process generates novelty autodynamically. Past changes bring on the following ones, so there is continuity absent in stochastic noise.34 Causality is transitive in the mathematical sense. Can causation be demonstrated with statistical correlation techniques? St-dy,,.^ 1J

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Autocorrelation differentiates bios from chaos but not from noise. Pearson's correlation coefficient R measures how closely two series change together. Autocorrelation is computed by calculating the Pearson's correlation coefficient between the time series and lagged copies. Periodic series display positive autocorrelation when the lag corresponds with the period; in these studies, we use lag 1 unless otherwise specified (Fig. 4.10). Time series of empirical data, 33

Patel, M . and Sabelli, H . (2003). Autocorrelation and Frequency Analysis Differentiate Cardiac A n d Economic Bios From 1/F Noise. Kybernetes 32: 692-702. 34 T h e term stochastic noise includes processes that contain strong deterministic components; e.g. Brownian noise is generated b y the conservation of random changes, which is a deterministic process.

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mathematical bios, and statistical noise (pink, brown) show high positive autocorrelation for at least 16 lags (Fig. 4.11). In contrast, there is a negative autocorrelation between successive terms for periodic series and for chaotic series generated by the process equation. Pearson's correlation coefficient in chaos is alternating and decreasing with lags. Chaotic series generated by the logistic equation resemble random data in showing no autocorrelation. Autocorrelation is not sufficient to distinguish biotic from stochastic series. In the process equation (Fig. 4.9), bios is clearly different from chaos; there is a sharp discontinuity between chaos (negative autocorrelation) and bios (positive autocorrelation).35 Interpreting these differences, in periodicity and chaos change embodies opposition, while in bios and in biological processes, change connects similars. Negative or no autocorrelation distinguishes many chaotic series from noise, except for the Rossler attractor36 that shows positive autocorrelation. Thus, autocorrelation can often but not invariably distinguish chaotic from random walks. Autocorrelation is a statistical indication of continuity and hence of dynamic identity. A series of random numbers has no autocorrelation because it has no unity or identity. Bios and random walks demonstrate identity. Autocorrelation reveals period 2 within chaos. Chaotic series generated by the process equation with gain below 3.9 show alternatively positive and negative correlation for at least 16 lags (Fig. 4.15). Correlation techniques show the presence of an underlying period 2 also during the early phase of chaos generated with the logistic equation. We thus coined the term period 2 chaos.37 While, in retrospect, this could have been inferred from observation of the time series, we have not seen it reported before. The overlap of bios with period 6 in the recursion At+i = At - At_i + g * sin(At+i) is self-evident (Chapter 3). Periodic processes may thus overlap with chaos or bios. In contrast, many descriptions of 35

Biotic series show enormous variability in autocorrelation according to initial value, number of data points in the series, and gain. Autocorrelation does not change with initial value or number of points analyzed for chaotic series. 36 Rossler chaos resembles bios in many respects. This is the only case we know in which deterministic chaos might be confused with stochastic noise. 37 Patel, M. and H. Sabelli. (2003). Autocorrelation and Frequency Analysis Differentiate Cardiac And Economic Bios From 1/F Noise. Kybernetes 32: 692-702.

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attractors in dynamical systems portray them as mutually exclusive. It is assumed that each initial point tends to one attractor, and the state space is decomposed into these different basins. Instead, overlapping patterns suggest coexisting generators. Similarly, simple pre-existing natural forms together may generate novel and complex patterns. Natural patterns often overlap; for instance, the weather shows periodicity in a certain scale and chaoticity in another.

Fig. 4.10 Pearson's autocorrelation coefficient (lag 1). RRI represents an average often 1 hour records from different persons, while awake and during sleep.

The autocorrelation between successive changes should differentiate causal from stochastic processes (Fig. 4.12).38 However, random change produces significant negative correlation between successive differences (R = - 0.5). While surprising, it is to be expected, as the terms that are being compared At_i - At and At - At+] have At in common. In this light, the smaller negative correlation observed with 38

An ongoing causal process may be expected to generate correlation between successive changes; a lack of autocorrelation in the time series of differences between consecutive terms may suggest a stochastic origin.

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cardiac and biotic series, and the 0 correlation found in economic data and random walks, actually indicate the existence of non-random components in these series.

Fig. 4.11 Pearson correlation coefficients calculated for time series generated with the process equation at various gains, for stochastic and heartbeat interval series. Top left: Period 2 chaos g = 3.65. Top middle: Chaos g = 4.1. Top right: Bios g = 4.61. Bottom left: Brownian noise. Bottom middle: 1/f noise. Bottom right: heartbeat interval series.

When the change is causal, i.e. when it carries information, the correlation between successive changes is asymmetric, it differs from 0.5. In random data, the autocorrelation of differences is negative (there is change to and from At) and symmetric (as it corresponds to random change), hence 1 over 2. A symmetry of opposites, as in randomness, carries no information. Regarding 0.5 as 1 over 2 points to the connection between correlation and information measures, and specifically associates asymmetry with information, as opposed to symmetry and randomness. This highlights the heuristic value of attending to the meaning of numbers, in this case, 2 as information.

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Fig. 4.12 Autocorrelation of the series of differences. Note that difference of random series shows negative autocorrelation.

Fig. 4.13 Correlation between series and difference of the series.

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Fig. 4.15 Partial autocorrelation in time series generated by the process equation with different gains, and others. Top left: heart beat intervals. Top middle: 1/f noise. Top right: Period 2 chaos g = 3.65. Bottom left: Chaos g = 4.1. Bottom middle: Bios 4.61. Bottom right: Bios g = 5.2.

Correlations between each term At and the difference (At - At+i) are high (R circa 0.7) for random data as well as for chaotic series (Fig. 4.13). In contrast, the correlation is small (< 0.3) or 0 for most heartbeat series, for mathematical bios (at low gain) and for 1/f noise (for random generators). The smallness of the correlation parallels the finding of novelty. In the process equation (Fig. 4.14), bios is clearly different from

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chaos; there is a sharp discontinuity between chaos (positive correlation) and bios (no correlation). In summary, correlation studies demonstrate that bios resembles noise, chaos resembles random and the overlap of aperiodic and periodic patterns. They do not differentiate causal from stochastic processes. Partial autocorrelation provides evidence for causation. The partial autocorrelation coefficient measures the degree of association between At and At+i, when the effects of other time lags - 1 , 2, 3,..., up to i - 1 are partialled out.39 Time series recorded from some natural processes known to generate novel patterns, heartbeat interval series (Fig. 4.15), respiration, climatic and paleoclimatic changes, and other natural processes show extended partial autocorrelations, indicating deterministic rather than probabilistic origin. Positive and negative partial autocorrelations are observed at different lags, clearly indicating a periodic pattern in the case of coral records of temperature. Positive and negative partial autocorrelation for several lags (3 to 8) are also observed in chaotic and biotic series generated by the process equation at relatively low gain, at a higher gain, biotic series correlate for only one lag. In the same manner, 1/f noise (Fig. 4.15 right) and brown noise correlate for only one lag, as expected from the random origin of change in these series. Autocorrelation indicates continuity. Autocorrelation points to any causal link, such as conservation, while partial autocorrelation signifies internal causation (autodynamism). This interpretation of partial autocorrelation as evidence for autodynamism is congruent with the origin and use of statistics as a technique to recognize causal relations in the human sciences where experiments are often impossible, unethical, or too costly. Statistical correlation is strong evidence for causality. Correlation measures the frequency with which a relation is observed, and therefore it can only be modified by a significant number of subsequent observations. Statistical correlation is thus more strongly established than a non-statistical relation, which can be refuted by finding a single exception (Popper).

39

Kendal, M. (1973). Time series. London: Charles Griffin.

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This interpretation is at variance with the current interpretation of correlation40 originating with Yule.41 The alleged divorce between statistical correlation and scientific evidence for causal processes stems from two misunderstandings. The first is the nature of proof: while correlation does not demonstrate causation, nothing in science (other than mathematics) proves. Scientific evidence can falsify but never prove (Popper). The other misunderstanding concerns the nature of causation. Correlation is atemporal; causation requires time. It is argued that correlations do not prove causation because they often result from a common antecedent. A common antecedent is a causal process. That At and Bt are correlated never implies that At causes Bt or vice versa. No contemporary entities can 'cause' one another. Only a past action can be a causative factor for the presently correlated entities. A correlation between coexisting processes indicates a past interaction between them. Also, causation is often a complex process involving multiple factors. The reduction of causation to simple linear causality, either At causes Bt+i or Bt causes At+i has long been superceded.42 Quantum mechanical entanglement is a significant case of determined correlation irreducible to classic causality. Observing that two processes are correlated leads a scientist to search for shared causal factors. To dismiss correlation as a likely result of chance leads one nowhere. A scientist who dismisses a correlation as "spurious" whenever he does not find an explanation will miss important leads. A most dramatic example is the correlation between cancer and smoking, denied for many years by a distinguished statistician. Causation is the most likely explanation for correlation. It should be considered first. Regarding processes as sequences of actions rather than a course of random events lead one to consider autocorrelation as a portrait of transitivity and causation. Global autocorrelation techniques differentiate chaos (negative autocorrelation), period 2 chaos, and bios (positive 40

Schield, M. (1995). Correlation, determination and causality in introductory statistics. American Statistical Association. 41 Yule, G. U. (1926). Why Do We Sometimes Get Nonsense-Correlations Between Time-Series? Presidential address. Journal of the Royal Statistical Society 99: 1-69. 42 Bunge, M. (1959). Causality and Modern Science. New York: Dover.

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autocorrelation) from random series. Partial autocorrelation techniques indicate continuity in many empirical series and in biotic series, differentiating them from correlated random walks in which innovations are generated by accidental events. These results support the hypothesis that heart rate variation, respiration, and other physiological processes represent biotic series generated by bipolar feedback rather than random walks. Bios is characterized by positive autocorrelation of the time series and decorrelation between the time series and the series of differences. These two characteristics differentiate it from chaos. As a creative process generates new patterns, its time series may be expected to demonstrate both continuity and diversification. Diversification can also be demonstrated for statistical noise, but only biotic series generated by recursions of bipolar feedback or by natural processes show both continuity and diversification. Diversification differentiates creative bios from periodic and chaotic attractors. Continuity distinguishes bios from statistical noise. Bios is characterized by both continuity and novelty, conservation and diversification, a coexistence of opposites to be expected in creative processes. 4.2.4 Power spectrum analysis: 1/f pattern, novelty and action In nature, many things oscillate. Periodic oscillations can underlie aperiodic complexity, as illustrated by the generation of chaotic and biotic patterns by recursions of harmonic functions. Natural processes as well as humanly created signals often encode information in the sinusoids that form a signal. Fourier analysis decomposes a complex (periodic or aperiodic) trajectory into a set of sine and cosine waves.43 The power spectrum represents a histogram of the frequencies of the sine and cosine waves into which the curve has been decomposed. In many aperiodic time series, the power of the periodic components into which the curve has been decomposed is inversely proportional to their frequency f. In the log-power/log-frequency plane, the spectra are straight lines, and can be described by a single parameter, the slope p\ 43 The horizontal axis is the temporal frequency (frequency = 1/ time) and the vertical axis is the power, which portrays the energy at each of these frequencies. In periodic series, peaks portray these periods.

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including (3= -1 (1/f or pink noise, which corresponds to the sound of waves crushing on a beach), p = -2 (brown noise), and larger exponents 2 > (3 > -4 (black noise). (3 = 0 corresponds to randomness (white noise); chaotic series can also have p = 0. Continuing the color analogy, many other terms have been coined; we shall use the term green to indicate P = 1 because green is the complementary to red. These patterns are represented in Fig. 4.16. Table 4.1 presents the p exponent for a number of time series. In many natural processes (astronomical, physical, biological and psychological), the power spectrum shows an inverse relation between frequency and energy. This so-called "1/f noise" appears in cosmic microwave background radiation (CBR) and other astronomical series, radioactive decay, chemical systems, blood pressure, fluid dynamics, electronic devices, optical systems, flood records, nucleotide sequences in DNA, prime numbers, blood pressure, network traffic, economics, music, and psychology.44 Power spectra of time series reveal significant properties of the process; for instance, the power spectrum slope P of heartbeat interval series is higher (p < 0.05) during wakefulness than during sleep.45 The ubiquitous appearance of 1/f patterns in significant processes indicates their origin in fundamental natural processes. Processes with 1/f and 1/f2 patterns can be generated by the combination of random changes, and are often referred to as "noise", a term that indicates random origin and suggests lack of meaning. This seems unlikely.46 1/f patterns can be generated deterministically, as demonstrated by the occurrence of harmonics in any type of oscillatory 44

Schroeder, M. (1991). Fractals, Chaos, Power Laws. New York: W. H. Freeman; Gilden, D. L. (2001). Cognitive Emissions of 1/f Noise. Psychological Reviews 108: 33-56; Handel, P. H. and Chung, A L. (1993). Noise in physical systems and 1/ffluctuations. New York: Amer. Institute of Physics Press, W.H. (1978). Flicker noises in astronomy and elsewhere. Comments in Astrophysics 7: 103-109; Butler, G.C. et al. (1994). Fractal nature of short-term systolic BP and HR variability during lower body negative pressure. Amer. JPhysiol. 267 (1 Pt 2):R26-33. 45 Patel, M. and Sabelli, H. (2003). Autocorrelation and Frequency Analysis Differentiate Cardiac And Economic Bios From 1/F Noise. Kybernetes 32: 692-702. 46 In 1965, Arno Penzias and Robert Wilson (who shared the 1978 Nobel Prize in physics for their discovery) found an "excess antenna temperature" in a radio receiver being constructed at the Bell Telephone Laboratories.46 Dicke and co-workers interpreted this "noise" as the cosmic microwave background radiation (CBR) they were seeking as a remnant of the big bang predicted by George Gamow in 1948. This anecdote shows the reality of "noise": a pattern that is not recognized as such parades as random.

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mechanism, mechanical or electrical. Music, which is created, illustrates a third process that can generate 1/f pattern.

Fig. 4.16 Four canonical types of aperiodic patterns. Left: time series. From top to bottom: Chaos At+1 = 3.9 * sin(At). RRI: R to R intervals in electrocardiogram. Bios generated with high gain At+1 = At. + 10 * sin(At). ARRI: difference between successive heartbeat intervals. Right: idealized representation of power spectrum: Y = log power; X = log frequency.

Measures of recurrence isometry (Section 4.6) distinguish these three types of 1/f pattern (stochastic, deterministic, and creative) but open to question the nature of pink noise. Pink noise shows novelty (lower than random recurrence) and no consecutive recurrence (Fig. 4.17). Many other series such as cosmic background radiation (CBR), distant galaxies, DNA nucleotide sequences, Nile river levels, and the S&P 500, also show negative p, novelty and no consecutive recurrences at any embedding dimension. These results suggest the existence of a

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nonrandom pattern characterized by novelty and negative p exponent, which we shall here call flux, because it is evident in the CBR. When 1/f noise is created using simple deterministic functions,47 we observe high recurrence and consecutive recurrence. Biotic series, cardiac or mathematical, show novelty, consecutive recurrence, and power spectra inversely proportional to frequency; in the process equation, p grows with the intensity of the gain, nearing -2 with intense feedback. Variants of the process equation generate series with p = -1 as heartbeat series (Chapter 5). In contrast, chaotic series generated by the process equation (or by the logistic equation) do not. The shift from f° to fp emerges exactly at the edge between chaos and bios. The electroencephalogram shows a clear inverse relation between energy and frequency in health but not in abnormal states48 (Table 4.2). Prime numbers represent novelty in the number series. The power spectrum of the prime numbers contained in the successive intervals of equal length 1=216 =65536 up to N=238 ~ 2.749 x 1011 displays 1/f13 behavior with the exponent p ~ 1.64.49 This slope beta does not depend on the length of the sampled intervals, suggesting some kind of selfsimilarity in the distribution of primes. Notably, the exponent P is similar to that observed in mathematical bios. There is no generally accepted explanation for 1/f patterns. The inverse power law applies to multiple levels of organization indicating self-similarity. Mandelbrot has indeed proposed that fractality accounts for 1/f noise. The underlying mechanism of fractality has not been identified. The biotic pattern generated by At+1 = A, + (g * sin(At)) ((At/|At|) * (At(mod 2%))) is interesting because, as heartbeat series, it shows 1/f power spectrum, novelty and homeostatic-like boundaries.

47

Procaccia, I. and Schuster, H. G. Functional renormalization group theory of universal 1/f noise in dynamical systems. Phys Rev 28 A, 1210-12 (1983). 48 Gibbs, F. A. and Gibbs, E. L. (1952). Atlas ofElectroencephalography. MA: Addison-Wesley. 49 Wolf, M. 1/f Noise in the Distribution of Prime Numbers. Physica A 241: 493-499, (1997).

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Fig. 4.17 1/f pattern generated deterministically (top) or stochastically (bottom). Time series, isometry, recurrence plots (N = 1000, radius 10, embedding 10). Embedding plots (N= 3500 and radius 0.1).

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Table 4.1 Power Spectrum Analysis, p exponent for the time series, the time series of differences, and the time series of cumulative values. N = 2000, 32 harmonics. Power spectrum exponent P o

•

T~>-J-J-

^

i

Isometry quantification

•

XT

i

Series Differences Cumulative Novelty Uniform random 0 -1 Brown noise Dow Jones Bios, g = 4.61 Corn price Silver price RRI awake (average, 10 subjects) Pink noise RRI asleep (average, 10 subjects) Logistic chaos g=3.99 Gaussian white noise Process chaos, g= 4.3 EEG |

0.10 -2.11 -1.91 -1.76 -1.71 -1.67 _lM

0.78 ~ -0.10 0.24 0.37 0.28 0.29

-1.00 ^ -0.28 0.00 0.06 0.63 |

Consecutive

recurrence NO HIGH dim, only YES YES YES YES

-2.00 -1.90 -2.00 -2.00 -2.02 -2.00 _2QQ

NO YES YES YES YES YES ^Y E § yes

1.01 ^

-3.01 _2m

YYES E§

YNO E

YE§

YE§

1.60 1.50 0.32 2.58

-2.01 -2.00 -2.00 -1.34

Q n

|

|

YE§

NO LOW dim, only NO NO NO LOW dim, only YES | YES

Table 4.2 Energy / frequency relation in the human EEG. Fast frequency Slow frequency

High Voltage Seizure Slow wave sleep

Low voltage Wakefulness Coma

What process, stochastic, deterministic, or creative, generates the 1/f patterns prevalent in nature? To investigate, we50 have found it useful to calculate the power spectra of the time series, its derivative (time series of differences), and its integral (time series of cumulative values). The power spectrum exponent is larger (more positive) for the time series of the differences, and smaller (more negative) for its integral. Differencing random walks generates a random series. Differencing brown noise generates a time series with an exponent near 0 (as random data). Differencing mathematical bios generates chaos. The average value for the P exponent for RRI (heartbeat interval) series recorded during wakefulness is near - 1 , for RRI differences is near 1, and for the integral 50 Patel, M. and H. Sabelli. Autocorrelation And Frequency Analysis Differentiate Cardiac And Economic Bios From 1/F Noise. Kybernetes 32: 692-702, 2003.

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of RRIs is -2, corresponding to pink, green, and brown patterns (Table 4.1). The same results occur with CBR series that will be discussed more in Chapter 6. Similarly, time series of economic processes show an inverse relation between frequency and power, while the time series of differences show a positive relation. The time series of differences between consecutive terms shows a positive exponent P also for series with white noise spectrum (uniform and normal random, process chaos). For many series the p of the power spectra of the integrals often hovers around -2, as brown noise, while the p of the power spectra of the series of differences between consecutive terms has a positive value, rather than 0 as expected from sequences of random events. For a given set of data, there is a positive correlation between the power exponent |3 of the series and that of the series of differences; the Pearson r is 0.68 for heartbeat interval series and 0.98 for CBR data. These observations suggest that in some cases different power spectrum patterns may represent the recording of different aspects of a single natural process, not necessarily different types of processes. Differencing

JW\ pink

/ ^\^

\ white )

Integrating Fig. 4.18 Effect of differentiating and integrating on the power spectrum of time series.

The human electroencephalogram (EEG) has a multiplicity of rhythms that show a clear inverse relation between energy and frequency in health but not in abnormal states.51 It has a near green spectrum, shows a near 1/f spectrum after integration, and the integral of the integral of the EEG has slope - 2 ; this suggests to me that EEG records the difference between consecutive terms of a process with a 1/f spectrum. In 51

Gibbs, F.A. and Gibbs, EX. (1952). Atlas ofElectroencephalography. MA: Addison-Wesley.

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a similar manner, speech shows a positive spectrum slope and its integral shows a 1/f spectrum. The fact that the time series of differences of many series with a 1/f spectrum, as well as random series, have a positive p may shed some light on the processes that generate them. Power spectrum analysis relates energy with time. Power is the statistical frequency of action quanta; temporal frequency is 1 over time. As a rule, physical energy is a function of frequency: the higher the frequency, the greater the energy. In 1/f patterns, the greater the frequency, the lesser the energy (power). In the EEG, frequency and amplitude are inversely related, as if maintaining some kind of homeostasis. Do these facts relate to each other? To explain black body radiation (such as the CBR), Planck postulated that radiation can be emitted only in multiples of a quantum h that has the dimensions of action = energy x time. We52 speculate that a similar phenomenon may account for the widespread 1/f spectrum found in natural processes. 4.2.5 Creative, conservative and attractive processes Natural processes diversify, indicating creativity. Among mathematically generated series, bios diversifies, while periodic and chaotic series converge to stable attractors. These results support the view that systems should be regarded as processes in continual evolution, rather than as homeostatic or chaotic. Table 4.3 Stability and diversification in canonical patterns. Determined patterns Steady state Periodicity Chaos Bios

Instantaneous: AA = At-At+1 Constant AA = 0 AA#0 AA/0 AA^ 0

Stability / Diversification Local: Lyapunov Global: Standard Deviation exponent (SD) as a function of N Negative No change ASD/AN = 0 Negative No change Positive No change Positive Diversification

52 Patel, M. and Sabelli, H. (2003). Autocorrelation and Frequency Analysis Differentiate Cardiac And Economic Bios From 1/F Noise. Kybernetes 32: 692-702.

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Bios Table 4.4 Features distinguishing canonical patterns.

Aperiodic patterns White noise Random walks Chaos

~

Bios

Sensitivity to inputs, partial correlation No No Yes

1

Yes

Periods and shifts No No Yes

|

Yes

Diversification, Novelty, Complexes No Yes No

[

Yes

Power spectrum 0 1/f 0 or 1/f

1

1/f

Measures of diffusion and diversification distinguish expansive, conservative, and converging processes. Creative natural processes and mathematical bios are expansive processes. Expansive processes also include mechanical diffusion and random walks. The S.D. of Brownian motion increases without bound as N increases; this is described as "infinite variance". Increases in volume, ranging from physical to cultural diffusion, are found at all levels of organization. There is inorganic, biological, economic and psychological growth. Many natural and mental processes also create information in the form of new patterns and structures. Expansion, innovation, and diversity are characteristic of physical evolution. Diffusion and diversification represent irreversibility. In contrast, mechanical processes are reversible; they conserve information and maintain their pattern. Random processes vary incessantly, but the pattern remains the same. Both mechanical and random processes are conservative; they maintain their initial degree of diversity. Many other processes converge to equilibrium, to a cyclic trajectory, or to chaos. These are stable attractors that, once reached, remains stable. As random series, chaotic processes change continually, but the more they change, the more they remain the same. While the process converges to the attractor, information is lost; once the process hovers within the attractor, information is conserved.

4.3 Phase Plane of Opposites: Energy and Information Abstract: Concrete opposites such as repulsion and attraction are similar and different, synergistic and antagonistic, and should thus be measured as orthogonal axes in the Cartesian plane (phase plane of opposites). Two- and three-dimensional plots are used to reveal and

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measure nonlinear opposites in clinical and research settings. Phase plane portraits of motivation and interpersonal relations show that opposites co-exist, and that they are complementary, often positively correlated or uncorrelated, not inversely proportional or mutually exclusive as implicit in the linear scales standard in psychology and sociology. Linear scales demonstrably distort data and promote pathogenic black-and-white thinking. Planar scales distinguish two distinct cognitive-affective styles, linear and bifurcating personality, demonstrate how the process of biculturation in immigrants goes beyond assimilation, and promote insight and tolerance. They also show that creative phenomena occur when the nonlinear opposites are both relatively intense and of similar intensity. Phase portraits can and should be considered in terms of opposites. The Cartesian plane, which plays a major role in understanding physical and mathematical phenomena,53 is widely used in nonlinear dynamics (return maps At vs. At+i, phase portraits At vs. At - At+i, and cobweb plots of recursions x vs. f[x]), but their significance as portraits of opposites is seldom considered. In fact, most sociological and psychological tests measure opposites with linear scales that drastically and irretrievably distort the facts, decreasing understanding through the generation of spurious data. Abstract opposites can be imagined to be linearly opposed, as positive and negative numbers. Real opposites such as femininity and masculinity, or harmony and conflict, always coexist and have many similarities. Conflict is not negative harmony, nor is femininity a negative masculinity. In natural as well as mental processes, opposites have a common origin, coexist and overlap, can wax and wane together, and interact in both a synergistic and antagonistic manner. Attraction and repulsion, harmony and conflict, like and dislike are complementary opposites. We are more likely to love and have conflicts with those persons with whom we are close than with strangers; similarly, desirable features and 53

For instance, complex numbers were discovered by Girolamo Cardano in the 1600s, but dismissed even by him until they were interpreted geometrically at the end of the 18th century as points or vectors in the Cartesian plane, now renamed the "complex plane". The number a + ib is simply the point having the coordinates a and b, or the vector connecting the origin to that point.

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undesirable cost often grow together regarding purchases. The difference between opposite motivations is the information that underlies the choice (selection or rejection), but the intensity of positive and negative feelings adds energy to the issue. Thus opposites are not polar opposites in a linear continuum. They are complementary actions that are similar and different, mutually reinforcing and in another way inversely proportional. For this reason, opposites must be represented on separate axes orthogonal, but not independent, as they partially depend on each other. The detection and measurement of coexisting opposites is hindered by standard analytic methods that assume opposites exclude each other, coexist only transiently, are antagonistic, or vary inversely to each other. Standard logic posits an absolute mutual exclusion of opposites. Correspondingly, categorical scales assume that opposites do not overlap. A linear conception of opposition is also implicit in probabilistic and fuzzy logic. In mechanics, linear opposites neutralize each other. The use of linear scales in sociology, psychology and economics involves an uncritical extrapolation from mechanics. The widely used Liker type scales portray opposites as polar ends of a linear continuum. As such, opposites necessarily neutralize each other, thereby generating the illusion of equilibrium. These scales force opposites into a linear relationship in which they appear to be inversely proportional, one increasing while the other decreases, when, in fact, they may vary to some extent independently of one another if each opposite is measured separately. There is thus a need for new methods to analyze opposites. Combining the phase plane of qualitative dynamics and the concept of coexisting and co-creative opposites, we developed the phase plane of opposites as a practical method to empirically and numerically study creative and contradictory processes. Identify the opposites are involved in the process. Measure them separately, and plot them on orthogonal axes in a Cartesian plane. Plot the trajectory of the process under study in this plane (Fig. 4.19). This allows one to examine the degree to which they overlap and vary synergistically rather than reciprocally. If opposites wax and wane in a reciprocal manner (as assumed by linear scales), this can also be demonstrated in the planar scale, as illustrated in Figs. 4.19 and 4.20.

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4.3.1 The diamond ofopposites in psychology The phase plane of opposites was developed in the context of clinical psychiatric practice to study the temporal development of family relations,54 and has also been applied to the study of self-concept (Fig. 4.19), choices,55 interpersonal relations,56 and personality (Fig. 4.20).57 In clinical practice, to avoid the psychological connotations of up and down, we stand the Cartesian plane on its zero vertex, and for the sake of simplicity, we call it the diamond of opposites. Measuring opposites on orthogonal scales, rather than as extremes of a single linear scale, allows one to portray how opposites coexist, and vary together. Data on either the left or the right quadrants represent cases in which one opposite clearly dominates over the other, either attraction or repulsion. The bottom quadrant signifies that both forces are of low intensity (neutrality). The top quadrant is occupied when opposites are both of high intensity (contradiction, ambivalence). Note that the vertical axis of the diamond represents energy, which is carried by both opposites; the horizontal axis represents their different sign, the simplest form of information. Plotting a person's perception of her/his interpersonal and work relations at different ages serves to identify significant issues, and reveals the existence of qualitative changes and bifurcations. Studies of multiple interpersonal relations showed that more than a third of healthy nursing students report over 30 % of their close relationships as contradictory; attraction and repulsion often correlated positively with each other. The neutral quadrant is always emptier than the contradictory quadrant in all plots, indicating that coexisting opposites create ambivalent bonds, not 54

Sabelli, H. (1989). Union of Opposites. Lawrenceville, VA: Brunswick. Carlson-Sabelli, L., Sabelli, H.C., Patel, M , and Holm, K. (1992). The Union of Opposites in Sociometry: An Empirical Application of Process Theory. The Journal of Group Psychotherapy, Psychodrama and Sociometry 44: 147-171. 56 Carlson-Sabelli, L., Sabelli, H., and Hale, A. (1994). Sociometry and Sociodynamics. In Psychodrama since Moreno: Innovations in Theory and Practice. Karp, Watson and Holmes (Eds); Raaz, N . , Carlson-Sabelli, L. and Sabelli, H.C. (1992). Psychodrama in the treatment of multiple personality disorder: A creation theory perspective. In Kluft, E. (Ed). Expressive and functional therapies in the treatment of Multiple personality disorder. (169-188). Springfield, IL: Charles Thomas. Sabelli, L.C. (1992). Measuring co-existing opposites: A methodological exploration. Doctoral dissertation, University of Illinois at Chicago. 57 Sabelli, H., Zarankin, S. and Carlson-Sabelli, L. (accepted for publication). Bios Data Analysis. Part 6. Opposition: The Phase Portraits in Psychology, Sociology and Economics. J. Applied Systems Studies. 55

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neutrality. In contrast, many depressed patients showed no trajectories in the contradictory quadrant. Only by measuring repulsion separately from attraction is one able to differentiate ambivalence and contradiction from neutrality and indifference. In the above graphs, we can differentiate linear from bifurcating personalities (Fig. 4.20). For some persons, as harmony and attraction grow, conflict and repulsion diminish. Such a linear personality may reflect a simple, low energy psychological make-up, or a neurotic inability to recognize and/or tolerate ambiguity. In contrast, in persons with bifurcating personality harmony and conflict are not inversely related; they show many relations in the contradictory quadrant. Only the plane of opposites reveals this personality type, characterized by intense harmonious and intense conflictual relationships, and frequent changes from one to the other. High-energy persons consistently have and seek high-energy relationships that often are not readily tolerated by others. This may lead to interpersonal conflicts. Bifurcators make friends and enemies, and are simultaneously attractive and repelling for many others. They elicit contradictory feelings even from their friends; their life includes numerous and important bifurcations and break-ups. Plotting his personal world in the phase plane can bring immediate insight to persons with clear linear or bifurcating personalities. Clinical observations indicate that bifurcating features are typical of bipolar (manic-depressive) illness and bipolar personalities. The same bifurcating lifestyle is also present in other highly creative persons. Highly contradictory processes are the most likely to produce change, be it creative or destructive. Persons with bifurcating personality are intensely introverted and intensely extroverted; they think intensely and feel intensely. In contrast, low energy persons display opposites to a low degree. To detect these important aspects of personality one has to use a phase plane of opposites. In contrast, the widely used Myers-Briggs Type Indicator58 based on Jungian personality theory assumes that there are dichotomous preferences, so alternatives are presented as forced choices, rather than 58

Myers, I. B. and McCaulley, M. H. (1985). Manual: A Guide to the Development and Use of the Myers-Briggs Type Indicator. Palo Alto, CA: Consulting Psychologists Press.

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separately. The person is thus judged to be extrovert or introvert, thinking or feeling. 10 10

"i

' j

T 22: illness

I '•• r < X 1-.

10-18

0-1

1

0

^ ^ ^ a s ^ 1

2

«-

4

2

1

h-^N

6

8

2 S :

i

'

t

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0 -I

Like/Approve

Q

, 2 Like

,

* *

|

*

i

,

,

,

6

8

10

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*

*

Fig. 4.19 Phase plane representations of feelings by a chronically depressed patient. Left: Temporal evolution of self-concept from age 18 to 38. There is a clear relation between self-concept and external events (illness, marriage) that is common in persons with low self-confidence. The linear inverse relation between positive and negative feelings is typical of a linear mode of functioning. Right: Interpersonal relations at age 38. Comparing these two plots allows one to differentiate personal versus situational factors. This patient is predominantly linear in her self-perception but includes contradictory relations in her personal world.

M •x

Linwr p«rtonatity

/

/Catartroph.sx

/

\

\

/

W*

Bifiirc»tlnsjs«rsonality

/

\

*

*

*

\

/

• w

WL *

\

•

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Fig. 4.20 Left: The diamond of opposites and it Phase portrait of the personal world (family, friends) of two persons with ^W

f

Love

^V

f

f

0 Conflict

drastically different interpersonal styles.development 4.3.2 Bipolar illness and creative

In the background of our notion of creativity as the product of bipolar feedback is our clinical experience with bipolar mood and the creativity associated with it. Briefly, bipolar illness includes episodes of elevated (mania) or decreased (depression) energy. During episodes of mania or

158

Bios

hypomania (mild mania), bipolar persons had greater energy, and thereby elevated mood, increased productivity, increased self-love and love in its multiple manifestations (sexuality, affection, and solidarity); they also experience greater negative feelings such as anger, anxiety, paranoia, and even depression. In other words, greater energy increases opposite feelings. Bipolar persons have passionate and chaotic personal and professional relationships. Figure 4.21 illustrates observations on a couple of bipolar persons. The metabolism of a neurohormone (phenylethylamine)59 that modulates energy and affect was decreased below normal in both spouses; such a neurohormone deficit may be the cause of the depression (priority of the simple). However, both spouses showed a peak in excretion the day of their divorce, denoting stress. This change illustrates the supremacy of the complex. A high proportion of close relations were intense and conflictual or mixed in both cases, illustrating the coexistence of opposites. Bipolarity is associated with increased creativity in patients and their relatives, as reported by many artists and psychiatrists and psychologists.60 Manic-depressives tend to be creative outside their 59

Sabelli, H. C. and Javaid, J. I. Phenylethylamine modulation of affect: Therapeutic and diagnostic implications. J. Neuropsychiatry & Clinical Neurosciences. 1995; 7:6-14; Sabelli, H. 2002. Phenylethylamine deficit and replacement in depressive Illness. In D. Mischoulon and J. F. Rosenbaum. Natural Medications for Psychiatric Disorders. Baltimore: Lippincottt Williams and Wilkins. Pp. 83-110. 60 Akiskal, H. and Akiskal, K. (1988). Reassessing the prevalence of bipolar disorders: clinical significance and artistic creativity. Psychiatry and Psychobiology 3(Suppl): 29S-36S; Akiskal, H. S. and Mallya, G. (1987). Criteria for the "Soft" Bipolar Spectrum: Treatment Implications. Psychopharmacology Bulletin 23: 68-73; Jamison, K.R. (1993). Touched with Fire. The Free Press, Macmillan Inc; Schildkraut, J.J., Hirshfeld, A.J., and Murphy, J. M. (1994). Mind and mood in modern art. Depressive disorders, spirituality and early deaths in the Abstract Expressionist Artists of the New York School. Am J Psychiatry 151: 482-488; Andreasen, N.C. and Glick, I.D. (1988). Bipolar affective disorder and creativity: implications and clinical management. Comprehensive Psychiatry 29: 207-217; Arieti, S. (1976) Creativity: The magic synthesis. New York: Basic Books; Barron, F., Harrington, D.M. (1981). Creativity, intelligence and personality. Annual Review of Psychology 32: 439-476; Braff, D.L. and Geyer, M.A. (1990). Sensorimotor gating and schizophrenia. Arch. Gen. Psychiatry 47: 181-188; Cattell, R.B. and Drevdahl, J.E. (1956). A comparison of the personality profile (16 P.F.) of eminent researchers with that of eminent teachers and administrators, and of the general population. Gen. Psych. 46: 248-261. Delias, M. and Gaier, E.L. (1970). Identification of creativity in the individual. Psychological Bulletin 73: 55-73; Lombroso, C. (1891). The Man of Genius, (original edition in Italian) London: Walter Scott; Ludwig, A.M. (1989). Reflections on creativity and madness. American Journal of Psychotherapy 43: 4-14; Ludwig, A.M. (1994). Mental illness and creative activity in female writers. American Journal of Psychiatry 151: 1650-1656; Rothenberg, A. (1971). The process of janusian thinking in creativity. Arch Gen Psychiatry 24: 195-205.

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affective episodes; manic subjects have a subjective feeling of creativity, although excessive energy during a manic episode actually interferes with creativity. Well relatives of manic-depressive patients often have bipolar personality and are highly creative in business, art, and science. Already Aristotle had noted that many eminent persons are afflicted by "melancholy", specifically describing manic-depressive illness.

Fig. 4.21 Observations in a couple of bipolar persons. Left: The metabolism of a neurohormone, phenylethylamine, is estimated by quantifying the daily excretion of its main metabolite. Right: Proportion of harmonic and conflictual relations (with close relatives and co-workers) evaluated with the phase plane of opposites (Section 4.3).

Fig. 4.22 Percentage of consecutive isometries in groups of healthy controls, and unipolar and bipolar depressed persons.

Extreme changes in energy and mood denote simpler causal processes. Consistent with this view, the percentage of recurrences and consecutive recurrences is greater in unipolar and bipolar depressed

160

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persons than in healthy controls, and much greater in psychotic manic patients.61 4.3.3 Sociometry: from catastrophe to co-creation Rumanian-American psychiatrist Jacob Moreno generated a set of methods for empirical measurement of personal interactions that are, at the same time, assessments and therapies.62 Moreno's sociometry owes its power to the combination of a clinical and therapeutic approach to social behavior with simple mathematical techniques that practitioners can readily apply. We expanded the sociometric test by using the phase plane of opposites (sociodynamic test). Studies of choice suggest that a theory of co-creation may be developed by conceptualizing the fold catastrophe as the simplest complexity generated by the interaction of opposites. In using planar plots in the study of choice,63 subjective evaluations of the intensity of the person's feelings and motivations regarding a given personal choice or a social policy are obtained using graphic scales or written questionnaires that contain separate scales for opposites. We have found these graphs useful to help persons express feelings that they do not dare to present when they are forced to make a choice.64 61

These observations are open to question because manic patients were treated with antipsychotic drugs. However, similar increases in recurrence isometry and consecutive recurrence were also found in psychotic patients who were not receiving anti-psychotic drug treatment for two for more weeks. Carlson-Sabelli L, Sabelli HC, Zbilut J, Messer J, Diez-Martin J, Walthall K, Tom C, Patel M, Zdanovics O, Fink P, Sugerman A. Cardiac patterns of emotions demonstrated by the process method: Psychotic patterns. New Systems Thinking and Action for a New Century: Proc. International Systems Society 38th Annual Mtg., B. Brady and L. Peeno (Eds.), Pacific Grove, CA, 1994, pp. 0419-0430. 62 Carlson-Sabelli, L., Sabelli, H., and Hale, A. (1994). Sociometry and Sociodynamics. In Psychodrama since Moreno: Innovations in Theory and Practice. Karp, Watson and Holmes (Eds). 63 Carlson-Sabelli, L., Sabelli, H.C., Patel, M , and Holm, K. (1992). The Union of Opposites in Sociometry: An Empirical Application of Process Theory. The Journal of Group Psychotherapy, Psychodrama and Sociometry 44(4): 147-171; Carlson-Sabelli, L., Sabelli, H., and Hale, A. (1994). Sociometry and Sociodynamics. In Psychodrama since Moreno: Innovations in Theory and Practice. Karp, Watson and Holmes (Eds). 64 Planar plots of opposites are particular useful to help persons to express opinions regarding issues that they find difficult to express in a linear scale for emotional reasons, such as negative evaluations of the government in a time of war. This was noted by E. Petacque in her interview of University of Illinois students during Gulf War I. [quoted by Sabelli, H. and L. Carlson-Sabelli. Sociodynamics: the application of process methods to the social sciences. Chaos Theory and Society (A. Albert, editor). I.O.S.Press, Amsterdam, Holland, and Les Presses de l'Universite du Quebec, Sainte-Foy, Canada (1995)]. The majority of students supported the government when given a linear scale that ranged

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Linear sociometric scales measure the hierarchy of choices, from first choice to rejections. The sociodynamic test65 uses a tridimensional scale in which the person also records the positive and negative feelings and motivations that underlie his/her choices and rejections. These opposite motivations are plotted in a diamond. Then the hierarchy of choices and rejections are plotted in a third axis (Fig. 4.24).66 When the shape of the choice outcomes is plotted as a function of the positive and negative motivations, one often finds nonlinearity that fits a simple fold catastrophe.67 Catastrophes are tridimensional forms regulated by two parameters, the simplest of which are regulated by two factors, asymmetric (a) and bifurcating (b). In our example, the sum of opposite motivations functions as a bifurcating control variable: at high intensities, choices and rejections are obtained. Each of the two possible outcomes occurs at one end of the asymmetric factor. At intermediate values, the outcome is determined by the bifurcating parameter: neutrality at low values and catastrophe at high values, i.e. one or the other of the two outcomes occur, and sudden switches from one to the other can occur. The difference between opposites functions as the asymmetric factor. An asymmetry between the opposites provides information regarding the outcome; when opposite forces are of similar intensity, both opposite outcomes are equally possible.68 We may thus interpret the abstract control variables of catastrophe theory in terms of interacting opposite processes.

between "strongly agree" and "strongly disagree" with the current policy. Yet, they showed extremely contradictory feelings when "approve/ agreement" and "disapprove / disagreement" were plotted in different scales. 65 Carlson-Sabelli, L., Sabelli, H., and Hale, A. (1994). Sociometry and Sociodynamics. In Psychodrama since Moreno: Innovations in Theory and Practice. Karp, Watson and Holmes (Eds). 66 This may be a pencil and paper exercise, but it is best performed in action, by drawing the diamond in the floor so the person can show his/her positive and negative feelings regarding a given choice by standing in the appropriate place, and can indicate choice or rejection by behavior such as lifting one arm or the other. 67 There are only a few cases of linear relation. 68 Carlson-Sabelli, L., Sabelli, H.C., Patel, M., and Holm, K. (1992). The Union of Opposites in Sociometry: An Empirical Application of Process Theory. The Journal of Group Psychotherapy, Psychodrama and Sociometry 44(4): 147-171.

162

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Fig. 4.23 Left: The Sociodynamic Test using the diamond of opposites to plot positive and negative motivations and feelings in orthogonal axes. Right: The relation between opposition, energy and information in the diamond of opposites. The plot of opposites is transformed into a plot of energy versus information by a 45° rotation.

These experiments lead us to interpret the bifurcating and asymmetric factors as mathematical representations of energy and information.69 As both positive and negative motivations contribute to the emotional energy involved in a choice, we regard the bifurcating factor as the energy provided by the sum of opposites. The difference between opposite motivations provides information regarding choices; we thus regard the asymmetric factor as a function of information. The identification of difference with information is congruent with the notion of change as the carrier of information.70 These considerations lead us to interpret the diamond of opposites as a portrait of energy and information (Fig. 4.22). Mathematical experiments indicate that these principles may apply beyond catastrophes to cascades of bifurcations, chaos and bios. Noting this equivalence has a practical application. The person may feel and perhaps express greater energy regarding a choice than expected by the reported positive and negative motivations. Such difference serves as a signal to reconsider conscious motivations, assisting the person to come in touch with additional, possibly unconscious, factors.

69

Sabelli, H. C. and Carlson-Sabelli, L. (1992). Process Theory: Energy, Information and Structure in the Phase Space of Opposites. Proceedings of the International Society for the Systems Science. Bateson, G. (1979). Mind and Nature: A Necessary Unity. New York: Dutton.

70

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Fig. 4.24 Catastrophe and co-creation. Left: A simple catastrophe generated by the competition of two attractors (P and N). The outcome (choice, plotted in the third dimension) is determined by the relative power of the opposite attractors. The bifurcating parameter of the catastrophe is the energy resulting from the sum of the opposites, and the asymmetric parameter is the difference between the two opposites. Right: The catastrophe may be interpreted as the simplest case if co-creation of complexity. When the trajectory reaches one pole or another, the state of the system is simple. Greater complexity occurs at the fold, when there is "ambivalence" between the two poles.

The phase plane of opposites reveals a significant association between creative processes and coexisting opposites. High-energy contradictory processes, either intrapsychic or interpersonal, have a great potential for creativity and destruction, and are easily influenced by small interventions. The capability to identify contradictions is thus useful to target issues that are most amenable to therapeutic intervention at a given time. Persons who have ambivalent feelings regarding enacting a protagonist role in psychodrama or similar group therapy exercises make more productive protagonists than persons who are indifferent or eager to become protagonists.71 Psychotherapy proceeds faster by targeting ambivalent, contradictory feelings and beliefs. The use of the diamond of opposites fosters insight and creativity as it helps the patient to become aware of coexisting opposites in himself and in others. We regard this catastrophe-like phenomenon as a model for cocreation by the interaction of opposites. At the two extremes of positive or negative motivation, there are simple outcomes, either choice or 71 Carlson-Sabelli, L., Sabelli, H., and Hale, A. (1994). Sociometry and Sociodynamics. In Psychodrama since Moreno: Innovations in Theory and Practice. Karp, Watson and Holmes (Eds).

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rejection. But when the opposite motivations are both intense, there is greater complexity from which new behaviors emerge. Placing issues in the contradictory quadrant does not portray only ambivalence; ambivalent participants in sociodynamic exercises spontaneously attempt to create a third alternative, such as a modified task, illustrating how nonlinear opposites foster creation.72 Catastrophes constitute the simplest case of organization. At each extreme, there is a simple state, either P (positive) or N (negative) in Fig. 4.24. The trajectory between these extremes shows a fold, a more complex region in which either of the two outcomes may come about. We thus regard a catastrophe as the creation of a tridimensional form by a two-dimensional opposition. Energy and symmetry increase complexity in catastrophes. Generalizing, in the interaction between processes, the difference between opposites P and N provides the information I: a = I(S) = g [ P - N ] , and the energy of both contributes to the total energy E of the system S, which for symmetric opposites is simply b = E(S) = V(P2 + N2). 4.3.4 The diamond of opposites in sociology Zarankin and I used the diamond of opposites to study the coexistence of Anglo-Saxon and Latino cultural worldviews in a sample of 64 working 72

Psychotherapy proceeds faster by targeting ambivalent, contradictory feelings and beliefs, as identified with the diamond of opposites. The use of the diamond of opposites itself fosters insight creativity by helping the patient to become aware of coexisting opposites in himself and others. In our clinical experience (Sabelli and Carlson-Sabelli, 1989), the most useful interventions are those that support to a large extend, but also challenge the patient's interpretations or beliefs ("partial contradiction"), as contrasted to confrontational interpretations and to Rogers' unconditional regard (Rogers, 1951). Using the diamond of opposites to choose the protagonist for a psychodrama or a gestalt exercise has made us realize that the most productive sessions obtain when the person has contradictory feelings regarding such role. Likewise the issues most profitably explored are those involving contradictory feelings. High-energy contradictory processes, either intrapsychic or interpersonal, have a great potential for creativity and destructiveness, and are easily influenced by small interventions. The capability to identity contradictions is thus useful to target issues that are most amenable to therapeutic intervention at a given time. On the other hand, excessive emotional energy, as often manifested by borderline personalities or by normal persons under stress actually clouds the intellect and prevents therapeutic resolution. In these cases, it is more useful to reduce emotional energy, and to focus on minor rather than large changes.

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Hispanic women.73 The test consists of pairs of opposite questions, such as "How important is it to you being fair? How important is it to you being loyal? For instance, if you have to decide who should get a job, and one of the applicants is a friend, how much value do you place on being fair, and treating equally friend and stranger? How much value do you place on being loyal to your friend? "1A The questions were directed to test commonly held ideas about differences between Latino behavior and mainstream American mores as reported in the literature,75 and as suggested by our clinical, educational,76 and personal 77 experience. For instance, the perception of time and schedules is often conceptually different. An Anglo-Saxon is presumed to start and end each activity on time, and he or she is therefore on time for the next appointment. A Latino is presumed to end the activity when the task is finished, and he or she is therefore often late for the next appointment. Anglo-Saxons are assumed to value honesty, and to disregard "honor" as childish or primitive.78 They feel guilt more often than shame. A Latino is presumed to value honor and heroism, and to regard minor breaches in honesty as inconsequential. They are 73

Zarankin, S. and Sabelli, H. (1996). Bi-culturality among Hispanic Working Women. The Union of Opposites in Psychosocial Testing and Education. Proceedings of the International Systems Society, 40th meeting. Sustainable Peace in the World System, and the Next Evolution of Human Consciousness M. L. W. Hall (Ed). Louisville, KE, pp. 691-702. 74 From a pool of 100 such questions, we here consider 22 pairs. Answers were reported as numbers from 0 to 100. Interviewees were specifically requested not to add up answers to opposite questions to a total of 100, and were given a written example of how answers to opposite questions may have independent values. The results are reported as mean + standard deviation for the entire group. 75 Cohen, R. E. (1987). Stressors: Migration and Acculturation to American Society. Health and Behavior: Research Agenda for Hispanics. Chicago: University of Illinois; Comas-Diaz, L. (1989). Hispanic/Latino Communities: Psychological Implications. The Journal of Training and Practice in Professional Psychology 4: 14-31; Falicov, C. (1982). Mexican Families. In Ethnicity and Family Therapy, M. McGoldrick, J. K; Fravega, H. (1989). An Ethnomedical Medical Perspective of AngloAmerican Psychiatry. American Journal of Psychiatry 146: 588-596; Hall, E. T. (1976). Beyond Culture. Garden City, NY: Doubleday; Torre, C. (1994). The Commuter Nation. Rio Piedras, P. R.: Editorial Universidad de Puerto Rico. 76 Zarankin, S. (1992). Psychoeducational Workshops: a Multidimensional Approach to Prevention and Treatment Intervention Program for the Latino Community. Doctoral dissertation, Illinois School of Professional Psychology. 77 Sabelli, H. (1997). Becoming Hispanic, Becoming American: Latin American Immigrants' Journey towards National Identity. Immigrant Experiences, P. Elovitz and C. Kahn (Eds). 78 Illustrating the racial bias that permeates much education, many psychology courses teach that honor (dignity versus shame) is more primitive than duty (innocence versus guilt), and thereby psychotherapists apply these concepts in their practice. Hispanic families are often described as "enmeshed", solidarity is omitted among normal feelings, and selfishness is regarded as normal.

166

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assumed to feel shame more often than guilt. Favoring a friend is regarded as unfair in Anglo-Saxon culture and as a duty in Latino culture. Hiring a friend and marrying a co-worker are discouraged in Anglo-Saxon culture, while they are regarded as desirable in many Latino cultures. Our study showed that opposite views coexisted in most interviewees.79 These and other empirical results indicate most of the stated "facts" about cultural differences reflect cultural stereotypes and are imbued by static models. The study of "cultural differences", for instance, neglects the influence of separation from the culture of origin, adaptation to a different culture, and the creative interaction of two cultures in each individual. While we all tend to accept what appears as universal within the context of our society, exposure to another culture reveals that there are options. Thus, each person feels free to choose the pattern newly encountered, retain the old one, or invent a new behavior. This study led us to propose a new concept: We define biculturation as a creative process of cognitive, affective and behavioral transformation that occurs when a person who grew up in one culture lives in another. Beyond assimilation and multiculturalism, biculturation creates novelty and complexity. Biculturation exemplifies co-creation. Notably, bilingualism is associated with more effective controlled processing in children. This bilingual advantage persists for adults and attenuates the negative effects of aging on cognitive control.80 Biculturation is not a special phenomenon applicable to particular individuals or populations. Civilization has evolved throughout the centuries through the intercourse of cultures, which is particularly strong in commercial and imperial centers such as the USA. Without interchange, culture becomes stagnant. Monoculture depletes the intellect just as agricultural monoculture depletes the soil. Based on the concept Contrary to anecdotal reports, the vast majority of Hispanic women considered being on time very important (95 + 11). Yet, many also considered it important to be natural and free from rigid schedules (55 + 33), and flexible to accommodate others (76 + 17). Likewise, contrary to common perceptions, Hispanic women valued fairness (91 + 13) as equally important as loyalty (87+ 18), and in fact, stress on loyalty correlated positively with stress on fairness (r = 0.568). Shame and guilt, often regarded as alternative responses, were found to coexist. When they felt they had done something wrong, Hispanic women experienced shame or guilt equally often. 80 Ellen Bialystok, E., Fergus I. M., Klein, R. and M. Viswanathan (2004). Bilingualism, Aging, and Cognitive Control: Evidence From the Simon Task. Psychology and Aging 204: 290-303.

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of co-creation, we view biculturation as a desirable creative process, and regard cultural uniformity as well as separation along ethnic or religious lines as highly detrimental. Current political debate moves between the assertion of AngloAmerican dominance demanding the assimilation of immigrants into a unitary national culture and the paradigm of identity politics that stresses the right to multiculturalism. Either of these two concepts subjects the person to the group, while biculturation is a process of individuation. Frightened by the increase in the Hispanic population, some ideologues want to specifically exclude Hispanic-speaking persons from the USA.81 The language we speak predetermines the way we think (Humboldt, Sapir, Whorf)82 and as a bilingual psychiatrist, I found that Spanish has helped me to detect and correct pathogenic social attitudes.83 Also, duty is regarded as one of the four giants of the soul in the Hispanic psychiatric literature84 but it is notoriously absent in much of the current psychiatric, sociological and sociobiological literature. "Negative" feelings such as guilt and shame are fundamental for ethics,85 just as "negative" emotions such as fear are essential for survival; the current fashion among self-styled psychotherapists to regard guilt and shame as "symptoms" portrays an unacceptable cultural deviation. In addition to their own culture, immigration itself provides unique experiences that contribute to cultural development.86

81

Huntington, S. P. Who are we? The Challenges to America's National Identity. Simon and Sinister, 2004. 82 Whorf, B. L. (1956). Language, Thought and Reality (ed. J. B. Carroll). Cambridge, MA: MIT Press. 83 For instance, it is significant that in English / is capitalized and you is not, while in Spanish Usted is capitalized and yo is not. It is particularly revealing to hear the question "How much are you worth?" meaning how much money do you have, and "number one" meaning oneself. As a psychiatrist, I regard these expressions as reflecting and promoting narcissistic social pathology. 84 Mira y Lopez, E. Cuatro gigantes del alma. Ed. El Ateneo, Buenos Aires, 1947. 85 When God saw how bad humans had become, Zeus sent them two gifts, guilt and shame, to help them improve their behavior; Jehovah sent the flood. 86 Immigrant Experiences. Personal Narrative and Psychological Analysis. Edited by P. Elovitz and C. Kahn, Fairleigh Dickinson University Press, 1997.

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4.3.5 The phase plane ofopposites in biotic equations At a given time, the interaction of opposites may result in a gradual or catastrophic switch between polar extremes, but as a process, interacting opposites co-create cycles, chaos and bios, as illustrated by catastrophic (Chapter 2) and biotic (Chapter 3) recursions. Computer experiments with biotic recursions show that the complexity of patterns also increases with the intensity and symmetry of opposites (Chapter 8). First, the complexity of pattern increases with the intensity (energy) of the feedback. Second, experiments in which the bipolar feedback is rendered asymmetric At+i = At + g * (q + sinAt) show that the pattern is most complex when the opposition is roughly symmetric (between 1 and -1) and decreases with asymmetry q. Notably, a plot of these experiments reveals a diamond ofopposites87 (Fig. 8.9). Summarizing, methods that assume a categorical distinction, or an inverse linear relation between them, cannot be valid or even fruitful; they prevent the recognition of bipolar relations, contradiction, ambivalence and intrapsychic conflict, and thus they conceal, rather than reveal, why and how change is engendered or prevented. This misrepresentation has practical consequences such as in psychological testing, public opinion polls, or the design of economic policy. The phase plane of opposites can and should be applied in educational contexts and sociological polls.88 The use of linear or planar scales to plot opposites is not a matter of choice, but of scientific validity.

87 There are chains of infmitations from g = n and |q| = 1, to g = 2K and q = 0. This diagonal chain of leaps (infmitations) together with the overall shape of the boundary between steady state and periods, period and chaos, and chaos and bio-parabios, forms the diamond ofopposites. 88 It is now being included in the qualifying exam for psychodramatists and has become a relatively standard method in sociometry.

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4.3.6 Psychogeometry:89 the trifurcation of anger, anxiety and depression Psychogeometry uses N-dimensional space representations to describe subjective reports of emotions and vegetative functions. I use these recordings in my practice to monitor the evolution of depressed and anxious patients. Daily reports of positive and negative emotions, as well as positive and negative events, are obtained for extended periods of time (1 month to three years) using a 0 to 9 scale.90 We have analyzed some of these data.91 We have also studied healthy adults in the same manner, and depressed and non-depressed persons incarcerated for major crimes.92 For visualization, triads of subjective feelings (such as anger, fear and depression) are plotted in a cube in which each axis represents 89

Carlson-Sabelli, L., Sabelli, H.C., Hein, N., and Javaid, J. (1990). Psychogeometry: The Dynamics of Behavior. Proc of the Internal Soc for the Systems Sciences 769-775; Sabelli, H.C., Patel, M., Carlson-Sabelli, L., Hein, N., and Harris, E. (1991). Psychogeometry, the Dynamic Analysis of Mood Processes. Proc of the Inaugural Meeting of the Soc for Chaos Theory in Psychology. San Francisco, CA; Sabelli, H.C., Carlson-Sabelli, L., Patel, M., Hein, N., and Harris, E. (1992). Psychogeometry, the Dynamic Analysis of Mood. Presented at The 145th Amer. Psychiat. Assoc. Washington, D.C.; Sabelli, H., Carlson-Sabelli, L., Levy, A., Patel, M. (1995). Anger, fear, depression and crime: physiological and psychological studies using the process method. Chaos Theory in Psychology and the Life Sciences, R. Robertson and A. Combs (Eds). Mahwah, NJ: Lawrence Erlbaum, pp 65-88. 90 Sabelli, H.C., Patel, M., Carlson-Sabelli, L., Hein, N., and Harris, E. (1991). Psychogeometry, the Dynamic Analysis of Mood Processes. Proc of the Inaugural Meeting of the Soc for Chaos Theory in Psychology. San Francisco, CA; Carlson-Sabelli, L., Sabelli, H.C., Hein, N., and Javaid, J. (1990). Psychogeometry: The Dynamics of Behavior. Proc Internat. Soc for the Systems Sciences 769-775; Sabelli, H., Carlson-Sabelli, L., Levy, A., and Patel, M. (1995). Anger, fear, depression and crime: physiological and psychological studies using the process method. Chaos Theory in Psychology and the Life Sciences, R. Robertson and A. Combs (Eds). Mahwah, NJ: Lawrence Erlbaum, pp. 65-88. 91 Subjects included adults of both sexes, single and married, with middle class occupations and education. They included healthy persons, patients with mild depression (dysthymic disorder), severe depression (unipolar or bipolar), and patients with problems in living without psychiatric dysfunction. Each person was asked to keep a daily inventory measured on a scale from 0 (none) to 9 (very intense) of positive and negative feelings toward a significant other (usually their spouse), levels of joy, depression, anger and rage, fear and anxiety, sexual feelings and behavior, sleep quality, as well as of positive and negative events. Each of these categories was the person's subjective evaluation of his or her overall feelings as experienced during the past 24 hours. Subjects were carefully instructed to plot separately positive and negative feelings, positive and negative events, not "average" them mentally. These reports were then used to monitor their current psychological state and symptomatology, in many cases for months and in some for three years. 92 Levy, A. B. (1991). A clinical study of the urinary phenylacetic acid (PAA) test of depression in prison inmates. A doctoral dissertation presented to the Department of Clinical Psychology, Brigham Young University; Sabelli, H., Carlson-Sabelli, L., Levy, A., Patel, M. 1995. Anger, fear, depression and crime: physiological and psychological studies using the process method. Chaos Theory in Psychology and the Life Sciences, edited by R. Robertson and A. Combs. Mahwah, New Jersey: Lawrence Erlbaum, pp. 65-88.

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one of these variables. The point determined by these three variables describes the state of the process at a given day. Plotting the successive states creates a trajectory, a qualitative portrait of the emotional patterns. These studies showed that positive (energy, joy, sexual arousal) and negative (anger, fear, depression) emotions are not inversely related; they readily coexist in many persons.93 These results support the notion of the union of opposites. Further, they also provide experimental support to the conflict theory of depression that we had advanced on clinical grounds.94 Traditional theories stress the interaction of opposites. In Freudian theory, which posits the conservation of energy, depression is anger turned inwards; it predicts the intensity of outward directed anger and depression to be inversely related. In Cannon's homeostatic theory, conflict poses an alternative: fight or flight. The emotional counterparts of these two behaviors are anger and fear. Cannon's fight-or-flight dichotomy has been interpreted through the mathematical model of catastrophes.95 Cannon's model predicts that anger and fear should be inversely correlated. Beyond opposites, we should consider triads. In fact, mammals have three responses to conflict: they may also surrender. The corresponding emotion is discouragement. Surrender is an effective defense because there is a biological taboo against intraspecies killing: victorious animals stop their attack against those who surrender. Thus, conflict produces a trifurcation between three defensive processes, not a dichotomy. We propose that when conflict occurs, the subject experiences anger, fear, and discouragement in various proportions. Rage, anxiety and depression are augmented, or pathological, manifestations of anger, fear and discouragement. This hypothesis predicts that the opposing emotions of 93 Carlson-Sabelli, L., Patel, M., Hein, N . , and Harris, E. (1992). Psychogeometry, the Dynamic Analysis of Mood. Presented at The 145th Amer. Psychiat. Assoc. Washington, D.C. 94 Sabelli, H . (1989). Union of Opposites. Lawrenceville, VA: Brunswick; Sabelli, H. a n d CarlsonSabelli, L. (1989). Biological Priority a n d Psychological Supremacy, a N e w Integrative Paradigm Derived from Process Theory. American Journal of Psychiatry 146: 1541-1551; Sabelli, H . C , Carlson-Sabelli, L., Javaid, J. I. (1990). The Thermodynamics of Bipolarity: A Bifurcation Model of Bipolar Illness and Bipolar Character and its Psychotherapeutic Applications. Psychiatry: Interpersonal and Biological Processes 53:346-367; Sabelli, H.C. and Carlson-Sabelli, L. (1991). Process Theory as a Framework for Comprehensive Psychodynamic Formulations. Genetic, Social, and General Psychology Monographs 117:5-27. 95 Zeeman, E. (1976). Catastrophe Theory. Scientific American 234:65-83.

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anger, fear and discouragement occur together.96 Statistically, anger, fear and depression were positively correlated in both healthy subjects and psychiatric patients.97 The results support the view of depression as a response to conflict, explaining its association with anxiety and anger, and providing a rationale for treatment (Chapter 16). In tridimensional space portraits, we could readily recognize by visual inspection several types of trajectories (Fig. 4.26). In most cases, the trajectories are aperiodic.98 Comparisons between depressed and nondepressed persons, as well as between women and men, showed significant differences, but the paucity of data does not allow for their definition as chaotic, biotic or stochastic. In contrast, the psychogeometric plots generated by incarcerated criminals show tight trajectories occupying a relatively small area of the state space near the zero point, with occasional spoke-like trajectories that spin off and rapidly return to the origin. We interpret these trajectories as point attractors (equilibrium). These equilibrium patterns were found in 67% of non-depressed jail inmates and were never found in any other person. Emotional indifference is expected in sociopathic individuals. That criminals, but not normal persons, showed equilibrium patterns, is at variance with the notion of health as equilibrium, and illness as disorder.

96

Sabelli, H., Carlson-Sabelli, L., Levy, A., and Patel, M. (1995). Anger, Fear, Depression and Crime: Physiological and Psychological Studies using the Process Method. Chaos Theory in Psychology and the Life Sciences, R. Robertson and A. Combs (Eds). Mahwah, NJ: Lawrence Erlbaum, pp. 65-88; Sabelli, H. (1989). Union ofOpposites. Lawrenceville, VA: Brunswick; Sabelli, H. (2001). The Co-Creation Hypothesis. In Understanding Complexity, G. Ragsdell and J. Wilby (Eds). London: Kluwer Academics/Plenum Publishers. 97 The correlation coefficients between anger, anxiety and depression were positive for both women and men. If opposites such as anger and fear were mutually exclusive, then increases in one should be accompanied by decreases in the other, with a negative correlation coefficient approaching -1. If these behavioral opposites are actually complementary aspects of a response to conflict, then they should be positively correlated, as it was indeed the case. These positive correlations contrast with Cannon's fight-or-flight dichotomy. Factor analysis likewise indicates anger, anxiety and depression are complementary aspects, rather than mutually exclusive alternatives. Anger and depression were found to be temporally associated in phase space trajectories, correlation matrices, and factor analyses, but the correlations were stronger for controls than for depressed patients. 98 In some well relatives of bipolar patients, spectrum analysis reveals noteworthy periodicities not only for emotions but also for reports of purportedly externally caused positive and negative events!

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Bios

Fig. 4.25 Psychogeometry. Trajectory of 70 daily reports of subjective feelings. Left: Positive, negative, and sexual feelings towards others. Right: Anger, fear, and depressions. Top: Healthy homosexual man. Middle: Young man with bipolar disorder, and cocaine addiction, just prior to his committing murder. Bottom: His mother.

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Fig. 4.26 Psychogeometry. Trajectory of 70 daily reports of subjective feelings. Left: days 1 to 70. Right: days 71 to 140. Note relative stability of pattern. Top: Anger, fear, and depressions in a man with unipolar depression treated with anti-depressants. Note high degrees of anger and anxiety. Middle and bottom: Psychotic middle aged woman.

174

Bios Table 4.5 Trajectory patterns of anger, fear and depression.

Trajectory type

Healthy

Equilibrium^

13 %

Center

Chaotic

Depressed patients 3%

3T%

1

56%

Depressed jail inmates 0%

15_%

|

82%

Non-depressed jail inmates 67%

8%

|

20%

%

|

92%

4.4 Information: Repetition, Rise, and Fall Abstract: Information is carried by patterns of repetition, rise and fall. Repetition carries greater information than change in a non-repetitive environment, and change conveys more information in a stable one. Empirical time series (heartbeat intervals, respiration, some economic and meteorological data), biotic series, and stochastic noise display more consecutive repetition than their shuffled copies, while chaotic series and some DNA base sequences show fewer consecutive repetitions. In evolving time series, consecutive repetition peaks at transitions from one pattern to another, and show distinct epochs within chaotic or biotic stages. Measuring rise and fall demonstrates triadicity in logistic chaos and quaternity in process chaos and bios. Repetition differentiates various phases within chaotic and biotic regimes. 4.4.1 Information: repetition and difference Computers, genetics and psychopharmacology make evident that information is a fundamental aspect of reality. Shannon considered the transmission of information as a statistical phenomenon, thus providing a way to determine the capacity of a communication channel." The quantification of information in terms of probability of occurrence, and its measurement through the calculation of entropy, however, is of limited usefulness in other contexts. Moreover, information theory can be developed (in part) with no mention of probabilities.100 Distinction may be regarded as the most basic form of information. There is no possible discourse without a distinction. The simplest case is 99

Shannon, C. E. (1948). A Mathematical Theory of Information. Bell System TechnicalJournal 27: 379-423, 623-56. m Griffith, J. S. (1971). Mathematical Neurobiohgy. New York: Academic Press, pp. 92-9.

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logical negation. The unit of information is likewise defined in terms of a distinction between two values. One value alone carries no information; its opposite must coexist for information to take place. Information is first and foremost carried by sign (positive or negative). According to SpencerBrown, distinction is the basis for mathematics. 101 He represents distinction by drawing a boundary to separate sides. Partition is neither necessary nor sufficient for distinction. It is not necessary, as distinction and hence information can arise from external or internal asymmetry, such as a magnet's polarity.102 It is not sufficient because a partition does not establish a distinction unless there is an asymmetry, difference or marking that differentiates the two sides. Information is often carried by the proportion between coexisting opposites rather than by their partition. Information is carried by action or stored by matter.103 It is a physical fact; actual information is a communication, depending as much on the observer as in the source. For instance, a sequence of DNA bases or of words carries a given information, or a different one, or none at all, according to the receiver. This does not imply that information is subjective. Information is an interaction that produces change, it is not just a distinction made by an observer. The mathematical basis of information is distinction, the difference of opposites, which may or may not involve separation. The physical embodiment of information is interaction. This dynamic and logical definition of information underlies and generalizes its statistical definition in Shannon's communication theory. Information needs to be defined in logical and dynamic terms, rather than statistical terms, because distinction and information exist in both deterministic and probabilistic systems. Physically, information is embodied by bifurcations. So understood, information is a universal physical dimension underlying all other more complex forms of information. Information consists of multiple levels ordered hierarchically (mathematical, physical, chemical, biological, social, psychological). 101

Spencer-Brown, G. (1969, reprinted 1979). Laws of Form. N e w York: E. P. Dutton. Sabelli, H. (2001). The Co-Creation Hypothesis. In Understanding Complexity, G. Ragsdell and J. Wilby (Eds). London: Kluwer Academics/Plenum Publishers. 103 Shannon, C.E. and J. Weaver (Eds.) (1964). The Mathematical Theory of Communication. Urbana, IL: University of Illinois Press. 102

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Even at the most elementary levels, information consists in a series of distinctions, determining 2, 4, 8 ...2N values. Feigenbaum's cascade of bifurcations 2°, 2, 22 ... 2N is a universal process that generates information in natural systems. One bifurcation generates a pair of linear opposites; two bifurcations generate two orthogonal pairs of linear opposites, and thereby complementary opposites (orthogonal, equally agonistic and antagonistic); bifurcation cascades generate multiple nonlinear opposites (partially synergic and partially antagonistic). Systems of 2N values allow for the dialectic coexistence of opposites, which is excluded as unacceptable contradiction by standard static logic. Bateson104 defined information in terms of change, or "news of a difference". Negation, a fundamental logical operation, is the change from one value to its opposite. Paraphrasing Spinoza and Hegel, we could say that information is negation. But assertion also carries information. In my view,105 in the midst of continual change, similarity and repetition carry information. We obtain information by noting the correspondence between an expected pattern and an input, more often than when we notice the difference between expected and received patterns. Matching, similarity and repetition carry information. The informational value of a signal depends on its relative frequency (Shannon). Whatever can be said to constitute a signal depends on the background. Existence implies the distinction of a figure from its background, to use the terminology introduced by Gestalt psychologists. Among structures, change conveys information because stability is the norm. In the midst of continual change, repetition carries information. Information is contained in the contrast between change and stability. Continuous random change carries no information. Conversely, stability or invariance do not per se represent information unless coexisting with change. Because processes are more abundant than structures in the universe, repetition usually carries more information than difference. Repetition is meaningful. Iteration is a repetition in time. Generic forms are iterated and thus produce complexity. Fractals are often generated by periodic repetitions. Genomes grow by duplication. The duplication of 104 105

Bateson, G. (1979). Mind and Nature. A Necessary £/«;/>> New York: Dutton. Sabelli, H. (1989). Union of Opposites. Lawrenceville, VA: Brunswick Publishing.

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information by books and computers revolutionized culture. Repetition of simple forms may generate periodicity or create complexity, as illustrated by arabesques, chaos, bios, fractals, and patterns produced by cellular automata. It may thus be expected that the quantification of repetitions may contribute to characterizing series with creative features and distinguishing them from random and chaotic series. The fact that both repetition and change carry information explains why statisticians regard information as inversely proportional to variance, in contradistinction to communication theorists who regard difference as information. For Bateson, information increases with variation. In contrast, standard statistics interprets variance as variability, and hence inversely proportional to information. This illustrates how repetition and change, albeit opposites, can both carry information. These considerations suggest that to analyze information, one needs to examine the proportion between repetitions and differences. I thus redefine information as opposition.106 Information always involves opposition. Perception itself requires contrast. True cannot even be conceived without reference to its opposites, lack of information (uncertainty, ignorance, unconsciousness, repression) and misinformation (mutation, error, lies, paraconsciousness). Opposition includes both repetition and difference, and difference includes rise and fall. Action At generates difference A,+i At, which may be positive (rise), negative (fall) or 0. Information I is carried by both change A and repetition (noA). I = A or noA. 4.4.2 Measuring repetition Repetition, rise and fall are elementary components of processes. Information is written in this three-letter alphabet. Kendal 107 introduced a method for the quantification of rise and fall. We have introduced the quantification of the sequence of repetition, rise and fall as a measure of

106 107

Sabelli, H. (1989). Union of Opposites. Lawrenceville, VA: Brunswick Publishing. Kendal, M. (1973). Time Series. London: Charles Griffin.

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information in time series.108 To implement these measures we have developed spreadsheets and Patel and Venkatachalapathy developed a Fortran program. Both are included in the CD-ROM. The percentage of all repetitions (consecutive or non-consecutive) is largest in periodic data, lower in heartbeat intervals, biotic series and logistic chaos, and even lower in process and Rossler chaos. Consecutive repetitions are calculated by measuring the difference or the ratio between consecutive terms and weighing them against a chosen radius of tolerance.109 In a similar manner, one counts rises and falls. It is reasonable to afford a margin of tolerance because very small differences between consecutive terms can be meaningless, and may actually result from arbitrary partitions introduced by sampling. First, the number of consecutive repetitions, rises and falls is calculated as a percentage of the total number of terms in the series. Second, the nine possible sequences of consecutive changes (e.g. rise-rise, rise-repetition, fall-rise, etc.) are identified, and their proportion is calculated as a percentage of the total number of possible cases. To differentiate determined pattern from random ones, the data At are shuffled to generate a random series As with the same mean and variance that will serve as a base for comparison.110 108 Sabelli, H., Patel, M., and V. K. Venkatachalapathy. (in press). Bios Data Analysis. Part 5. Action and Information: Repetition, Rise and Fall. Journal of Applied Systems Studies, special issue edited by H. Sabelli. 109 Measuring the ratio is convenient because the same radius of tolerance (e.g. greater than 1.001 or less than 0.999) can be applied to all series, but it is not applicable when there are 0 terms. When measuring differences between consecutive terms, the radius of tolerance used may become crucial; it must be adjusted to the range of differences between consecutive terms AAt; the range of the series At is not relevant. For empirical data, the radius r must be equal or larger than the precision of the measurement, as this is an unavoidable degree of uncertainty; for instance, we record heartbeat intervals with a precision of l/128th of a second, so we may take this value as r. In mathematical recursions, tolerance may be defined as a fixed percent of a significant parameter such as step size in random walks or gain g in recursions. To compare diverse empirical series, one may set r to be a proportional to the value of the previous term or to the mean of the absolute value of the differences between consecutive terms in the series; results obtained with the same fixed radius of tolerance for different series may be misleading. Alternatively, the data must be standardized. Examining a number of series and comparing a variety of criteria for tolerance, as illustrated in the experiments described below, led us to conclude that, to characterize pattern, it is useful to test a range of tolerances rather than a single one. The program developed by Patel and Venkatachalapathy (in the CD-ROM) thus compares the difference between consecutive terms with a series of tolerance radii (0.001, 0.1, 0.2,... 0.5 percent of the preceding term). 110 Shuffling is performed by pairing each member of the time series with a triple of consecutive it digits, and then sorting the latter in ascending order. This procedure is performed several times with different segments of n digits to obtain several shuffled copies for comparison. Repetition generated by chance can be expected to occur as often in At as in As. The number of repetitions recorded in a

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Consecutive repetition measures the density of points in the diagonal of a return map (Fig. 4.27). The time series of heartbeat intervals, respiration, air temperature, and economic processes show a relatively high percentage of consecutive repetitions. Shuffling the data markedly reduces these percentages.

Fig. 4.27 Counting consecutive repetitions may be understood as sampling diagonal in the return map. The number of points is much less in chaotic series generated by the process equation than in shuffled copies, while the number of terms in the diagonal is larger in the other three cases.

Fig. 4.28 Measuring repetition differentiates among biotic series. Consecutive repetition calculated by measuring the ratio between successive terms.

given shuffled copy is subtracted from the number of repetitions recorded in the original series. A

word of caution: the range of the series is relevant to the choice of the ratio of tolerance when we compare a series and its shuffled copy. For instance, a random walk has the same number of consecutive repetitions as the random series used to generate it, but shuffling reduces consecutive repetition only in the random walk.

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Significant differences are found between sleep and wakefulness in series of heartbeat intervals and in the series of differences between consecutive heartbeats (Fig. 4.29), indicating that consecutive repetitions portray physiological processes. Among mathematically generated times series, the frequency of repetition is largest in random walks and biotic series. Periodic data, by necessity, show no consecutive repetitions; after shuffling, their frequency is approximately 100/p percent, where p is the period. Consecutive repetitions are variable in chaotic series. Among chaotic series, logistic, process and Sprott's chaos show less consecutive repetitions than their shuffled copies, while Henon, Rossler and sine chaos are more repetitious.

Fig. 4.29 Average and S.E. of 12 records. Tolerance radius = l/128th second.

Fig. 4.30 Measuring repetition differentiates similar types of chaos. Series generated by trigonometric feedback with or without a conserved term show relatively low percentage of consecutive repetitions, which is higher than in shuffled copies in one case and lower in the other. Consecutive repetition calculated by measuring the ratio between successive terms.

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Fig. 4.32 Process equation At+1 = At + g * sin(At). Percentage of consecutive repetitions in time series generated at constant gains during the periodic, chaotic and biotic phases. Tolerance = 0.1 * absolute value of difference between consecutive terms. There are no repetitions during periodic phases, including the overlap of period 2 with chaos. Repetitions are observed in aperiodic series, chaotic and biotic. Repetitions peak at the onset of aperiodic chaos (end of period 2) and at the onset of bios. Intrachaotic and intrabiotic periodicities and infmitations are clearly detectable by a lack of consecutive repetitions.

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In evolving time series, consecutive repetition peaks at transitions from one pattern to another and shows distinct epochs within chaotic or biotic stages. In the logistic equation (Fig. 4.31), there are no consecutive repetitions during the initial phase of chaos, when this aperiodic pattern coexists with a period two ("period 2 chaos"). Repetition emerges when the two branches of chaos unify. Their number peaks soon thereafter, followed by a dip, which precedes a dramatically sharp rise at the upper limit of chaos. Hence, there are two peaks of repetition, one at the onset of aperiodic chaos and the other at its end. These various phases of the chaotic regime are not detected by either visual observation of the time series or by standard statistical measures. Repetitions are of course absent during intrachaotic or intrabiotic periodicities. In the process equation (Fig. 4.32), consecutive repetition reaches two peaks, one at the onset of aperiodic chaos and the other at the onset of bios. There are three distinct phases during the chaotic regime: (1) no repetition during "period 2 chaos"; (2) a peak when the two branches of chaos unify at the end of period 2 (g = 3.9) followed by a gradual decrease up to g = 4.3; and (3) a subsequent increase. Neither visual observation of the time series nor standard statistical measures distinguish these phases within the chaotic regime. During the biotic phase, the percentage of consecutive repetitions oscillates above the range observed in chaos. Repetitions are absent during the infinitations and periodic patterns that periodically interrupt bios when the feedback gain equals an integer multiple of n. Consecutive repetitions peak when the gain equals 1.5TI, 2.5K, 3.5n, etc. There is a complex pattern of variation in the proportion of repetitions between these extremes. Again, neither visual observation of the time series nor standard statistical measures reveal these peaks. The variation in the number of repetitions as a function of the gain in the shuffled copy follows the same pattern during the biotic phase (except for the interspersed periodicities) but the amplitude of variation is less. Shuffling affects the percentage of consecutive repetition because it randomizes the sequence but does not alter the proportion of repetitions. In summary, the simple quantification of consecutive repetitions distinguishes different types of time series. Leaving out the trivial cases of steady states and infinitations, consecutive repetitions are high in

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biological and economic series as well as in random walks and biotic series, that is to say, in series that display creative features. This differentiates them from periodic series in which consecutive repetitions are absent, and from chaotic series in which repetitions are lower. Two types of chaos can be distinguished by considering the effect of shuffling. The quantification of consecutive repetitions also distinguishes otherwise indistinguishable stages in the chaotic as well as in the biotic phases of the logistic and the process equations. Particularly interesting is the fact that there are peaks of repetition at points of transition between different phases, such as in the beginning of chaos, and in the transition between chaos and bios. There are also periodic peaks during the biotic phase of the process equation when the gain equals 2.5, 3.5, 4.5, ... multiples of %. This complex pattern of variation in the rate of consecutive repetition illustrates the power of measuring consecutive repetitions as an analytic method. process equation. Radius = 0.1 % of mean absolute difference I

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Consecutive repetition relates to stability, but peaks of consecutive repetitions coincide with transformation of pattern, as illustrated by

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transitions into and out of chaos for the logistic and the process equations. In natural processes, state changes coincide with transient stability; for instance, the temperature of boiling water remains stable. 4.4.3 Rise and fall The quantification of sequences of rise, fall and repetition allows one to analyze pattern. The program developed by Patel and Venkatachalapathy considers sequences of nine consecutive terms. For the sake of simplicity let us consider only sequences of three terms, and only rise and fall. We thus have only four possible cases: rise followed by another rise in value, rise-fall, fall-rise, and fall-fall. This simple scheme allows one to differentiate various types of chaos and of bios. Let us consider first periodic series. Period 2 (rise, fall, rise) generates a predictable distribution. Period 3 has two possible patterns, but period 3 generated by the logistic equation shows only one of them: rise followed by rise and then fall; fall never follows fall. This is not predictable. More complex periodic series, such as sine waves, include all types of sequence, but sequences of like terms (rise followed by rise or fall followed by fall) are by far the most common. This we dub polar modality. Random and related series (n digits, Cantor) also include all types of sequence, but in this case, the alternation of opposites (rise-fall or fall-rise) is more frequent (central modality); this is readily understandable, as the series are bounded, but it is nevertheless prima facie surprising. Finally, series generated by the Weierstrass equation show the same proportion of all four types of sequence (uniform modality). We see four types of chaos: (1) Period 2 chaos (as generated by the logistic and the process equation) produces a rise-fall alternation. (2) Logistic chaos, Henon chaos and the tent map show only three sequences; fall never follows fall. (3) In Lorenz, Rossler and Sprott A chaos: all types of sequences occur, and sequences of like terms (rise followed by rise or fall followed by fall) are the most common. (4) In Ikeda and process chaos, there is a central distribution. Notably, sine At+i = g * sin(At) and cosine At+) = g * cos(At) reiterations show triadic distribution at low gain and central distribution at higher gain.

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In heartbeat interval series, the percentage of accelerations and decelerations is different: there are more decreases than increases, in both healthy persons and in patients with CAD. This may be because behavioral excitement occurs faster than relaxation. Among empirical series, economic data and air temperature show uniform modality, ocean temperature shows polar modality. There are three types of mathematical biotic series, with uniform, central, and polar modality, depending on the generator and its parameters.

Fig. 4.34 Repetition, rise and fall of various empirical series, and their shuffled copies. Tridimensional representation shows the percentage of nine possibilities: rise followed by fall, repetition or rise (white columns), etc. Proportion means here the relative frequency of each category.

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In summary, quantification of rise and fall distinguishes different kinds of chaos and of bios, and also detect differences in empirical series. The study of longer sequences can provide more information. Research on this direction is being pursued with a new program being developed by Patel and Venkatachalapathy that considers sequences of nine consecutive terms. To fully evaluate pattern, we also find it useful to evaluate the proportion between consecutive terms.111 Continuous proportion (Fig. 4.35) measures the stability of ratios between consecutive terms of the time series A t / At+i = At+i / A t+2 . n Our pilot experiments suggest that consecutive proportions may be useful to characterize some types of data. For instance, the rate of consecutive proportions is low in 1/f (pink) noise in comparison to cardiac and biotic series. In general, continuous proportions are abundant in creative processes (cardiac, economic, meteorological and mathematical biotic series), and scarce in random and chaotic data. Table 4.6 Distinguishing patterns with rise and fall. Sequences Four: Rise - Rise (R - R); Rise - Fall (R - F); Fall - Rise (F - R); Fall-Fall ( F - F ) . Three (no F-F)

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The empirical results shown indicate that the measure of repetitions, rise and fall reveals meaningful patterns, as illustrated by the differences 1

'' There are many different types of proportion. There are several types of proportions, among which we estimated arithmetic proportion (At+2 - At+i)/(At+i - At) = 1 +1, geometric proportion (At+2 A,+i)/(A,+i - At) = (At+2/At+i) +1, and harmonic proportion (At+2 - At+i)/(At+1 - At) = (At+2/At) + t. 112 The difference (At/At+1) - (At+i/At+2) is computed, and whenever it is smaller than a chosen tolerance (range /100), a continuous proportion is counted. If the result is less than a chosen tolerance t (e.g. 0.1) and there is no repetition of values such as At ~ At+1, we count a continuous proportion. We calculate continuous proportions as a percentage of the total number of terms in the series. The data is shuffled and the percentage of continuous proportions recorded after this randomization is subtracted from the value obtained in the original series. Preliminary experiments have been reported in Patel, M. and Sabelli, H. (2003). Autocorrelation and Frequency Analysis Differentiate Cardiac and Economic Bios from 1/f Noise. Kybernetes 32: 692-702.

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found between heartbeat interval series obtained during sleep and wakefulness. We shall not attempt to analyze the empirical data in this introductory presentation, but focus instead on specific findings of general interest regarding statistics: The uneven distribution of rise and fall sequences in uniform random data contradicts the commonly held expectation that series of random events can produce any pattern whatsoever, and yet it is the unavoidable consequence of the existence of boundaries.

Fig. 4.35 Percentage of continuous proportions in various time series.

Fig. 4.36 Tolerance radius 0.1. Continuous proportions are low during periodicity and the early phase of chaos.

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The low consecutive repetition rate found in DNA base sequences is at variance with the notion that DNA sequences are random walks. Low rate of consecutive repetition is found in some chaotic series but the presence of novelty differentiates DNA from chaos. At this time we do not have any model that fits DNA sequence data. The high consecutive repetition rate with a polar modality of rise and fall sequences found in series of Pacific Ocean temperatures can be modeled by biotic series, and it is at variance with random or Brownian or pink noise models. Heartbeat interval series differ from pink noise in their much higher rate of consecutive repetition and the uniform modality of rise-fall sequences while pink noise shows central modality. These observations contradict the commonly held assumption that heartbeat interval series represent pink noise. On the other hand, one can construct biotic series with high consecutive repetition, uniform modality of rise and fall sequences, and 1/f power spectrum as observed with heartbeat series. These results, considered together with measures of novelty and nonrandom complexity, point to the need to shift from the random models dominating statistical thinking in the earlier twentieth century to the new dynamic models emerging at its end. More specifically, the results obtained with many empirical series are compatible with bios generated by bipolar feedback and characterized by high repetition and novelty rather than with chaos that shows low repetition and no novelty. 4.4.4 Contiguity In natural as well as in biotic series and statistical noise, changes are often gradual and sustained; random or chaotic processes produce continual changes of the same order of magnitude as the total range of the series. Conservation implies continuity or, in discrete series, the similarity between consecutive terms, which we shall call contiguity. Contiguity is the "continuity" of discrete series. We explored several measures of contiguity. Counting the number of midline crossings for small (N=5) and larger (N=100) sets of consecutive terms in the series and calculating their ratio differentiates sinusoidal, chaotic and random series (ratio 0.7 to 1) from mathematical bios, random walk, pink noise,

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and empirical series such as heartbeat intervals (healthy, cardiac and psychotic persons), electroencephalogram, Ocean temperature, atmospheric temperature, oil prices, and corn prices. In contrast, cosmic background radiation (Chapter 6) and the S&P500 index (Chapter 15) resemble random data. Similar results are obtained by computing crossings of the moving average. 4.5 Trigonometric Analysis of Opposites Abstract: Computing sine and cosine of each term in a time series allows one to explore the opposite components of a process when only one time series is available. This transformation is used in a number of analytic techniques that allow one to distinguish a variety of patterns, including several types of chaos and normal from pathological heartbeat series. "It is a deep magic that contraries can be brought forth after a point of unity has been found" (Giordano Bruno). Given that interacting opposites play a fundamental role in natural and human processes, how can one study complementary subprocesses when only one time series is available? This is a matter of practical importance in many cases. For instance, heart rate is largely determined by the opposing actions of the accelerating sympathetic and the decelerating parasympathetic nerves. Measuring their relative contribution is clinically relevant,113 but only one set of data, heartbeat intervals, is readily available. To study opposite subprocesses, we calculate the sine and cosine of each term in the series, thereby decomposing a single time series into two complementary surrogate series (sine and cosine transforms). Sine and cosine are paradigmatic of complementary opposites. Sine and cosine are orthogonal to each other, sharing one dimension, time. They wax and wane out of phase (displaced by nil) but not independently. Orthogonal means % of a rotation, NOT independence. Sine and cosine transforms thus provide a two-dimensional framework in which to project a time series and examine the relation between its opposite 113 Malik, M. and Camm, J. (1995). Heart Rate Variability. Armonk, NY: Futura Publishing Company.

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components. We114 have introduced trigonometric transformations as a strategy to develop numerical analyses and plots.

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Fig. 4.38 Top: Healthy subject. Bottom: Patient with Coronary Artery Disease (CAD). Left: Time graphs of heartbeat intervals computed by measuring the interval between R in the electrocardiogram (RRI). The series appears erratic in this one-dimensional plot. Middle: Complement plots of the same data. RRI of healthy subject form Mandala, while complement plot of RRI of CAD patient seems incomplete, and has significantly less distinct transitions. Right: Trigonometric plots. 114 Sabelli, H. (2000). Complement Plots: Analyzing Opposites Reveals Mandala-like Patterns in Human Heartbeats. International Journal of General Systems 29: 799-830; H. Sabelli, and L. Kauffman.. Bios Data Analysis. Process Methods to Analyze Creative Processes. Part 7. Opposition: Trigonometric Analysis in Time Series Journal of Applied Systems Studies, special issue edited by H. Sabelli.

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4.5.1 Trigonometric model Circular forms represent an infinite number of linear diametric opposites, and therefore include orthogonal vectors and all degrees of partial opposition in between. Congruently, sinusoidal forms are embodied in fundamental processes and structures. Light waves, the paradigmatic carrier of information, consist of mutually orthogonal electric and magnetic fields that vary in a sinusoidal fashion; accordingly, sine and cosine are natural models for information. Proteins and ribonucleic acids characteristically exhibit a helical structure. Helices and spirals have been recognized as archetypical from ancient mythologies to dialectics. Trigonometric functions thus model essential features of opposition. The notion of co-creation is modeled by recursions of trigonometric functions described in Chapter 3. Congruent with trigonometric models for creative processes, we develop their trigonometric analysis. Trigonometric analysis decomposes a complex series into two orthogonal and opposite components. Trigonometric transformations are widely used in time series analysis. Fourier analysis decomposes a complex time series into a (potentially infinite) series of sine and cosine components. Such trigonometric decomposition portrays the frequency range of energy. The trigonometric decomposition into sine and cosine components portrays informational oppositions. We take the relation between sine and cosine functions as a mathematical model for complementary opposition, because it involves reciprocity and orthogonality. This trigonometric definition of complementary opposition115 captures in part, and makes more rigorous, its philosophical conceptualization without exhausting it. In fact, trigonometric analyses of empirical data to be described in this article suggest expanding the concept of co-creative opposition to include uncorrelated opposites and partial opposites, i.e. partial agonists and partial antagonists that are neither linear nor orthogonal (Fig. 4.39). Caveat: Trigonometric transformations and plots depend on the range of values of the time series examined. This article presents results

115 Sabelli, H. and Kauffman, L. (1999). The Process Equation: Formulating And Testing The Process Theory Of Systems. Cybernetics and Systems 30: 261-294.

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obtained with the original data, as well as some examples of the effects of standardizing the data to the 0 to 2TC range. A wide spectrum of opposites Orthogonal"Complementary, not independent Partial antagonists / / /

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4.5.2 Complement plots We calculate the sine and cosine of each term in the series to generate two surrogate series, the sine and cosine transforms. Complement plots are generated by plotting the cosine and sine transforms in the X and Y axes, and drawing a straight line between successive points to represent transitions. In the complement plot, the value of each term in the times series (modulo 2n) corresponds to a point in a circumference. The vertical axis is the sine scale and the horizontal axis is the cosine scale, with zero in both scales corresponding to the center of circumference. The plot is circular for series of numbers with a range equal to or larger than 27t. Complement plots reveal pattern in the heartbeat interval series of all healthy persons (Figs. 4.35 and 4.37) and many cardiac and psychiatric patients. The connecting lines generate a set of concentric rings; no diameters cross them, indicating that consecutive terms are never linear opposites. Many persons spontaneously describe this pattern as a Mandate.116 Mandate patterns are obtained in some cases with extremely large sets of data (e.g. N=7000). In other cases, the pattern is 116 Sabelli, H. (2000). Complement Plots: Analyzing Opposites Reveals Mandala-like Patterns in Human Heartbeats. International Journal of General Systems 29 (5): 799-830.

Bios Data Analysis

] 93

demonstrable for any relatively small set, let us say N =500, but becomes blurred for larger samples as the range of RRI values changes. The Mandala pattern is absent in heartbeat series recorded from patients with severe cardiac illness (Chapter 5). It is also absent in some psychotic patients (Fig. 4.40 bottom right), regardless of whether or not they are treated with anti-psychotic medication. This indicates a psychological modulation of cardiac timing.

Fig. 4.40 In the RRI series of a healthy person (top left), there are 6 rings, and the inside circle is empty (consecutive terms never are linear opposites). In the shuffled copy (top right), one can barely discern a circular pattern of multiple rings, and there is no empty central circle (consecutive terms often are linear opposites). The Mandala pattern is present in most patients with coronary artery disease (bottom left), but it is absent in patients with severe psychosis (bottom right). N=2000.

Mandala patterns in natural time series, and the modeling of these biotic patterns by the process equation, point to the importance of complementary opposition in vital processes. For process theory, complementation is harmonic and oppositional in both the mathematical and the human sense of the terms.

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Fig. 4.41 Rounded-off time series display distinct patterns not readily observable in the original data. Mandala patterns are observed for biotic series and for random walks but not for random data. N = 500.

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Similar Mandala patterns are detected in other empirical time series, including some economic and meteorological time series.117 Shuffling the data to eliminate temporal order while leaving the statistical distribution unchanged completely obliterates the Mandala pattern (Fig. 4.40 top right). Mandala patterns occur only in integer series. Many empirical data are integers. Non-integer times series can be rounded off; this often reveals otherwise hidden pattern (Fig. 4.41). The generation of the Mandala pattern requires a sufficient range of data (larger than 2n). In some series, it is necessary to expand the range by multiplying each term by a constant. Complement plots of non-integer random numbers and Brownian noise are uniform (Fig. 4.41), while biotic series generate patterned plots. Complement plots of integer random numbers generate simple forms. A Mandala pattern of concentric rings is present in integer biotic series generated by the process equation At+i = At + g * sin(At) and by random walks with integer steps (greater than 2 and less than 13). Shuffling destroys these patterns. Complement plots generated by the process equation At+i = At + g * sin(At), are highly asymmetric; when delay is introduced as in At+1 = At + g * sin(At_i), the complement plot of biotic series is symmetric, as observed in heartbeat data. This illustrates the ability of this technique to differentiate otherwise very similar patterns. Critical requirements for the generation of the Mandala pattern appear to be integer action and a moderate range of variation between successive terms. However, chaotic series generated by the process equation do not show a Mandala pattern even after expanding their range by multiplication, so the difference between chaotic and biotic patterns is not due to the range of the data. The fact that remarkable regularity can be obtained by graphing data in a complement plot when the same data appear irregular in return maps points to the vital dialectic of complementary opposites in natural processes. This is understandable in the case of heart rate variation that is generated by the opposing actions of the sympathetic and

117 Sabelli, H. (2000). Complement Plots: Analyzing Opposites Reveals Mandala-like Patterns in Human Heartbeats. International Journal of General Systems 29 (5): 799-830.

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parasympathetic nerves. It is also readily explainable by interactions of consumption and production in economic processes. As phase portraits and return maps, calculating the sine and cosine of every member of a time series serves to explore bi-dimensional patterns of change. As phase portraits and return maps, complement plots eliminate time to reveal pattern. But complement plots also eliminate the magnitude of change, as the same sine and cosine obtain for numbers equal modulo 2n. By eliminating time and energy, complement plots ignore action, focusing exclusively on information. 4.5.3 Trigonometric time graphs To consider the magnitude of changes, we also generate two surrogate time series by adding the successive terms of the series of sines and of the series of cosines: Si = 0 SHi = St + sin At, C t+ i= Q + cos At, Q = 0. and

Fig. 4.42 Time series and trigonometric walks of heartbeat series (left) and of sine and cosine forms of the process equation. Note the symmetry of the sine and cosine walks in heartbeat series.

For the sake of brevity, we shall refer to these series as sine and cosine walks (Fig. 4.42). Comparing series generated by symmetric bipolar feedback such as At+i = At + g * sin(At) + g * cos(At) with series generated by asymmetric bipolar feedback, either At+i = At + g * sin(At) or At+i = At + g * cos(At), shows that trigonometric walks and trigonometric plots clearly differentiate asymmetric from symmetric

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opposition. In almost all empirical time series examined, the sine and cosine walks are of markedly different magnitude, and hence the trigonometric plots are highly asymmetric. This indicates that natural opposites do not wax and wane together in a quantitatively related fashion. These observations can be quantified by measuring correlations and ratios as shown in Fig. 4.42. Trigonometric plots, however, provide much of the same information. 4.5.4 Trigonometric plots Trigonometric plots are generated by plotting the cosine and sine walks in the X and Y axes. Dekking and Mendes-France118 use such plots, which they called "curlicues" by analogy with architecture, to study mathematical curves, measuring their properties in terms of entropy. We interpret these plots as portraits of opposites in empirical and mathematical series.

Fig. 4.43 Mathematical biotic series can generate different types of trajectories, both curvilinear and superficial. 118

Dekking, M., and Mendes-France, M. (1981). Uniform Distribution Modulo One. Journal Fur die Reine und Angerwandte Mathematik 239: 149-153.

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Fig. 4.44 Trigonometric plots of chaotic series. Note the differences in the horizontal and vertical scales. Logistic, Henon, and Ikeda's chaos show simple linear trajectories.

Fig. 4.45 Heartbeat intervals (RRI) of a healthy person: Left: time series. Middle: trigonometric plot. Right: trigonometric plot of a shuffled copy.

Trajectories in the trigonometric plot are classified by Dekking and Mendes-France according to their dimensions. The curve is surrounded by a region of width w, and the area A of this region that lies inside a circle of radius R is measured. The dimension is the limit (if one exists) of logA/logR. A curve is said to be linear if its dimension is 1, and superficial if its dimension is greater than 1. We further distinguish four types of trajectories by their visual appearance into (Figs. 4.43 and 4.44):

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linear as in logistic chaos or periodic data, curvilinear as in Rossler chaos), mottled superficial as in Lorenz chaos, and uniform superficial as in process chaos. Linear plots indicate that opposition is linear in Henon, Ikeda and logistic chaos (Fig. 4.44). Uniform superficial plots indicate orthogonal uncorrelated opposites in process chaos. Consideration of these simple mathematical series clarifies how sine and cosine walks provide information regarding opposites that generate a given process. The logistic recursion involves the multiplication of linear opposites At and (1- At); this generates a two-dimensional (quadratic) chaotic process. Its trigonometric plot represents the linearity of the opposition by the linearity of its trajectory, and the bidimensionality of the process by its diagonal orientation. In contrast, process chaos is generated by trigonometric functions that involve a circle of opposites -i.e. nonlinear and bidimensional opposites. Correspondingly, the trajectory in the trigonometric plot is a rectangular area; there is no correlation between sine and cosine walks.

Fig. 4.46 Trigonometric plots of RRI of patients with CAD. Some trajectories are superficial, as observed in healthy hearts. Curvilinear trajectories appear in the heartbeat series of patients with severe cardiac illness.

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Fig. 4.47 Trigonometric plots of RRI series of psychotic patients. Some trajectories are superficial. Curvilinear trajectories appear in the RRIs of profoundly psychotic patients.

Fig. 4.48 Empirical series show both curvilinear and superficial trajectories.

Trigonometric plots of many empirical series, mathematical bios (Fig. 4.43), some chaotic series (Lorenz, Rossler), random data, and stochastic noise display curvilinear trajectories (actually resembling curlicues) or mottled superficial plots. These patterns indicate partial opposition -i.e. the opposite components are neither linear (as in logistic chaos) nor orthogonal (as process chaos), but instead they display an intermediate degree of nonlinearity. Heartbeat intervals of healthy persons show superficial trajectories (Fig. 4.45). In contrast, curvilinear trajectories appear in some heartbeat

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series of patients with severe cardiac illness (Fig. 4.46). Curvilinear trajectories are also found in profoundly psychotic individuals who are cardiologically healthy (Fig. 4.47). Linear, curvilinear and superficial trajectories obtain in physical, meteorological, biological, and economic time series. Thus, in spite of their simplicity, trigonometric plots distinguish different types of chaos, of bios, and of empirical time series, including heartbeats from healthy and ill individuals (Fig. 4.48). 4.5.6 Quantification of trigonometric transforms and walks To quantify these observations, for each series we measure: (1) the ratio of the sine transform over the cosine transform; (2) the ratio of the sine walk over the cosine walk; (3) the correlation between sine and cosine transforms; and (4) the correlation between sine and cosine walks.119 Figure 4.50 illustrates typical observations in heartbeat interval series in healthy persons. There is no correlation between sine and cosine transforms, and there is a positive correlation between sine and cosine walks. Ratios between sine and cosine transforms as well as ratios between sine and cosine walks are near zero and highly variable. In contrast, in severely psychotic persons, sine to cosine ratios can be stable for relatively long periods of time. The ratio of the walk in the sine axis to that in the cosine axis shows symmetric patterns (cosine walk/sine walk ratio near 1) for many natural processes, including heartbeat intervals from most healthy, CAD patients, and psychotic persons. Some cardiovascular and psychiatric patients, however, show highly asymmetric graphs. This abnormality is independent of the linear or superficial character of the curve. The cosine walk is much larger than the sine walk for a wide variety of time series, physical and mathematical. Consideration of simple mathematical series clarifies how sine and cosine walks provide information regarding opposites that generate a given process. Consider the logistic model in which there are linear opposites At and (1-At) that multiply, thereby generating a twodimensional (quadratic) chaotic process. Its trigonometric plot represents 119

Caveat: correlations between walks are highly dependent on the size of the sample.

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the linearity of the opposition by the linearity of the trajectory, and the bidimensionality of the process by its diagonal orientation (Fig. 4.51). Both characteristics are also expressed by a near 1 correlation between sine and cosine walks, and the relatively near 1 average of sine/cosine ratios. Consider chaos generated by sine or cosine process equations, in which the trigonometric functions constitute a circle of opposites. Their trigonometric plots represent the nonlinearity and the bidimensionality of the opposition by the area covered by the trajectory; correspondingly, there is no correlation between sine and cosine walks, and the average of sine/cosine ratios is far from 1. The biotic series generated by these same sine or cosine process equations at higher gain, however, generate curvilinear trajectories, show significant correlation between sine and cosine walks (as logistic chaos), and far from 1 average of sine/cosine ratios (as process chaos).

Fig. 4.49 Quantification of trigonometric transforms (left) and walks (right). Left; Top: time series, 2nd row: series of cosine transforms, 3 rd row: series of the ratio of the sine transform over the cosine transform, bottom row: Pearson's Correlation Coefficient between sine and cosine series calculated for epochs of 500 values. Right; Top: series of sine and cosine walks, middle row: ratio of sine walk to the cosine walk, bottom row: Pearson's Correlation Coefficient between sine and cosine walks calculated for epochs of 500 values.

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Fig. 4.50 Trigonometric analyses of heartbeat interval series in a healthy (top) and a psychotic (bottom) person. Quantification of trigonometric transforms (left) and walks (right). Left: Top: time series; 2nd row: series of cosine transforms; 3 rd row, series of the ratio of the sine transform over the cosine transform; Bottom row: Pearson's Correlation Coefficient between sine and cosine series calculated for epochs of 500 values. Right: Top: series of sine and cosine walks; Middle Row: ratio of sine walk to the cosine walk; Bottom Row: Pearson's Correlation Coefficient between sine and cosine walks calculated for epochs of 500 values.

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Fig. 4.51 Asymmetry of sine and cosine walks versus series in sine and cosine process equations.

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Fig. 4.52 The sine transform correlates negatively (R — 1 ) with the series of differences between consecutive terms for all phases. Otherwise no other correlation is found during the biotic phase of the recursion. The cosine transform correlates negatively with the series and the differences during the steady state and during the transition from high periodicity to period 2 chaos; they correlate positively during bifurcation, unifurcation and period 4.

Fig. 4.53 The sine transform correlates negatively (R ~ -1) with the series of differences between consecutive

4.5.7 Discussion The sine and the cosine transform correlate negatively during the steady state, suggesting that opposites are in equilibrium. They correlate negatively during periodicity, indicating complementary. They correlate

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either positively (sine recursion) or negatively (cosine recursion) during period 2 chaos. Opposites are uncorrelated during bios, and positively or negatively correlated during infinitation. Polar opposites must be expected to be negatively correlated; complementary opposites should be positively correlated. The apparent independence of opposites in biotic series generated by deterministic equations cannot be interpreted as statistical independence. The observation of this lack of correlation in bios indicates instead a complex nonlinear relation. This concept includes and supersedes the standard concept of linear opposites as well as the notion of opposites as complementary advanced by dialectics, Taoism, quantum mechanics and systems theory. In summary, these experiments show that trigonometric analysis of time series is useful to distinguish various types of patterns and to identify the different types of opposite subprocesses that generate them. The results obtained with empirical series indicate that natural creative processes are constituted by nonlinear, asymmetric, and uncorrelated opposite subprocesses. Opposites are bidimensional (nonlinear) because they include both synergistic and antagonistic components; in contrast, mechanism regards opposite processes as linear (polar) and inversely correlated. Trigonometric analyses demonstrate various degrees of "partial" opposites with various proportions of synergism and antagonism, in contrast to philosophical formulations of complementary opposites that regard them as waxing and waning together, implying correlation, symmetry and orthogonality. This notion of bidimensional opposites is congruent with concepts currently advanced in the natural sciences such as superposition of opposites in quantum mechanics and the importance of partial agonists and partial antagonist drugs in synaptic pharmacology. The nonlinearity of opposites provides a theoretical explanation for the significance of nonlinearity in the dynamics of complex processes. What is the relation between the abstract opposition measured by sine and cosine transforms and actual oppositions such as sympathetic acceleration and parasympathetic deceleration of heart rate? We conjecture that any given process integrates a plurality of subprocesses, rendering them interdependent. For instance, because physiological processes are integrated by the central nervous system, the firing of the

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sympathetic and parasympathetic nerves reflects changes in RRI regardless of their cause -mechanical, hormonal, neural, or psychological. In a similar manner, changes in supply and demand reflect changes in the economy regardless of their cause. We thus surmise that changes in the sine and cosine transform reflect, albeit in an abstract and simplified manner, changes in the coexisting opposing subprocesses that make up any given process. In the sine process equation, the series and the series of differences correlate during steady state, periods, chaos and bioperiods, and do not correlate during bios and leaps (infinitation). Sine and cosine transforms correlate positively during steady state, logistic-like period 2 chaos, leaps, and bioperiod 2, negatively during unifurcation. In the sine and cosine process equations, the series and the differences correlate to each other during the prebiotic phases and in bioperiods, but not during biotic or ballistic diffusion. As expected, the differences between consecutive terms are inversely proportional to the sine transform in the sine equation, and to the cosine transform in the cosine equation. The sine walk is directly proportional to the series during steady state, and infinitation, and is inversely proportional to the series during periods, bioperiods, and chaos. Trigonometric walk generated by the integration of the sine or cosine transforms of a trended series (like ascending numbers) is of course, a sinusoidal function, and the trigonometric walk of a sinusoidal series is a trended series of ascending numbers. Thus if there are in nature structures that will "compute" the sine of actions and integrate them, one may expect that linear change would produce an oscillatory pattern, and that oscillation will produce linear change. This is illustrated by AC-DC converters. Such a structure would function as a "translator" of information from linear to oscillation and vice versa. Such translators are likely to exist in nature because there is a relation between linear quantities and periodic cycles. It is interesting the linear and periodic processes will generate each other because the combination of these two forms is the generator of the process equation.

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4.6 Novelty and Causation (Recurrence Isometry Method) Abstract: The quantification of isometric vectors demonstrates creativity (novelty + causality) and differentiates it from order (causation without novelty) andfrom random innovation (novelty without causation). Lower isometry recurrence than random defines novelty, the central characteristic of creative processes (bios and stochastic noise), in contrast to order as defined by greater recurrence (periodic and chaotic series). Consecutive recurrence portrays causation including periodicity (consecutive recurrence at periodic intervals), causality (low dimension consecutive recurrence), and integration (high embedding dimensions). Chaos is causal, Brownian noise is integrative, and cardiac and mathematical bios are both. A process is a sequence of actions. As action is quantity, an important feature that characterizes a process is the cumulative result of the actions that compose it. This is the norm. To compare processes, it is thus cogent to compare their norms and test whether they are the same (isometry) or different. Isometry also provides a meaningful measure of information carried by similarity and repetition. The measurement of individual repetition (Section 4.4) has limited value. A much more powerful tool is the recurrence method introduced by Eckmann and co-workers120 and further developed by Zbilut and Webber.121 A recurrence is a measure of the repetition of pattern through the comparison of vectors (sequences) of successive terms in a time series. These vectors are compared and, when

120 Eckmann, J. P., Kamphorst, S. O. and Ruelle, D. (1987). Recurrence Plots of Dynamical Systems. Europhysics Letters 4: 973-977. 121 Webber, Jr., C. L. and Zbilut, J. P. (1994). Dynamical Assessment of Physiological Systems and States using Recurrence Plot Strategies. Journal of Applied Physiology 76: 965-973; Webber, Jr., C. L. and Zbilut, J. P. (1996). Assessing Deterministic Structures in Physiological Systems using Recurrence Plot Strategies. In Bioengineering Approaches to Pulmonary Physiology and Medicine, M. Khoo (Ed). New York: Plenum Press, pp 137-148; Zbilut, J.P. and Webber, Jr., C. L. (1992). Embeddings and Delays as Derived from Quantification of Recurrence Plots. Phys. Lett . A 171: 199-203; Zbilut, J. P., Giuliani, A., and Webber, Jr., C. L. (1998). Recurrence Quantification Analysis and Principle Components in the Detection of Short Complex Signals. Phys. Lett. A 237: 131-135; Zbilut, J. P. and Webber, Jr., C. L. (1998). Quantification of Heart Rate Variability using Methods Derived from Nonlinear Dynamics. In Analysis and Assessment of Cardiovascular Function. G. Drzewiecki and J. K.-J. Li (Eds.). New York: Springer Verlag, pp. 324-334.

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found to be alike, a recurrence is counted and / or plotted.122 One may also measure the mean distance between recurrences. Caveat: It is not feasible to compare all vectors, so recurrence quantification programs randomly sample the data. The Bios Data Analyzer uniquely states how many vector pairs are tested and allows the researcher to decide this number. There are several ways in which recurrence can be defined and measured. We have introduced the terms isometry and similarity to distinguish two types of recurrence measurements currently used.123 Isometry recurrence indicates vectors with comparable the same length.124 Similarity recurrence requires that two vectors be alike in length and direction.125 Consecutive recurrence is the number of recurrences that follow each other; e.g. if vector yt is recurrent with vector yt+m, then vector yt+i is recurrent with vector yt+m+i. Consecutive recurrence is calculated for isometric and for similarity recurrences. The rates of recurrence observed in the time series are compared with those obtained on shuffled copies of data.126 Isometries increase or decrease with shuffling, while similarities only decrease with shuffling. 122

Given a discrete series A b A2, ..., AN, one constructs the sequence (vector) of D successive members Aj; Aj+i, Aj+2, ..., starting with every term AN of the series. Given a continuous series, one constructs the sequence yi of D successive members starting with data points at regular intervals d: yi = (Aj, Ai+A, Ai+2 2 and d > l.The number D of terms in the vector is called the embedding dimension, and the interval d is called the lag or delay. 123 Sabelli, H. (2001). Novelty, a Measure of Creative Organization in Natural and Mathematical Time Series. Nonlinear Dynamics, Psychology, and Life Sciences. 5: 89-113. Sabelli, H. and A. Abouzeid (2003). Definition and Empirical Characterization of Creative Processes. Nonlinear Dynamics, Psychology and the Life Sciences 7(1): 35-47. 124 The length of each vector is measured by calculating its Euclidean norm (the square root of the sum of squares of its members). These norms are then compared to one another. Two vectors are considered isometric if the absolute value of the difference between their Euclidean norms is smaller than a chosen cutoff radius. When two vectors are isometric (i.e. they are equal within the tolerance determined by the chosen cutoff radius), a recurrence is counted. For instance, if we choose a cutoff radius of 0.1, as we do in most of our experiments, and we consider embedding 2, then the vectors yj = and yk = are recurrent if V(Aj2 + Aj+i2) - V(Ak2 + Ak+i2) < 0.1. 125 Two vectors are recurrent when the Euclidean norm of the distance between the vectors (the square root of the sum of squares of the differences between their members) falls below the selected cutoff radius. For instance, if we choose a cutoff radius of 1, and we consider embedding 2, then the vectors yj = and yk = are recurrent if V[(Aj - Ak)2 + (Aj+i - Ak+])2] < 1. 126 Recurrence rate is the observed number of recurrences as a percentage of the total number of possible recurrences, which is the number of data points squared. The rate of consecutive recurrence rate is the observed number of consecutive recurrences as a percentage of the observed number of recurrences. Net recurrence is the number of recurrences in the original series minus the number of recurrences in the shuffled copy.

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Our most important result is the observation that many natural processes regarded as creative as well as mathematical bios have less isometry than their shuffled copy. This property, being less recurrent than random, defines novelty, an essential characteristic of creative processes. Periodic processes show more isometry than their shuffled copy when the embedding coincides with the period. Thus creativity and order are opposite departures from randomness. Random

1.2-1

0 -I

0

0.6 -I

0 -| 0

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Bios -^— BDA shuffled

0.4 - I

,

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RQA shuffled

A A / W ^ l / l

Embedding

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Fig. 4.54 Isometry plots show results calculated with RQA program (plain lines), and with BDA program (lines with circles). Top: Random series. In RQA, number of isometries increases with embedding, while in BDA, this number remains the same. Bottom: Bios. There is quantitative difference between RQA and BDA, but qualitatively, both programs show the same results.

Novelty may be quantified as the difference or the ratio between original series and its shuffled copy. Caveat: Several shuffled copies of a given time series should be obtained, because both random sampling of vectors and randomization by shuffling introduce variability. We have spent many days pursuing mirages in the time series of Tt digits. Another Caveat: Periodic series that demonstrate recurrence at the corresponding embedding appear to be novel at other embedding dimensions; long

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periodicities are thus misrepresented when only one, low embedding is computed. Embedding plots of sine waves and of sunspots illustrate this. Similarity recurrences decrease with shuffling in all the time series we have examined. We thus focus on isometry in this and previous publications, but the currently available programs for recurrence quantification measure only similarity recurrences.127 The Bios Data Analyzer (BDA) measures both types of recurrence. Figure 4.56 shows that net isometry and net similarity vary independently of each other. Net consecutive isometry and net consecutive similarity also vary independently. It is thus cogent to employ both measures. OR.

o

Expanding random series 25 I

Embedding

so

0

1.4 i

Embedding

50

a

160 i

Embedding

so

°

Embedding

so

Fig. 4.55 A random series with expanding boundaries may show only novelty or novelty plus consecutive recurrence at higher embeddings, depending of the rate of expansion.

Fig. 4.56 Comparison of isometry and similarity measures of recurrence using Webber and Zbilut's quantification programs. 127 Webber and Zbilut's older programs measured isometry. Webber and Zbilut's current program measure similarity recurrence, and include more features than the BDA.

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There are some differences between the measures obtained with the Bios Data Analyzer (A. Sugerman) and with Recurrence Quantification Analysis (Webber and Zbilut). 4.6.1 Consecutive recurrence and causation Recurrences are consecutive when they are generated non-randomly. Periodic data shows periodic increases in consecutive recurrences of isometry at embedding dimensions corresponding to the period. In random data, there is slow increase in consecutive recurrence with embedding, resulting from the integration of successive terms of the series by embedding. Thus, consecutive recurrence beyond that observed in shuffled data indicates nonrandom order.128 Consecutive recurrence129 at low embedding dimensions demonstrates causation. Thus, we observe it in many empirical series and in mathematical chaos and bios, but not in stochastic processes. Consecutive recurrence at high embeddings indicates integration, i.e. the accumulation of actions, so it is larger in random walks and in mathematical bios than in their shuffled copy, but not in chaos. Natural and mathematical biotic series thus show consecutive recurrence at both low and high embeddings with a minimum at intermediate embeddings. Measures of consecutive recurrence thus distinguish between deterministic and stochastic creative processes. Distinguishing deterministic chaos from colored noise is one important problem in time series analysis for which several algorithms have been proposed. We found partial autocorrelation useful (Section 4.2). Isometry analysis distinguishes bios from noise when partial autocorrelation fails to do so, a point that is significant regarding economic data (Chapter 15), and it also distinguishes two types of nonrandom causation. In biotic recursions, the conserve term accumulates information, while the change term represents the transmission of information from one stage to the next (causation). Bios includes both (Fig. 4.57). 128

Small range random series, including n, have high consecutive recurrence at low embeddings. Webber and Zbilut use the term determinism for consecutive recurrence. This is in keeping with the usage of the term by mathematicians. Physicists and philosophers regard determinism as a theory. 129

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Consecutive recurrence isometry

>V

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/ I

^

din

^

-\

9

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Fig. 4.57 Bios has consecutive recurrence isometry both on low and high embeddings.

4.6.2 Isometry histograms Deterministic feedback and stochastic change most likely coexist in many physical, biological and economic processes. We130 have developed a simple method to estimate their relative contribution. We compute the Euclidean norm for 2, 3, 4, 6, ...23...50 embeddings. Isometries are measured in the histogram of Euclidean norms. Each series At is compared with 5 shuffled copies As, and all results refer to these comparisons. A Pareto distribution of frequencies allows one to measure the change in isometry between the original data and the average of its shuffled copies As. We compare the frequencies F of At and As by bin in an effort to distinguish ordered, creative and random components of the process under study (Fig. 4.58). F(At) > F(As) defines order; in fact we find that F(At) > F(As) in periodic series. F(At) = F(As) implies random flux since shuffling does not change the frequency. A chaotic series is the same as a random flux by this measure. F(At)
130 Sugerman, A. and H. Sabelli (2003). Novelty, Diversification and Nonrandom Complexity Define Creative Processes. Kybernetes 32: 829-836.

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Fig. 4.58 Order, novelty, and flux of empirical and mathematical series.

This rough method complements the results obtained with recurrence analysis. It allows one to evaluate to what extent order and novelty coexist in a given series. It also permits to the entire series rather than sampling it as in recurrence analysis. Biotic processes combine order, novelty and flux (Fig. 4.58). 4.7 Complexes: Recurrence and Wavelet Plots Abstract: The analysis of time series with recurrence methods detects episodic patterns (complexes) in creative processes. In contrast, uniform plots are found in random and chaotic series. Complexes are demonstrable in human heartbeat intervals, economic series, meteorological series, DNA sequences, some literary texts, as well as in biotic series generated by recursions of bipolar feedback and in stochastic noise. Creative processes form and transform patterns and structures. Creativity, complexity and change are inseparable. The formation and

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transformation of pattern can be examined in recurrence and wavelet plots. The recurrence method is a powerful tool to study transient changes and non-stationary patterns. Yet, recurrence plotting and quantification are often restricted to the analysis of stationary epochs. Instead, we record long samples and interpret recurrence plots as time graphs that portray the transformation of one pattern into another.131 Recurrence time graphs may be uniform or may reveal relatively transient patterns that we call complexes.132

t

Fig. 4.59 Recurrence plots with isometric (radius 10) and similarity (radius 50) recurrences generated with Webber and Zbilut's RQA.

To construct recurrence time graphs, vectors starting with 1st, 2nd, 3 rd ... ith data points are plotted along the horizontal and the vertical axes, generating a square matrix. A recurrence is indicated by placing a dot at 131 Carlson-Sabelli, L., Sabelli, H. C , Zbilut, J., Messer, J., Diez-Martin, J., Walthall, K., Tom, C , Patel, M., Zdanovics, O., Fink, P., Sugerman, A. (1994). Cardiac Patterns of Emotions demonstrated by the Process Method: Psychotic Patterns. New Systems Thinking and Action for a New Century: Proceedings of the International Systems Society 38th Annual Meeting, B. Brady and L. Peeno (Eds.). Pacific Grove, CA, pp. 0419-0430; Carlson-Sabelli, L., Sabelli, H., Patel, M., Messer, J., Zbilut, J., Sugerman, A., Walthall K., Tom, C. and Zdanovics, O. (1995). Electropsychocardiography. Illustrating the Application of Process Methods to Comprehensive Patient Evaluation. Complexity and Chaos in Nursing 2: 16-24; Sabelli, H., Carlson-Sabelli, L., Patel, M., Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological Portraits: A Clinical Application of Process Theory. In Chaos Theory in Psychology, F. D. Abraham and A. R. Gilgen (Eds). Westport, CT: Greenwood Publishing Group, Inc., pp. 107-125. 132 Carlson-Sabelli, L., Sabelli, H. C , Zbilut, J., Patel, M., Messer, J., Walthall, K., Tom, C , Fink, P., Sugerman, A., & Zdanovics, O. (1994). How the Heart Informs about the Brain. A Process Analysis of the Electrocardiogram. In Cybernetics and Systems 2, R. Trappl (Ed). London: World Scientific Publishing.

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the intersection marking the coordinate address of the two data points beginning the similar vector sequences. As the same vectors are represented in the horizontal and the vertical axes, a diagonal line is created (because the vector corresponding to each data point is identical with itself), and all other recurrences are plotted twice, symmetrically, on both sides of the diagonal.133 Recurrence time graphs are compared with those obtained on copies of data randomized by shuffling.

Fig. 4.60 Recurrence plots of heartbeat intervals (top) and their shuffled copies (bottom) generated with Webber and Zbilut's RQA. 10 embeddings. Left: isometric recurrences, radius 1. Right: similarity recurrences, radius 10. Complexes are evident in plots of the data, and they are erased by shuffling. Shuffling increases the number of isometry recurrences, while it decreases the number of similarity recurrences. 133 These graphs are commonly referred to as recurrence plots, but we use the term time graph to stress the fact that the diagonal represents time.

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The time graphs of similarity and isometry recurrences are alike (Figs. 4.59-4.61). Plots of time series of processes such as heartbeat intervals and other biological data, many economic processes, some DNA base sequences, and some literary texts, show recurrence-rich epochs that we call complexes, which are separated by interruptions of pattern. Among mathematical models, biotic patterns and random walks also display complexes separated by interruptions. In contrast, stable, periodic and chaotic time series generate uniform patterns in which the same form occurs throughout.

Fig. 4.61 Isometric (left) and similarity (right) recurrence plots of biotic (top) and chaotic (bottom) series. Isometric (radius 1) and similarity (radius 10) plots are generated with Sugerman's BDA.

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Episodic patterning (i.e. complexes) is the main temporal characteristic of complex, creative processes. Complexes indicate complexity. The term "complex" was chosen to point to the essential connection between complexity and change. Selecting stationary periods precludes the study of pattern transformation. Complexes thus distinguish creative processes from stable states such as found in conservative processes and chaotic attractors. The cumulative addition of chaotic series generates series similar to mathematical bios, but, in most cases, the recurrence time graph is uniform, without separate complexes, unlike those observed in empirical series or biotic series generated by bipolar feedback. Recurrence time graphs allow one to study the form of complexes. Short line segments parallel to the main diagonal indicate sequences of consecutive isometries; they are prominent in plots of patterned time series, while plots of random data show few if any such lines. Complexes have a lattice structure: an origin, a series of forkings and joints, and an ending. Within this structure, complexes display a diversity of forms. Preliminary studies134 indicate that in heartbeat interval series, the form of complexes appears to be associated with emotions and behavior.

Fig. 4.62 Complexes in healthy (left) and schizophrenic (right) subjects.

134 Sabelli, H., Carlson-Sabelli, L., Patel, M., Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological Portraits: A Clinical Application of Process Theory. In Chaos Theory in Psychology, F. D. Abraham and A. R. Gilgen (Eds). Westport, CT: Greenwood Publishing Group, Inc., pp. 107-125.

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The number and duration of complexes can be quantified. Using visual observation, we have found a greater number of interruptions in heartbeat series in schizophrenic than in normal subjects (Fig. 4.62).135 We are currently developing computer techniques to quantify the rate of pattern transformation. Complexes are extremely similar in plots of isometry and similarity recurrences, indicating that both describe the same process.

Fig. 4.63 Wavelet plots of biotic and chaotic series: bios (top left), chaos (top right), bios shuffled (bottom left), chaos shuffled (bottom right).

135 Carlson-Sabelli, L., Sabelli, H. C , Zbilut, J., Messer, J., Diez-Martin, J., Walthall, K., Tom, C , Patel, M., Zdanovics, O., Fink, P., Sugerman, A. (1994). Cardiac Patterns of Emotions demonstrated by the Process Method: Psychotic Patterns. New Systems Thinking and Action for a New Century: Proceedings of the International Systems Society 38th Annual Meeting, B. Brady and L. Peeno (Eds.). Pacific Grove, CA, pp. 0419-0430.

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Shuffling the data abolishes the partition of recurrences into complexes; the temporal distribution of recurrences becomes uniform. Shuffling completely eliminates similarity recurrence. Episodic patterns at various scales, including complexes separated by interruptions and long epochs separated by major shifts, can also be shown in wavelet plots136 of natural processes, biotic series and stochastic noise, and they are also absent in random, chaotic or periodic series (Fig. 4.63). Table 4.7 Four elementary types of aperiodic series

Pattern (recurrence and , wavelet plots) Uniform Episodic (Complexes)

„ Stochastic

_ , Causal

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Chaos Bios

4.8 Arrangement, a Measure of Nonrandom Complexity Abstract: The generation of complexity defines a process as creative. Current measures of complexity are inadequate because they assign highest complexity to random processes. The ratio of consecutive recurrences to total recurrences in a time series, which we call arrangement, is high in time series of physiological recordings and economic processes, and in biotic series generated by recursions of bipolar feedback. Arrangement is low in random, periodic and chaotic series. Thus, arrangement provides a measure of nonrandom complexity that correlates with an intuitive notion of complexity.

136 Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. Wavelets were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last two decades have led to many new wavelet applications.

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4.8.1 Definition of complexity The production of complexity is the fundamental feature of evolution, from elementary particles to brains. Simpler processes generate higher, more complex ones. Biological and psychological phenomena are the most complex processes known, and should therefore be considered as paradigmatic of complexity. Complexity has become a major focus of research in contemporary science.137 However, there are multiple definitions of complexity; many of them are counterintuitive and nonempirical. Confusion stems from use of the term "complexity" to mean both organization and randomness.138 In common language, the term "complexity" (Latin, to plait together) implies (i) a composite made of many different parts and relations; (ii) a complicated, not readily understandable entity; and (iii) a higher level of organization. The term "higher" is congruent with the vertical organization of the body from head to feet. When supernatural explanations were de rigueur, what we now call complex was called "higher". The "chain of being" was regarded as a hierarchy: minerals < plants < animals < human body < soul < angels < God. This hierarchical view was congruent with the hierarchical organization of ancient and medieval societies. In our times "it is flirting with sin if one says that a worm is a lower animal and a vertebrate a higher animal, even though their fossil origins will be found in lower and higher strata".139

137 Casti, J. L. and A. Karlqvist. (1995). Cooperation and Conflict in General Evolutionary Processes. Wiley; Chaitin, G.J. (1990, revised third printing). Algorithmic Information Theory. Cambridge University Press; Ragsdell, G. and J. Wilby. Understanding Complexity. London: Kluwer Academics/Plenum Publishers; Cohen, J. and I. Stewart. (1994). The Collapse of Chaos: Simplicity in a Complex World. N e w York: Viking Press; Chaitin, G.J. (1990). Information, Randomness & Incompleteness, 2 n d edition. World Scientific; Chaitin, G.J. (1992). Information-Theoretic Incompleteness. World Scientific; Chaitin, G.J. (1995). T h e Berry paradox. Complexity 1:1, pp. 26-30; Li, SpringerM and P. Vitanyi. (1993). An Introduction to Kolmogorov Complexity and its Applications. Verlag. 138 Crutchfield, J. P. (2003). When Evolution is Revolution. In J.P. Crutchfield and P. Schuster. Evolutionary Dynamics. Oxford: Oxford University Press. Recognizing this fact, Crushfield regards these two meanings as complementary rather than opposite and the confusion as pregnant with possibilities. I regard "complementary" and "opposition" as inseparable (a complementarity that is indeed pregnant), but I regard terminological vagueness as laden with obscurity rather than pregnant with possibility. 139 Bonner, J. (1980). The Evolution of Complexity. Princeton University Press.

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Complexity has a mathematical definition in the notions of complex and hypercomplex numbers. Geometrically, a complex number is twodimensional. Extending this notion, we can define the complexity of a process or system as the number of its dimensions. A biological process is complex because it has all the physical dimensions of non-biological processes plus additional dimensions that describe its biological organization. This concept may provide a definition of complexity that corresponds to the idea of "higher". The term complexity implies that processes at higher levels are systems composed of simpler ones. Higher processes have the same composition as simpler ones, differing only in their form or organization. By way of contrast, medieval philosophies regarded psychological processes as made of a different substance, the soul, capable of a separate existence. Mind and spirit were supposed to reside in the soul, and the soul was regarded as being simple and unitary. Clearly, emotional and mental activity cannot reside in a simple substance but requires a functioning brain. Stating the first general principle of evolutionary theory, Lamarck asserted that complexity of function requires complexity of organization.140 In systems theories, complexity is regarded as the result of combination of parts into a whole; thus, the local is regarded as simple and the global as complex. But complexity is not a simple function of the number of parts. Biological complexity is not a function of the number of genes: the worm Caenorhabditis elegans has 18,424 genes, the fruit fly Drosophila melanogaster 13,601, and humans about 35,000. This difference appears to be too small to account for the wide difference in the complexity of function.141 Similarly, the complexity of an ecosystem is not solely defined by the number of species, but requires consideration of the types and number of interactions among them. The complexity of networks among persons, computers, or species similarly depends on their spatial structure and not solely on the number of nodes and links.142 As complexity 140

Bateson, G. (1979). Mind and Nature. A Necessary Unity. New York: Dutton. Szathamary, E., Jordan, F. and Pal, C. (2001). Can genes explain biological complexity? Science 292: 1315-1316. 142 Lloyd, A. and May, R. M. (2001). How viruses spread among computers and people. Science 292: 1316-1317. 141

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evolves as the result of evolutionary "tinkering" rather than preconceived design, the number of components involved in a given function may far exceed the minimal number required to perform it. Conversely, a whole can be less than the sum of its parts. A heap is simpler than the atoms that compose it. Multiplicity of parts is a necessary but not sufficient condition for complexity. Further, complexity can emerge in individuals as they differentiate and mature within the system. In these cases, the system has priority, and is simpler than the individuals. For instance, social systems are prior and simpler than the human individuals, and hot plasma preceded the differentiation of galaxies in the early universe. A macroscopic system is often simpler than its component parts. Human organisms are more complex than the larger systems in which we live; galaxies are not made more complex by the local development of complexity such as human life. Large systems can be less complex than their contents: sand dunes are constructed by simpler mechanical interactions than the quantum mechanic laws that govern the structure of the component atoms. Even social processes are largely unaffected by the psychological life of most individuals. Since systems may be more or less complex than their component parts, it seems more appropriate to regard dimensionality as the definition of complexity. Notwithstanding, a larger system is obviously more complex than a smaller system of the same dimensionality. Thus, complexity has at least these two complementary aspects. Current science employs the term "complexity" to refer to many different things, labeled "topological complexity", "algorithmic complexity", etc.143 One current view of "complexity" is systematically anti-systemic; it paradoxically discards the generation of complexity by 143 It is not surprising that complexity has many aspects, and therefore that there are several different types and measures of complexity. M. Koppel (Complexity, depth and sophistication. Complex Systems 1: 1087-1091, 1987) distinguishes between "total complexity", which includes entropy, and "meaningful complexity" which captures structure. F. Papentin ( On order and complexity. I General considerations. Journal of Theoretical Biology 87: 421-456, 1980) divides complexity into "organized" and "unorganized" components. M. Anand and L. Orloci, (Complexity in Plant Communities: the notion and quantification. Journal of Theoretical Biology 179, 1980) measuring complexity with a communication-theoretical parsimonious code, found that entropy measures only one component of complexity. For an excellent review, see Ilachinski, A. (2002). Cellular Automata. Singapore: World Scientific.

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the formation of collective systems. According to this view, each entity is independent, and remains so when grouped. Global behavior is determined by the action of each individual, which is simple and independent, like a grain of sand. Complexity is the appearance of global behavior. Emergence is defined as the appearance of complexity in a grouping of entities when no single one of them directs all others, and there is no rule in the system that dictates global behavior. (This is not how philosophers defined emergence.) Under this strange definition, temperature and entropy should be regarded as complex because they are collective properties "emerging" from the aggregate entities. The algorithmic complexity of a finite sequence of bits144 is measured by the size of the smallest program that generates it. Algorithmic complexity can thus be used to describe mathematical series, but it is not applicable to empirical processes. Also, algorithmic complexity is formally incomputable, although estimates can be obtained with a version of algorithmic information theory that utilizes a particular universal Turing machine by working with a specific general programming language.145 Also, algorithmic complexity is so defined that random sequences turn out to be more complex than biological processes. Algorithmic complexity is a measure of randomness, and randomness is not what is usually meant by complexity, either in ordinary language or in scientific discourse. Thus, Nobelist Gell-Mann146 states, algorithmic complexity is not a valid construct of real complexity. It would be desirable to formulate a definition of nonrandom complexity that is operational, valid, and applicable. By operational, I mean measurable and computable. By valid, I mean that it would correspond, albeit approximately, to the usual meaning of the term. By applicable, I mean that it measures the complexity of empirical time series, not only that of mathematical series. Such a definition of complexity may be achieved by integrating it within evolutionary theory and grounding it in empirical observations. Biological and psychological 144 Kolmogorov, Solomon, Martin-Loef, Chaitin, and others, see Li, M. and Vitanyi, P. (1993). An Introduction to Kolmogorov Complexity and its Applications. Springer-Verlag; Chaitin, G. J. (1996). How to run algorithmic information theory on a computer. Complexity 2: 15-21. 145 Chaitin, G. J. (1996). How to run algorithmic information theory on a computer. Complexity 2(1): 15-21. 146 Gell-Mann, M. (1994). The Quark and the Jaguar. New York: W. H. Freeman.

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processes are more complex than physical ones, and in turn physical processes are more complex than random flux. We should thus consider a measure of complexity valid when it provides high values for biological processes and mathematically generated biotic series, intermediate values for chaos, and low values for random or simple periodic processes. This criterion to identify complexity may be regarded as a matter of definition. However, it corresponds to the usual meaning of the term complexity. From a purely pragmatic perspective, methods that identify biological and psychological complexity may be useful tools. On these grounds, we proposed that the ratio of consecutive to total recurrence ("arrangement") measures nonrandom complexity in time series.147 4.8.2 Arrangement The measure of nonrandom complexity to be described here is based on empirical studies148 in which we found that the ratio of consecutive isometries over the total number of isometries is high in heartbeat interval series and low in random series. This observation suggested to us that this ratio might provide a valid measure of complexity. This possibility was later supported by studies comparing time series of various degrees of complexity.149 The term arrangement was chosen to avoid adding yet another meaning to the term complexity. Arrangement is the ratio of consecutive isometries to total isometries. It is high in time series of physiological recordings 147

Sabelli, H., Carlson-Sabelli, L., Patel, M . , Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological Portraits: A Clinical Application of Process Theory. In Chaos Theory in Psychology, F. D . Abraham and A . R. Gilgen (Eds). Westport, CT: Greenwood Publishing Group, Inc., p p 107-125; Sabelli, H . (2001). Arrangement, a measure of nonrandom complexity. Systems Analysis Modelling Simulation 42: 395-403. 148 Sabelli, H.C., Carlson-Sabelli, L., Patel, M , Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological portraits: A clinical application of process theory. In Chaos Theory in Psychology, F. D . Abraham and A . R. Gilgen (Eds). Westport, CT: Greenwood Publishing Group, pp. 107-125. Republished in Russian C H H E P F E T H K A H n C H X O J I O r H f l 1: 184-209, 1997. 149 Sabelli, H . (2001). Arrangement, a measure of nonrandom complexity. Systems Analysis Modelling Simulation 4 2 : 395-403; Sabelli, H., Sugerman, A., Carlson-Sabelli, L., Kauffman, L., and M. Patel (accepted for publication). Bios Data Analysis. Process Methods to Analyze Creative Processes. Part 8. Recurrence Isometry: Measures of Novelty, Order and Nonrandom Complexity. Journal of Applied Systems Studies, special issue edited by H. Sabelli.

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(electrocardiogram, electroencephalogram, electromyogram, respiration), economic time series (Dow-Jones Industrial Average; prices for crude oil, corn, gold, silver; exchange rates for American, British, Canadian, Danish, Japanese, European, currencies), and biotic series generated with recursions of bipolar feedback At+i = At + g * sinAt, that is to say, complex processes (Fig. 4.64). Arrangement is low in simple series, including simple speech sounds, oceanic temperature changes during El Nino, random data, periodic series, and chaotic series. In periodic series, arrangement increases with the complexity of the periodicity (period 2 < period 4 < period 16, etc). In series generated by the process equation (Fig. 4.65), arrangement increases from steady flows to bifurcation cascades, to period 2 chaos, to chaos, to bios, to infinitation, in contrast to isometries and consecutive isometries that decrease from periodicity to chaos to bios. Neither the ratio of consecutive recurrence to total recurrence nor either one of these measures alone correlates with complexity when similarity recurrence is measured. The Lempel-Ziv complexity relative to white noise is maximal for the static and the dyadic phase, diminishes with successive bifurcations, is minimal for chaos, and increases significantly during the biotic phase.

Fig. 4.64 Arrangement for series of 1000 terms calculated with 50 embeddings and cutoff radius 0.1.

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UsefUl comparisons among numerical series with widely different range of values can be made by measuring recurrence and arrangement at the Median Embedding Dimension (MED), which is defined as the embedding at which 50% of the isometries are consecutive (Fig. 4.66

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top).150 The MED does not correlate with complexity. It is highest in random and chaotic data. It is low in some periodic and non-periodic empirical data. As shown in Table 4.8, the MED of empirical time series are of the same order of magnitude as those for biotic series, and much lower than those observed with random and chaotic series, and 1/f noise. Regardless of their MED, arrangement is high in complex series, including 1/f noise, and lower for simpler series. Although arrangement and the MED obviously measure different types of complexity, both markers indicate that heartbeat interval series recorded from healthy persons are more complex than those recorded from patients with psychiatric illness. This is consistent with the view that cardiac rate and variability are largely determined by higher central nervous system activity. Table 4.8 Arrangement at the Median Embedding Dimension (M.E.D.) Isometry measured with delay 1, cutoff radius 0.1. (RRI = heartbeat intervals) Random (uniform) 1/f pink noise Logistic chaos Process chaos g = 4.3 Bios g = 4.61 Bios g = 4.65 Bios g = 4.66 Bios g = 4.7 Healthy RRI (N=31) Coronary disease RRI (N = 9) Depressed RRI (N = 51) Bipolar depressed RRI (N=9) Affective psychoses RRI (N=45) Schizophrenic RRI (N=9) Dow Jones Industrial Average Corn El Nino Paleoclimate marker (Seychelles)

M.E.D. (mean+ S.E.) 214 120 363 345 18 21 53 78 60 + 4 36 + 12 37 + 2 52 + 17 41+3 25 + 8 10 35 37 331

Arrangement 16 97 15 12 42 57 189 289 61 + 4 61 + 20 49 + 2 62 + 20 49+3 34 + 11 54 98 58 15

150 Sabelli, H.C., Carlson-Sabelli, L., Patel, M., Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological portraits: A clinical application of process theory. In Chaos Theory in Psychology, F. D. Abraham and A. R. Gilgen (Eds). Westport ,CT: Greenwood Publishing Group, pp. 107-125.

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Shuffling the data prior to calculations decreases arrangement in biotic series, and increases it in the case of periodic data. These results indicate that arrangement correlates with our intuitive notion of complexity. In the case of chaotic series, shuffling decreases arrangement al low embeddings (as for bios) and increases arrangement at high embeddings (as for periodic series), indicating two different forms of organization. Arrangement is reduced by shuffling for physiological and economic data, regardless of the embedding dimension. This is consistent with the notion that these processes are creative and exhibit a biotic pattern. 4.8.3 A focus on creativity The consistent generation of complexity in cosmological, biological and human evolution point to accounting and measuring complexity by focusing on its generation by causal processes. In contrast, Chaitin argues that the most important application of complexity theory "is to show the limits of mathematical reasoning. And in particular what I've constructed and exhibited are mathematical facts that are true for no reason. These are mathematical facts that are true by accident. And since they're true for no reason you can never actually prove logically whether they're true or not. They're sort of accidental mathematical facts... analogous to the outcome of a coin toss, because an independent toss of a fair coin has got to come out heads or tails but there's no reason why it should come out one or the other. And I've found mathematical facts that mirror this very precisely." In the spirit of pragmatism that analyzes ideas by their practical implications, let us compare the implications of different notions of complexity. Consider the notion that the complexity of a system "emerges" from the individual action of its components, so the V pattern of flying geese is the appearance resulting from the biologically determined behavior of each individual goose. In the same manner, individual instincts for self-preservation and acquisition determine the economic system. The corollary is that the status quo lasts forever, the natural result of biological law. Explaining social behavior by individual biology is not a politically neutral hypothesis.

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From the perspective of creative processes, individual behavior is more complex than its biological basis. Biology belongs to the species; it determines social behavior in each individual organism. This shared behavior generates a social system that in turn serves as a cradle in which individual organisms differentiate. Both social and personal developments are modified by present circumstances and past history. As a result, there is diversity of social systems, and an even larger diversification of individuals. Pursuing self-preservation, biology generates solidarity, not only selfishness. These two different scientific concepts of complexity represent contrasting ideologies: the first one is individualistic and deterministic; the second is creative: determined biological processes create social systems and individuated persons, and individuals create new social organization. Determinism cannot explain natural diversity and hinders motivation to create and individuate. There are two ways of looking at the relationship of evolution and dimensionality. Attributing the generation of novelty to random processes implies that evolution is a reduction from the infinite dimensions of randomness to the many fewer dimensions of attractors and ordered structures. Attributing the origin of complexity to the interaction of simpler entities implies an expansion in the number of dimensions. Equating complexity with disorder renders random-like chaos exemplary of complexity; "How does chaos emerge from simplicity?" becomes the foremost question.151 In contrast, defining complexity as biological-like poses a different question: what simple processes create novelty? 4.9 Simplicity and Complexity: Embedding Plots Theory and method begin with the definition of dimensions. Dimension organizes physical theory and empirical measurement. Dimensions are quantifiable. Further, one can define a limited set of dimensions and define all others in terms of the dimensions taken as fundamental. The 151 Crutchfield, J. P. (2003). When Evolution is Revolution. In Evolutionary Dynamics, J.P. Crutchfield and P. Schuster (Eds). Oxford: Oxford University Press.

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concept of dimension provides physics with a logical power that all other sciences aim to attain. As much as possible, one wishes to measure complex processes in terms of physical dimensions. In addition, it would be desirable to extend the concepts of dimension to describe biological organization. Medical care starts with measuring physical dimensions: temperature, energy (such as amplitude of the pulse or of respiratory movements) frequency of actions (such as respiratory and heart rate), and mass (weight). However, a clinical description also adds descriptions of form, such as color, shape, consistency, and so on. All processes are physical entities, and hence should be described in terms of physical dimensions.152 However, standard physics does not concern itself with communication and organization, two fundamental features of chemical, biological, and psychological processes. Dimensions of information and form are also necessary to describe concrete subatomic, cosmological, and geological structures. Thus, Yates153 indicated the need for defining new dimensions describing information and form. These dimensions have not been identified as yet, but it may be possible, in principle, to investigate them mathematically by creating series of lags, differences and embeddings. Bios analysis is based on the concept that mathematical dimensions represent abstractions of actual dimensions of reality. An evolutionary perspective must focus on the creation of complexity rather than on complexity itself. The scientific study of complexity must start with simplicity. Simplicity is the foundation of complexity in nature, and reduction is the most successful strategy in science. "Fundamental" implies simple. Simple and complex coexist. We cannot consider one without the other. Simpler processes contain (and are contained within) the more complex processes they generate. Simple and complex processes are embedded into one other. The simple encodes the complex, so simple and complex determine each other in an asymmetric fashion: priority / supremacy. 152 Most physical quantities can be expressed in terms of combinations of five basic dimensions. These are mass (M), length (L), time (T), electrical current (I), and temperature (D). These five dimensions have been chosen as being basic because they are easy to measure in experiments. There are dimensionless quantities such as the numbers and trigonometric functions, and many others. 153 Yates, F. E. (1987). General Introduction. In Self-Organizing Systems. The Emergence of Order, F. E. Yates (Ed.). New York: Plenum Press.

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Creativity consists in the generation of higher dimensions by simple (low dimensional) processes. Evolution is a process of dimensiogenesis, i.e. an increase in the number of dimensions of form, in contrast to notions of creation of lower dimensional order by an infinitely complex source -either random or supernatural. Complexity is composed of multiple simplicities in time, space, and organization. Simple origins originate complexity. Simple processes have priority and are creative. They pre-exist, co-exist and outlast the complex organization they generate. They are universal components to be measured in every complex processes. Whatever complexity pertains to the totality of a process or system, it must be embodied in the sequence of its constituents in time and space. In a process, complexity is embodied in both rapid and slow variation in the time series. These considerations indicate that to analyze complexity, one needs to record time series for a sufficiently long time, and with an appropriately high sampling rate. The time series of creative process may thus be expected to contain both high dimensional complex components and their low dimensional simple generator. A cause is by definition simple. In contrast, random processes are high dimensional. The time series of stochastic processes generated by random innovations will not contain simple components. To better study both simple and complex components of a time series, we plot isometries as a function of the duration of the vector (embedding plots). These plots allow one to study simple and complex components of processes from a single time series. Particularly useful are embedding plots of isometric recurrences denoting repetition and consecutive recurrences denoting order. Periodic series show 100% isometry when the vector is an integer multiple of the period, indicating that the embedding dimension represents the time dimension of the component being examined. Low dimensional order is particularly evident in embedding plots of consecutive isometries, and notoriously absent in 1/f noise. Deterministic causation is also suggested by strong autocorrelation, and partial autocorrelation.154 Stochastic series do not 154 Patel, M. and H. Sabelli. Autocorrelation And Frequency Analysis Differentiate Cardiac And Economic Bios From 1/F Noise. Kybernetes. 32: 692-702, 2003.

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show partial autocorrelation. Creative organization displays both order and novelty; random creation displays novelty without order. The number of dimensions portrays the complexity of a process. Embedding plots differentiate five types of aperiodic series: random (indistinguishable from its shuffled copies), chaotic (low dimensional order and high dimensional randomness), stochastic (low dimensional randomness and high dimensional novelty and order), biotic (low dimensional order and high dimensional novelty), and prebiotic (novelty without consecutive recurrence). In creative evolution, simple, low dimensional processes generate complex, high dimensional patterns. To study creativity one needs to measure simplicity and complexity, rather than complexity alone. The time series of processes that evolve from simple to complex may be expected to contain both high dimensional complex components and the simpler low dimensional processes that generate them. In contrast, deterministic processes conserve their original form and dimensionality, so mechanical as well as chaotic processes have only simple low dimensional components. Random processes are highly complex in the sense that each change represents an independent event; thus stochastic series in which complex organization is generated by random changes display only complex components. The method of delay and embedding allows one to measure simple and complex patterns coexisting in a single time series. The concept of dimension organizes notions of quality, quantity, and complexity into a theoretical framework. Early philosophy considered quantity, quality (which meant property but also rank) and order (inferior and superior) as separate categories. Classification is the core of Aristotelian logic and of modern mathematical logic and set theory. In contrast, a process viewpoint regards qualities as dimensions. With the advent of modern science, the quantitative acquired dominance. This shift reflected a switch to a monetary economy, some sociologists argue, but this ignores intrinsic scientific reasons that are far more fundamental. Within this quantitative frame of mind, qualitative considerations were often regarded as primitive or inferior quantitative analyses. Inferior and superior became simple and complex. Analysis of the complex into its simple components became the most fundamental method of science

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from physics to psychology, and reduction became the core of scientific philosophy. In our times, quality has gained ascendancy again. Mandelbrot155 discovered scale invariance (for short, "scaling") meaning structures in which magnifying one of the parts of an entity reproduces the original totality.156 The discovery of scaling has diverted attention from the relation between quantity and quality. In the area of time series analysis, this manner of thinking attempts to account for complex processes in terms of simple (low dimensional) attractors. "Embedology" attempts to determine the correct dimension at which a process must be analyzed. Focusing on creative processes requires another change in perspective. To study creativity it is necessary to measure both simple and complex components by analyzing time series at multiple embeddings. Instead of reduction, we must attend to both the priority of the simple and the supremacy of the complex. Scalar differences are significant. Numbers are also forms. Quantity, quality and order must be considered together, in a dialectic fashion. Dimension etymologically means measure, but the term has a more complex meaning. Dimension is a quantity such as size: if you ask someone the dimensions of an object, he will probably tell you its length, width and height. A physicist will also consider weight, momentum, and electrical charge. Each of these dimensions represents a quality.157 In addition to the quantitative and qualitative aspects of dimensions, there is a third aspect, complexity: what is the number of dimensions that describe the system under consideration? A dimension involves quantity, quality and complexity: sqd, where s is a magnitude in a given scale, q is the quality such as distance or time, and d is the number of dimensions in

155 Mandelbrot, B. B. (1977). The Fractal Geometry of Nature. New York: W. H. Freeman and Company. 156 "Scale free" meaning repetition. A straight line is "self-similar" because any line segment is straight. In addition to linear organization, there is another fundamental set of self-similar entities, namely fractals. Mathematical fractals are complex yet self-similar objects, showing the same pattern at small and large dimensions; natural fractals, such as coastlines, are not exactly self-similar, but show statistical self-similarity. 157 Quantity, quality, and measure (dimension) constitute one of Hegel's dialectic triads. Dimension offers a better model for quality than standard logic, which describes qualities as classes defined by their well-defined extension. Real classes have fractal and highly permeable boundaries.

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this quality, such as 3 for space. These aspects are not independent from one other.158 A physical process is described by a multiaxial system of fundamental dimensions such as energy, mass, time, position, velocity, electrical charge, etc. A fundamental quality is one that is orthogonal to all others within the universe. It follows that the interaction among qualities are multiplicative, nonlinear. Fundamental dimensions provide a theoretical framework. Dimensional analysis of a process provides meaningful insights on physical processes. The standard physical dimensions are also useful to describe biological, social and psychological processes. These physical dimensions are sufficient in physics because this science focuses on general processes. Physics does not account for specific features such as the form of mountains and continents. Features of information and form are even more important in biological and human processes. It seems thus desirable for biologists to define informational and morphological dimensions.159 A bridge towards this larger system of dimensions is offered by the mathematical concept of dimension. It extends the usual concept of spatial dimensions. In physical space, the position of an object is defined by three coordinates; in the same manner one defines a point in the abstract space defined by any coordinate or reference system. The number of coordinates required to specify each point is called the dimension of this space. The set of coordinates that defines a point forms a vector. Caveat: Statisticians use the expression "orthogonal dimensions" to mean "independent dimensions". Height and width are orthogonal but seldom independent, as illustrated by the size of planets and the changes

158

When the order of magnitude is large, one of the three dimensions of space cannot be separated from time; we thus speak of light-years to refer to stellar distances. Galileo highlighted the dependence of quality on quantity. Ants walk on vertical walls, while heavier animals cannot. Levels of organization often represent orders of magnitude. In processes, frequency is associated with size (atoms vibrate faster than large objects) and complexity is associated with diversity in the frequency spectrum. 159 Yates, F. E. (1987). General Introduction. In Self-Organizing Systems. The Emergence of Order, F. E. Yates (Ed.). New York: Plenum Press.

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in size of balloons compressed in one dimension or the other. The use of the term dimension in nonlinear dynamics is also approximate.160 There are multiple mathematical measures of dimension. Euclidean, topological and fractal dimensions are commonly employed to characterize natural processes.161 Topological and Euclidean dimensions may or may not coincide, but both assume only integer values. Fractal dimensions can be non-integer, and thereby characterize fractal objects. Fractal dimensions quantify how the small-scale forms are related to the larger scale forms. Such fractality cannot be observed in natural time series; for instance, if the wind velocity changes between 1 and 2 m/sec in 1 minute, it does not follow that it will fluctuate between 24*60 m/sec and 2*24*60 m/sec in one day.162 A noninteger capacity (or Hausdorff) dimension163 characterizes many but not all fractals.164 The Hausdorff dimension is one among the infinite number of fractal dimensions that can be measured. The correlation dimension calculates as the number of points that have a smaller (Euclidean) distance than some give distance r, and the relative count C(r) as the total count divided by the squared number of points as r is varied: D2 = lim log C(r) / log r, r-^0. The correlation dimension is lower for chaos than for bios, and much higher 160

It is stated that we must make sure that the statistical analysis of a certain sample involves independent values, as dependent values bias our estimations. The same philosophy is applied for the reconstruction of attractors and the estimation of the correlation dimension. How such independence is proven is, in my view, often open to question. 161 The Euclidean dimension of a configuration is 1 if it is embedded on a straight line, 2 if it is embedded in a plane, and 3 if it is embedded in space. Thus, a curve may be two or threedimensional. The topological dimension of a curve is 1, just as for straight lines, because it is divided by one point; similarly, surfaces are continua of topological dimension 2, and space is a continuum of three dimensions. 162 Tsonis, A. A. (1992). Chaos: From Theory to Applications. New York: Plenum. 163 Consider a line (or the side of a square or a cube) of length L, and divide it into N straight-line segments of length r. If the scale unit r is sufficiently small, the length L of a smooth line is approximately equal to the product N * r (as r tends to 0, N * r approaches a finite limit, the length L). A similarity dimension D is defined by the relation between the number of parts required to reproduce the original form to the scale change. In the case of complex fractal curves, as we reduce the size of our ruler r, the product N * r does not converge to a finite value, but it grows indefinitely, as r now enters finer and finer twists of the curve. The German mathematician Hausdorff found that N * rD stays finite for some critical value DH of the exponent D, tends to 0 for larger values of D, and flies to infinity for smaller values. The Hausdorff dimension is defined as the limit of the ratio of the logarithm of the number of parts to the logarithm of the inverse of their size r as r tends to 0: DH = limlogN/log(l/r). r-»0 164 In Multifractals and 1/f noise (Springer, New York, 1999), Mandelbrot explicitly rejects his earlier definition of fractals in terms of noninteger Hausdorff dimension as a mistake to which he was led by social pressure for "rigorous" definitions.

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for their randomized copies. The correlation dimension of the time series of differences between consecutive terms is also lower for chaos and for bios than for random series, indicating that the series are not random walks. 4.9.1 Embedding method One can reconstruct the phase space of a process by using a single record of some observable x(t) by using the method of delays and embedding.165 The state of the system is represented by a state vector X(t) constructed by using x(t) as the first coordinate, x(t + x) as the second coordinate, and x( t + (n — 1) x) as the last coordinate, where x is a suitable delay parameter and n is the embedding dimension. One can visualize easily tridimensional space, and more dimensions by using color and other forms of representation. For higher dimensions, one can compare sequence of consecutive terms that form the vectors constructed starting with each term of the time series, and calculate recurrences of various functions. Figure 4.67 illustrates this method. In the context of chaos theory, embedding methods are used to calculate the dimension of the attractor. In the case of mathematical series in which there is an attractor, one can describe it by embedding the attractor in a coordinate space166; the embedding dimension is the lowest possible dimension of such space.167 There are solid mathematical bases for the method, but its application to empirical data is not 165 Packard, N.H., Crutchfield, J.P., Farmer, J.D., and Shaw, R.S. (1980). Geometry from a Time Series. Physical Review Letters 45: 712-716; Ruelle, D. (1991). Chance and Chaos. Princeton, NJ: Princeton University Press; Takens, F. (1993). Detecting Nonlinearities in Stationary Time Series. InternationalJournal of Bifurcation and Chaos 3: 241; Gershenfeld, N.A. (1992). Dimension Measurement on High-Dimensional Systems. Physica D 55: 135-154; Guillemin, V. and A. Pollack. (1974). Differential Topology. Prentice-Hall; Eckmann, J.P., Kamphorst, S.O. andD. Ruelle. (1987). Recurrence Plots of Dynamical Systems. Neurophysics Letters 4: 973-977; Zbilut, J.P. and C.L. Webber Jr. (1992). Embeddings and Delays as Derived From Quantification of Recurrence Plots. Physics Letters A 171: 199-203; Zbilut, J.P., Webber, C. L. Jr., P.A. Sobotka, et al. (1993). Recurrence Analysis of Heart Rate Variability. J. Am. Coll. Cardiol. 21 (2, Suppl. 4A): Abstract No. 439-5. 166 Actually, the series may be embedded into any type of smooth manifold. A manifold is a geometric model including cylinder, tori, etc. A smooth manifold does not possess self-intersections. 167 Note, however, that only attractors that are topological structures (points, limit cycles, tori) are submanifolds of the manifold in which they are embedded. Attractors that are fractal sets are not submanifolds [Tsonis, A. A. (1992). Chaos: From Theory to Applications. New York: Plenum].

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straightforward. How can we proceed in the case of natural processes, in which we do not know the embedding dimension, or even whether or not there is an attractor? In fact, creative processes cannot be expected to have an attractor. Notwithstanding a number of procedures have been devised, and multiple articles have debated the issue of what is the appropriate embedding dimension. These methods are based on Whitney's theorem,168 which requires infinite data. Thus, when we are dealing with finite data sets, the word "embedding" is used loosely.

Fig. 4.67 Lorenz chaos shows pattern on low embeddings.

A number of guidelines have been offered regarding the minimum number required and the maximum number allowed in the choice of embeddings. A relatively low number is usually chosen in the search for low dimensional attractors, and in the fear that a high number of According to Whitney's theorem, any smooth manifold of dimension m can be smoothly embedded in n = 2m + 1 dimensions. If the dimension of the manifold containing the underlying attractor is m, then embedding the data in a dimension n > 2m + 1 preserves the topological preserves properties of the attractor such as dimension, positive Lyapunov exponents, etc.

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embeddings may introduce misleading errors. Using Webber and Zbilut's recurrence quantification169 we have constructed "embedding plots" that graph the percentage of recurrence as a function of the number of embeddings used in their computation,170 and found that periodicity can only be detected at the corresponding embedding. For instance, it is necessary to use 365 embeddings to detect annual periodicity in daily data. Thus each embedding identifies a significant form present only at that temporal dimension. Natural processes often show different patterns at various durations; for instance the weather has seasonal as well as daily periodicity, but between these two periodicities there is an aperiodic pattern that has chaotic features171 and also biotic novelty, diversification, and nonrandom complexity.172 These observations indicate that complexity cannot be measured at one embedding, no matter how chosen. We thus introduced embedding plots173 to study both low and high dimensional components of a process from a single time series. To this effect, one constructs vectors of 1, 2, 3, ..., N consecutive terms starting with each term of the time series, compute statistical and dynamical measures for each set of vectors, and plot these parameters as a function of the duration of the vector. These embedding plots allow one to study simple and complex components of processes from a single time series. 169 Webber, Jr., C. L. and Zbilut, J.P. (1994). Dynamical Assessment of Physiological Systems and States using Recurrence Plot Strategies. Journal of Applied Physiology 76: 965-973. 170 Sabelli, H., Carlson-Sabelli, L., Patel, M., Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological Portraits: A Clinical Application of Process Theory. In Chaos Theory in Psychology, F. D. Abraham and A. R. Gilgen (Eds). Westport, CT: Greenwood Publishing Group, Inc., pp. 107-125; Sabelli, H., Carlson-Sabelli, L., Patel, M., and Sugerman, A. (1997). Dynamics and Psychodynamics. Process Foundations of Psychology. Journal of Mind and Behavior 18: 305334. 171 Lorenz, E. N. (1993). The Essence of Chaos. Seattle: University of Washington. 172 Sabelli, H. (2000). In Peoria, the Weather is Biotic. General Systems Bulletin 29: 9-10. 173 Sabelli, H., Carlson-Sabelli, L., Levy, A., and Patel, M. (1995). Anger, Fear, Depression and Crime: Physiological and Psychological Studies using the Process Method. Chaos Theory in Psychology and the Life Sciences, R. Robertson and A. Combs (Eds). Mahwah, NJ: Lawrence Erlbaum, pp. 65-88; Sabelli, H., Carlson-Sabelli, L., Patel, M., Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological Portraits: A Clinical Application of Process Theory. In Chaos Theory in Psychology, F. D. Abraham and A. R. Gilgen (Eds). Westport, CT: Greenwood Publishing Group, Inc., pp 107-125; Sabelli, H., Carlson-Sabelli, L., Patel, M., and Sugerman, A. (1997). Dynamics and Psychodynamics. Process Foundations of Psychology. Journal of Mind and Behavior 18: 305-334; Sabelli, H. (2001). Arrangement, a measure of nonrandom complexity. Systems Analysis Modeling Simulation 42:395-403.

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The number of terms in the vector is the time dimension, i.e. the duration being examined. Just as one could portray a complex physical form, let us say a sculpture, by measures of width at different heights, one may reveal the form of a process by measures of variance, recurrence, or correlation at different durations. Particularly useful are embedding plots of isometric recurrences174 denoting repetition, and consecutive recurrences denoting order. The pattern generated by these measures when plotted as a function of vector duration175 portrays the temporal pattern of the process. For instance, when the process includes periodicities, characteristic features of the series, such as recurrence, appear only at the corresponding embedding (Fig. 4.68). Periodic series show 100% isometry when the vector is an integer multiple of the period, indicating that the embedding dimension represents the time dimension of the component being examined. This is obvious for periodic series; the same concept may be 174

Sequences (vectors) of 1, 2 ...d,..., D successive members of a time series are constructed, starting with each data point. The length d of the vector is the "embedding dimension". We use a range of embeddings, from 1 to D = 100 or more, as required by the data. For each vector, we calculate the Euclidean norm (the square root of the sum of the squares of its terms). Recurrence analysis is performed by the quantification of isometric vectors, using a cutoff ratio of 0.01 and a delay of 1, as described before. In this description, the terms recurrence and isometry are taken as synonymous. At each embedding, we quantify: (i) Recurrence and novelty: Isometry rate is the number of isometries as a percentage of the total number of possible isometries in the sample (N x N / 2). Lower isometry in the series than in its randomized copies indicates variation at a faster rate than expected from accidental change, which defines novelty. (ii) Consecutive isometry and causation: the number of isometries that follow each other; e.g. if vector x, is recurrent with vector xt+m, then vector x,+1 is recurrent with vector xt+m+i; consecutive isometry is calculated as percentage of total isometry. Larger consecutive isometry in the series than in shuffled copies indicates deterministic causation. At low dimensions, this shows simple causality; at periodic intervals, it indicates periodic causation. (iii) Recurrence entropy and order: sequences of consecutive isometries are arranged according to their length, and their statistical entropy is measured in bits. Higher entropy in the series than in its randomized copies indicates order. (iv) Arrangement and nonrandom complexity: the ratio of consecutive isometry to isometry rate, which previous studies indicate is correlated with nonrandom complexity. Higher arrangement in the series than in its randomized copies indicates nonrandom complexity. Each series is compared with shuffled copies. A difference between the series and shuffled copies in any one of these measures indicates nonrandom pattern at the corresponding embedding dimension. By definition, a simple process displays pattern at a specific embedding dimension (and at its multiples). Complexity is intuitively defined by the demonstration of multiple components in the time series. 175 In this case, it seems preferable to speak of "vector durations", but we may refer to them as "embedding dimensions" with the understanding that this use of the term embedding is at best informal.

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generalized to aperiodic ones. The morphology of a process is represented by the features observed in the corresponding time series in the range of vector durations being examined. Just as an object may display different forms at various amplifications, a process may display different patterns at different durations. Form can be coded as information (e.g. the digital coding of visual or musical patterns). Sequence creates organization in reality as well as in analysis. Just as the tridimensional spatial sequencing of energy generates material systems, sequences in time generate complexity. Meaningful information may be carried in two different ways: as local patterns and as large global patterns. To detect these two types of pattern, one needs to examine short and long series, using small and large embeddings. Embedding dimensions are dimensions of the time required to encode a given piece of information. 60 -i

Sine wave

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The abstract concept of dimension opens many doors. First, it allows us to apply it to time series. Second, it provides an intuitive scale of complexity in terms of the number of dimensions (1 < 2< 3 etc). Third, in embedding plots of recurrence, it connects temporal duration as a scale analog of dimensionality. In connecting embedding dimensions with temporal duration, we return to the relation of scale with quality envisioned by Galileo. Fourth, it allows us to define noninteger, fractal dimensions. Scalar quality and scaling (fractal) qualities are complementary aspects of quality.

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For embedding plots of isometric recurrence, in random data, isometry rate is practically zero at low embeddings and consecutive isometry is low at all embeddings. This follows from the fact that a random event is independent of the preceding ones.176 Random sequences of few values, e.g. the digits of n, show a peak of isometries at low embeddings, but the same is observed in shuffled copies. This is why determination is measured by comparison with shuffled data. ^"v^. Pacific ocean temperature, radius 0.01

i -3 I

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Fig. 4.69 Embedding plot of net recurrence isometry of water temperature in the Pacific Ocean and two shuffled copies. Peaks at around 365 embeddings and marked increase in isometry with shuffling (novelty) show the coexistence of periodicity and bioticity. Plasmodium chromosome 7 initial segment 35

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176 In Webber and Zbilut's program, isometry increases with the number of embeddings because the Euclidean norms of longer vectors become more similar to each other. Consecutive isometry and arrangement also increase gradually with embedding, as consecutive vectors have greater proportional overlap as embedding increases. In Sugerman's BDA, there is very little difference in values regarding embedding.

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Fig. 4.71 Embedding plots of series generated by the process equation at increasing gains. N=1000, radius 0.1.

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Fig. 4.72 Embedding plots of time series generated by chaotic and stochastic series. N = 1000, radius 0.1. Pink noise shows no determination at any embedding. Brownian noise does not show low dimensional determination. The Rossler chaotic attractor shows novelty and arrangement as does bios, but it differs from bios in showing no consecutive recurrence at low dimensions and strong periodicity.

Periodic series generate periodic embedding plots. When the embedding is an integer multiple of the period, there is a maximum of isometry, consecutive isometry approaches 100%, recurrence entropy is

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maximal, and arrangement is minimal. This is illustrated by the sequence of DNA bases in a telomere (Fig. 4.70). In sinusoidal distributions of data, as illustrated in Fig. 4.68, there are periodic variations in isometry as a function of the number of embeddings, with peaks when the embedding equals half the period. When multiple periodicities are present, each is denoted by a peak at the corresponding embedding.

Fig. 4.73 Embedding plots of empirical series with biotic properties.

Embedding plots, I surmise, portray the form of complexity.

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Figure 4.71 illustrates the evolution from periodicity to chaos and bios in the process equation. Periodic series show high isometry, consecutive isometry and entropy, but no complexity; arrangement is equal to or lower than in shuffled copies (top row). When chaos is combined with periodicity (second row), isometry and recurrence entropy are markedly decreased, while arrangement increases - chaos is more complex than periodic cycling. Consecutive isometry, recurrence and arrangement decrease with embedding indicating low dimensional causation.

Fig. 4.74 Embedding plots of non-biotic empirical series.

Chaos shows high consecutive isometry only at low dimensions, indicating simple causation. At higher embeddings, the proportion of consecutive isometries decreases to that observed in random data (although there may be peaks associated with coexisting periodicity). This is consistent with the fact that chaotic processes produce random-

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like disorder. Chaotic series show greater isometry than their shuffled copies at all embeddings; this differentiates chaos from random, biotic, and stochastic series, as well as from some empirical series studied here. Arrangement is very high at low embeddings, and it is lower than in shuffled copies at higher embeddings, indicating short duration complexity. Figures 4.71-4.72 illustrate these results for chaotic series generated by logistic and process equations; similar results are obtained with other chaotic series. There are significant differences among chaotic series regarding recurrence entropy; e.g. compared to shuffled copies, recurrence entropy is lower in logistic chaos and higher in process chaos at low embeddings and in Rossler chaos at all embeddings. 4.9.2 Biotic and stochastic aperiodic series Isometry, consecutive isometry, recurrence entropy and arrangement generally increase with embedding in almost all aperiodic series. As illustrated by time series generated by the process equation (Fig. 4.71), embedding plots clearly distinguish chaotic from biotic series. The percentage of isometric recurrences is lower in biotic series than in shuffled copies (novelty) while it is higher than in shuffled copies for periodic and chaotic series. Bios shows high consecutive recurrence at all dimensions, indicting causation (low dimension) and integration (high dimension). The difference between these two processes is indicated by nonlinearity. Embedding plots of mathematical bios, heartbeat interval series, and corn prices exhibit a very significant non-linearity: the number of consecutive isometries first sharply decreases with increasing embedding, and then gradually increases with further embedding; the inflection point lies circa embedding 6. Most other empirical series do not show such nonlinearity. Bios shows arrangement at all dimensions. Heartbeat intervals, respiration, electroencephalograms, annual series of air and ocean temperature, and many economic data show the same pattern as bios, namely: (1) higher isometry and consecutive isometry than shuffled copies at low embeddings, which is compatible with bios but not stochastic noise; and (2) lower isometry and greater consecutive isometry than shuffled copies at high embeddings, creative features absent in chaos. These results contrast with well-known ideas regarding

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heart rate variation, which is assumed to be either chaotic or stochastic, and weather, which is taken to be prototypical of chaos. The proportion of consecutive isometries approaches 100 percent within the range of embeddings examined in many of the nonrandom aperiodic series (stochastic, chaotic, biotic, empirical). A descriptor of this process is the Median Embedding Dimension (MED), which is the embedding at which 50 percent of the isometries are consecutive.177 We choose the median embedding dimension to measure arrangement (Fig. 4.66). The MED is moderate (e.g. circa 50) in mathematical bios and in empirical data and much higher in random and chaotic data (circa 300). In the case of cardiac beat intervals, the MED is much higher in healthy subjects than in cardiovascular or psychiatric patients (see Chapter 5). At high embeddings, Brownian noise shows novelty, consecutive isometry and arrangement just as biotic series do. At low embeddings, Brownian noise resembles random data.178 Pink noise, as well as Brownian noise, shows less isometry than randomized copies at high embeddings. Consecutive isometry is not larger than in shuffled copies. This differentiates pink noise from most empirical series with a 1/f pattern such as heartbeat intervals. It also distinguishes pink noise from Brownian noise and from bios. 4.9.3 Coexisting patterns Multiple embeddings are necessary to detect single or multiple periodicities. Further, embedding plots allow detection of the coexistence of multiple patterns. Embedding plots show that periodicity and chaos coexist in many series, at variance with their standard conceptualization as mutually exclusive attractors. The time series generated by the process and logistic equations at relatively low gain 177 Sabelli, H., Carlson-Sabelli, L., Patel, M., Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological Portraits: A Clinical Application of Process Theory. In Chaos Theory in Psychology, F. D. Abraham and A. R. Gilgen (Eds). Westport, CT: Greenwood Publishing Group, Inc., pp. 107-125. 178 At low embeddings, Brownian noise shows only slightly larger numbers of consecutive isometry than in a shuffled copy (Fig. 4), and not the initial peak observed in biotic and some empirical series. Random walks constructed with small integer steps show peaks of isometry and consecutive isometry at low embeddings, but the same is observed in shuffled copies.

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(period 2 chaos179) show a monotonic increase in isometry with the number of embeddings (as observed with chaos) and a decrease in isometry with shuffling, denoting periodicity. Rossler (Fig. 4.72) and Lorenz chaos also have strong periodic features. Embedding plots of Pacific Ocean temperature (Fig. 4.69) not only show annual periodicity but also display a biotic pattern of daily variation: the percentage of isometries is low and increases with the number of embeddings. Shuffling increases isometry (novelty) and decreases consecutive isometry and arrangement, denoting determined and complex pattern. These experiments illustrate the use of embedding plots to analyze complex processes with multiple components, which are often found in natural processes. Power spectrum analyses detect multiple periodic patterns and measure the power exponent of aperiodic patterns. Embedding plots are not very sensitive in detecting periodicities, but describe and measure coexisting periodic and aperiodic patterns. 4.9.4 Choice of embeddings These results are relevant to often-asked questions regarding the choice of embedding for the quantification of isometries. There is a legitimate concern that a high number of embeddings may introduce errors, as the number of isometries often increases with the number of embeddings in aperiodic data. Yet, using a high number of embeddings does not make everything appear as recurrent. Isometry remains very low for heartbeat series, DNA sequences, stochastic noise and mathematical bios at very large embeddings. The same patterns of distribution of isometries appear in recurrence plots of time series constructed at low and high embedding dimensions; increasing embedding only sharpens the complexes. Regardless of the number of embeddings used to compute them, the series of Euclidean norms amplify and sharpen the pattern of the time series without changing it, as illustrated in Fig. 4.2. High embeddings are necessary to measure seasonal periodicities (Fig. 4.69). Pattern does not consist of a single form with a unique dimension that requires a 179 Patel, M. and H. Sabelli (2003). Autocorrelation And Frequency Analysis Differentiate Cardiac And Economic Bios From 1/F Noise. Kybernetes 32: 692-702.

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particular embedding to be detected. Rather, a pattern is a complex form that has different shapes at different durations, and therefore requires a wide range of embeddings in order to be portrayed. There is no one embedding that can portray a complex process. 4.9.7 Recurrence diversification To measure diversification, the percentage of isometries is evaluated in samples of increasing duration. The number of isometries decreases with the duration of the sample for biotic series but not for random or chaotic series (Fig. 4.75). This result reflects a diversification of pattern that is absent in stationary series. ;

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4.9.8 Embedding plots operationally define creativity Embedding plots uniquely identify creativity. Intuitively, a process is creative when a simple cause generates novelty and complexity. Embedding plots provide a quantitative portrait for creative processes as displaying low dimensional order (cause) and high dimensional novelty and nonrandom complexity (arrangement). This provides a clearly defined (i.e. measurable) definition for creative processes that corresponds to the intuitive meaning of the term and to empirical data. Recurrence measures at low and high embedding dimension characterize causal order and creative organization (Table 4.9). Isometry represents repetition. Organization is creative; it displays novelty. Order is stable and hence recurrent. Order is characterized by high isometry and high consecutive isometry. These features of order reoccur in periodic data at embeddings that are integer multiples of the period(s). They are

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observed at low embeddings in aperiodic data generated deterministically such as chaotic and biotic series. Causal determination implies continuity; therefore neighboring terms will be similar to one other. Thus, Webber and Zbilut,180 who quantify isometry at low embeddings, regard consecutive isometry as a measure of "determinism". Actually consecutive isometry demonstrates pattern and indicates different types of causation according to the embedding, periodic peaks of consecutive recurrence indicate a periodic generator, slowly increasing consecutive recurrence indicate the cumulative effects such as the integration of random events to generate a random walk, and consecutive recurrence at low embeddings indicates causality. Biotic series, whether in empirical data or generated by recursions, shows a high proportion of consecutive recurrences at both low and high dimensional embeddings, with a clear inflection point in embedding plots. This indicates that biotic series involve two nonrandom processes: causation (as in chaos) and integration (as in Brown noise). The inflection point hovers about 6 for heartbeat interval series. Brown noise shows consecutive recurrence at high embeddings only; at low embeddings it displays the same proportion of consecutive recurrences as shuffled copies. This indicates that Brown noise is produced stochastically by random increments, but it becomes deterministic as result of the integration of these successive changes. The embedding plot shows no inflection point. Creative biotic organization displays both order and novelty; random creation displays novelty without order. Embedding plots differentiate biotic from stochastic series, a distinction that cannot otherwise be readily achieved.

Fig. 4.76 Recurrence diversification: Recurrence analysis of a time series of heartbeat intervals recorded from a healthy man.

180

Webber, Jr., C. L. and Zbilut, J.P. (1996). Assessing Deterministic Structures in Physiological

Systems using Recurrence Plot Strategies. In Bioengineering Approaches to Pulmonary Physiology and Medicine, M. Khoo (Ed). New York: Plenum Press, pp. 137-148.

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Fig. 4.77 Embedding plots differentiate bios from chaos and noise. Table 4.9 Distinguishing canonical patterns using embedding plots Technique:

Isometry

Dimension:

Low I High

Consecutive . . . Arrangement T Isometry

Recurrence entropy

Low I High

Low I High

Causality

Property:

Low I High

Order

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Low embedding dimensions

High

High embedding dimensions

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+

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Lower than in shuffled copies

Chapter 5

The Biotic Pattern of Heart Rate Variation and Other Physiological Processes

Abstract: Heart rate variation, an indicator of cardiac health, appears to be erratic and has been described as chaotic or stochastic. However, a set of studies1 of time series of intervals between R waves (RRI) in electrocardiograms shows a pattern characterized by diversification, novelty, nonrandom complexity, and asymmetry that we regard as prototypical of bios. These patterns are similar to those generated by recursions of bipolar feedback, which in the body could result from sympathetic acceleration and parasympathetic inhibition. The pattern of heartbeat intervals shows 1/fpower spectrum but it is differentiated from 1/f noise by the demonstration of consecutive recurrence indicating causation. Episodic patterns (complexes) are associated with behavior; 1 Carlson-Sabelli, L., Sabelli, H.C., Zbilut, J., Patel, M., Messer, J., Walthall, K., Tom, C , Fink, P., Sugerman, A., Zdanovics, O. (1994). How the heart informs about the brain. A process analysis of the electrocardiogram. Cybernetics and Systems'94 2: 1031-1038, R. Trappl (Ed.). Singapore: World Scientific; Carlson-Sabelli, L., Sabelli, H. C , Zbilut, J., Messer, J., Diez-Martin, J., Walthall, K., Tom, C , Patel, M., Zdanovics, O., Fink, P., Sugerman, A. (1994). Cardiac Patterns of Emotions demonstrated by the Process Method: Psychotic Patterns. New Systems Thinking and Action for a New Century: Proceedings of the International Systems Society 38th Annual Meeting, B. Brady and L. Peeno (Eds.). Pacific Grove, CA, pp. 0419-0430; Sabelli, H., Carlson-Sabelli, L., Patel, M., Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological portraits: A clinical application of process theory. Chaos Theory in Psychology, edited by F. D. Abraham and A. R. Gilgen. Westport, CT: Greenwood Publishing Group, Inc., pp. 107-125; Sabelli, H., Carlson-Sabelli, L., Levy, A., Patel, M. (1995). Anger, fear, depression and crime: physiological and psychological studies using the process method. In Chaos Theory in Psychology and the Life Sciences, R. Robertson and A. Combs (Eds). Mahwah, New Jersey: Lawrence Erlbaum, pp. 65-88; CarlsonSabelli L., Sabelli H. C , Patel, M, Messer, J, Zbilut, J., Sugerman, A., Walthall K., Tom, C. and Zdanovics, O. (1995). Electropsychocardiography. Illustrating the application of process methods to comprehensive patient evaluation. Complexity and Chaos in Nursing 2: 16-24; Sabelli, H. (2000). Complement plots: analyzing opposites reveals Mandala-like patterns in human heart beats. InternationalJournal of General Systems 29: 799-830.

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heart rate variation represents the cardiac component of neurophysiological patterns. Temporal patterning and quantification of isometric recurrence detect changes in cardiac and psychiatric patients. 5.1 Research Strategies Beat to beat intervals provide a portrait of a fundamental timing in the organism. This timing can be precisely measured by the interval between R waves in the electrocardiogram (R wave is the wave with the largest amplitude). To determine the R-to-R interval (RRI), we sample the electrocardiogram once every 128th of a second. The rhythm of the heart is normally determined by a pacemaker (the sinoatrial node) located in the posterior wall of the right atrium. The cells of the node spontaneously oscillate, about 100 per minute. This intrinsic rhythm is continually slowed down by the parasympathetic nerve to 60-80 beats/min, and it is accelerated by the sympathetic nerve during emotions or exercise. The rhythmic contractions of the heart can be so regular that Galileo used his pulse to time the swings of a pendulum in the cathedral at Pisa. However, heart rate is not strictly periodic. Since ancient times, physicians have known that the patterns of the pulse portray the patterns of emotions. The reader may remember the Arabian Nights story of the wise physician who recognized a woman in love by the acceleration of her pulse when her beloved entered the room. As the heart supplies oxygen and foodstuff, and brain determines behavior, there is a close relation between the activities of these two organs. The brain accelerates or slows down heart rate adapting it to the global activity of the organism. Emotional states2 and diurnal rhythms affect cardiac function 2

Chesney, M. A., Sevelius G., Black, G. W., Ward, M. M., Swan, G. E., and Rosenman, R. H. (1981). Work environment, type A behavior, and coronary heart disease risk factors. Occupational Medicine 23: 551-555; Dalack, G. W. and Roose, S. P. (1990). Perspectives on the relationship between cardiovascular disease and affective disorder. Clinical Psychiatry 51: Suppl 4-9; Elliot, R. S., & Buell, J. C. (1985). Role of emotions and stress in the genesis of sudden death. Journal of the American College of Cardiology 6: 95B-98B; Ewing, D. J., Hume, L., Campbell, I. W., Neilson, J. M., Clarke, B. F. (1980). Autonomic mechanisms in the initial heart rate response to standing. Journal of Applied Physiology 49: 809-814; Reidbord, S. P. and Redington, D. J. (1992). Psychophysiological processes during insight-oriented therapy: further investigations into nonlinear psychodynamics. Nervous and Mental Diseases 180: 649-657; Malliani, A. (1991). Sympathovagal interaction during mental stress. Circulation, Supplement H, 83: 43^9; Redington, D. J. & Reidbord, S. P. (1992). Chaotic dynamics in

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and pathology. For this reason, the heart mirrors our emotions and behavior, and the ancients regarded the heart as the seat of the soul. As it is required for life, cardiac function has priority, but for this very reason it is controlled by the brain, the function of which has supremacy. Heart rate variation (HRV) contains information; it does not represent perturbations by external or internal noise. It is variation, not variability. Physical and emotional temperatures determine heart rate, arithmetical calculations reduce blood flow, emotions elicit specific patterns patterned sequences, not mere beat-to-beat changes. As behavior and emotions are organized processes, so are heartbeat sequences. Studying the rhythms of the heart thus requires consideration of both muscular contraction and subjective emotion, physical and emotional temperature, person and universe. The human heart marks the rhythm of the life each person co-creates with her/his world. Figure 5.1 shows that variation in RRI series resembles mathematical bios and does not resemble chaos. We recognized in RRI series the prototype of a new pattern that we subsequently called bios.

Fig. 5.1 Biotic and chaotic series. Left: Time graph of heartbeat intervals computed by measuring the interval between R in the electrocardiogram (RRI). Middle: Biotic series generated with the process equation. Right: Chaotic series generated with the same equation.

Figure 5.3 illustrates the 1/f "pink" noise-like patterns we find in wavelet plots, resembling those we observe in bios but not in process or autonomic nervous system activity of a patient during a psychotherapy session. Biological Psychiatry 31: 993-1007; Porges, S. W., McCabe, P. M. & Youngue, B. G., (1982). Respiratory-heart rate interactions: Psychophysiological implications for pathophysiology and behavior. In J. Cacioppo, R. Petty (Eds.), Perspectives in Cardiovascular Psychophysiology. New York: Guilford Press, pp. 223264; Yeragani, V. K., Pohl, R., Balon, R.,Ramesh, C , Glitz, D., Jung, I. & Sherwood, P. (1991). Heart rate variability in patients with major depression. Psychiatry Research 37: 35-46.

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logistic chaos. RRI series resemble 1/f noise also in low Hurst exponents (indicating anti-persistence). Wavelet plots vary markedly during the day, and often show a lower power exponent during sleep (Fig. 5.3). This variation is more readily expected from biotic processes than from a chaotic attractor. 15 -i

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Fig. 5.3 Wavelet plots of RRI of a healthy subject. Left: Awake. Right: Asleep.

Phase plane pictures show that cardiac and mathematical biotic series generate a patterned trajectory. Complement plots reveal a regular pattern of concentric rings in RRI series and integer biotic series, absent in chaotic or random series (Fig. 5.4). Partial autocorrelation, low

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Lempel-Ziv complexity,3 and patterned series of differences also indicate determined causation.

Fig. 5.4 Complement plots of heartbeat interval series. Left: The XY plot of the sine (Y axis) and the cosine (X axis) of the RRIs reveals an amazingly regular pattern (Mandala). N = 1000. Middle: Complement plot of RRI recorded from infant with severe congenital cardiac illness. Right: Complement plot of shuffled series of healthy person. N = 1000.

Simple visual comparison demonstrate obvious differences between recurrence plots of RRIs (showing "complexes") and plots of computergenerated random, periodic, or chaotic data. One can also visually distinguish the smaller patterns characteristic of electrocardiograms of healthy subjects from the larger patterns observed in CAD and in psychotic subjects (Fig. 5.5). Numerical measurements of RRI series confirm statistically the visual portraits. In both psychotic and CAD patients, the percentage of recurrences is greater than in controls (Table 5.1), indicating repetitiveness. Psychotic patients also have a significant greater percentage of consecutive recurrences. These results indicate a greater degree of order in these patients than in healthy subjects, at variance with the view of illness as disorder (see later). Regardless of these differences between healthy subjects and patients, cardiac data from all groups had a much smaller percentage of recurrences than random, normally-distributed, periodic or chaotic data with similar S.D. This is surprising since one would have expected that the variability of biological processes would be less than that of random series. This conclusion is confirmed by the equally unexpected finding 3

Sprott, J. C. and Rowlands, G. (1995). Chaos Data Analyzer. New York: American Institute of Physics.

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that shuffling cardiac data to eliminate temporal order of RRIs (while not changing mean and S.D.) increased the percentage of recurrences. This is novelty.

Hg 5 5 Recurrence plols of RRIs of healthy subjects (lop), subjects with CAD (middle), and psychotic patients (bottom) 10 embeddings, radius 0.1. 2000 points.

Another way to compare different patterns is to examine how the number of recurrences varies with the number of RRIs included in each sequence (embedding). As shown in Fig. 5.6, the number of recurrences first decreases and then increases with increasing numbers of embeddings in cardiac data. In a few electrocardiographic recordings, small oscillations in the percentage of recurrences with increasing embeddings suggest the presence of some periodicity. Embedding plots (Fig. 5.6) best characterize heartbeat interval series as biotic: they show novelty, nonrandom complexity, and causation.

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Further evidence for biotic pattern includes partial autocorrelation (Section 4.2). RRI series show asymmetric statistical distributions, as observed with mathematical bios, but not with most random, periodic and chaotic series. Entropy measures demonstrate asymmetry in CAD patients. As a result, the entropy of RRIs is a reductionjn CAD patients (3.404 + 0.350 for 10 bins) in comparison to healthy controls (3.809 ± 0.219). The difference is small but robust, as it was observed during diverse activities. Entropy is transiently reduced further during episodes of angina. Periods of low entropy are also found during early morning hours, a time of greater vulnerability and increased death rate. The slope of the entropy-bin regression line for cardiac beats does not differ significantly from that of random numbers, nor is it significantly different in CAD patients. As estimated by entropy measures, RRI series have the same diversity in healthy persons and in CAD patients, almost as high as that of random data. In healthy subjects, the entropy of interval differences is lower than that of RRIs. Likewise the entropy of differences of differences, up to the fifth, are lower than the entropy of the RRI series. In this respect, RRI series are markedly different from both mathematical bios and 1/f noise. RRI series from CAD patients show marked deviations from this pattern. Heartbeat (RRI) series show a high correlation (Pearson's R = 0.8 to 0.99) between successive values, low correlation between RRI and ARRI (R = 0.15 to 0.25), and variable or no correlation between successive ARRIs (R = - 0.04 to 0.21). In all these respects, heartbeat intervals resemble 1/f noise and bios.

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5.2 Homeobios: Diversification Without Diffusion Cardiac bios is nonstationary but bounded, in contrast to the series generated by the process equations described in Chapter 3 that diffuse away from their basin of origin. RRI series thus show local diversification (with or without global diversification) and little, if any, local or global diffusion. There are several ways in which one can mathematically generate bounded biotic series ("homeobios", Fig. 5.6), such as by the addition of a negative feedback term to the recursion: (5.1) At+1= At + g *sin(At) - 0.01 *(Ar 31*7t). It is also possible to generate mathematically bounded bios with recursions in which the trajectory is attracted to a static value such as Bt+1 = B t + g * sin(Bt) - k * ( B t - BO, (5.2) where k typically is 0.001. One can also generate bounded bios with homeobiotic recursions in which change is a function of At and its opposite 1/At, such as (5.3) Ct+1 = C, + sin(g*Ct) + sin(g/Ct). This recursion illustrates a process that can maintain homeostasis other than negative feedback. The time series generated by Dt+1 = D t + sin(5*Dt) + sin(5/D,) - 0.005* (Dt - Dj) (5.4) diversifies only locally. Homeobios is also generated by (5.5) Et+1 = Et + g * sinEt+1 - k*(H-Et) where H is the homeostatic attractor and k is smaller than 1. The recursion: (5.6) Ft+i = Ft + g * sinFt+1 - (Ft/[Ft]) * Ft.(modulo g/2) where [Ft] is the absolute value of Ft, (Ft/[Ft]) is 1 or - 1 , and Ft.(modulo g/2) provides a biotic negative feedback and generates biotic series with 1/f power spectrum, roughly unimodal histogram, bimodal (but not U shaped) histogram of differences, low Hurst, pink-like wavelet plot, and novelty, but no complexes. All of the time series generated by these recursions show diversification without diffusion (Fig. 5.8). Thus, diffusion is not the essential characteristic of bios. Homeobios may thus provide a simple

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model for physiological processes that are both creative and maintained homeostatically.

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Recurrences (isometry and similarity) cluster in complexes, which display a relatively small number of distinct forms. This suggests the idea of an alphabet in which messages can be written. Complexes appear to be associated with activities, emotions or symptoms.4 A lattice pattern

4

Sabelli, H., Carlson-Sabelli, L., Patel, M., Zbilut, I , Messer, J., and Walthall, K. (1995). Psychocardiological portraits: A clinical application of process theory. Chaos Theory in Psychology, edited by F. D. Abraham and A. R. Gilgen. Westport, CT.

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of recurrences was observed in a number of patients who concomitantly reported brief feelings of fear or anxiety.

Fig. 5.9 Factor processing of heartbeat intervals (N=1000) in two healthy persons (left and center) and during angina (right).

5.3 Factor Processing Assuming that the evolution of a process is a function of non-linear interactions between opposing factors, we introduce factor processing as a method to identify them from the data contained in a time series.4 We generate time-delayed replicas (e.g. from 1 to 30 lags), calculate their correlation with the original time series, then identified the statistically significant factors that describe these 30 variables and rotated them to separate orthogonal opposites. Using a symbol to indicate the order in which each variable (lag) appeared in each factor, we plot the factor loadings for each one against the factor loadings of the other. The plot of the three most significant factors in tridimensional space produces a unidirectional trajectory for heartbeat interval series, such as inverted U shape (Fig. 5.9), representing change in the predominance of factor 1 to that of its opposite factor 2; often the trajectories folded partially or markedly, even cycling between opposites. Factor analysis of RRI series from normal subjects revealed 3 to 5 factors. Recordings from patients with coronary artery disease often show only 2 factors. During the few episodes of angina recorded in this group of patients, the plots became disorganized, as observed with plots of random data. The plots also become extremely disorganized during sleep in some depressed patients.

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5.4 Electropsychocardiography One of the practical applications of studying the rhythms of the heart is to reveal unconscious and/or unreported emotions. Behavior is organized in hard-wired processes including sleep, dreaming, emotions, and other action patterns.5 Emotions are processes, not states, consisting of ordered sequences of actions from trigger to consummation (unless interrupted by whatever reason). Action pathways include outward behavior, subjective feeling, and physiological changes, among which cardiac phenomena are prominent. Cardiovascular patterns differ according to states of happiness, sadness, anger and fear.6 Redington and Reidbord7 have observed suggestive relations between electrocardiographic recordings and verbal content during an hour of psychotherapy in two patients. Thus, the electrocardiogram may be used to read unconscious emotions.8 The patterns may be useful to distinguish various kinds of personality, emotional states and disorders, and as well as predicting cardiovascular events. EPCG constitutes both an experimental testing of this hypothesis and a clinical application of bios data analysis.9 We have begun studies in this direction (Fig. 5.10). 5 Young, J. Z. (1978). Programs of the Brain. London: Oxford University Press. Killeen, P. R. (1992). Mechanics of the animate. Journal ofExperimental Analysis of Behavior 57: 429-463. 6 Schwartz G. E., Weinberger, D. A., and Singer, J.A. (1981). Cardiovascular differentiation of happiness, sadness, anger and fear following imagery and exercise. Psychosomatic Medicine 43: 343364. 7 Redington, D. J. and Reidbord, S. P. (1992). Chaotic dynamics in autonomic nervous system activity of a patient during a psychotherapy session. Biological Psychiatry 'SI: 993-1007. 8 Sabelli, H., Carlson-Sabelli, L., Patel, M., Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological portraits: A clinical application of process theory. Chaos Theory in Psychology, edited by F. D. Abraham and A. R. Gilgen. Westport, CT; Carlson-Sabelli L., Sabelli HC, Patel, M, Messer, J, Zbilut, J., Sugerman, A., Walthall K., Tom, C. and Zdanovics, O. (1995). Electropsychocardiography. Illustrating the Application of Process Methods and Chaos Theory to the Comprehensive Evaluation of Coronary Patients. Complexity and Chaos in Nursing 2: 16-24; Sabelli, H., Carlson-Sabelli, L., Levy, A., Patel, M. (1995). Anger, fear, depression and crime: physiological and psychological studies using the process method. Chaos Theory in Psychology and the Life Sciences, R. Robertson and A. Combs (Eds). Mahwah, New Jersey: Lawrence Eribaum, pp. 65-88. 9 Illustrating a process approach, we obtain long recordings and study them as a function of time, with particular attention to the rise and fall of patterns, rather than focusing on instantaneous snapshots of presumably stationary processes. Illustrating the arithmetical hypothesis, we study cardiac recordings in 0, 1, 2, 3 and further dimensions. Recording electrical (physical) energy to study biological (heart function) and psychological (portrait of behavioral patterns) processes together, via a mathematical description, embodies a methodological monism, making practical use of the philosophical concept that reality is indivisible.

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Fig. 5.10 Recurrence plots of heartbeat intervals recorded during reports of anxiety by two different patients.

In some experiments, we obtained simultaneous twenty-four hour recordings of the electrocardiogram in marital couples, in order to study how their emotions change together. Notably, many couples in conflict avoided such recordings, as one or both partners feared that they would reveal who started their fights! Thus, the attempt to gather data served a psychotherapeutic purpose. In another exploration (to be discussed in future publications), I monitored heart rate during psychotherapy, recording the pulse with a plethysmograph and observing it with an oscilloscope placed on the back of the patient. Evident changes in heart rate now and again revealed unexpressed feelings and thus served to raise questions timely. 5.5 Biotic Health, Ordered Illness One of the practical reasons why nonlinear analyses of heartbeat intervals are of interest is because linear analyses fail to be diagnostic.10 For instance, only 30% of the several hundred thousands of persons a year who die due to cardiac fibrillation are ever diagnosed as high risk 10 Bunde, A., Kropp, J., and Shellnhubber, H.J. (2002). The Science of Disasters. Berlin: SpringerVerlag.

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patients. Figures 5.5, 5.11, 5.12 and Table 5.1 present experiments comparing healthy controls with cardiovascular and psychiatric patients. Patients with coronary artery disease, depression or psychosis have lower arrangement, lower Median Embedding Dimension (MED), indicating lesser complexity and increased order. Illustrating the supremacy of the complex, cardiac patterns (Fig. 15.13) are altered in psychotic patients.

Fig. 5.11 Comparison of RRI series (N=3500) from healthy persons (N=32), depressed persons (N=52) and psychotic persons (N=46). Isometry measures at Median Embedding Dimension (MED). Table 5.1 Heartbeat interval series from healthy, coronary and psychotic patients. Samples of 3500 data points per patient, recorded during wakefulness. RRIs measured in units of l/128th seconds. Probability of differences between each patient group and healthy controls, using one way analysis of variance: * p < 0.05; ** p < 0.01. Recurrence measures obtained with 5 embeddings, cutoff radius 0.1. Healthy CAD Psychotic Bios Process Chaos Normal controls patients patients (J=4.7) (J=4.5) random # of samples 30 30 20 1 1 ~ 1 Average 97.3 113.5** 88.0 83.5 99.0 100 SJX 12.3 12.5 9.1 * 6.9 O43 12 0.004 12 Coefficient of variation 12.6 11.6 10.5 0.08 % Isometric recurrence 0.62 0.81** 0.8** 1.23 32 1.1 ^ ^ ^ ^ ^ % Consecutive gQ n g recurrences ~ Arrangement ] 14.5 [ 14.6 | 18 | 41 | 2.1 \ 3.5

These results suggest that biological organization consists in the creation of a multiplicity of patterns, not in the homeostatic maintenance of any one pattern, whether regular or chaotic. Summarizing their findings and ideas, nonlinear dynamicists have pointed to scale invariance and universality as organizing principles of cardiac activity

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and other complex systems. From this perspective, health is disorder and illness is excessive order,11 at variance with standard medical nomenclature that identifies illness with disorder. I agree with the notion that illness often represents excessive order,12 but disorder is not as accurate description of health. Instead, cardiac patterns represent complex and novel organization.

Fig 5.12 Isometry measures of RRIs from healthy, depressed, psychotic and patient with CAD.

Fig 5.13 Left: Complement plot of RRI from a psychotic patient. Right: Isometry recurrence plot of normal electroencephalogram, N = 1950, embedding 50, radius 5. 11 "Let us start with a question. If you were going to describe a disease, say heart disease, which word would you reach for - order or disorder? Until very recently, nearly every physician would answer "disorder". Now, increasing numbers would not. Researchers are observing that an "ordered" sequence of heartbeat intervals very often indicates the presence of heart disease, and that a "disordered" sequence of heartbeat intervals is a pretty clear indication of a healthy heart. Stanleya, H.E., Amarala, L.A.N., P. Gopikrishnana, P., Ivanova, P.Ch., Keittb, T.H., and Pleroua, V. (2000). Scale invariance and universality: Organizing principles in complex systems. Physica A 281: 60-68. 12 Sabelli, H. (1989). Union of Opposites. Lawrenceville, VA: Brunswick; Sabelli, H., CarlsonSabelli, L., Patel, M and Sugerman, A. (1997). Dynamics and psychodynamics. Process Foundations of Psychology. J. Mind and Behavior 18: 305-334. Special issue edited by L. Vandervert. Understanding Tomorrow's Mind: Advances in Chaos Theory, Quantum Theory, and Consciousness in Psychology.

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5.6 Biotic Patterns in Other Psychological Processes Biotic patterns are also observed in other physiological variables (Figs. 5.14 to 5.17). Among them, the biotic patterns of respiration may be useful to study brain function because there is a remarkable alternation in predominance between opposite nostrils that parallels the activity of the opposite brain hemispheres.13 Electroencephalograms (EEG) show distinct complexes, novelty, arrangement and significant consecutive recurrence and recurrence entropy at high embeddings, with only small consecutive recurrence at low embeddings. It is difficult to distinguish biotic from stochastic pattern from these findings; note that each electrode in an EEG recording picks up the activity of roughly a million neurons, and that the EEG has been useful to study primarily neurological rather than psychological phenomena. Seizure patients do not show initial peak in the isometry plot (Fig. 5.17). Partial autocorrelation

0

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Combs, A., & Winkler, M. (1995). The nostril cycle: A study in the methodology of chaos science. In R. Robertson and A. Combs (Eds.), Chaos theory in psychology and the life sciences. Mahwah, New Jersey: Lawrence Erlbaum. Brown, T. L., & Combs, A. (1995). Constraint, complexity, and chaos: A methodological follow-up on the nostril cycle. In R. Robertson & A. Combs (Eds.), Chaos Theory in Psychology and the Life Sciences. Hillsdale, NJ: Lawrence Erlbaum Associates; Block, R. A., Arnott, D. P., Quigley, B., Lynch, W. C. (1989). Unilateral nostril breathing influences lateralized cognitive performance. Brain Cogn. 9(2):181-90; Jella, S. A., Shannahoff-Khalsa, D. S. (1993). The effects of unilateral forced nostril breathing on cognitive performance, hit J Neurosci. 73(l-2):61-8.

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Fig. 5.15 Diversification and diffusion of the time series of EEG, EMG, and respiration.

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Fig. 5.16 Embedding plots of respiration, electromyogram and electroencephalogram recordings (awake).

In conclusion, physiological oscillations are not the inevitable byproduct of physical structure such as the vibrations of a bridge. They are functional, associated with particular ongoing processes, and phylogenetically preserved. While periodicities are notable, several physiological processes also show biotic features including erratic pattern, partial autocorrelation (Fig. 5.14), diversification (Fig. 5.15), novelty, consecutive recurrence (Figs. 5.16 and 5.17), and 1/f power spectrum. These observations indicate that the aperiodic changes contain information.

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Fig. 5.17 Embedding plots of EEG recordings from healthy subject with eyes open (A) or closed (B) and from an epileptic patient during seizure free intervals (C and D), during seizure activity (E). Records obtained from www.meb.unibonn.de/epileptologie/science/physik/eegdata.html.

Chapter 6

The Biotic Expansion of the Universe

Abstract: Time series analysis of the distribution of galaxies recorded in two recent surveys show a biotic pattern of expansion. This points to a mechanism for the expansion of the universe, namely the expansion of a chaotic process generated by the interaction of fundamental opposites. The spatial distribution of galaxies shows biotic features at relatively short distances. Cosmic background radiation series show novelty within the dodecahedral framework demonstrated by Luminet and co-workers. These results suggest that simple ordered forms, rather than random flux, created the complex universe. Cosmology offers a unique opportunity to study creative processes. The creation of the universe is "Creation" par excellence. Notably, we can observe creation. As a result of the combination of vast distance that separates our Milky Way from other galaxies with the finite velocity of light, the farther away we look, the further back into the past we see. We observe distant galaxies as they were millions of years ago. What appears as a spatial distribution also involves time. Literally, we observe history. The visible "structure" of the universe is the pattern of an ongoing process. The distribution of galaxies as a function of the age of the universe thus offers data for testing general worldviews: creative evolution, entropic decay, or randomness. This chapter describes re-analyses of data reported in recent surveys of the distribution of galaxies and the cosmic background radiation

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(CBR). These time series analyses 1 demonstrate the features of novelty that indicate creative evolution. There is also evidence for deterministic causation that points to a nonrandom creative process (bios) that could account for the nonrandom spatial distribution of galaxies and contribute to the expansion of the universe. 6.1 A Brief Overview of Current Concepts Long after evolution was recognized in biology, physical processes have been regarded as universal and permanent. Static views have dominated Western cosmology, both religious and scientific. Einstein's universe is static, uniform and finite. The notion of an evolutionary universe, first envisioned by philosophers, entered modern cosmology with the Soviet cosmologist Alexander Friedmann, and became accepted through the discoveries of the American astronomer Edwin Hubble.2

Alexander Friedmann

Edwin Hubble

While chemical and biological evolution involve diversification, novelty and increased complexity, cosmologists still regard cosmological

1 Sabelli, H. and Kovacevic, L. (2003). Biotic Expansion of the Universe. International Conference on Advances in Internet, Processing, Systems, and Interdisciplinary Research. Electronic Publication IPSI-2003. 2 The universe is globally expanding, possibly at an increasing rate. [Perlmutter, S. (2001). Supernovae, Dark Energy, and the Accelerating Universe. AIP Conference Proceedings 596(1): 253274.] Bands corresponding to various chemical elements are redshifted in the light spectrum from distant galaxies., indicating that these galaxies are receding from us. Assuming that our location in the universe is not special, it implies that all galaxies are receding from each other, i.e. the universe is expanding. Galaxies within the same cluster do not recede from each other, and they may even approach each other. Expansion is global; gravitation predominates locally. This opposition between the global and the local is central to process theory (Chapter 9).

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change as random fluctuations within a stationary random process. The notion of a uniform distribution of matter, implying a universal geometry, was explicitly stated by Einstein, who argued that any agglomeration of matter would disperse uniformly with time. Friedmann conserved the notion of a uniform distribution of matter in his model. Uniformity still prevails in contemporary models. It involves several different aspects: universality,3 regularity, isotropy,4 and lack of center.5 Mandelbrot6 expands the cosmological principle to assert that the laws of nature are always the same; this notion excludes creative evolution. Just as the universe is not temporally static in time, it is not spatially uniform. Empirically, the distribution of galaxies is highly heterogeneous and dynamic for at least 1000 Mpc, approximately 3000 million light years. There is a huge hierarchy of structure and motion. The galaxies -some 100 billion of them in the observable universe- journey through space in clusters bound by gravity, which in turn form superclusters of thousands of galaxies stretching many hundreds of millions of light years across space. These superclusters are arranged in filaments or sheet-like structures, between which there are gigantic voids of seemingly empty

3 Universality is stated by the "cosmological principle", proposed by Einstein (1917) and formalized by E. A. Milne (1930). He asserted that the laws of nature are the same everywhere at any given instant of time. Thus, the observable universe is a fair sample of the universe. Following Occam's razor, we must assume that the entire universe obeys the same laws of physics discovered in the observed universe. Note, however, that the hypothetical "Big Bang" is regarded as an exception, as the known laws of physics may not apply at these extreme conditions. 4 Isotropic means that the physical properties of space are not dependent on the direction in which they are measured. This appears to be generally true, though there is a significant asymmetry between the north and south galactic caps, in galaxy density and in the cosmic microwave background radiation. 5 The concept of a universe without center is called the "Copernican principle". Antiquity vacillated between man-centered and God-centered worldviews, the latter standing for the former in a disguised way. Thus the earth was placed at the center of the physical universe. As an expected reaction, natural philosophers advanced the notion that the universe has no center. This view was already proposed by Nicholas of Cusa and Bruno, and it was later on adopted by Einstein and Hubble. It is today regarded as central to both the standard and the fractal models for the distribution of galaxies in space. It is not, however, self-evident. Everywhere in the universe we see local centers: the atomic nucleus, the sun surrounded by planets, galaxies spiraling around an axis, black holes at their center. A finite universe by necessity has a geometrical center. Copernicus placed the sun at the center of his system, so the notion that there are no special places in the universe cannot be properly called the "Copernican principle". 6 Mandelbrot, B. B. (1975). The Fractal Geometry of Nature. New York: W. H. Freeman and Company.

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space.7 Stars, galaxies, clusters of galaxies, and superclusters demonstrate an irregular hierarchical structure, which in a way continue the sequence of quarks, nuclei, atoms and molecules at the small end of the scale. The universe appears to be a hierarchical system rather than a random distribution. The standard cosmological model interprets the cosmological principle to mean that the universe is homogeneous and isotropic. A random stationary origin is assumed based on Occam's razor.8 The observable hierarchical structure in the distribution of matter is explained as local fluctuations, which are assumed to be confined to scales less than a few hundred million light years. These and other observations indicating a far-from-uniform distribution of galaxies have led to a formulation of a weaker hypothesis, namely that the universe is uniform, homogeneous and isotropic only in a large scale and only in a statistical sense. Most models of the universe thus ignore its hierarchical structure.9 The Polish-American researcher Benoit Mandelbrot10 proposed an alternative model: a self-similar fractal geometry generated by stationary stochastic processes. A fractal model of the universe has been developed

7

Galaxy counts averaged within spherical regions of radius 30h-l Mpc fluctuate around the largescale mean by about 30%. If one includes progressively fainter galaxies in our count, one would expect the number to increase at a certain rate if their distribution is truly uniform; in fact, the number of galaxies increases more slowly than expected. The distribution of nearby galaxies is notoriously non-homogenous, and some structures extend to remarkable distances. For instance, our own galaxy, the Milky Way and the Andromeda galaxy are moving toward each other; in turn both of them and some fifteen other smaller galaxies (the Local Group of galaxies) are moving towards the enormous Virgo supercluster, which, along with a second supercluster, is speeding toward some mass known as the Great Attractor. A "Great Wall" of galaxies has been found 750 million light years long. Stochastic processes could not generate such massive structure. 8 Support for uniform distribution is provided by the correlation function method advanced by astrophysicist P. J. E. Peebles of Princeton University. This method gives correlation lengths of 5-10 Mpc, in contrast to the observation in galaxy maps of structures with over 50 Mpc. The discrepancy between correlation lengths and observable structures that are ten times larger suggests that the method may not be reliable. 9 "While there are allusions to clustering in most works," comments Mandelbrot, "serious theoretical developments hasten to sweep it under the rug, claiming that on scales beyond some large but unspecified threshold galaxies are uniformly distributed." The standard model simply dismisses the empirical evidence of pattern as fluctuations within a statistically homogenous and isotropic universe. However, a number of researchers have considered the possibility that clustering may continue on very large scales. 10 Mandelbrot, B. B. (1975). The Fractal Geometry of Nature. New York: W. H. Freeman and Company.

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by Pietronero and coworkers.11 Many investigators agree that galactic structures are fractal up to a distance scale,12 i.e. fractality may be limited to the local universe (less than 500 Mpc). Both the standard and the fractal models regard the galaxy space distribution as the result of stationary stochastic processes. The pattern of the process does not evolve with time. In this sense, these are static concepts. Yet, intergalactic distance is convoluted with time. The study of the macroscopic distribution of matter is not geometry but history. The expansion of space, the synthesis of elements in the core of stars, and the generation of complex aggregates of matter ranging from atoms to galaxy superclusters indicate that the universe is a process of creative evolution, that is to say, nonstationary and largely causal. Evolution speaks against stationarity, and the hierarchical organization of the groupings of matter from atoms to superclusters of galaxies speaks against random distribution.13 6.2 The Universe as a Creative Process: Empirical Study Friedmann's interpretation of relativity and Hubble's discovery of the expansion of the universe moved us beyond the static view of the universe that dominated human thought from Aristotle and Ptolemy to Newton and Einstein. We view the universe as an ongoing process of creative evolution that continues to generate heterogeneity in the distribution of matter. To test this view, Lazar Kovacevic and I 14 have examined the distribution of galaxies as a process, seeking to identify its

11 Pietronero, L. (1987). Physica A 144: 257. Pietronero, L., Montuori, M., and Sylos Labini, F. (1997). Proceedings of the Conference Critical Dialogues in Cosmology, N. Turok (Ed.). World Scientific. 12 Baryshev, Y. and Teerikorpi, P. (2002). Discovery of Cosmic Fractals. New Jersey: World Scientific. 13 Other evidence for nonrandom organization is the form and mass of galaxies. Galaxies have many features in common, such as a dense nucleus, a faint outer region or envelope, and a dark matter halo. Many galaxies show spiral-shaped arms, which emanate from or near the nucleus and gradually wind outward to the edge. Many galaxies are of the same order of magnitude as the Milky Way, and seldom if ever, they are four times bigger. 14 Sabelli, H. and Kovacevic, L. (2003). Biotic Expansion of the Universe. International Conference on Advances in Internet, Processing, Systems, and Interdisciplinary Research. Electronic Publication IPSI-2003.

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creative features. We regard the distribution of galaxies as a time series, and analyze it accordingly. The data analyzed are obtained by the remarkable observational efforts of researchers at the Las Campanas Observatory in Chile15 ("Las Campanas Redshift Survey," abbreviated LCRS) and the AngloAustralian Observatory16 ("The 2-degree Field Galaxy Redshift Survey," abbreviated 2dFGRS).17 6.2.1 Time-space distribution Time can be measured from the redshifts, but it is, however, not obvious how such a series should be constructed. We have thus generated several types of time series along the z-axis. These time series are compared with shuffled copies.18

15 Las Campanas Redshift Survey (http://manaslu.astro.utoronto.ca/~lin/lcrs.html) was conducted by Stephen Shectman (Carnegie Observatories), Paul Schechter (MIT), Gus Oemler (Yale/Carnegie), Bob Kirshner (Harvard), Douglas Tucker (Fermilab), Stephen Landy (Berkeley), Yasuhiro Hashimoto (Yale), and Huan Lin (Toronto). The observations were carried out at the Carnegie Institution's Las Campanas Observatory in Chile. Shectman, S. A., Landy, S. D., Oemler, A., Tucker, D. L., Lin, H., Kirshner, R., and Schechter, P. (1996). The Las Campanas Redshift Survey. Astrophysics Journal (online) 470: 172. Available: http://arxiv.org/abs/astro-ph/9604167. 16 The 2dF Galaxy Redshift Survey (http://www.mso.anu.edu.au/2dFGRS) was conducted by Matthew Colless (Australian National University), Steve Maddox (University of Nottingham), and John Peacock (University of Edinburgh). Colless, M. (1999). First Results from the 2dF Galaxy Redshift Survey. Phil. Trans. Roy. Soc. Lond. Available: http://arxiv.org/abs/astro-ph/9804079. 17 The LCRS covers over 700 square degrees in 6 strips, each 1.5 degrees x 80 degrees, three each in the North and South galactic caps. After filtering the data, we analyzed 25322 galaxies. The 2dFGRS covers more than 100,000 galaxies spread over 2,000 square degrees in both South and North galactic caps. The survey was not complete at the time of our study, so there were discontinuities in the data. Thus, in addition to studying the entire sample (over 95,000 galaxies), we also analyzed two continuous strips 17 generated by cropping the data. Analyses are carried out for the entire set of 2dFGRS as well as separately for the six strips from LCRS and the two strips from 2dFGRS. Analyses of the eight strips and of the pooled data generate similar results. The data for each galaxy consist of redshift (z), and two angles: Right Ascension (RA), and Declination (DEC). We used 1950 coordinates. The distance d is calculated by d = v IH where H is Hubble constant and v is radial velocity, which is redshift multiplied with the speed of light c. Both surveys measure redshifts for more than 1000 Mpc, measuring RA in a narrow range of declination. In our analyses, we disregarded declination. From the redshift, we calculate the distance d from us along the z-axis that represents space-time. The data are studied as numerical series along the z-axis representing time and space, and as a function of right ascension representing only space. 18 In approaching the data, we considered two difficulties: the greater the distance, the wider the area we can observe, and greater luminosity is required to detect the galaxy. To deal with these issues, we compared the entire data with the set of galaxies within 600 Mpc. Essentially the same results were obtained in these series.

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Let us focus first on the temporal series formed by computing the number of galaxies in one Mpc bins (Fig. 6.1). Note the similarity in the temporal distribution in both surveys. All analyses in this section refer to these series. These time series display all the features that characterize cardiac and mathematical bios: novelty, causation (consecutive isometry or "determinism", partial autocorrelation), and nonrandom complexity (arrangement), asymmetry, expansion, diversification, and contiguity.

Fig. 6.1 Number of galaxies per Mpc in 2dFGRS and LCRS (each includes all the galaxies from the survey). This figure shows the number of galaxies observed at different ages of the universe - e.g. the number of galaxies per Mpc at 1000 Mpc represents the number of galaxies when the universe was 10.7 billion years old (present age 13.7 billion years).

6.2.1.1 Recurrence analysis The temporal pattern of the number of galaxies per Mpc as a function of the age of the universe was studied by measuring recurrence isometry. Recurrence plots of temporal series (Fig. 6.2) show episodic patterns (complexes) as observed with other creative processes. Shuffling erases this organization in separate complexes. Similar results are obtained for continuous strips and for the non-continuous set of all galaxies in each survey. Shuffling also increases the number of isometric recurrences. This is an indication of novelty, a property of creative time series. Embedding plots of temporal series show the four characteristic features of creative biotic patterns: novelty, determination, high dimensional entropy, and arrangement. This is observed for entire surveys (Fig. 6.3) as well as for individual strips from each of them (Fig. 6.4). Among deterministic series, novelty is the defining feature of bios that differentiates it from chaos.

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Fig. 6.2 Recurrence plots for continuous strips from Las Campanas and 2dFGRS surveys. Isometric recurrence computed with 20 embeddings, delay 1, and cutoff radius 20. N=1000. Recurrence plots in the original series show complexes (left, middle, and top right). Shuffling (bottom right) destroys the pattern, eliminating the complexes.

Fig. 6.3 Embedding plots of temporal series of galaxies (thin lines with circles) and of shuffled copies. Cut-off radius 0.1. From left to right: Isometry, consecutive isometry, entropy of consecutive isometries, arrangement. Embedding plot of temporal series of galaxies in 2dFGRS, number of galaxies per 0.5 Mpc (top), and 1 Mpc (bottom). These two graphs show the same results, demonstrating that the size of epochs does not determine the observed pattern.

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Fig. 6.4 Embedding plots of the individual strips from the 2dFGRS and from the LCRS. Thin lines with circles represent the original series, and bold lines represent shuffled copy. Cut-off radius is 0.1.

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Consecutive isometry is an indication of determinism; a high proportion of consecutive isometries at low embeddings indicates causation. Temporal series show a higher proportion of consecutive isometries than their shuffled copies at low as well as at high embedding dimensions. This is also observed with mathematical bios, but not with random series. Chaos shows determinism only at low embeddings, and statistical noise only at high embeddings. Corresponding to their determinism, the entropy of consecutive isometries is also high in these series as observed in determined processes. Finally, the ratio of consecutive isometries to total isometry, which we call arrangement, and regard as a measure of nonrandom complexity, is higher in galactic series than in their shuffled copies. 6.2.1.2 Frequency analysis: Wavelet plots

Fig. 6.5 Wavelet plots of temporal series for galaxies. Left: 2dFGRS (top) and shuffled copy (bottom). Middle: LCRS (top) and shuffled copy (bottom). Pattern is evident in original series, while it is erased in shuffled copies. Right: Examples of individual strips.

Wavelet plots (Fig. 6.5) demonstrate temporal changes in power spectrum indicating nonstationary patterns equivalent to the complexes

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observed in recurrence plots. Such patterns are absent in shuffled copies and in random series. 6.2.1.3 Statistical analyses Statistical analyses demonstrate asymmetry and partial autocorrelation (i.e. transitivity), two essential characteristics of action that differentiate action from random change. Statistical analyses also demonstrate diffusion and diversification, which are characteristic of creative processes. Also, the statistical quantification of isometry appears to indicate causation rather than random change. Histograms of temporal series show multimodal and highly asymmetric distribution (Fig. 6.6). Asymmetry is an essential feature of fundamental natural processes (Pasteur's cosmic asymmetry). Asymmetry and multimodal distributions are characteristic of creative processes and of mathematical bios, and absent in random data and in most chaotic series.

Fig. 6.6 Histogram of temporal series for continuous strip from Las Campanas surveys and for sample of 95000 galaxies in 2dFGRS. Asymmetry and multimodality is evident.

The time series of temporal series shows diffusion, while shuffled copies do not. Diffusion is best demonstrated by measuring the increase in the mean-squared displacement (M.S.D.) as a function of the number of embeddings.

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Creativity implies diversification, which we measure as the increase in variance with time, i.e., either with the duration of the series (global diversification) or with embedding (local diversification). Temporal series shows local diversification while shuffled copies do not. The S.D. largely increases (global diversification) as a function of the number of terms in temporal series, while shuffled copies do not show changes. Creativity implies diversification beyond diffusion, and therefore an increase in the ratio of diversification over diffusion. In contrast, increasing the size of the sample can be expected to increase uniformity, and therefore decrease the ratio of diversification over diffusion. In temporal series, the ratio decreases for global measures and increases for

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local measures (Fig. 6.7). Local diversification beyond local diffusion indicates creative diversification. The deterministic generation of the pattern of galactic distribution is confirmed by partial autocorrelation (Fig. 6.8 left and Table 6.1). Table 6.1 Partial Autocorrelation The partial autocorrelation coefficient measures the association between At and At+k when the effects of other time lags (1,2,3..., up to k-1) are partialled out. Lag 2

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the histogram method demonstrates their coexistence in temporal distribution of galaxies (Fig. 6.8 right).

Fig. 6.8 Left: Partial autocorrelation for temporal series in 2dFGRS (95000 galaxies) and LCRS (25000 galaxies). Right: Computing order, novelty, and flux using the histogram method.

6.2.1.4 A bioticpattern Results similar to those reported above were found in both entire samples and the eight separate strips examined. The differences noted among the strips witness the heterogeneity of the distribution of matter in the universe. This heterogeneity is well known. The new information added by the current analyses is the characterization of observed pattern. The distribution of galaxies along the time-space z-axis shows diversification, novelty, and nonrandom complexity (arrangement), ruling out chaos. Consecutive isometry and partial autocorrelation demonstrate that the series is causally determined rather than stochastic. We thus conclude that temporal series display a biotic pattern. It is not possible to dismiss these biotic features as variability unless one can demonstrate that random fluctuations can produce the biotic pattern observed in time series analyses. Random distributions do not produce diversification, novelty, arrangement and asymmetry. Much less can we expect that such features will be observed in every direction.

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6.2.1.5 Further evidence for causation Nonrandom novelty is the core of the concept of creative processes. In the temporal distribution of galaxies being examined, novelty can be demonstrated not only in temporal series but also in the series of differences between consecutive terms in the series. Complexes in recurrence plots are found in the series of differences (Fig. 6.9), and not in their shuffled copies. This shows that the series is determined rather than stochastic. In all but one, novelty is evident at high embeddings (Fig. 6.11). Wavelet plots (Fig. 6.10) do not demonstrate pattern in the differences between consecutive terms of temporal series.

Fig. 6.9 Complexes in series of differences between consecutive terms of temporal series. Recurrence of isometries computed with 20 embeddings, delay 1, and cutoff radius 20. 2dFGRS 0-1 RA strip. Recurrence plot show complexes in series of differences (left). Shuffling destroys the pattern, eliminating the complexes (right).

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Fig. 6.11 Embedding plots of the series of differences of temporal series for individual strip from the LCRS and form the 2dFGRS. Thin lines with circles represent the original series, and bold lines represent shuffled copy. Cut-off radius is 0.1. Difference of Galaxies by Mpc, Las Campanas, 12 degrees Declination 20

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embeddings because it is generated by the addition of random changes, but it shows consecutive isometry at high embeddings, revealing the deterministic accumulation of random changes. In biotic series, one can demonstrate determinism in the series itself at low and high embeddings. One also finds consecutive isometry in the series of differences between consecutive terms of the series (Fig. 6.11). The time series of differences of temporal series shows global and local diffusion and diversification (Fig. 6.12). However, decrease in ratios show that there is no diversification beyond diffusion. 6.2.1.6 Expansion and creativity -the bios hypothesis The significance of finding a biotic pattern in the distribution of galaxies lies in the expansive nature of bios. Finding biotic features for at least 2.5 billion years indicates that biotic expansion must have been operative for a significantly large era of cosmic evolution. The process that generates bios may cause or contribute to the expansion of the universe. In temporal series, local diversification exceeds local diffusion (Fig. 6.12). This is typical of bios (Chapter 4). The process of expansion may play a fundamental role in the evolution of the universe, as it does in other creative processes; for instance, quantitative growth is necessary for qualitative maturation. The demonstration of diversification, novelty, and arrangement (nonrandom complexity) shows that the evolution of the universe represents a creative process, as contrasted to the hypothetical decay towards entropic disorder. Finding biotic features for at least 2.5 billion years indicates that biotic expansion must have been operative for a significantly large era of cosmic evolution. The process that generates bios must thus contribute to, or cause, the expansion of the universe. We do not propose that the expansion of the universe is biotic without some trepidation, particularly as our research group does not include cosmologists. Notwithstanding, we are simply describing the results obtained with simple and understandable analyses of the data collected by well-known scientists to whom we give the credit. The notion of a biotic expansion is not entirely new. Bios is an ongoing chaotic process

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and the notion of ongoing chaotic inflation has been advanced by the Russian cosmologist Andrei Linde, now at Stanford.19 6.3 The Spatial Distribution of Galaxies Another way to examine the temporal evolution of galaxies is to examine their spatial distribution at different ages of the universe. The same data discussed above is analyzed, but in this case we partition the data in 100 Mpc epochs and construct numerical series of the distribution of galaxies along the right ascension axis. Data is divided into 100 Mpc epochs, and redshift is sorted by the Right Ascension. Analysis is done on the redshift series for each epoch, and for each strip. Epochs are then compared. 6.3.1 Recurrence plots Recurrence plots show clusters of isometric vectors (complexes) separated by brief interruptions. These complexes are observed in the epochs from 0 to 600 Mpc, and become less evident at greater distance (Fig. 6.14) when compared with shuffled copies. Embedding plots of z in 100 Mpc epochs show two distinct patterns (Fig. 6.13). In the range between 100 and 600 Mpc, the plots show high dimensional novelty, determination, and nonrandom complexity. The recurrence plot shows complexes. In other epochs (up to 100 Mpc and beyond 600 Mpc), there is high dimensional novelty and nonrandom complexity, and no determination. This pattern can be produced by stochastic series. 6.3.2 Wavelet portraits andfrequency analysis Wavelet plots show nonrandom organization in the range between 100 and 700 Mpc (Fig. 6.15). The phase identified as biotic by recurrence analysis is within these limits (100 to 600 Mpc).

19 Linde, A. (1990). Quantum Cosmology and the Structure of Inflationary Universe. Particle Physics and Inflationary Cosmology. New York: Harwood.

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Fig. 6.13 Embedding plots of spatial series of galaxies in Las Campanas survey.

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Fig. 6.14 Recurrence plots of spatial series of galaxies from 2dFGRS 0-1 radians RA strip. Plots of 100 Mpc epochs are plotted in the increasing order from top left (0-100 Mpc) to bottom right (800-900 Mpc). Recurrence of isometries computed with 20 embeddings, delay 1, and cutoff radius 10.

Results show that between 100 and 600 Mpc, pattern is biotic. There is also significant partial autocorrelation for the distribution of galaxies in space from 100 to 800 Mpc. In contrast, up to 100 Mpc and beyond 600 Mpc, embedding and recurrence plots resemble 1/f noise. In summary, we find creative features in the distribution of galaxies not only with regard to distance, where space is convoluted with time, but also in right ascension, which is purely spatial dimension. This is to be expected, because structures by necessity acquire the form imparted by the processes that create them. The spatial distribution of galaxies as a

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function of time shows three stages: an apparently random pattern at very large time-space redshift; a pre-biotic pattern characterized by novelty without evidence for causation at large redshift, a biotic pattern characterized by consecutive recurrence (continuity) at smaller redshift, and again novelty at small redshift.

Fig. 6.15 Wavelet plots of spatial series of galaxies from 2dFGRS 0-1 radians RA strip. Plots of 100 Mpc epochs are plotted in the increasing order from top left (0-100 Mpc) to bottom right (800-900 Mpc).

The standard model postulates large-scale statistical randomness for the entire universe, and, in particular, that such randomness should be detectable at large redshifts. The fractal model postulates fractality in the

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local universe (less than 500 Mpc). Our recurrence analyses are largely consistent with both predictions. 6.4 Cosmic Background Radiation: Novelty and Archetype The universe is much older than the galactic surveys analyzed above. We can learn about the earlier stages in the evolution of the Universe by observing the radiation that originated in the early universe. From our provincial terrestrial perspective, we can imagine the faint microwave glow surrounding us like a distant wall of fire, and the tiny fluctuations in the temperature (and other properties) of the ancient light as the writing on the wall that reveals what the universe is made of. But reality is just the opposite: the CBR originates in a universe that is much smaller than the one we inhabit. The standard model postulates the generation of an extremely hot radiation that cools off as the universe expands.20 This cosmic microwave background radiation (CBR) currently is 2.726 ±0.010 °K above absolute zero (microwave portion of the electromagnetic spectrum).21 The CBR portrays photons bouncing off a hot gas cloud of free electrons and nuclei that filled the universe when it was about 400,000 years old, some 13.7 billion years ago.22 Today, the CBR photons bear a unique imprint of the state of the Universe at 'recombination' time.23 It provides an image of the infant universe when 20 For every matter particle in the Universe there are 10 billion photons. Most photons in the Universe are cosmic background radiation, invisible to the eye. As the Universe continued to expand over the last 15 billion years, the wavelength of the C B R photons also increased from the original gamma-ray energies (size comparable to atomic nuclei) to microwave wavelengths (size comparable to human body). 21 The C B R temperature increases with increasing redshift as predicted b y hot Big Bang cosmology. (Srianand, R Petitjean, P. and C. Ledoux. (2000). T h e cosmic microwave background radiation temperature at a redshift of 2.34. Nature 408, 931 - 935.) 22 Photons move through the universe as they propagate through the atmosphere: light moves freely through clear air but is scattered b y water droplets in a cloud. A t the high temperatures prevailing in the early universe, photons were continually scattered b y collisions with hydrogen nuclei. A s the Universe expanded, the plasma cooled; when the universe reached one hundred millionth its present size, electrons a n d protons combined to form hydrogen atoms. Photons interact very weakly with neutral hydrogen, the scattering stopped, and since then, the primordial photons have traveled freely through the Universe, redshifting to microwave frequencies as the Universe expanded. 23 Actually, the CBR polarization may also contain clues to later periods in the evolution of the Universe. When the first stars and quasars started shining almost a billion years after the

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it last was a glowing ball of plasma. Just as we can see clouds by looking through the air, but cannot see beyond the clouds, in the same manner maps of the temperature of the CBR portray the surface of last scattering. We can look through much of the universe back to when it was opaque because most of the CBR photons were scattered by their interaction with matter. The Cosmic Background Explorer (COBE) satellite found that the CBR is astonishingly uniform in every direction (isotropic); variations in matter-energy density are only 17 parts in 1,000,000. This isotropy of the CBR indicates a fundamental oneness of the universe. The CBR also provides evidence for a fundamental twoness (Fig. 6.16), a dipole anisotropy. This dipole results from a Doppler effect as the Earth moves with respect to the microwave background at about 600 km/s. Physicists assume that in addition to this dipole due to our motion, there is a true "cosmic dipole". Observations also demonstrate the existence of a quadrupole, and octapole, all the way to extremely small fluctuations; there is a sequence 1, 2, 4, 8... many as in bifurcation processes.

Fig. 6.16 The dipole anisotropy in the Cosmic Background Radiation exemplifies the deep-seated asymmetry and twoness of the universe.

The Wilkinson Microwave Anisotropy Probe (WMAP), a NASA satellite, is currently (2004) observing the CBR. The pictures delivered by this satellite show that the universe is geometrically "flat", and about 13.7 billion years old. Power spectrum analysis is one of the primary

recombination epoch ("the end of the dark ages"), the ultraviolet radiation re-ionized all the hydrogen in the Universe, providing a fresh opportunity for a few per cent of the CBR to scatter and become polarized.

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tools used by researchers to analyze numerical data.24 The shape of the CBR angular power spectrum directly traces acoustic oscillations of the photon-baryon fluid in the early Universe. Acoustic oscillations passing through extrema at the time when photons and baryons decoupled are observed in the CBR angular power spectrum as a harmonic series of peaks. The location of the first peak provides evidence25 for a Euclidean geometry of the Universe. Such a nearly "flat" Universe 26 would be described as a small piece of an enormous hypersphere. The CBR is not only a remnant of the past; it is the flux within which the galaxies exist, and it portrays the form of space. What is the size27 and the large-scale topology28 of the Universe? Is the Universe spatially infinite, containing an infinite amount of matter (open universe), or is it spatially finite, containing a finite amount of matter (closed universe)? 6.4.1 The dodecahedral universe In an infinite flat space, waves from the Big Bang would fill the universe on all length scales. Data from the first year of operation of WMAP reveal that the large-scale fluctuations across the sky are much weaker than would be expected in an infinite universe. The power spectrum of anisotropies shows a distinctive set of peaks when the anisotropy is 24 The photons behave as a gas, and produce sound waves just as traveling compressions and rarefactions of air produce waves that we hear as sound as they strike our ear drum. Temperature fluctuations of the CBR may be expressed as a sum of spherical harmonics just as sounds may be expressed as a sum of ordinary harmonics. A musical note is the sum of a fundamental, a second harmonic, a third harmonic, and so on. The relative strengths of the harmonics determine the tone quality. 25 De Bernardis, P. et al. (2000). A flat universe from high-resolution maps of the cosmic microwave background radiation. Nature 404: 955 - 959. 26 In a flat space, parallel lines stay the same distance apart and never meet (as in Euclidean space), as contrasted to a 'negatively curved' space in which parallel lines diverge from one another and never meet (a three-dimensional analogue of a Lobachevsky space) and a 'positively curved' in which parallel lines converge and eventually intersect (the three-dimensional analogue of the surface of a sphere). 27 Positively curved space sections are necessarily closed, but both flat and negatively curved space sections can be finite if their connectivity is more complex than in Euclidean space; or example, in a flat toroidal space, as you exit right you enter left, and space is finite. A complex topology allows the possibility that distant points within the universe may be connected in some regular fashion. For example, the surface of the cylinder has the same curvature as a plane (you can wrap a sheet of paper around a cylinder without tearing it) but has a different topology. Just as an ant walking on a paper cylinder could return to its starting point without ever having to turn around, light may wrap around the real universe.

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compared between regions of sky separated by small angles. On large angular scales (typically for regions more than 60° apart), there is remarkably less power in the quadrupole than expected.29 The low quadrupole implies a cut-off on the wavelengths of the three-dimensional harmonics. A possible explanation is that space is finite: just as water waves cannot be larger than their container, and the vibrations of a bell cannot be larger than the bell itself, the density fluctuations in space cannot be larger than space itself. The WMAP observations are compatible with a finite universe that has no boundary, but wraps around like a sheet of paper rolled into a cylinder. Jean-Pierre Luminet and coworkers30 interpret the data to indicate a Poincare dodecahedral space (Fig. 6.17). One of the important implications of Luminet's concept is the development of complex organization from a relatively simple mathematical archetype.

Fig. 6.17 The dodecahedral universe (left) as proposed by Luminet and co-workers (Chapter 6). This figure was kindly provided by mathematician and MacArthur Fellow Jeff Weeks, from Canton, New York. The figure at the right shows how opposite faces are connected in Poincare's dodecahedron.

A Pythagorean philosopher, mathematician and astronomer, Timaeus of Locri (Magna Graecia, now southern Italy) proposed that the 29

The dipole cannot be observed because it is obscured by the dipole that results from a Doppler effect as the Earth moves with respect to the CBR. 30 Luminet, J. P. et al. (2003). Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background. Nature 425: 593 - 595.

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dodecahedron is the shape that envelops the whole Universe in the fifth century BC,31 perhaps because it is the most complex of the five regular solids that we now call the Platonic bodies. The notion of geometric archetypes was also prominent among Renaissance scientists. Luminet (Fig. 6.17), who is also a composer, a poet and a painter, predicted the dodecahedral shape of the universe years before measuring it.32 The Big Bang origin and the dodecahedral form of the CBR call to our minds Heraclitus fire and logos. Bringing them back is not an unnecessary display of erudition. Heraclitus process theory is the foundation for a process method of analysis that leads one to search for creativity rather than determinism or randomness. Heraclitus' concept of universal opposites is realized in the CBR as dipole anisotropy and as the continuity between opposite faces in Poincare's dodecahedron. Period 12 is prominent in the cascade of bifurcations generated by the process equation; 12 = 22*3 belongs to the Sarkovskii's series. The observation of numerical patterns 2 (dipole), 22 (quadrupole), 23 (octapole), 12 (dodecahedron) indicates a noteworthy structure in the CBR. 6.4.2 The cosmic background radiation and the evolution of the universe While the observable Universe displays a rich hierarchical pattern of galaxy clusters and superclusters, the isotropy of the CBR indicates that the early Universe had a spatially homogeneous and isotropic geometry. There are, however, small anisotropies in the CBR temperature that arise mainly from density fluctuations in the early universe: photons traveling from denser regions do more work against gravity and therefore become cooler, while photons from less dense regions do less work against gravity and arrive warmer. An image of the early Universe thus remains imprinted in the temperature anisotropy of the CBR.33 Within the "Hot

31

Giomini, C. (2003). Timaeus's insight on the shape of the universe. Nature 425: 899. Luminet, J. P. (2001). L 'Univers Chiffonne. Fayard. Anisotropies on angular scales larger than 2° are dominated by the gravitational redshift the photons undergo as they leave the density fluctuations present at decoupling (Sachs, R. K. and A.M. Wolfe. (1967). Perturbations of a cosmological model and angular variations of the microwave background. Astrophysics Journal 147: 73-90). Anisotropies on smaller angular scales are enhanced 32 33

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Big Bang" model, the formation of the large-scale structure we see today (galaxies, stars and planets) could be explained as the result of the growth of gravitational instabilities during an early period of rapidly accelerating expansion (inflation). "Gravitational instability" models propose that a Gaussian random field of initial fluctuations seeded the structure-formation process. These slight "ripples" were then magnified by the effect of gravity as the small, initially overly dense, areas attracted additional mass. It is further speculated that these ripples would evolve independently during the early stages of this expansion, but that as the structures grow in mass, they would interact with each other in nonlinear ways by phase correlations.34 In the beginning, the phases are random. This corresponds to a state of minimal information that is regarded as maximum entropy. As information flows into the phases, the information content increases and entropy decreases. (Models that assume random origin require evolution against the law of maximization of entropy.) In my view, gravitational attraction, being a fundamental force of nature, must work along with the maximization of entropy rather than against it. Entropy maximization consistently involves the aggregation of matter and the formation of systems, not only the dispersal of energy. Also, the dodecahedral structure found by Luminet and coworkers in the CBR data indicates causal processes rather than stochastic ones. In addition, the disproportion between the observed heterogeneity in the distribution of galaxies and the remarkable isotropy of the CBR suggests that causal and creative processes, possibly sensitive to initial conditions, may have operated throughout the history of the universe. Consider then the hypothesis that the early Universe embodies, since its origin, asymmetry and harmonic feedback that would create periodic, chaotic and biotic fluctuations. We may envision these initial fluctuations as interacting with each other in nonlinear ways from their very inception at the very early stages of the expansion of the Universe. These initial fluctuations in the radiation could nucleate additional mass thereby generating large and heterogeneous structures. by oscillations of the photon—baryon fluid before decoupling (Hu, W., Sugiyama, N. and Silk, J. (1997). The physics of cosmic microwave background anisotropies. Nature 386: 37-43). 34 Coles, P. and Chiang, L-Y. (2000). Characterizing the nonlinear growth of large-scale structure in the Universe. Nature 406: 376 - 378.

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6.4.3 Experimental study This is the concept that Lazar Kovacevic and I set out to test, with the understanding that we are considering it only from the perspective of numerical series analysis. In fact, our strategy is to analyze a complex multidimensional system by sampling linear numerical series. We have analyzed the WMAP sky temperature maps that were made available for public use by NASA in 2003.35 The data provided in each frequency map includes the thermodynamic temperature (in mK) for each pixel. WMAP observes five frequency bands between 22 and 90 GHz.36 We selected a number of iso-latitude rings from the maps converted into the RING numbering scheme, and we constructed numerical series of temperatures.37 Wavelet plots show significant structure, which is erased by shuffling (Fig. 6.18 top). Recurrence plots of series of CBR (Fig. 6.18 bottom) show episodic patterns (complexes) that are erased by shuffling. Shuffling also increases the number of isometric recurrences, indicating novelty. Novelty is readily demonstrable in embedding plots (Fig.

35

Galactic foreground signals are distinguishable from C B R anisotropy b y their differing spectra and spatial distributions. Multiple frequency coverage is needed to reliably separate them. W M A P sky maps are in the Galactic Coordinate System and use the "HEALPix" format of sphere pixelization developed b y Gorski, Wandelt, and Hivon. Some of the results in this paper have been derived using and Wandelt 1999) package, currently the HEALPix (Gorski, Hivon, http://www.eso.org/science/healpix/. HEALPix is an acronym for Hierarchical Equal Area isoLatitude Pixelisation of the sphere. HEALPix is a genuinely curvilinear partition of the sphere into exactly equal area quadrilaterals of varying shape. The base-resolution comprises twelve pixels in three rings around the poles and equator. W e used a suite of Interactive Data Language (IDL) software tools for working with H E A L P i x format maps. IDL is made b y the Research Systems, Inc. (RSI). W e are thankful for the use of this software. 36 These maps are labeled K, Ka, Q, V , and W-Band (22.8, 33.0, 40.7, 60.8, and 93.5 GHz). Each band h a s bandpasses. W e used several types of maps: (a) Temperature maps for each of ten differencing assemblies (each pixel in a m a p represents a sky temperature for the bandpass appropriate to the differencing assembly), (b) Temperature maps for each of five frequencies (these maps are derived from the individual differencing assembly maps), (c) Foreground Cleaned Maps: temperature maps from which template foregrounds have been removed (the Galactic (Milky Way) foreground signal is removed), (d) Internal Linear Combination (ILC) M a p (reduced-galaxy m a p produced via linear combination technique). Altogether, w e analyzed 22 different maps. W e also analyzed low and high resolution maps, and observed that they give somewhat different results. 37 The iso-latitude rings located between the upper and lower corners of the equatorial baseresolution pixels, the equatorial zone, are divided into the same number of pixels: Neq = 4xJVside. Most of our series are from this zone and have 2048 data points but away from the equator where the recordings contain foreground signal from our galaxy.

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6.21).38 The percentage of consecutive recurrence is the same in shuffled copies. This is consistent with random generation; it is also observed in DNA sequences that cannot possibly be random. Partial autocorrelation is not significant in any of the series examined, suggesting random generation. However, the dodecahedral structure of the CBR indicates causal processes rather than stochastic ones.

Fig. 6.18 Wavelet (top) and recurrence (bottom) plots of the series (left) and of the shuffled copies (right). Complexes are blurred, not separated by distinct interruptions.

38 Recurrence quantification showed some differences between samples according to frequency band and type of processing, and much less differences according to spatial distribution. The exception is the equatorial area, which is "contaminated" with the galactic foreground signal. This is in agreement with the fact that ILC map (with foreground signal completely removed) shows the same results for the whole map, while Foreground Cleaned Maps (as well as other temperature maps) do show differences between equatorial and non-equatorial areas, because the foreground removal is not applicable to regions near the Galactic plane.

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Fig. 6.19 Series of iso-latitude series show variable degrees of autocorrelation, which is more noticeable in series recorded with high resolution.

Fig. 6.20 Power spectrum exponents (slope in the logarithmic scale) of CBR series and series of differences.

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Fig. 6.21 Embedding plots for vl band at several iso-latitudes. In all cases, we observed novelty and arrangement. Embedding plot for differences between consecutive terms in thevli2hl band.

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Power spectrum analysis show negative (3 (ranging from -0.14 to 1.16) for the CBR series and positive [3 (ranging from 0.65 to 1.58) for the series of differences (Fig. 6.21). Histograms of these are symmetric. The CBR does not show global or local diversification. From the autocorrelation analysis, we conclude that there is a wide range of values of autocorrelation, which is usually small but larger than in shuffled copies (Fig. 6.19). Likewise, there are small but larger than shuffled partial autocorrelations (Fig. 6.22).

Fig. 6.22 Top: CBR series at several latitudes show small partial autocorrelation (except for those near the equator) yet larger than observed in shuffled copies. Numerical series are constructed using iso-latitude rings. Bottom: Numerical series constructed using one ring from the ILC map (ring is chosen from the middle of the top "hemisphere" of the map).

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6.4.4 A creative inflnitating universe These studies demonstrate novelty in both the CBR and the distribution of galaxies suggesting that nonrandom creative processes, possibly highly sensitive to initial conditions, generated, and continue to generate, the observed structure of the universe. The CBR is a quasi-symmetric flux differencing from uniform randomness in displaying anisotropy, tridimensional harmonics, dodecahedral shape, novelty, and 1/f power spectrum. The distribution of galaxies along the temporal axis displays biotic features of fractality, diversification, novelty, and nonrandom complexity. Bios is characterized by a great sensitivity to initial conditions that may explain the development of enormous heterogeneities in the current distribution of matter and energy starting from an extraordinarily homogeneous initial state as evident in the CBR. The notion of a creative universe implies that the topology of the Universe may change with time. Aristotle's picture of space was a series of concentric spheres that sustained the heavenly bodies, altogether a finite ball. Ptolemy formulated this view in scientific terms -erroneous, but scientific. Dante integrated this view of the universe with Christian theology in La Divina Commedia. In Dante's magnificently integrated vision, the ascending planetary spheres that envelop the earth in Ptolemaic astronomy culminate in the divine sphere inhabited by God. Below the earth surface, a symmetric sequence of circles forms hell. Since the 17th Century, with the invention of the telescope, the predominant model of the universe has been infinite space. In the nineteenth century, scientists became uncomfortable with the idea of an infinite universe. The only universe in which we can predict astronomical trajectories is a relatively small universe in which we could obtain all the data needed to make calculations and predictions. However, as the notion of a boundary to space was not appetizing, a solution was found in the form of a wraparound universe. Einstein proposed a spatially closed universe to solve the problem of boundary conditions at infinity. In my view, the universe is neither finite nor infinite. The universe is finite and inflnitating. This issue will be pursued in a later Chapter (Mathematical Genesis).

Chapter 7

Novelty in DNA

Abstract: DNA base sequences show novelty (indicating creativity), and low entropic diversity (indicating nonrandom organization). Genetic combination can create new traits and may play a major role in the emergence and evolution of species. The creative role of DNA in development and evolution suggests that also non-biological creation may result from the unfolding of simple, transmitted generic forms. The striking structural characteristics of DNA suggest what these generic forms may be. Nucleoproteins are the matter of life in our planet, from the simplest viruses to humans. In fact, given the stringent requirements for coding information biochemically (Chapter 13), they may be truly universal, i.e. also present in extraterrestrial life forms. In the planet, the genetic code is almost universal. The same codons are assigned to the same amino acids in the vast majority of genes in microorganisms, plants, and animals. RNA and DNA can transmit words across species, thus allowing for genetic transfers that may play a major role in evolution (Chapter 13). The chemistry of life is not arbitrary; organization at higher biological level depends on organization at the simpler chemical level. Thus, the chemical structure of DNA and RNA may indicate necessary requirements for creativity. Current models, however, assume stochastic organization and stationarity in the sequence of DNA bases. It has been further speculated that much DNA has no function ("junk DNA") and is therefore meaningless and "selfish".1 Actually, the vast majority of

1

Dawkins, R. (1989) The Selfish Gene. Oxford Paperbacks.

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genetic material in organisms from bacteria to mammals consists of noncoding DNA segments, which are interspersed within the coding regions. In humans, every cell contains approximately two meters of DNA, but about 97 percent of the genome is non-coding. In addition to the "coding" regions that determine the proteins a species can synthesize, genomes are built up of protein-coding and other classes of DNA sequences that are combinatorially formatted to carry out multiple other tasks (e.g. start and stop sites for transcription; processing signals for primary transcripts; control signals for level of expression and dynamic access at right time and place; identifiers for coding sequences that must be coordinately or sequentially expressed, and many others).2 The gene as a functional genetic unit actually encompasses not only the DNA that is transcribed into RNA but also the surrounding DNA sequences that regulate transcription.3 The functional unit may extend over hundreds of kilobases of DNA. Genetic functional units may, and often do, overlap. Genes are regulated by chromatin (formerly thought to be passive packaging material) that in turn, responds to signals received from the cytoplasm.4 Meaningful information is thus carried and transmitted not only as local patterns but also as large global patterns that could be detected by examining long series with large embeddings. 7.1 Analysis of DNA Sequences The analytic methods developed here may be useful to study biomolecules such as proteins and nucleic acids that consist of long chains. In particular, the quantification of isometry, which allows one to detect novelty, may be useful to analyze "junk DNA". We are currently examining the potential usefulness of bios analysis by examining DNA base sequences from Plasmodium falciparum (strain 3D70), a protozoan that produces malaria, and the yeast Saccharomyces cerervisiae.

2

Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K. and Watson, J. D. (1994). Molecular Biology of the Cell, 3rd ed. New York: Garland; Gerhart, J. and Kirschner, M.. (1997). Cells, Embryos, and Evolution. London: Blackwell. 3 Dillon, N. (2003). Positions, please... Nature 425: 457. 4 Turner, B. M. (2001). Chromatin and gene regulation. Oxford: Blackwell Science.

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Series of cytosine, or guanine, content per epoch (as percentage of the number of bases) in which successive epochs overlapped, show asymmetric distributions, aperiodic patterns, power inversely proportional to frequency, local diversification without diffusion (Fig. 7.1 left), complex wavelet and recurrence plots, (but not complexes separated by interruptions) (Fig. 7.1 right), novelty, consecutive recurrence, and nonrandom complexity (Fig. 7.2). Series of cytosine, or guanine, content per epoch (as percentage of the number of bases) in which successive epochs did not overlap show novelty and nonrandom complexity, but no significant consecutive recurrence (Fig. 7.3). Also in human DNA, the pattern of cytosine plus guanine is aperiodic, and power is inversely proportional to frequency.5

Fig. 7.1 Percentage content of guanine in Yeast chromosome 1, first 5000 bases. In this and related experiments, the percentage of guanine content is calculated for epochs of 100 to 500 bases. In this experiment, epochs overlap (first point is average of 1-100 bases, second is average of 2-101, and so on). Left: Graph shows that there is local diversification without diffusion. Right: Recurrence plot of the same series. Cutoff radius 10, embedding dimension is 100.

5

Heilig, R et al. (2003). The DNA sequence and analysis of the human chromosome 14. Nature 421: 601-607.

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Fig. 7.2 Embedding plot of series of percentage content of guanine in Yeast chromosome 1. Series constructed with overlapping epochs shows a biotic pattern. Cutoff radius is 0.1.

Fig. 7.3 Embedding plot of series of percentage content of guanine in a series constructed with non-overlapping epochs. Cutoff radius is 0.1.

In other studies, we code the bases numerically (adenine 1, cytosine 2, guanine 3, and thymine 4) so the sum of complementary bases is always 5.6 These sequences of DNA bases show aperiodic patterns, except for telomeric periodic segments. The aperiodic series show power inversely proportional to frequency, complexes, novelty and arrangement, without consecutive recurrence (Figs. 7.4-7.7), diversification or partial autocorrelation. The distribution of sequences of repetition, rise and fall was examined in chromosome 1 of the Plasmodium and found to be is identical in the series and in shuffled copies, for both coding and non-coding segments. Recurrence plots and quantification did not show much morphological differences in either coding or non-coding segments, using either similarity of isometric recurrence. These analyses show novelty without consecutive recurrence in either case. Pizzi and Frontali showed that in some eukaryotic genomes, introns and intergenic tracts 6

The program, written by A. Sugerman, is included in the BDA.

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exhibit highly recurrent patterns with correlated properties distinguishing them from the low-recurrence regimen present in exons.7

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7 Frontali, C. and Pizzi, E.. (1999). Similarity in oligonucleotide usage in introns and intergenic regions contributes to long range correlation in the Caenorhabditis elegans genome. Gene: 87-95.

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Fig. 7.6 Embedding plot of the initial 2000 bases in the DNA of the chromosome 7 of the Plasmodium falciparum strain 3D7. There is a period 7 for almost 100 embeddings (top panel), and aperiodic changes at higher embeddings.

Fig. 7.7 Embedding plot of bases 4000 to 6000 in the DNA of the chromosome 7, as in Fig. 7.6. Note novelty (negative net isometry) and high arrangement.

Novelty without consecutive recurrence is compatible with a stochastic process, although it is difficult to imagine that DNA sequences could be generated randomly. Measuring entropy as a function of the number of bins (process entropy, Chapter 11) distinguishes DNA from random data. The entropy of guanine content is near 2 when computed with 2 bins (near uniform random distribution) and less than random when computed with larger numbers of bins, thus demonstrating near

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symmetry but reduced diversity. The entropy of DNA base sequences is almost 1 when measured with two bins, and differs more from random data when measured with 3 and 4 bins (Fig. 7.8), indicating less diversity. In contrast, random walks show the same diversity as random. The results obtained with these measures of process entropy are noteworthy because the entropy of DNA base sequences has been found to be near uniformity. ,

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7.2 Alphabetical Bios These results clearly rule out random, periodic and chaotic pattern. Novelty indicates a creative process. In the case of single base sequences, the presence of consecutive recurrence indicates a biotic pattern. However, analyses of sequences encoding all four bases do not show consecutive recurrence. Obviously, the method determines to some extent the conclusion. This is not exceptional: in science as in any other field of endeavor, facts have priority but methodology and interpretation have supremacy (see Priority of the Objective and Supremacy of the Subjective, Chapter 9). In mathematical experiments with discrete

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recursions we identified two creative mechanisms, the addition (integration, accumulation) of parts into a totality (as observed in bios and random walks) and bipolar feedback. The data does not seem to fit entirely with either biotic or stochastic pattern, but these are only pilot experiments. Language offers another mechanism. From a purely physical perspective, information is carried by repetitions and difference, but most informational systems involve a limited number of possible cases, a closed alphabet, such as the letters in a language, whose combination generates an open, boundless universe. Language demonstrates how alphabets can create enormous diversity and complexity. In a similar manner, a small number of chemical elements creates a potentially infinite diversity of molecules. The four DNA bases constitute the alphabet, which combined in triplets spells out the 22 amino acids that in turn form sequences that encode proteins. They also combine in more complex ways to transmit information as mentioned above. Novelty in DNA sequences emerges in such alphabetic context. Ongoing analyses of texts show a diversity of patterns. In any case, these preliminary experiments indicate that measures of creative features such as novelty are relevant to the study of DNA sequences. The observed heterogeneity is at variance with the stationarity explicitly or implicitly assumed by stochastic and information theoretic models. The demonstration of organized patterns is also at variance with the strange notion that DNA segments that do not encode instructions for making proteins are "junk" and "selfish". 7.3 Selfishness Is Not In Our Genes Sociobiologists propose that genes are the units of selection, and that organisms are simply carriers of genes. "/ am treating a mother as a machine programmed to do everything in its power to propagate copies of the genes which reside within it" states Dawkins in The Selfish Gene. However, genes cannot be selfish because they do not have a self; they cannot see into the future and cannot possibly care whether their replicas are present in future genomes. Further, the various biological definitions

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of gene are extremely more complex than the simple notion portrayed by sociobiologists - genes as defined functionally do not necessarily coincide with specific sequences. Sociobiologists claim that solidarity and generosity, which they call "altruism" and find paradoxical, is the result of the selfishness of our genes. We are generous with those who share our genes because in that manner we ensure the survival of those genes (the concept of inclusive fitness). Sociobiological theories involve imaginative calculations of generosity as due to genetic overlap.8 These "calculations" do not take into account that (1) we share much with our spouses, with whom we do not share genes (according to sociobiological calculations); (2) we share over 99% of our genes with chimpanzees;9 (3) we share a large proportion of our genes with remote species such as mushrooms and worms, and surprisingly we tend to like flowering plants and hate snakes, at variance with the proportion of genes we share with them; (4) the number of human genes is not known; and (5) the role of genes in determining behavior is not known. 10 Genetic and cultural differences interact.11 Each person receives from the parents not only genes but also education. Biological, social and psychological processes cannot be assumed to be independent without proof; most often, they must be largely synergistic, in which case empirical data will show stronger effects for a given cause, say biological, than is actually the case. A large 8

The altruistic behavior of animals contradicts the most fundamental tenet of Darwinian evolution. Thus, evolutionists have struggled for a long time attempting to explain animal altruism. Sociobiologists explain it by the notion of "inclusive fitness." This means that one should consider not only the consequences of the altruistic behavior of the individual, which may be negative, but also the benefits of other individuals who possess the same allele. This is "inclusive fitness", a concept originating with R. A. Fisher's (The Genetical Theory ofNatural Selection. Oxford: Clarendon, 1930.) and J. B. S. Haldane's The Causes ofEvolution (London: Longman, 1932). The calculus of inclusive fitness was developed by Hamilton, W. D. (1964). J. Theor. Biol. 7: 1-16. 9 King M. C. and Wilson, A. C. (1975). Evolution at two levels in humans and chimpanzees. Science 188: 107-116. 10 Changeux's paradox serves as a word of caution regarding genetic explanations: one can understand how the earthworm's 18,000 genes govern the development of its 959 cells, but how some 30,000 human genes determine 1011 cells with 1015 connections? [Changeux, J.-P. (1997). Neuronal man: The Biology of Mind. Trans. L. Garey. Princeton Univ. Press.] 11 The effect of a gene depends on interactions with the environment. For instance, a genetic variation that affects the gene for monoamine oxidase A (an enzyme that destroys some of the neurotransmitters involved in aggressive behavior), facilitates antisocial behavior only in victims of childhood abuse [Caspi et al. (2002). Science 297: 851].

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number of articles on sociobiology are devoted to explaining "paradoxes", namely that human beings as well as animals defy the tenets of sociobiology by displaying altruism with genetically unrelated strangers. Altruistic behaviors are characterized by sociobiologists as "maladaptative"; they account for them by proposing that the human brain now applies "ancient tendencies to cooperate", prevalent in pre-industrial societies, "perhaps as result of religion".12 The so-called paradoxes consist of data that contradict the sociobiological hypotheses. When facts contradict hypotheses, intellectual honesty demands to call them refutations, not paradoxes. 7.4 The Genetic Theory of Evolution Genetics was born as a theory of creative evolution. In the 18th century, the Swedish physician and biologist Carolus Linnaeus, known as the botanical pornographer for his interest in the sexual life of plants, proposed that new species are produced by sexual intercourse among different species, generating hybrids. His metaphor was transformed into science in the mid 19th century by the Augustine monk Gregor Mendel. Living in the liberal milieu of educated Catholicism, Mendel considered Lamarck and Darwin's theories of evolution. Their critics had pointed out that if the characteristics of the parents were blended, then a mutation would be blended out, just as a single drop of white paint would be in a gallon of black (Fig. 7.9). Mendel incorporated this refutation into evolutionary theory -illustrating the difference between creative thinking and merely critical thinking (Chapter 18). He hypothesized that traits must be carried by discrete particles and tested this idea experimentally. Through statistical analyses, he showed that heredity could be explained by the existence of pairs of opposite genes -alleles. Evolution is a cocreation of opposites. (Opposition is also built-in the helical structure of DNA discovered by Watson and Crick). An imaginative hypothesis, a carefully designed experiment, and enormous work were necessary, and could have been sufficient to develop a new science, except that 12

Johnson, D, Stopka, P. and Knights, S. (2003). The puzzle of human cooperation. Nature 421: 911-912.

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Mendel's experiments were ignored. In 1900, the Dutch botanist Hugo de Vries rediscovered Mendel's laws, and, to his credit, credited Mendel. Many scientists concluded that mutation was the main driving force in evolution. Darwin's theory fell out of favor, just as Lamarck's has now, until combined with genetics by J. B. S. Haldane, Sewall Wright, Theodosius Dobzhansky, and Ernst Mayr. Notably, genetics, born as a theory of evolution, was misinterpreted as supporting static views of human nature, applauded by some as supporting racism and sexism, and rejected by Soviet Marxists as "bourgeois Mendelism". Still today, there is much pseudoscience relating purported genetic differences to intelligence.13 Genetics actually refutes racism.14 Generation 1

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As a science, genetics is not only at the forefront of medical research, but also genetic processes, including horizontal genetic transfer (Chapter 13), are recognized as essential components of evolution. Such genetic transfers may actualize the generation of new species by genetic combination. Genetic combination may also arise in other ways. The traditional view that genetic change comes from accidental sources such as radiation, or from inevitable errors in the replication process, is belied by the existence of DNA proofreading and repair systems that are remarkably effective at removing these mutations. Starting with the work 13

Lewontin, R. C , Rose, S. and Kamin, L. J. (1984) Not in our genes. Pantheon Books, New York. Genetic analyses show that all of humanity varies less genetically than does a typical wild population of chimpanzees [Kaessmann, H., Wiebe, V. & Paabo, S. (1999). Science 286: 11591162; Kaessmann, H., Heissig, F., von Haeseler, A. & Paabo, S. (1999). Nature Genet. 22: 78], refuting the very essence of racism. 14

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of Barbara McClintock15 in the 1940s, it is now established that the vast majority of genetic change results from the action of cellular biochemical systems that act on DNA. Mobile genetic elements constitute a large fraction of the DNA in some species of plants and animals, and about 43% of the human genome16. These mobile genetic elements operate at the DNA level in both prokaryotes and eukaryotes, and can generate large-scale non-random rearrangements of the genome. Genetic change is primarily biological. Feedback processes in which living organisms actively reorganize their genomes, rather than stochastic processes, appear to drive evolution at the molecular level. New species may thus arise from the combination of DNA words into new "sentences" and "dialogues". Genomes continually interact with cellular components, mainly proteins. Through such molecular interactions, cells continually carry out "computations". Thus, cells can reorganize the genome in response to needs. New functions can rise by the cut-and-splice rearrangement of genetic modules. James Shapiro of the University of Chicago17 considers that genetic novelty may result from the rearrangement of these modular components. In this way, genomes can be altered locally, regionally or globally. Such rearrangements might originate new species. Recapitulating, Aristotle regarded development as guided by a final cause. Today we regard the genome as the "final cause" of development. It causes change, but it does not determine the outcome, because development is creative. A "final cause" is a generator, not an attractor (see Chapter 3). Linnaeus and Mendel expanded this view to account for evolution as the result of the recombination of generators. This view is further elaborated by the work of McClintock and of Margulis (Chapter 13). Genetic recombination may replace natural selection as the mainstay of evolutionary theory. 15

McClintock, B. (1987). The Discovery and Characterization ofTransposable Elements. New York: Garland. 16 International Human Genome Sequencing Consortium. Initial sequencing and analysis of the human genome. Nature 860-921, 2001. 17 Shapiro, J. A. (1992). Natural genetic engineering in evolution. Genetica 86: 99-111; Shapiro, J. A. (1999). Genome system architecture and natural genetic engineering in evolution. Annal. NYAcad. Sci. 870:23-35; Shapiro, J. A. (1999). Transposable elements as the key to a 21st Century view of evolution. Genetica 107: 171-179.

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In support of a major role for genetics in evolution, let us note that increasing complexity does not appear to be explained by selection because bacteria are as adapted as mammals. An intriguing solution is that progressive evolution is actually due to the relaxation of selection. It is thus argued that the complexity of eukaryotes emerged from random genetic drift.18 Empirical data are at variance with the implications of this hypothesis regarding genome size in relation to trophic level and body size, suggesting an adaptative interpretation of genome enlargement.19 The organization and reorganization of physical or genetic material may be expected to be constrained by their structure. DNA embodies generic forms in its structure. DNA is formed by discrete units, ordered in a linear sequence. It comprises two pairs of complementary opposites, a feature that accounts for its capability to conserve and transmit information. Triads of bases encode information (codons). Finding a tetrad is intriguing, as two orthogonal pairs of opposites are necessary and sufficient to generate biotic patterns (Chapter 8), and period 4 is prominent in the process equation (Chapter 3). As in other long polymers, such as proteins, the chain often adopts a helical form that materializes harmonic motion (2°°). Also, genomes are modular; they are hierarchically organized systems composed of assemblies of smaller and larger modular genetic elements (segments of protein coding sequences, regulatory sites, repetitive DNA elements, chromatin domains). Given the universal role of DNA and RNA in living organisms, this chemical organization is unlikely to be arbitrary. The chemical encoding of biological information highlights the creative role of alphabetical organization. Taking genetics as a model, one may speculate that combination and recombination of informationrich forms may be a major factor in all creative processes, just as biological development and evolution originate with the genome. I speculate that the chemical structures of RNA and DNA embody a "cosmic gene",20 meaning simple generic forms that repeat fractally at all 18

Lynch, M. and Conery, J. S. (2003). The origins of genome complexity. Science 302: 1401. Vinogradov, A. E. (2004). Testing genome complexity. Science 304: 389. 20 Sabelli, H. and Carlson-Sabelli, L.. (1996). A cosmic gene? A biological model of complex systems. In honor to James Miller. Proc. International Systems Society, 40th meeting, Louisville, Kentucky, July 14-19. Sustainable Peace in the World System, and the Next Evolution of Human Consciousness, M.L.W. Hall (Ed.), pp. 531-542. 19

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levels of organization. We have speculated that this "cosmic gene" includes numerical constants and Bourbaki's mother structures of mathematics (Chapter 9). One may thus expand the genetic theory of biological evolution to all creative processes. Because genetic combination and recombination are constrained by chemical structure, they are not stochastic processes such as the proverbial monkey who, typing at random, can hardly be expected to produce Hamlet. In the same manner, the combination of elementary particles to form atoms, the combination of atoms to form molecules, and all other creative combination of parts into systems cannot be stochastic processes. Creation may be the necessary result of necessary mathematical forms that we can see embodied in the genome and that also appear, in a different manner, in the standard model of eight pairs of opposite elementary particles, the distribution of electrons in pairs in atomic orbitals, and the periodic table of elements with its bifurcation at higher atomic numbers.21 In mutation-selection theories of evolution, the chemical structure of DNA is not a factor, mutations are regarded as random, most DNA is regarded as "junk", and evolution is order created by selection against the law of entropy. In a genetic theory, the chemical structure of DNA embodies and portrays generic forms that create both stable structures (order) and novel organization in both physical and biological processes, thereby increasing entropy (Chapter 11). The biosphere is teeming with genes; even in one of the world's most nutrient-impoverished environments, the Atlantic Ocean, millions of new genes have been discovered.22 Genes are not blueprints; there are too few genes to specify particular developmental outcomes in humans. Genes are active agents.23 This offers a model for the creative functioning of physical regularities and mathematical archetypes.

21

The series of actinides and lanthanides may be interpreted as a bifurcation (Sabelli, H., 1989. Union ofOpposites. Lawrenceville, VA: Brunswick). Venter, C , Remington, K., Heidelberg, J. et al. Environmental Genome Shotgun Sequencing of the Sargasso Sea. Science 304: 66-74, 2004. 23 Marcus, G. The Birth of the Mind. Basic Books, New York, 2004.

Chapter 8

Bios Hypothesis

Abstract: Mathematical experiments show that the generation of biotic series with features of novelty, diversity and complexity requires intense action, complete conservation, and harmonic (bipolar, bidimensional, quasi-symmetric and diverse) feedback, indicating the necessary conditions for creative (bios-like) thinking and action. Asymmetric opposites generate trended bios (parabios). A range of asymmetries generates a complex pattern (bias) of synchronous actions. It is proposed that biotic and parabiotic generators are generic processes operating at all levels of organization and that they play a major role in evolution. The empirical studies described in Chapters 4 to 7 identify biotic and stochastic patterns (Table 8.1), and also indicate that other natural processes often show novelty. Bios may account for some of the many patterns that show a preponderance of lower frequencies (negative P power spectrum exponent) and novelty. However, these two features often appear together in natural processes (cosmic background radiation, DNA sequences) in which we find no evidence for causation. Is this form of novelty another name for chance? In my view, its association with 1/f power spectrum and with complexes indicates the existence a generator and excludes randomness. This indicates the need to search for other forms of deterministic creativity. The generation of 1/f patterns by filtering does not address the issue. In the analysis of empirical series, we did not find random processes. Random and chaotic series, albeit often regarded as creative, are patternless, as it is evident in recurrence plots. They do not generate the features that characterize natural creative processes. The oft-quoted 318

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notion that any pattern whatsoever can emerge from random change is belied by actual observations. The sequence of n digits, which is the most random sequence ever found, never includes biotic features such as novelty, diversification, expansion, and complexes. What processes generate these creative features like diversity, novelty and complexity? 8.1 The Concept of Bios Bios is a new mathematical concept grounded on empirical studies. Bios is (1) defined by newly developed analytic methods to measure diversification, novelty, and complexity; (2) exemplified by complex biological processes such as series heartbeat intervals that do not diffuse; and (3) generated mathematically and, we propose, also in nature, by the interaction of opposites as in bipolar feedback. Bios serves as a model for creative and causal processes in which simple interactions generate a complex outcome. Simple origin means causation by low dimensional interactions, and implies that the process of creation is natural, rational, understandable, and in principle controllable. Stochastic processes, albeit often considered simple, are in fact complex insofar as each random event is a new phenomenon; random events are not controllable. Complex outcome implies increasing diversity, novelty, nonrandom complexity (higher dimensionality), greater informational content, and intricate form, including self-similar fractal structure. Complex outcome excludes predictability and reducibility to simple levels, but allows for control. We use the term bios to name a family of simple creative processes that generate irregular, multifractal patterns with 1/f spectrum such as observed in a wide variety of natural processes rather than complex forms such as anatomical or artistic. These patterns have been regarded up to now as chaos or noise, but are clearly distinguishable from them. The concept of bios must be compared with those of chaos and noise. Chaos is an unpredictable, erratic, irregular, fluctuation among (multivalued) opposites. Chaos has been described as "deterministic random", meaning that it appears random but is generated by a simple, welldetermined process. We speak of chaos when a deterministic system

320

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governed by simple equations behave unpredictably. The hallmark of chaos is sensitivity to initial conditions, absent in true random series.

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Noise (stochastic time series) are statistical time series such as those generated by the addition of random changes. However, the same patterns can be generated deterministically. The term noise is also misleading insofar as these series display significant patterns that appear in significant natural processes. Noise also shows an unpredictable, erratic, irregular, alternation of (multi-valued) opposites. Notably, noise can produce diversity, novelty and nonrandom complexity. Stochastic processes are generated externally. Creative processes generate themselves (autodynamism) through interaction with their environment. Bios is generated by bipolar feedback. Biotic patterns meet the definition of chaos, and displays additional features that differentiate bios from low dimensional chaos: (1) expanding phase space volume; (2) episodic patterns separated by interruptions (complexes) rather than stationarity; (3) properties associated with creativity, namely diversification, novelty and nonrandom complexity -this excludes periodicity. Bios resembles natural processes and human language in continually generating new patterns. In contrast, an attractor, including chaotic attractors, is changeless -the more it changes, the more it stays the same. The biotic pattern is expansive and bipolar -it travels in both positive and negative directions (enantiodromia). Expansion is observed in many physical processes, from the expansion of the universe to the expansion of human populations. Enantiodromia is also widespread - cosmological evolution and entropic decay, evolution and extinction of biological species, growth and ageing of individual organisms, economic development and reversed development, rise and fall of nations and empires, social progress and decline. Enantiodromia has clear implications regarding economic and social strategies. Bios is also characterized by: (1) asymmetric rather than symmetric statistical distribution, (2) high auto-correlation (Pearson's correlation), (3) anti-persistence (Hurst exponent < 0.5), (4) patterned wavelet and recurrence plots resembling those obtained with 1/f noise, and (5) ring patterns in complement plots. In contrast, to random series, bios is characterized by determined novelty and determined recurrences rather than abundant recurrence and low determination.

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Bios is a class of patterns. Different types of biotic patterns obtain in series of heartbeat intervals in healthy and sick individuals, in various physiological, meteorological and economic processes, and in series generated by different recursions of trigonometric functions. The definition of bios is evolving. It is being developed based on the analysis of empirical time series and numerical series generated by difference equations. We first looked upon bios as a pattern, but we have come to regard it as a process, namely harmonic (bipolar and diverse, hence bidimensional) feedback. A lack of a more precise definition at this stage in our research should not be surprising. Although the concept of chaos has proved extremely useful, there still is no definitive characterization of chaos. Its definition still remains somewhat ambiguous; there are at least sixteen different definitions of chaos.1 In the same manner, the concept of fractal has no rigorous definition and Mandelbrot thinks that such a definition is unnecessary and could be useless and even harmful.2 In the process equation, bios occurs after chaos, as the series expands beyond the initial basin of attraction. However, what defines a creative process such as bios is diversification, not non-stationarity. Mathematical bios such as that generated by the process equation has a non-stationary mean and a non-stationary SD. But there are a number of variants of this recursion that generate bios with a stationary mean and a non-stationary SD such as observed with cardiac data. In the process equation, there is another fundamental difference between the biotic and chaotic phases, namely the emergence of low frequencies. Biotic series have a broad but non-uniform fp power spectrum, in contrast to chaotic series that often have a white noise-like f° power spectrum. (This is the case for chaotic series generated by bipolar feedback and by the logistic recursion, but there are chaotic series with fp power spectra.) Biotic processes may account for many of the widespread 1/f patterns. 1 Kaplan, D. and Glass, L. Understanding Nonlinear Dynamics. Springer-Verlag, 1995. For instance, Smale's definition of chaos by the presence of a transversal homoclinic point is based on the proof that homoclinic points imply chaos, but the converse has not been formalized; further, Smale allows for "some borderline cases in which this may not be exactly right". In many cases, it is not possible to demonstrate chaos unequivocally in empirical data, differentiating it from random. 2 Mandelbrot, B. B. Multijractals and 1/f Noise. Springer. New York. 1998.

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Is bios new?3 I have asked myself the question, but after some reflection I came to the conclusion that it is trivial. As bipolar feedback is widespread in nature, biotic patterns have been encountered numerous times. Real phenomena by necessity are rediscovered many times. Bios, as chaos, has been found again and again, but it has been labeled noise. There is a great difference between bios and noise. First, bios is generated causally, while noise is a stochastic process. Second, bios implies meaningful change, whereas noise implies a meaningless one. Biotic patterns appear in many processes ranging from astronomy to economics. To continue using the term "noise" is inappropriate, and misguiding. What may be noise in radio communication is the pattern of creative processes. The cosmic microwave background radiation first appeared as "noise" (Section 4.2). Bios has also been labeled chaos and deterministic diffusion, but has not been recognized as a separate pattern. Many empirical and several mathematical time series labeled chaotic (including weather models developed by Lorenz) show biotic patterns. The integration of some chaotic series produces bios. Biotic patterns are also generated by a number of nonlinear equations described by Chirikov4 and others, and investigated as a model for deterministic diffusion without remarking on a new pattern distinct from chaos, or on the concept of biotic feedback. We interpret bios as a prototype for natural creation, and we identify the recursions that generate it as a simple example of widespread processes of causal creation. I wish then to echo Ueda's disclaiming of priority for finding a pattern observed by many. Our study concerns the concept of bios and bipolar feedback as a creative process. The cocreation of opposites is a fundamental philosophical concept. As a model 3

The same question has been asked regarding fractals and chaos. Before he discovered the fractal geometry of natural forms, mathematicians had found some "mathematical monsters," points out Mandelbrot. Poincare had found chaos in the 19th century and, even before, Newton realized that planetary orbits may require divine intervention to remain regular. With oriental elegance, Ueda explains that, even when at this time many researchers attribute to him the discovery of chaos, he remembers how chaotic series were repeatedly found in the research projects carried out in the laboratory where he worked, but its director, interested in regular, periodic, beautiful configurations, simply disregarded them. Ueda recognized that it was worthwhile to study these chaotic series. 4 Chirikov, B. V., Lieberman, M.A., Shepelyansky, D.L., and Vivaldi, F. (1985). A Theory of Modulational Diffusion. Physica 14D: 289-304; Geisel, T. and Nierwetberg, J. (1982). Onset of Diffusion and Universal Scaling in Chaotic Systems. Physical Review Letters 48: 7-10.

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for natural processes, bios must be compared with chaos, noise, terminal dynamics5, Levy flights6, and cellular automata models7. In their discussion of terminal dynamics, that they also call "non-Lipschitz" and "nondeterministic" dynamics, as they are unhappy with each of these terms, Zak and co-workers describe "good" instabilities that lead to evolution, progress and creativity. They regard noise as a possible deterministic system that we cannot explain. Like fractals and chaos, bios represents the recognition of a pattern, not the finding of an object. Naming serves to define concepts. The concept of bios represents a step towards a theory of creative processes and its application to human behavior. It points out that a seemly exceptional type of chaos actually constitutes the rule in a wide variety of natural processes, and allows one to explain a large number of phenomena considered by most to be stochastic processes generated by accidental change. What is new is the concept of biotic pattern as a sign of causal creation and the concept of biotic feedback (bipolar, bidimensional, and diverse) as an apparently widespread creative process operating at all levels of organization. Also new is the focus on creative processes as contrasted to determinism and probability, and the application of these concepts to thermodynamic, biological, social, and psychological matters. 8.2 Biotic Factors: Action To study what principles are necessary for creation, we experiment with various recursions, examining the effect of altering their components on the pattern of the time series generated. The three major factors are action, opposition and conservation (Fig. 8.1).

5

Zak, M , Zbilut, J.P., Meyers, R. E. (1997). From Instability to Intelligence. Berlin: SpringerVerlag. 6 West, B. J. and Deering, B. (1995). The Lure of Modern Science. Singapore: World Scientific. 7 Ilachinski, A. (2002). Cellular Automata. Singapore: World Scientific; Wolfram, S. (2002). A New Kind of Science. Winnipeg: Wolfram Media.

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Fig. 8.2 A recursion is computed as a difference equation (At = 1) and as a differential equation using Euler's approximation (At = h). When h is small (left), the discrete recursion generates a complex logistic-like trajectory while the differential equation generates simple exponential growth. When h is larger, the logistic trajectory is observed even if the time steps are very small (right).

The need for action is obvious. Equations generate numbers; only recursions generate pattern. Without action, without iteration, there is no pattern. The intensity of action is given by the magnitude of the parameter. Its intensity determines pattern. In both biotic and logistics development, complexity increases with the intensity of the parameter, from equilibrium to periodicity to chaos to bios, and then decreases as linear infinitation or blow-up. Thus, maximum complexity occurs at

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moderate values of the parameter, as expected;8 there is a nonlinear relation between quantity and quality (Chapter 9). Notably, the process equation At+i = At + k*t*sin(At) and the diversifying equation At+i = At + sin(At*k*t) generate very similar patterns. This similarity is noteworthy because obviously x*sin(y) is not the same as sin(x*y). The two parameters have a different function: g represents the feedback gain (intensity or energy), while J represents diversity (frequency or information). A simple comparison illustrates this point: if we compute the sine wave g*sin(At*J), the amplitude is determined by g and the frequency by J. Both energy (gain) and information (diversity) contribute to power, as expected from intuition. The quantic nature of action is often critical for the generation of bios and certain types of chaos. The logistic differential equation generates a simple curve while the difference equation generates a complex trajectory. Similarly, the process difference equation generates periodicity, chaos and bios, but the corresponding differential equation generates only convergence to a steady state regardless of the feedback gain. The Rossler attractor, which is generated by a set of differential equations, can also be generated by a set of difference equations. The comparison of differences and differential equations provides a mathematical stage upon which to scientifically examine the category of discrete versus continuous. As all other general ideas (categories), these concepts emerge as a pair of opposites. As in other cases, the opposites transform into each other. Differential equations can be approximated by discrete recursions. Consider the numerical solution of the equation dx/dt = t - x2 by Euler's method. If the step size h is small, a simple curve is obtained, but if h is somewhat large, the computed values fluctuate at each step, first periodically and then chaotically, generating a logisticlike bifurcation diagram. This has been regarded as a breakdown in Euler's method.9 What is seen as error in the computation of a differential equation may instead be interpreted as a signal generated by a difference equation. What is an error or a signal depends on our 8

Galaxies and atoms are less complex than living organisms. Taking life and mind as the highest known entity, maximum complexity occurs at moderate temperature, moderate frequency and duration, and moderate size. This is in line with the Apollonian notion of moderation. 9 Acheson, D. (1997). From Calculus to Chaos. Oxford University Press.

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perspective: mutation is an essential mechanism for genetic variation from a process perspective, but is an error from a static perspective. The shift from continuous to discrete mathematics is likewise a change in perspective. From the perspective of discrete processes, one may regard h as a feedback gain rather than as a time step; a logistic-like trajectory is also obtained when the time steps are small if h is sufficiently large (Fig. 8.2). Approximating differential equations with Euler's method shows us that there often is continuity between the discrete and the continuous extremes. This dialectic of the continuous and the discrete applies to the real world, e.g. quantum and classic mechanics. In almost every process, there are both discrete and continuous transformations at different levels of organization. As the level changes, there is transformation from continuous to discrete or vice versa. The pattern and rate of change of the parameter determines the development of pattern. Notably, the gain at which new patterns emerge is lower when the rate of change of the parameter g or J is lower. Alternating the sign of the gain increases the amplitude of the biotic phase, whereas random increments decrease it. 8.3 Biotic Factors: Opposition, Symmetry and Asymmetry Chaos is generated by nonlinear (two-dimensional) opposition; for instance, the logistic recursion is quadratic. Bios also requires twodimensional opposition, such as trigonometric feedback. The same sequence of patterns, from asymmetric steady state to bios, can also be generated by replacing the trigonometric function by a pair of numbers such that r2 = At2 + Bt2, At+i = A, + ABt, and Bt+1 = Bt - A At.10 In this process, the change of one quantity acts to change the other, its opposite. This creates circularity and movement. Sine and cosine are paradigmatic of out of phase, complementary opposites. This experiment indicates how the coexistence of complementary opposites implies an infinity of oppositions.

10 Sabelli, H. and Kauffinan, L. (1999). The process equation: formulating and testing the process theory of systems. Cybernetics and Systems 30: 261-294.

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Opposition is a kind of symmetry, but opposites may be asymmetric in magnitude. To investigate the relevance of symmetry to creativity, we introduce a biasing term q in the process equation: (8.1) At+1 = At + g * ( q + sin(At)), or

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The patterns generated by the equation are nested: simple steady states at the bottom (low energetic gain g) and the sides (total asymmetry, q = 1 or -1), periodic patterns immediately inside, then chaotic patterns, then parabiotic patterns, and, at the core, with high g and no asymmetry (q = 0), the biotic pattern. This general pattern is interrupted by a chain of infinitations that starts at g = n for the totally asymmetric cases, and reaches 2n for the total symmetric case (q = 0). This diagonal chain of infinitations repeats at higher multiples of n. Whereas extreme asymmetry precludes complexity, a small degree of asymmetry fosters the emergence of periodic, chaotic, biotic and

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catastrophic patterns at lower g. For instance, biotic patterns start at g = 4.604 when q = 0 and at progressively lower g as q increases up to 0.3. We regard the relation between At, g and q in the process equation as an experiment regarding the relation between action, energy and opposition (information). In these equations, the gain g represents the energy of the bipolar feedback and q provides asymmetry, which provides information. One might think that the equality of opposite outcomes represents lack of information and therefore asymmetry represents information. Actually maximal complexity (bios) occurs only when the opposites are symmetric; at maximal asymmetry (q = 1 or -1), the pattern is a simple steady state (Fig. 8.5).

Fig. 8.4 Introducing asymmetry decreases the threshold for bios.

Fig. 8.5 Time series generated by the process equation at gain 2.8 (left) and 3.2 (right). In the symmetric case (extreme left, q = 0), period two is generated. As asymmetry increases (from 0 at the left to 1 at the right) we observe an increase and then a decrease in the complexity of pattern.

A small asymmetry slightly reduces the gain required to generate bios (Fig. 8.4). In a similar manner, at low gains, small asymmetry increases, and large asymmetry decreases, the complexity of pattern (Fig.

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8.5). Alternating a positive and negative asymmetry (e.g. q is positive for odd iterations and negative for even iterations) generates complex patterns at lower gain than the symmetric recursion with q = 0. Figure 8.6 illustrates several different ways in which kinetic symmetry fosters the generation of complex biotic patterns. The same effect occurs when one alternates the sine and cosine functions (Fig. 8.6). Kinetic symmetry is more creative than static symmetry.

Fig. 8 6 Process equations At+1 = At + gt * (qt * cos(At)) calculated with Aj = 0, and alternating positive and negative values of the asymmetry term q (this page), the gain g (next page top row), the conserve term At (next page middle row), or the trigonometric function sine and cosine (next page bottom row). These recursions (black trajectories) are compared with the same recursions without alternation (white trajectories). In the first two rows only, the points are connected. Alternation reduces threshold for complex patterns in all cases.

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Fig. 8.6 (Continued.) Process equations calculated with (black) and without (white) alternation of the trigonometric function.

As biotic patterns obtain only when opposites are largely symmetric, the fact that cardiac beat series show a biotic pattern suggests that the opposite actions of accelerating and decelerating nerves and hormones that regulate cardiac intervals must then be largely symmetric -this is to

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be expected, as marked cardiac acceleration or deceleration can be lethal. On the other hand, some economic processes show a parabiotic pattern that combines biological-like creativity with asymmetric trends (Chapter 15). It is perhaps significant that trends, when extreme, lead to infinitation, a catastrophic acceleration that provides a mathematical metaphor for economic crises.

Fig. 8.7 Sensitivity to asymmetry. With slight variations of q, pattern changes drastically.

Fig. 8.8 The relation between opposition, energy and information in the patterns generated by the equation At+1 = A, + g * [q + sin (At+1)], in which the gain g represents the energy of the bipolar feedback and q (which ranges between 1 and -1) provides asymmetry.

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8.5 Biotic Factors: Conservation To examine the role of the conservation in feedback processes, we will compare recursions with and without a conserved term, which, for the sake of brevity, we shall call walks and reiterations. In recursions of trigonometric functions: only walks generate bios; reiterations generate only chaos. Conservation produces an equivalence of opposites. Sine and cosine walks generate similar time series. Sine and cosine reiterations are markedly different.

Fig. 8.9 Time series generated by reiteration of the sine and cosine functions. In this and following figures, X axis: g t = k*t. Y axis: At. These time series are computed with initial value 1. The left graph shows the sequence of bifurcation trees leading to chaos, interrupted by periodic convergences to one or two values. The time series is transversed by two sine bands, one corresponding to the sine of g,, the other to its opposite. Each bifurcation tree resembles that generated by the process equation, with unifurcations, expansions of chaos, and a prominent period 4. Right: The graph shows the initial bifurcation tree. Note the initial logistic-like tree followed by an abrupt expansion of chaos at g = %, that becomes bipolar and includes a prominent period 4. Note the occurrence of unifurcation in the second tree.

At+i = k * t * sin(At) generates sequences of bifurcations leading to chaos. Chaos is unipolar up to gt = n, at which point it expands and becomes bipolar. The time series converges to period two (1 and -1) when the gain equals 2.5 n, 4.5n, etc., and to one value (either 1 or - 1 , alternating) when the gain equals 1.5 n, 3.5rc, etc. (computing the recursion with a fixed g). These convergences are followed by new bifurcation trees and chaos. The time series display two major sinusoidal bands, one corresponding to the sine of gt, the other to its opposite; these bands cross at integer multiples of TT. The bifurcation tree resembles the process equation before the emergence of bios: it includes a prominent period 4, and an abrupt expansion of chaos. The eye connects the missing

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limb of the unifurcation with the newly emerging component of chaos. The shape of the initial linear phase, together with the initial expansion of chaos at g = 7i, suggests that the entire series starts with a unifurcation.

Fig. 8.10 Time series generated by At+1 = A,*cos(gt). Top left: The sequence of bifurcations organized by a band that corresponds to the cosine of gt. Top right: detail of the initial bifurcation tree showing the features of a logistic development but also an abrupt expansion shortly after the onset of chaos. Bottom left: Detail of the first chaotic expansion (k*t = 4.19). Note also period 3 at g = 4.34. Bottom right: Similar development is produced by At+1 = cos(At*gt).

The cosine reiterations At+i = k * t * cos(At) and At+i = cos(At*(k * t)) generate sequences of bifurcations culminating in chaos. The time series are organized by bands corresponding to the cosine of k*t. The trees are similar to that observed with the logistic equation, without unifurcations and with a prominent intrachaotic period 3 (Fig. 8.10). This chaos, however, is bipolar. Also, the pattern of bands is different from that observed in the logistic equation, and there are abrupt expansions of chaos beyond the cosine band. When k*t nears integer multiples of % (including 0), the time series converges to one value (1 for k*t equal an even multiple of n and -1 for odd multiples of JI), then bifurcates (one of the legs corresponding to the cosine band), generating 2N periods and

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chaos, to converge again at the next integer multiple of 71. As k*t becomes larger, the intervals between bifurcations in these trees become shorter, leading more rapidly into chaos.

Fig. 8.11 Effects of changes in the conserved term of the process recursion. Middle left is a plot of recursion where conserved term is exact (h=l). Even small changes in conserved term cause drastic changes in the pattern.

The chaotic series generated by reiterations of trigonometric function are the same regardless of the gain, and the basin of attraction is infinite. Thus the conserve term increases diversity for the initial fixed point and for the chaotic and biotic trajectories. Why the cosine reiteration

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generates logistic-like period 3 chaos while the sine reiteration generates period 4 chaos is not evident to me. Sine and cosine are also very different in recursions computed modulo m as the circle map. Thus, the process of integration of the bipolar feedback performed by the presence of a conserved term in biotic equations erases the effect of the asymmetry between sine and cosine opposites. Conservation implies continuity or contiguity in time and space. Chaotic trajectories are characterized by high divergence. The feedback must be bipolar, because only bipolar changes can conserve structure. Recursions of unipolar feedback such as the logistic equation are largely insensitive to the absence of the conserved term. As illustrated by the trifurcating equation, (Chapter 3), there are many possible forms of the conserved term that can generate bios. However, even small reductions in the conservation of the previous action, as generated by introducing a multiplier m ^1 in the conserved term At+; = At * m + k * t * sin At generates major changes in the time series (Fig. 8.11). The most prominent changes are the separation of the initial logistic part of the bifurcation cascade (m=0.99) and a reduction of bios to chaos (m = 0.99). Other changes include the replacement of leaps by an expanding oscillatory pattern followed by a long-lasting highly trended chaotic pattern (m=0.999), the abolition of unifurcation (m =0.9), and the appearance of prominent period 3 as in the logistic chaos (m=0.8). The conserved term is necessary because it integrates the sequence of chaotic changes into a biotic pattern. The integration of chaotic series (logistic chaos, process chaos, Ikeda's attractor, Henon's attractor, Lorenz's attractor, sine map, shift map, and sine reiterations at some, but not all, gains) produces aperiodic patterns resembling bios (novelty, diversification and nonrandom complexity) but without partition into episodic patterns (complexes). Bios is an integration and an expansion of chaos. Integration is also the creative process in the generation of stochastic noise from random data. Increasing the conservation by multiplying At by a factor h greater than 1 adds a trend to bios and inhibits its development at specific values. There is a marked nonlinearity in this effect: increasing the conserved term by 1.00001 prevents the development of bios and the subsequent

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leap, while such an effect is not observed at lower (1.000001) or higher (1.0005) values of h. Not only is conservation necessary; exact conservation is required. This indicates the importance of conservation in creation. It is also consistent with the role of conservation in actual processes. Energy-matter is conserved. Conservation and integration reflect the stability and nucleation of matter. Complex processes require simple foundations, historically and concurrently. Intelligence requires memory, and education. Creation often results from incorporating and refuting (in part) preexisting knowledge (Chapter 18). In physical as well as in intellectual processes, meaning is given by context, which includes two aspects, the interdisciplinary and the historical. In physical as well as in intellectual creation, conservation is essential. Therefore, a generator that is not sensitive to the presence or absence of a conserved term, such as the logistic, cannot model creative processes. Bipolar feedback generates low dimensional consecutive recurrence. Integration of chaotic changes, similar to the generation of Brownian noise by the addition of random events, produces high dimensional consecutive recurrence. Understanding how bios is generated has practical implications: it guides the development of analytic methods and it provides practical tools for humane human action. In summary, experiments with the biotic equation suggest that a simple generator of creative change consists of physical action, informational opposition, and feedback. In some sense, we may say that the process equation reflects three fundamental components of nature. In the past, prediction was considered as the hallmark of science. After the discovery of chaos, this criterion was no longer applicable. In our times, control appears to be the characteristic of scientific understanding. As supernatural interventions, random events are not controllable. In contrast, chaos, albeit unpredictable, is (partially) controllable.11 Bios is in principle even more readily controllable because of its greater sensitivity to change. This renders the study of chaos and bios eminently practical.

11 Ott, E., Grebogi, C. & Yorke, J. A. (1990). Controlling Chaos. Phys. Rev. Lett. 64: 1196-1199; Pecora, L. M. & Carroll, T. L. (1990). Synchronization in Chaotic Systems. Phys. Rev. Lett. 64: 821-824.

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The biotic equations illustrate two generic forms worth emphasizing, asymmetry and the relation between quantity and quality. All bifurcations are asymmetric. Pattern depends of the value of the gain. Changes in gain determine non-linear changes in the outcome of iterations, instantiating Hegel-Engels dialectic law according to which continuous changes in quantity produce discontinuous changes in quality. With regard to changes in the initial value of At, the dependence of quality on quantity is limited, as they affect the value but not the pattern of the time series generated at various values of g. The notion of creative feedback integrates but also radically changes dialectic, cybernetic, and dynamic concepts. Creative feedback as the engine of evolution contrasts with negative feedback as a stabilizing mechanism such as postulated for biological homeostasis and even for the planet (Chapter 14). 8.6 Biotic Systems: Co-Creating Recursions To build a theory of creation, one can mathematically generate "toy universes", systems or webs of interconnected equations that may be explored after the fashion of cellular automata. In nature, feedback must be, as a rule, mutual, because the components of a system necessarily interact repeatedly. As natural entities never are isolated, mutual feedback also occurs among systems. Circular, mutual, or dialectic causation, is thus much more common than one-sided causation. Mathematical instantiation of mutual feedback generate enormously rich patterns, many of which show organic form that in some recursions repeat in a fractal fashion. A pair of interlocked equations generates organic-like patterns that display fractal repetition in time selves.12 Figures 8.12 and 8.14 present examples of generation of organic forms in two and three dimensions. Mutual feedback may be expected to involve greater delay for the input received from the other process than for the changes induced by each process upon itself (Fig. 8.15).

12

Kauffman, L. and Sabelli, H. (2003). Mathematical Bios. Kybernetes 31: 1418-1428.

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Fig. 8.12 The generation of organic forms by the interaction of two process equations. X axis: At+1 = A, + 0.1*Bt*sin(Bt). Y axis: Bt+1 = Bt + 0.01*A,*cos(At). Initial values Ai = Bj = 1. The progressive development of complex pattern with iteration is presented in the sequence of XY graphs A, B, C, D, and E. Note how each larger pattern contains and repeats at a larger scale the previous ones (fractality).

Cascades of recursions generate progressively more complex processes (Fig. 8.17) suggesting how complexity may develop. Sequences are creative processes that can generate complex patterns from simple origins, as illustrated by the cascade of equations in Fig. 8.17. The output of one feedback system generates the gain for the

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following system. In contrast, a circuit involving a number of feedback processes in which the gain of the first is determined by the output of a later member in the system such as At+i = At + Et *sin(At), Bt+i = Bt +At *sin(Bt), CH-I = Q +Bt *sin(Ct), D,+1 = Dt +C, *sin(Dt), and Et+1 = Et +Dt *sin(Et), generates a stable chaotic attractor. Thus, in mathematical experiments, mutual feedback produces two types of attractor according to the number of processes involved, even or odd. Two process equations can create a chaotic attractor,13 i.e. a bounded trajectory that is chaotic at the microscopic level and looks periodic at the macroscopic level. One or three recursions generate boundless trajectory that we will call a "biotic attractor". (The average of trajectories originating with a wide range of initial values is near TT at low values of the gain but then departs to high positive or negative values.). The biotic attractor is infinite. This notion to me appears relevant regarding thermodynamics and evolution.

Fig. 8.13 Multiple tridimensional views of the Sabelli Attractor A t+ , = A t + B, *cos(A t ) and B t + 1 = B t + A t *sin(B t ). The third dimension is the sum sin(A) + cos(B).

13 Sabelli, H. (1999). Process theory: mathematical formulation, experimental method, and clinical and social application. Toward New Paradigm of System Science, P. Y. Rhee (ed). Seoul: Seoul National University Press, pp. 159- 201.

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Fig. 8.14 These are 3-dimensional co-creating equations with more and more iterations. At+1 = At + 0.1 *B, *sin(Bt); Bt+1 = B, +0.01*Ct *cos(Ct); Ct+1 = Ct +0.1*A, *sin(At). Note: axes are normalized.

Fig. 8.15 Mutual feedback with delay. Left panel shows the complex braid generated by one time series At, and the simpler increase in the other series Bt until it reaches the biotic phase. The right diagram shows A, in greater detail. Note that its initial pattern combines chaos with period 8.

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Fig. 8.16 Mutual feedback between process equations. Top panels computed with slow increase in gain, lower panels computed with faster gain increase. Black points represent values and white lines represent transitions from consecutive values. Note the overlap of period 2 with a periodic (top) or a biotic (bottom) pattern in the At series.

Fig. 8.17 Cascades of biotic recursions: At+i = A, + Et *sin(At), B,+1 = B, +At *sin(B,), Cm = Q +Bt *sin(Ct), and Dt+i = Dt +C, *sin(Dt).

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8.7 Bias Another way of examining the expanding patterns generated by bipolar feedback is to consider the outcome of multiple coexisting recursions and examining the increasing the biasing parameter q beyond the 1 and -1 extremes of the trigonometric function. Parabiotic patterns vary as a function of q in a complex and periodic manner. When q is high, the time series appears to be simple but the series of differences between consecutive terms reveals complex periodic repetitions of pattern as a function of both the intensity (energy) and asymmetry (information) of the feedback (Figs. 8.18).

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Fig. 8.18 Process equation with high asymmetry generates complex periodic patterns that can be detected in the time series of the differences. At q = 0, the patterns observed are period 2 (top left and top right), bios (bottom left) and infmitation (bottom right).

To examine the spatial structures created by parabiotic processes, we plot the distribution of values At generated by At+i = At + gx * (qy + sin (At)) after N iterations of a given initial value calculated with a range of gains g and of the biasing parameter q. The range of actions At increases with q, with g, and with the number of iterations. A complex pattern

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emerges after as few as 10 iterations (Fig. 8.19). In three dimensions, we see a central body with a number of legs. The central body has an overall triangular shape with a series of nucleations that increase in number (1, 2, 3, 4, ...) as a function of g (Fig. 8.20). The sign of q determines trend. A complex form occurs in the range between -1 and 1 q, and at higher and lower intervals. Varying the initial value does not affect the pattern. We are just beginning to explore this pattern, which we call bias, because it represents the nonrandom ever-expanding complexity generated by biotic and parabiotic processes. It consists of complementary opposite asymmetries, and it presents a cascade of nucleations. Bipolar feedback generates divergence, bifurcation and enantiodromia in space (bias). Bios occurs whenever opposites are symmetric, at the center of bias, or whenever two asymmetries compensate each other as illustrated by recursions in which either g or q show alternative values. Metaphorically, "centripetal" systems of forces produce bios and "centrifugal" systems produce bias. 8.9 Bios Hypothesis Summarizing, bios can be clearly defined as a pattern displaying causal and creative features generated by action, bipolar feedback, and integration. Bios is generic, being found in diverse processes ranging from the distribution of galaxies to physiological processes and, as we shall see, in meteorological and economic processes. The widespread occurrence of biotic patterns indicates that bipolar feedback is a generic process. It is thus cogent to relate it to fundamental physical processes. Physically, the intensity of the feedback corresponds to the energy of the system, and the coexistence of opposites corresponds to information. It is intuitively obvious that creativity is generated by the combination of energy and information. The biotic model also shows that pattern increases with gain g and the symmetry of opposites (low q). This corresponds to the bifurcating and asymmetric parameters of a catastrophe. The appearance of a diamond in plots of mathematical pattern in the g-q plane is particularly suggestive.

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Bios models reveal the importance of opposition in many different ways. To begin with, the development of bios requires both change and conservation. Bipolar opposition is required, but it must be quasisymmetric, and a small asymmetry is more effective than full symmetry. Even more effective is the alternation of opposites, and this may be regarding trigonometric function, gain g, or asymmetry q.

Fig. 8.19 The distribution of values A, generated by At+1 = At + gx * (qy + sin (At)) after 10 (left), 100 (middle), and 1000 (right) iterations of Ao = 1 value calculated with a 0 to 8 range of gains g and a range -2 to 2 of the biasing parameter q. The pattern is almost completely formed after as few as 10 iterations. Larger iteration increases the range of the distribution.

The complex distribution of synchronous actions generated by the coexistence of multiple parabiotic degrees of that we have dubbed bias is another case in which the distribution of actions displays a remarkable pattern as a function of bifurcating energy and bipolar information. The pattern generated by biotic evolution grows with the intensity of the feedback. This is congruent with evolution, and at variance with notions such as entropic disorder or an omega point of evolution. There is instead a pattern, bias, that grows in extension and complexity (up to periodicity) with the energy and asymmetry of the feedback, but only at its center there is bios, which corresponds to the greater complexity that is observed in natural processes. Creation, I speculate, results from the interaction of relatively intense and quasi-symmetric opposites that produces bipolar change and expansion beyond bounded attractors.

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Fig. 8.20 Tridimensional scatter plots of multiple computations of the process equation At+i = At + g * (q + sin(At) (x-axis) at multiple values of gain g (y-axis) and asymmetry parameter q (z-axis). Each point represents nth iteration (2000th for top plots, and 1000th for bottom plots). Initial value of A = 1; the values of the parameters g (y-axis) and q (z-axis) are kept constant in the recursion.

What does the study of bios contribute to a general theory of processes? Biotic feedback provides a mathematical and mechanical

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realization of the notion of creation via the interaction of opposites, thereby linking dialectics and cybernetics. However, bios analysis and biotic feedback indicate that creation (rather than cybernetic control or dialectic struggle) must be regarded as the core feature of natural processes. Mathematical and empirical bios also show that opposites can vary autonomously rather than complementarily. Asymmetry produces bias, and symmetry produces bios; neither generates equilibrium. Albeit simple information is provided by the inequality of opposites, it seems that the evolution of complexity requires the symmetry of opposites. Studies with walking equations indicate that kinetic symmetry is more efficient than static symmetry to produce complexity. The interaction of opposites produces either catastrophe (infinitation at q =1) or co-creation (q=0 or qt+i = qt * -1). The catastrophe itself is a tridimensional co-creation of planar opposites. Opposites thus create structures in higher dimensions than themselves, which can function as attractors; in this way, opposition may bootstrap evolution. For instance, as discussed in 4.3, positive and negative motivations determine choice, but in turn choice functions as an attractor that determines motivation. Notably, when symmetry is maximal (q = 0), not only complexity is maximal but also action is minimal (less positive and less negative). One is tempted to connect this observation with the Taoist concept of "noaction" (which actually means low intensity action14) and with the physical principle of least action. In brief, biotic dynamics, meaning conservation, bipolar, diverse, mutual and hierarchical feedback generating expansion, appears to be a basic generator. Creative phenomena involve growth such as the physical expansion of intergalactic space, ecological spreading out of species, the growth of young organisms, the extension of social systems (tribe, nation, federation or empire) and the expansion of chaos into bios. Biotic expansion is present even in homeostatic biological systems. This is the biotic hypothesis. Chapter 9 integrates it within the context of a general theory of creative processes, and examines the role of tetrads in bios. 14 Sabelli, H. The Union of Opposites: from Taoism to Process Theory. Systems Research 15: 429441, 1998. Reprinted: The union of opposites: North and South, East and West, Korea and America. (1999) in Toward New Paradigm of System Science. JP. Y. Rhee editor. Seoul: Seoul National University Press, pp. 251-27'4.

Chapter 9

Creation Theory

Abstract: Creation is a continuing evolutionary process from simple generic forms to complex organization (dimensiogenesis). Creation Theory advances an evolving set of hypotheses regarding generic regularities or principles operative in natural and mental processes: (0) Non-zero, non-random flux. (1) Asymmetric action. (2) Iterative opposition (information). (3) Triadic chaos and materialization. Matter represents the equilibrium of opposite actions in three dimensions. (4) Tetradic biotic creation (bipolar, mutual and hierarchical feedback). (5) Priority of the simple and supremacy of the complex. (6) Infinite complexity of the attractor of evolution. Creation Theory postulates advances an integrated set of hypotheses regarding natural and human processes according to which a small set of simple principles (Fig. 9.1) creates complexity through their recursion and combination (Fig. 9.2). Although very general, these hypotheses are scientific insofar as they are grounded in empirical data, mathematically formulated, testable by empirical and mathematical experiments, and practically applicable. We have gradually developed these hypotheses in a series of articles and books,1 using the term Process Theory to stress 1 Sabelli, H. (1989). Union ofOpposites. Lawrenceville, VA: Brunswick Publishing. Sabelli, H., and Carlson-Sabelli, L. (1989). Biological Priority and Psychological Supremacy, a New Integrative Paradigm Derived from Process Theory. American Journal of Psychiatry 146 1541-1551. Sabelli, H. C. (1991). Process Theory, a Biological Model of Open Systems. Proc. Internal. Soc. Systems Sciences. 2:219-225. Sabelli, H. (1991). Process Theory, a General Theory of Natural and Human Systems . Proc of the Internal Soc for the Systems Sciences. 3:168-174. Sabelli, H. (1999). Process theory: mathematical formulation, experimental method, and clinical and social application. Toward New Paradigm of System Science.?. Y. Rhee editor. Seoul: Seoul National University Press, pp 159201. Sabelli, H. (2001). The Co-Creation Hypothesis. In Understanding Complexity. Ed. by G.

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continuity with previous thinkers from Heraclitus to contemporary mathematical dynamics. Our formulation of Process Theory is extensively reviewed by Francois in the International Encyclopedia of Cybernetics and Systems.2 The discovery of novelty in empirical processes and the development of mathematical models for them (bios) has led us to the conclusion that creative processes constitute the core of natural and human reality. This is Creation Theory.

Fig. 9.1 Schematic representation of five primordial forms present at all levels of organization: (0) Flux: formless non zero-dimensional energy fluctuations. (1) Action: flow of energy in one directional time). (2) Opposition: bi-directional, two dimensional interaction of energy (causation) and (information, including synergistic and antagonistic components), tridimensional nucleation (matter) and radiation of energy, and tetrads of orthogonal opposites. A system is formed by a central material core, a web of energetic interactions, and a field of communication expanding in space and time.

Ragsdell and J. Wilby. Kluwer Academics/Plenum Publishers. London. Sabelli, H. (2003). Mathematical Development: A Theory Of Natural Creation. Kybernetes 32: 752-766. 1

Francois, C. (1997) Internal. Encyclopedia of Systems and Cybernetics. Milnchen: Saur. Articles on Action; Action graphs; Complex, supremacy of; Creation (Co-); Opposites, union of; Priority of the simple; Process theory; Process Method; Process thermodynamics; and Sublation. Because of its date of publication, the Encyclopedia does not include some of the central concepts of process theory, such as bios, novelty, and the process equation.

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Creation results from the interaction of universal mathematical forms, such as numbers and algebraic structures. Ever-present flux is the substance that embodies these mathematical generators, rendering them physical rather than merely mathematical. The universe is a creative process that originates with simple generators that are mathematical forms and physical dimensions: (0) energy flux, (1) unidirectional time, (2) bi-directional information, and (3) tridimensional mass. Their interaction continually generates higher dimensions. Time and information are orthogonal, creating bidimensionality. The equilibrium of pairs of opposites in three dimensions is a convergence that produces the stability of matter. The generators are generic. They occur in processes at multiple levels of organization. The dimensions of space are not fixed and determined. Space does not have 3, 4 or 11 dimensions, but an ever-increasing number of dimensions —infinitating but not infinite. Dimensions are a process of dimensiogenesis. Dimensiogenesis is a bootstrapping process of ever-increasing complexity (autogenesis).3 THREE MODELS OF CREATION: SUPERNATURAL, RANDOM AND MATHEMATICAL Supernatural acts of creation I

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3 Individual

processes are autodynamic; organisms are autopoietic; dimensionality is autogenic.

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9.0 Novel Non-Zero Energy Flux Non-Zero hypothesis: At all levels of organization, there are fluctuations of energy throughout time and space, characterized by novelty and often displaying a predominance of slow over high frequencies. The simplest organization is the apparent uniformity (lack of organization) of flux. All fields have fluctuations; at any given moment their actual value varies around a mean value, which in the vacuum at zero temperature corresponds to half the energy of a photon. Physical space is full of energy in constant fluctuation, spontaneously creating and destroying pairs of opposite particles. Virtual particles are real; they exert measurable force (Casimir effect).4 Space is not empty. There is no absolute vacuum. There is no absolute rest, no absolute zero. There is no absolute 0° temperature (Nernst theorem, also known as the third law of thermodynamics). Existence, action and organization do not oppose emptiness; rather, they oppose disordered change, noise, and heat. Flux may approach but never attain zero. This is the Non-Zero hypothesis.5 There is always something rather than nothing. This flux can be molded into physical processes by necessary mathematical relations (Chapter 10). Flux, I propose, is the substance that constitutes the universe when molded by mathematical generators. Flux is not a particular property of the simplest level of organization: there are small, continuous, irregular, directionless, symmetric fluctuations at all levels of organization. This reappearance of flux at all levels of organization represents a notable self-similarity. Flux is interspersed with local, discrete and asymmetric actions, and, at least at non-quantum levels of organization, it is composed of actions. Flux is a collective variation, not a property of individual entities. Flux and action are inseparable. Random flux could, in principle, generate any 4

The Casimir effect is a small attractive force that acts between two close parallel uncharged conducting plates as result of quantum vacuum fluctuations of the electromagnetic field. The Dutch physicist Hendrick Casimir realized in 1948 that between two plates, only those virtual photons whose wavelengths fit a whole number of times into the gap should be counted when calculating the vacuum energy. The energy density decreases as the plates are moved closer which implies there is a small force drawing them together. 5 Sabelli, H. (1999). Process theory: mathematical formulation, experimental method, and clinical and social application. Toward New Paradigm of System Science. Y. Y. Rhee editor. Seoul: Seoul National University Press, pp 159- 201.

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type of asymmetric, ordered action.6 On the other hand, multiple causal changes may create disordered flux: friction produces heat, deterministic equations generate chaotic number series, and individual human actions can produce unpredictable and often chaotic consequences. Macroscopically symmetric flux may be composed of microscopic asymmetric and discrete actions. Action and flux are same in substance and differ in intensity. In quantum processes, Planck's constant divides the flux of virtual particles from action. Is flux random? "Random" means galloping, not uniformity. Flux is not randomly uniform. Experimental results indicating novelty and 1/f spectrum in the cosmic background radiation suggests that natural flux is novel and thus presumably organized rather than random. The expansion of space introduces a strong deterministic component into global flux; as discussed in Chapter 4, expanding random series display novelty. Novelty occurs in many series presumed random but unlikely to be so, such as DNA base sequences. Perfect random patterns appear only in the series of n digits, which is determined.7 In many cases, novelty is associated with 1/f patterns are common in nature and even in psychological processes. The labeling of such patterns as noise is an assumption without empirical support. The reproduction of such pattern by filtering does not provide understanding regarding its genesis. Fluctuation excludes static values of energy, time, position or momentum. Absolute values are abstract approximations; concrete processes always fluctuate. At the quantum level, this is Heisenberg's uncertainty principle, Ax*Ap > h/2n, which relates changes in position and momentum. As entities continually interact with each other, there are always changes and thus there are ranges of position and momentum rather than a static point defined by single values of both. "Uncertainty" may not result from observation but from the existence of continual interactions that generate flux as an objective component of nature. The changes introduced by observation are just one case among these many 6

It remains to be proven that this actually happens. We have not found biotic patterns in it digits. Yet in principle, in a totally random system, every configuration has the same probability, so local asymmetry (meaning directed action) would be a frequent and unavoidable consequence. 7 The most random sequence is the series of digits of % [Pincus, S. M and Kalman, R. (1997). Not All (Possibly) "Random" Sequences are Created Equal. Mathematics 94: 3513-3518].

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interactions. In fact, the mathematical formulation of Heisenberg's principle contains no reference to the observer.8 This interpretation of Heisenberg's principle as flux provides a realistic formulation of quantum uncertainty. Heisenberg's thought experiment demonstrates that complex actions, such as observation, produce marked changes even in the simplest flux. Observation does not produce "uncertainty"; it illustrates the supremacy of the complex. This effect of more complex actions upon simpler flux may be expected to have significant consequences. The generation of flux by the coexistence of multiple actions might account for novelty and broad power spectrum. The uncertainty relation also connects energy and time. The widespread 1/f pattern represents an inverse relation between frequency (I/time) and power (which is a form of energy). How do these two regularities relate to each other? Uncertainty is often regarded as a refutation of determinism. Determinism is incorrect because human observations and other interventions affect processes at every level of organization, including the quantum level, but also the biological and the psychological. Determinism is incorrect in the sense that there is a fundamental uncertainty smaller than the smallest certainty; there is no fundamental order underlying uncertainty. Yet also probabilism is wrong, because there is certainty larger than the uncertainty. Every uncertainty is a blurring around a larger certain value. 9.1 Asymmetric Action The first principle of Creation Theory proposes that asymmetric action is the one and sole constituent of the universe. In mechanics, action A is the difference in kinetic energy KE and potential energy PE integrated over time: A = I (KE - PE) dt. The physical dimension of action is energy

8

Popper, K. (1956, reprinted 1982). Quantum Theory and the Schism in Physics. Totawa, NJ: Rowman and Littlefield; Bunge, M. (1981). Scientific Materialism. Dordrecht, Holland: D. Reidel Publishing Company.

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multiplied by time.9 Energy and time do not vary independently from each other. Time and energy are inseparable; they are quantum conjugates just as position and momentum (Heisenberg's principle). As most other fundamental concepts, the notion of action emerged from human actions, but it is defined most clearly and rigorously by physics. The difference between equilibrium and action as the simplest condition differentiates creation theory from other conceptions of dynamics. From a process perspective, the first principle of thermodynamics states that energy is continually transformed; this includes the quantitative conversion of one form of energy into another. (From a static perspective, the principle is formulated as the conservation of energy.) This change of energy is action. We can extend this definition of action to all levels of organization; e.g. cardiac action involves force, duration and frequency of contraction. If action units are roughly equal in energy, their rate provides a coarse measure of energy consumption. This is in fact roughly true for cardiac rate and energy consumption. Because action results from both energy and time, a very small force can produce a momentous effect when acting for a long time, as illustrated by the proverbial drop of water eroding the rock. Planck discovered that energy is emitted only in integer multiples of a constant h = 6.5 x 10"26 ergs sec. Einstein realized that this was indeed fundamental. Planck-Einstein's quantum h has the dimension of both energy and time, i.e. action, not energy alone. Since the quantum is the smallest unit of existence, nothing is simpler than action. The physical basis of information also is an action, namely communication10 of an energetic or material carrier. Matter also is a form of action. Matter and energy interconvert. Matter is the transient, local, and partial arrest of this energy flow. Also the vacuum state appears to be composed of actions that are short-lived and symmetrically distributed, so we perceive the collective set as empty. The world around us and within us is one in

9

The dimensions of action are ML2/T, in which M is mass, L is length, and T is time. Angular momentum likewise has the dimensions of action; this rotational character of action is significant; e.g. light follows the path of least action trough the curvatures of space-time. 10 Shannon did not develop a theory of information, but, as he clearly stated, a theory of communication.

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composition, and many in form, as in Heraclitus' aphorism "one is many, and many is one". Energy and time are common to matter and mind. Natural and mental processes are thus made of one and the same "substance", namely action. This commonality allows physical processes and ideas to interact in brain. Psychological processes are flows of physical energy in a complex brain. Thought is action at the physical level (electrochemical changes in neurons), but also socially and psychologically. There are discrete, directed (asymmetric), causative, and interactive changes, which is to say, actions, at all levels of organization. Action is an archetype homologically repeated at every level of organization. Action is cause. Action causes change; a process is a sequence of actions. In contrast, the Copenhagen interpretation of quantum physics assumes that the conjoint change of energy and time implicit in the quantum nature of action implies uncertainty. Linear and nonlinear dynamics do not describe two types of processes, but two types of components present in real processes. Periodic, chaotic or biotic patterns include within them a linear component. Linear methods thus describe many important features of actual processes. Action involves quantity, order, and numerical forms. Actions are thus numerical. Action embodies one as oneness of substance, unidirectionality in time, units. Yet action also has an intrinsic duality; energy and time being inseparable complementary opposites ("conjugates" in quantum mechanics). Here we encounter the coexistence of unity and duality, the union of opposites described by Heraclitus. From a practical perspective, time series measure one dimension, either intervals between discrete actions or intensity of energy at fixed time intervals. Processes are ordered sequences of actions. The essential properties of action correspond to the properties that define partial order and thereby lattices,11 one of the mother structures of mathematics (Chapter 11 Partial order is rigorously described by the mathematical relation < (as in "less than"), which is reflexive (for all A, A < A), asymmetric (or, more exactly, anti-symmetric, A < B and B < A if and only if A = B) and transitive (if A < B and B < C, the A < C). A partially ordered set is a set of elements organized by this ordering relation. Natural numbers form a totally ordered set (one number is either smaller or larger than another); actions are a partially ordered set, as there are multiple, probably infinite number of coexisting actions. A simple way of visualizing order is the

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10). This correspondence between physical action and mathematical partial order has four important implications: (1) It allows one to study action in time series by studying asymmetry and transitivity (see Chapter 4). (2) It points to what I regard as the physical basis of Pasteur's cosmic asymmetry. (3) It corresponds to fundamental order that Einstein proposed as underlying quantum probability. (4) It is congruent with the notion that physical reality emerges from the embodiment of necessary mathematical relations; action is the form that flux takes when molded by asymmetric order (Chapter 10). Note also the psychological / philosophical / ideological shift of interpreting lattices as models of action rather than as a model for order. Recognizing action as the one and only constituent of nature is consistent with the fundamental place of the principle of least action as a basis for Einstein's relativity. The principle of least action stems from optics,12 but there are many fundamental optimality principles in physics13 and in biology.14 In probability and statistics, there are "least squares" and maximum likelihood; minimax principles are basic to game theory and some models of mathematical economics. I propose that least action expresses the inseparability of action and information. Each and every action carries information. Each and every information requires an action. Thus, one unit of action (quantum) corresponds to one unit of arrow. In a partially ordered set, two or more arrows can diverge from one element (e.g. bifurcation), and two or more arrows can converge to one element (e.g. synthesis). 12 The one and only possible route of light from one point to another is a straight line in the time graph of action -however crooked the trajectory may appear to our eye. If a ray of light from some point A reaches a mirror at point P and is reflected to point B, the rays AP and PB make equal angles with the mirror. Another way of stating this well known fact is to say that the distance AP + PB is as small as possible. This is the minimum principle for optics discovered by Heron of Alexandria (circa 60 AD). Fermat generalized Heron's minimum principle for optics as a principle of least time in 1662. Fermat discovered that both the reflection and the refraction of light appear to obey a single principle of least time, rather than least distance. Feynman proposed that light actually travels by every possible path from the source to the eye, bouncing off mirrors at all kinds of angles, so the least action path results from the composition of all these different paths. 13 A principle of least action was developed by Pierre Louis Maupertuis (1461-1554) regarding the motion of mechanical systems: it asserts that, of all the possible paths consistent with the conservation of energy, a system will move along the path that minimizes action. For Maupertuis this "perfection" was "proof of the existence of Him who governs the world." Hamilton, in 1883, noted that action is either least or greatest -but no other . He commented, "The quantity pretended to be economized is in fact often lavishly expended", which he regarded as a refutation of Maupertuis' theological interpretation. Yet from another cultural perspective, one could regard lavishly expenditure as better suited to cosmic infinity than economizing. 14 Rosen, R. (1967). Optimality Principles in Biology. New York: Plenum Press.

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information (bit). Opposition is an action, not simply a property such as duality, or the pairing of two classes of complementary entities. Actions always allow for, and eventually lead to, opposite actions.

Topology: Henri Poincare and Rene Thorn

9.2 Opposition: Symmetry, Information, and Co-Creation The second principle of Creation Theory proposes that opposition is a universal and iterative process that generates information. Opposition is universal in extension, quality and dimension. Twoness is primordial, as embodied in the two dimensions (energy and time) of action, and in the two values of the simplest form of information (logical distinction). The number and complexity of oppositions grow from universal twoness to quantum superposition and entanglement, to local differentiation and global co-creation. This is not an eclectic compromise among quantum mechanics, logic, and dialectics but an evolutionary view of opposition that has scientific significance and practical application.15 Superposition is fundamental to physics, and to 15 Some scientists may question the usefulness of a general and abstract concept of opposition that includes quantum superposition, logical no-contradiction, dialectic coexistence of opposites, and catastrophic and harmonic generators. Undoubtedly such an abstract concept is too vague to guide much research, yet it is sufficiently concrete as to direct us to seek both symmetries and asymmetries, not just one or the other, in physics, to indicate the uselessness and misleading nature of linear scales that most sociologists and psychologists use, and to suggest an expansion of mathematical logic to include dialectic synthesis. General concepts play a dual role, descriptive and

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the design and construction of quantum computers. Logical no contradiction is essential in mathematics. Dialectic oppositions create natural and human processes. Opposition involves many aspects to be examined: (1) Universality: Opposition is universal in time, space, quality, and complexity. All processes contain pairs of opposite and complementary components at every level of organization, such as quantum conjugates (energy and time), positive and negative elementary particles and biological sexes.16 There are opposites in every quality or dimension17 (except irreversible time).18 In an N-dimensional process, there are 2N orthogonal pairs of opposites. There is a boundless number of different forms of opposition. Opposition is universal not only in time and space, but also in quality: there are infinite forms of opposition. Polar (linear) opposites occur in simple processes, neutralizing each other and generating equilibrium. Processes generate oppositions (cascades of bifurcations) forming lattices of increasing complexity and cycles of mutual feedback that generates new patterns (chaos, bios). Processes

normative. To be applicable, we need a clear notion of opposition that must be sufficiently abstract to be applicable to different situations and disciplines, sufficiently concrete to guide practice, sufficiently simple to be promptly remembered, and, foremost, sufficiently close to the truth to be useful. In contrast, much of our thinking and many of our actions are determined by general, clear, and widely accepted black and white concepts of opposition that are at odds with reality, and that promote dysfunctional behavior (Chapter 17). 16 There is opposition at every level of organization: (a) Physical: positive protons and negative electrons, position and momentum, energy and time, Pauli's exclusion principle, (b) Biological: growth and decay, complementary DNA strands, levo and dextro forms of biomolecules, anabolism and catabolism, sympathetic and parasympathetic nerves, (c) Human: cooperation and conflict; supply and demand; workers and dominant classes, (d) Logic: continuous and discrete, quantity and quality, true and false. Every structure has a right and a left, a top and a bottom. "Twoness" is universal, but it is manifested in multiple and diverse ways: bifurcation, pairing, duality, antagonism, information, and quantum superposition. 17 Mario Bunge (Scientific Materialism, D. Reidel Publ. Dordrecht, Holland, 1981) objects to the universality of opposition by pointing out that chairs do not have anti-chairs. His objection does not apply to actions (there always is an opposite action), to informational values (every statement can be negated), and to fundamental categories of entities such as electrons. There are no anti-chairs but there are anti-electrons (positrons) and the action of sitting down is opposed by the action of getting up. Opposition is a pairing of actions; opposites alternate with each other periodically and aperiodically, and through their interaction they influence each other and create new entities. 18 Time is unidirectional except in our minds. Energy and time may be considered opposites insofar as they are paired, inseparable (neither exists without the other), and vary inversely to each other in the sense that, for a given action, the smaller the change in energy, the larger is the change in time, and vice versa. This is often expressed as saying that the more precisely we know the change in energy the more uncertain is the change in time, but this interpretation is a philosophical overlay.

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evolve through differentiation into complementary (but asymmetric) opposites, and their subsequent interaction. Ionic dissociation, biological speciation, embryological differentiation, and the formation of pairs of virtual particles in the void within the boundaries of the Planck constant, exemplify how separation generates, at least transiently, complementary opposites. The division of elementary particles into fermions that obey Pauli's principle and bosons that tend, on the contrary, to form pairs and larger aggregates, points to the fundamentality and heterogeneity of opposition. (2) Coexistence and mutual implication of opposites ("complementarity"): Opposition is tautological: A if and only if no-A. Right and left necessarily coexist in objects. Internal and external processes are inseparable: action is interaction; change is exchange; information is communication. Every physical entity is both a particle and a wave (Bohr's quantum complementarity). Opposite states coexist at the quantum level (superposition principle). Further, evolution and decay coexist (enantiodromia), and social processes progress and retrogress, contrary to one-sided views of social progress and of entropic decay. The coexistence of opposites applies to opposition itself: opposites are united and separated, synergistic and conflictual, fundamentally similar and fundamentally different. The mutual implication of opposites captures one aspect of the several meanings given to "complementarity" in philosophy19 and differs significantly in other respects. In biotic processes, opposites may wax and wane together, reciprocally, or autonomously (Chapter 4.3). This lack of correlation indicates a complex nonlinear relation rather than independence. One observes that opposites change in an uncorrelated manner in many processes.20 This autonomy of opposites is essential for

19 Complementarity has been discussed in the context of Greek physiology, Chinese Taoism, Medieval scholasticism, German dialectics and the Copenhagen interpretation of quantum mechanics, among others. Linear opposites vary inversely, as one wax, the other wanes. Complementary angles vary in such a way. In philosophy, complementarity refers to the coexistence of opposites. This implies both synergy and antagonism; opposites should therefore be represented in orthogonal axes, and may be expected to vary proportionally to each other. 20 Psychological tests that measure opposite emotions, opposite motivations, and feminine and masculine characteristics (references in section 4.3) show that opposites can vary in an apparently independent manner, rather than inversely or complementarily. Mania and depression are extremes

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creation. Opposites are not complementary in the sense that their sum equals the totality. Opposites are included in group structures of complementary types, which often include 3 or more members (at variance with two-valued logic and dialectics). (3) Union and bifurcation of opposites: Opposites often emerge through bifurcation from a common origin; they as a rule remain inseparable, and influence each other. The superposition of opposites is primordial, and leads to their eventual separation. In macroscopic processes, opposites coexist, but separated in time, space or quality. Positive and negative charges necessarily coexist in every atom, but in different particles. Male and female necessarily coexist in the same species but usually in different individuals. Life and death coexist but separate in time or place. Every living organism eventually dies, and while alive it is continually replacing its cells, literally living and dying at once. Poincare's dodecahedron (and its embodiment in the cosmic background radiation, Chapter 6) illustrates the connection of opposites at macroscopic levels. The concept of coexisting opposites contrasts with the traditional focus on boundaries between physical systems or between logical classes; it must be replaced by the notion that opposites are distinct but united. (4) Similarity and difference: Opposites are more similar than complementary (Antonio Sabelli).21 Similar spouses make better marriages than couples with complementary personalities. Chemically, covalent bonds are stronger than ionic bonds. Similarity implies equality in some respects and difference in others. Opposites are partial, nonlinear, neither perfectly similar and synergic, nor completely different and/or antagonistic. (5) Synergy and antagonism: Opposites often are both synergistic and conflictual; we have our greatest conflicts with family members, of a linear continuum of mood and energy, but in mixed affective disorders mania coexists with depression (Chapter 16). Anger and fear often coexist and enhance each other (Chapter 4.3). 21 Though the two are not contradictory, the difference between similarity and complementary cannot be overstated. Complementarity involves inseparability and difference, and highlighting difference often serves to rationalize inequity in human processes. To say that masculine and feminine are complementary is obvious; to say that they are similar opposes a long tradition of sexism. To say that terrorism and anti-terrorism (or imperialism and anti-imperialism) are complementary is obvious; to say that they can be similar may be regarded as anti-patriotic.

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friends and co-workers, that is to say with those we are closest to and we love the most. This notion of opposition as including both harmony and conflict corresponds to the notion of bipolar feedback. It is fundamentally disparate with the notions of competition and conflict as a motor of change of Malthusian ideology, capitalist economics, Darwinian evolutionary theory, and Marxian class struggle. (6) Linearity: Opposites differ in quantity in one or more dimensions. They coexist in a continuum in a reciprocal relation in which as one property (e.g. synergism) waxes, its opposite wanes, but both coexist at each point. For instance, the degree of structural similarity of chemicals to a hormone places them in order from agonists (synergic but also competitive) to partial agonists to partial antagonists to full blockers. This notion is useful to generate change; e.g. pharmacologists synthesize antagonists by modifying the length of the carbon chain in a drug molecule. The quantitative relation between opposites underlies the notion of opposition as polarity; even at the extremes, each opposite contains the other in a diminished form, as represented symbolically by the yin/yang of Taoism and as clearly observed in fractals (Fig. 2.2); also dialectics posited the interpenetration of opposites. In a cyclic trajectory, the poles represent a turning around, a reversal of the directionality of the trajectory to the pole. Probabilistic and fuzzy logic improve on traditional views that view opposites as classes separated by boundaries, but it still fails to capture complementarity. Opposition cannot be reduced to quantitative difference -anti-matter is not a deficit of matter, evil is not a deficit of goodness. (7) Bidimensionality: Paired entities can both cooperate and conflict, be similar in some ways and different in others, be partially united and partialled separated. In the same manner, good and evil, feminine and masculine, and every other pair of complementary opposite properties overlap to some extent. Thus opposites cannot be conceived as poles of a linear continuum. Even further, both opposites may increase or decrease more or less autonomously. As opposites coexist, a portrait of reality is either consistent and incomplete, or complete and "contradictory", said Hegel. To understand reality we need to take two complementary views, just as to see a sculpture we must view it from several angles. This implies that opposites are orthogonal, not polar.

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Opposition is bidimensional, not linear. Opposites are nonlinear additive in one dimension and subtractive in another. This requires representing opposites in at least two separate dimensions (i.e. a plane). Each of the two opposite vectors is decomposed into two orthogonal components, one corresponding to the properties they share and the other portraying their differences. In the same manner, each vectors is decomposed into two orthogonal components, one corresponding to the ways in which they are synergistic and the other portraying their antagonism (Fig. 9.3). The plane allows representing linear, complementary and partial opposites, and showing similarities and differences between opposites. One thus needs at least two dimensions to represent oppositions (Fig. 9.3). The prototypical case is orthogonal opposites. All other cases may be understood as mixed cases of linear and orthogonal interactions. Concrete opposition is always nonlinear. Linear opposites are abstractions that very often distort thinking just as linear scales invariably distort data (Chapter 4.3). Nonlinearity implies that opposition must be nonlinear. Yet, in spite of current interest in nonlinear phenomena, most thinkers generally consider opposites as polarities in a linear continuum. In Boolean logic there are two opposites.22 The nonlinearity of opposition may be represented with trigonometric models (Fig. 9.4) employed for the modeling of bios and for time series analyses; they corresponds to helical, spiral and circular patterns and symbols (e.g. DNA, galaxies, dialectic helices, Mandalas). (8) Multidimensionality and multiplicity of opposites: Synergism and antagonism, union and separation, similarity and difference, are different distinctions that do not overlap. For instance, cooperation occurs among similar as well as among different organisms; likewise conflict is observed between similar organisms that compete with each other as well as among predators and prey. Thus each of these properties 22 While the concept of action as the universal substance is consistent with standard viewpoints, this notion of opposition is at variance with current concepts. Opposites are commonly regarded as classes, rather than actions; as separate rather than continuous (Spencer-Brown's concept of distinction); as mutually exclusive (logical principle of no contradiction, which is applied in information theory and in computer science); and as neutralizing each other (mechanical concept of equilibrium) rather than co-creative. Those who recognize the union of opposites, regard them as conflictual (Darwinian evolution, capitalist economics, Marxian class struggle, dialectic philosophy) or as integrated and harmonic (Bohr's complementarity, and some systems theories).

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represents an axis orthogonal to the others. Nonlinear dynamics allows one to understand rationally and rigorously the coexistence of opposites by separating them in different dimensions. Being multidimensional, every entity can have more than one opposite. True information opposes false, error, lie, ignorance, unconsciousness, and secret.

Fig. 9.3 Two-dimensional representation of opposition. Top: Vector representation of linear (polar), orthogonal (dialectic, complementary), and partial opposites. Unidimensional scales are valid only to describe abstract entities such as numbers. Concrete oppositions must be represented in at least two dimensions, such as action and sign. Bottom left: Two-dimensional representation of opposition. Each of the two vectors is decomposed into two orthogonal components, one corresponding to the properties shared by both opposites (energy, time, etc) and the other portraying their differences and / or antagonism. The energy of the system is proportional to the sum of opposites while information is proportional to their difference. Bottom right: The synergy and divergence of opposites is illustrated for the first bifurcation in the time series generated by the process equation.

(9) Mutual determination: Opposites mutually determine and transform each other. At the quantum level, two particles that have interacted in the past continue determining each other even after they are separated (entanglement), no matter how distant they are from each other (quantum nonlocality). Opposites also determine each other at the

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macroscopic level. Action elicits reaction; antibiotics generate resistance. Our behavior evokes similar responses in our opposites. Cooperation evokes cooperation. Aggression triggers counteroffensive reactions. Repression fosters revolution. Terror produces terror.

Fig. 9.4 Trigonometric model of opposites. Sine and cosine are paradigmatic of complementary opposites that are reciprocal and orthogonal. Top left: two coexisting bifurcations (positive /negative and internal/external) determine a circle of opposites; the bifurcations increase with the energy of the system (such as the feedback gain in a mathematical recursion). Bottom left: The increase in bifurcation with the energy of the system is represented by the expansion of the sine wave (bottom). Top right: a qubit, consisting of two opposite Boolean connected by intermediate states. Bottom right: a similar circle of opposites occurs at macroscopic levels; e.g. agonist and antagonist agents or states are bridged by the existence of intermediate agents or states.

(10) Levels: Opposite processes display three different forms of interaction according to the magnitude and complexity of the level of organization: superposition at the quantum level,23 logical separation in 23

At the quantum level, elementary particles have two distinguishable "Boolean" states (e.g. horizontal polarizations: ]0> = <->, and vertical photon polarization |1> = J). A unit of quantum information (quantum bit or 'qubit'), such as an atom or nuclear spin, can also exist in a continuum of intermediate states resulting from the superposition of these opposites. Superpositions are represented mathematically as complex linear combinations of the basis states |0> and |1>. With regard to any measurement, these superposition states behave like the basis states |0> with a certain probability and like |1> with a certain probability. Thus, the intermediate states cannot be

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time, space or relation at macroscopic local levels, and creative complementarity at global, systemic levels (co-creation).24 In the quantum world, there are at least four values: two basis states and two opposite forms of superposition (two types of diagonal polarizations). Pairs of qubits, such as two photons in different locations, can exist in four (2N) Boolean states |00> |01> |10> |11>. They can also exist in all their possible superpositions: the quaternity of orthogonal, bipolar opposites is contained in a circle.25 The intermediate states represent two separate complementary paths from one Boolean pole to the other. Thus, superposition is not a linear continuum but a continuous circular sequence of intermediate values (Fig. 9.4). The qubit is the physical reality that supports the trigonometric model of opposition. Superposition is extremely fragile, and a qubit must eventually go to a single state in a process known as decoherence. Decoherence arises from the constant, unavoidable interaction of these systems with their natural environment, explaining why macroscopic systems possess their classical physical properties. Macroscopic entities thus also acquire logical properties, i.e. opposites are mutually exclusive, as postulated by traditional and mathematical logic. (11) Information and misinformation: Opposition is the physical substrate of information: information is necessarily carried by energetic or material tokens26 and it is encoded by difference27 or by repetition (Chapter 4.4). Two values are necessary and sufficient to encode information: positive and negative states of computer components, true and false value in logic, action or resting potential in neurons. distinguished, even in principle, from the basis state |0> and |1>, in contrast, with the intermediate states of a classical bit (such as voltages between the standard 0 and 1 values) that can be reliably distinguished. Two quantum states are reliably distinguishable if and only if their vector representations are orthogonal; thus |0> and |1> are reliably distinguishable by one type of measurement, and diagonal polarizations by another, but no measurement can reliably distinguish a vertical from a diagonal polarization. 24 Sabelli, H. (2001). The Co-Creation Hypothesis. In Understanding Complexity, G. Ragsdell and J. Wilby (Eds). London: Kluwer Academics/Plenum Publishers. 25 Among the possible states generated by the superposition of opposites, there are some in which neither qubit is by itself in a definite state, but the pair is in a definite state. This situation is called an "entangled state" (Schrodinger). 26 Shannon, C. E. (1948). A Mathematical Theory of Information. Bell System Technical Journal 27: 379-423, 623-56. 27 Bateson, G. (1979). Mind and Nature. A necessary unity New York: Dutton.

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Information is difference or distinction, embodied in changes of action. Uniformity carries no information. Information implies the local separation of opposites that coexist in the process. As processes always contain at least two different states, there always is information. Opposites may be identical except for their sign, which thus carries information. Notably, the separation of elements into separate sets is not sufficient for distinction. Spencer-Brown28 defines distinction by partition but notes that marking is also necessary. Information is carried by the asymmetry of opposites, i.e. one opposite predominates at a given point and its opposite predominates at another; partition is neither necessary nor sufficient for distinction. The Moebius ribbon and fractals shows that opposition does not necessitate on boundary; the Klein bottle portrays the unity of the internal and the external (Fig. 9.5).

Fig. 9.5 The Moebius ribbon, the Klein bottle and a fractal illustrate that opposites are not determined by boundaries. The Klein bottle can be realized in 4-dimensional space; the tridimensional picture depicts a self-intersection which is not really there.

28

Spencer-Brown, G. (1969, reprinted 1979). Laws of Form. New York: E. P. Dutton.

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Where information is possible, so is misinformation. The two are inseparable. True and false are opposites orthogonal to all others, so each entity has at least two opposites, its true opposite and its own false self. There is false information, false intellectuals, false innocence, as discussed in relation to anti-immigrant sociologists (Chapter 4.3.4), innocent economic fraud (Chapter 15), and sociobiological accounts of human selfishness (Chapters 13 and 16). The opposite of innocence is not guilt, which brings about a change in behavior, but false innocence. The opposite of knowing is not ignorance, which can be readily conquered, but faith, dogma and prejudice. (12) Symmetry and asymmetry are complementary opposites. Opposition often is the symmetry that results from the alternation of two opposite asymmetries in time or space. The experiments described in Chapter 8 indicate that, even when simple information is provided by the inequality of opposites, the evolution of complexity requires the symmetry of opposites, and further, that in this respect, kinetic symmetry is more efficient than static symmetry. Two asymmetries make symmetry; this is the "asymmetry" of symmetry. Conversely, asymmetries are often paired; this is the "symmetry" of asymmetry. Opposition is a form of symmetry, but many bifurcations are asymmetric (Chapter 3). Fundamental opposites (e.g. sexes, brain hemispheres, beta decay) show meaningful asymmetries. Cosmological "symmetrybreakings" and biological differentiation also illustrate that partitions are as a rule asymmetric. An opposition represents symmetry, but it consists of an asymmetric action as illustrated by a screw, a wheel, or a cyclic engine. Intriguing possibilities, however, emerge from the consideration of symmetries, as it is evident in both physics and mathematics. The Russian physicist Vladimir Kulish of Singapore University proposes a Null principle: as soon as some quality becomes manifested, its opposite becomes manifested at the same time, and the quantitative measure of that opposite quality is exactly equal to the quantitative measure of the manifested quality.29 This could explain the origin of the universe as paired with an anti-universe. It seems to me that symmetry and 29

Ghista, D. N., and Kulish, V. V. (2003). Theory of Consciousness and Cognition. Internationa! Conference on Internet, Processing, Systems, Interdisciplinaries (IPSI-2003), Sveti Stefan, Montenegro, October 5 — 11.

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asymmetry must be fundamental, if not the most fundamental opposites, the mathematical equivalent of action and information. Being united and different, a pair of opposites may be regarded as the asymmetric poles of a unitary process. Groups model symmetry mathematically. Groups of three are common and fundamental; elementary particles, crystals, and many other physical structures and processes display a group structure that includes opposites and closure. Processes are groups. (13) Opposition as a cyclic engine: Kinetically, opposition is an action; every action involves opposition insofar as it is change from the previous action. In mechanical processes, equal and opposite linear forces can neutralize each other, producing static equilibrium. In nonlinear systems, opposites neutralize each other only at low energy. Bifurcation occurs at higher gain,30 generating an alternation of opposites. A wave is an alternation of opposites, rise and fall. Period 2, is ubiquitous in natural and human processes: odd and even, day and night, sleep and wakefulness, conjugated carbons in aromatic rings, walking, wax and wane of tides, and many others, including the proverbial question regarding the chicken or the egg. The Necker cube, in which two alternative interpretations of an ambiguous figure exclude each other and yet each lead to the other, is another clear example. In these cases, opposites coexist globally, but are separated locally. They alternate in space and/or time (Hegel-Engels1 law of negation of the negation).31 Neither opposite has absolute primacy, but each predominates in different respects and at different times. Dominance alternates, so the one that has priority is overcome by the greater complexity of the other (supremacy), but then the roles reverse again. Bifurcation is also a quantitative phenomenon: the greater the intensity of the gain, the larger the separation of the opposite outcomes. Further, energy becomes a bifurcating factor for catastrophes and for co-creations. Increasing intensity also increases the number of bifurcations, generating periodicity, chaos and bios. Dynamically, opposition is the interaction of two attractors, as in a catastrophe; two attractors are by necessity synergic in one dimension 30 In the process equation, A t+ i = A, + g * sin(A t ) to be described in Chapter 3, the parameter g represents the feedback gain (intensity or energy). 31 Engels, F. (reprinted 1940). Dialectics of Nature. N e w York: International Publishers.

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and competitive in another dimension. Two nonlinear forces can produce cycling, which consists is an asymmetric action that goes from one opposite to the other and back without changing direction. This unidirectional implication of opposites may thus operate as a motor (e.g. cyclic engines). The cycle of opposites may in fact be the engine of creation. Internal opposite components render processes autodynamic. (14) Co-creation: Nonlinear interactions produce bifurcation and thereby complexity: opposition is the simplest form of complexity. Opposition develops novel forms and 21, 22, 23,...2°° dimensions through a process of iterated differentiations (in processes) and distinctions (of ideas) homologous to the cascade of bifurcations in mathematical recursions. If there are N properties or dimensions, there are 2 N opposites. Period 2°° is the circle, which includes infinite pairs of diametric opposites, orthogonal vectors, and all intermediate types of opposition. Unidirectional action and circular opposition form the trigonometric model of opposites (Fig. 9.4). Rotation around this circle displays a directional asymmetry. Such a cycle of opposites may create form (water cycles shaping the environment) or organization. Radiation and material waves are exemplary of sinusoidal cycling. Sine and cosine make a tridimensional process. Cascades of bifurcations also generate period 3, chaos and bios in mathematical recursions; we can expect similar complexity in natural processes. In biology, differentiation into two branches represents the most elementary step in growth, development, and evolution. In physics, cosmological evolution consists in a sequence of "symmetry-breakings", meaning the differentiation of an original uniform state into two opposites. In mathematics, bifurcation into opposites plays a central role in the generation of pattern.32 In turn, bifurcations are created by the interaction of opposites, such as At and (1-At) in the well-known logistic equation and the positive and negative values of the sine function in trigonometric recursions. Similarly, bifurcations are created by the interaction of opposite forces in physical processes. Oppositions cause evolution and evolution generates opposites. In mechanics, opposites neutralize each other; in non-mechanical processes, opposites co-create 32

Feigenbaum, M. J. (1983). Universal Behavior in Nonlinear Systems. Physica D: 16-39.

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equilibrium, novelty, complexity and structure (co-creation hypothesis). The separation of opposites (bifurcation) creates information. Creation is the generation of information. What distinguishes causal creation (such as bios) from stochastic processes (such as Brownian noise) is that the creative change results from oppositions within the process (including the entity and system to which it belongs), i.e. internal information (information) rather than from accidental interactions. 9.3 Tridimensional Materialization To create is to make material. The third principle of Creation Theory acknowledges the creation of relatively stable, continuous, tridimensional structures at all levels of organization. Processes create structures.33 Materiality is universal. Materialization is a process: highly energetic processes create matter. Linear and equal opposites create equilibrium; tridimensional equilibrium creates matter. Stabilization generates structure, not equilibrium. The relation between stability, tridimensionality, topological continuity, and mass is apparent, but not understood. The relation between energy (E), information (I) and matter (M) is contained in Einstein's famous formula E=mc2 relating energy to mass (m). E is physical energy, but social and psychological energy are forms of physical energy. M stands for pattern and structure, as matter is the fundamental structure of the macroscopic world. Information is provided by change between opposite values, in short by frequency. Indeed the quantity of information that can be communicated is limited by the frequency of the energy carrier. Hence I < c2, as the velocity of the light c is the maximal attainable. E=mc2 represents the extreme case in which the rate of communication of information has reached its maximum, and hence equality, in both directions; energy can then convert into mass. More generally, the formation of structure is fostered by the energy of the system, and by the equality of the mutually opposing forces (1 = 0). 33

For this reason, I reserve the term structure to mean tridimensional material form. I use pattern to refer to processes, and organization to refer to higher dimensional forms, but, since use varies, I do not make a definition out of this personal use of the words.

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The relation between E, I and M as related aspects of systems is manifested in many different physical laws such as Coulomb's law: V = i *R, where current i carries information and resistance R is a function of the material circuit. It is also manifested in human processes, such as the relation between labor (E), wealth (M) and technology (I) in economic value. Generalizing, E = M * I. Energy creates matter. Also matter transforms into energy, but, in the evolution of the universe, energy has formed matter to a larger extent than matter becomes energy. Thus we may write the inequality E~—•I'M The nucleation of energy within a tridimensional global, continuous and expanding space generates discrete local, multiple, discrete, and asymmetric and asymmetric units (structures). In turn these material particles and systems nucleations of energy asymmetrically distributed in the continuous and apparently symmetric global space. Atoms, stars, galaxies, and black holes form simultaneously with the radiation of energy and the expansion of space. Mass thus becomes distributed in a range of densities, from black hole to matter to radiation to (low energy) information to (apparently empty) space. Nucleation and expansion are the elementary forms of opposition in three dimensions. Processes nucleate particles to form material structures (including matter itself), and also drive the expansion of systems, including space. Structures are stable but they accelerate processes by conducting energy, catalyzing change and conserving information. Structures result from the equilibrium of equal and opposite forces but almost invariably they are asymmetric. At all levels of organization, structures are composed of units (elementary particles, atoms, molecules, cells, organisms, stars) separated by (apparently) continuous space, and combining to form systems. These units are extended and continuous34 in space. None has been shown to be indivisible. At fundamental levels of organization, there are a limited number of classes of units (e.g. chemical elements, 34

Continuity is a defining feature in topology.

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amino acids) that combine to form an unlimited number of systems at a higher level (e.g. molecules, proteins). These combinations generate diversity, novelty and complexity in the same manner as a limited alphabet creates words and language. Every system displays energetic, informational and material aspects, distinct but inseparable (Chapter 2.3.3), because action, information and matter are universal (triadic monism). For instance, the electron has mass, charge, and information. From a system's perspective,35 energy, matter and information are the three components of nature; we36 conceptualize energy, information and matter as three inseparable aspects of each system.37 Energy flux and flow (action), opposition (information), and structure (matter) are universal forms. They are distinct but inseparable aspects of every process, rather than separate components. For instance (Fig. 2.3), a nerve impulse is an action current (energy flow), a signal (information) carried by a difference in potential (opposition), a sodium influx (material composition), and a transformation in the conformation of the membrane (material structure). However, the relative importance of these three aspects seldom is proportional. Systems have a material core, a larger energetic field, and a larger and expanding informational field (Fig. 9.6). This model of concentric spheres reminds one of the Mandala. Whitehead pointed to this pattern of organization for the solar system: a material, high-energy core (sun), an energy field (planetary system), and an unlimited radiation of information (light) into colder space. This concept of self-centered system also applies to personal systems (Section 16.2). In this light, the idea of system's boundaries needs to be reformulated. Space separates one solar system from another. In organism, membranes are specialized structures that serve to channel communication. 35

Miller, J. G. (1978). Living Systems. McGraw-Hill Book Company. New York. Sabelli, H. C. and Carlson-Sabelli, L. (1992). Process Theory: Energy, Information and Structure in the Phase Space of Opposites. Proc of the Internal Socfor the Systems Science. 37 Both conceptualizations are useful. The materialist notion of separate components serves to differentiate between physical or metabolic processes that are primarily concerned with exchanges or energy and matter, and informational processes in which the carrier is to a large extent irrelevant e.g. energy and mater supplying food versus information carrying hormones and drugs. On the other hand, the process conceptualization in term of aspects points to the inseparability of the two types of processes. Physical structures are formed because energy and matter always carry information; likewise food also brings information to the organism. 36

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Fig. 9.6 A system is formed by a central material core, a surrounding web of energetic interactions, and a field of communication that expands in space and time.

Creative processes are generic (Thomson's "principle of mass production", producing only a limited number of types of entities at each level of organization (Mill's "principle of the uniform structure of nature"). Entities of the same type are exchangeable in many interactions; hence we call them "modules".38 Just as one hydrogen atom may replace another, different persons may replace one another regarding social roles (generation, sex, profession, etc), a fact witnessed often in the generic ways in which persons react to others. Some levels of organization consist of a small number of types of units (e.g., chemical elements, DNA bases, primary colors, emotions), which constitute the alphabet in which higher levels of a potentially infinite number of members (molecules, genes, colors, feelings) are constructed. All processes contain, create, and destroy structure (subatomic particles, biological organisms, etc). Material structure also is a universal feature of processes. Matter itself is a structure, a tridimensional separation between masses of energy: this is Descartes' definition of matter as extension. Stable structures conserve information. They conserve "memories" of the processes that generate them. All structures 38

Sabelli, H. (1989). Union of Opposites. Lawrenceville, VA: Brunswick Publishing; CarlsonSabelli, L., and Sabelli, H.C. Modular Organization of Human Systems: A Process Theory Perspective. Proc of the Internat Socfor the Systems Science, 1992.

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embody in their three dimensions the unipolar asymmetry of action, the bipolar asymmetry of information, and the hierarchical asymmetry of cocreation.39 Structures portray the processes (past and present) that create them. Atomic and molecular orbitals present cosmic forms. Macroscopic structures also display the asymmetry and discreteness of action, globular, spiral (galaxies) and helical (proteins, DNA, RNA) forms of opposition, tridimensional fractal chaos and bios (e.g. river shores display the biotic flow of water; the distribution of galaxies may reflect a biotic expansion of the universe). Formation is transformation. Energy-mass is conserved, and to a certain extent, so is information. Identity depends on informational continuity: energy continually flows, and the material composition of systems, particularly complex organisms, also changes fairly rapidly. (Consider for instance the daily renewal of the cells that line our stomach and the continuity of Jupiter's Great Red Spot). However, informational continuity often depends largely on material continuity. Corresponding to Aristotle's efficient, formal and material cause, effects have energetic, informational and material causes. In the case of system formation by assembly, the two or more precursors become material components of the newly formed entity. Otherwise, co-creative interactions are as a rule unequal (Fig. 9.7). All causative agents provide energy and information, but often only one has material continuity with its consequent. Thus, what we do, feel and think now has material continuity with who we were, although it also depends on external inputs. In the same manner, a child has material continuity with the mother (literally, mother and matter are one and the same word); mother and father provide the same amount of nuclear genetic information, but the maternal ovum provides the cytoplasm and the mitochondrial DNA, and the mother's body provides matter directly to the fetus. There are two types of continuity, material and informational, at each moment in the course of a person's or a system's life, and also in generational jumps. To state the obvious: The 39

As discussed in Chapter 2, Even our anatomy embodies the unidirectionality of physical action as front and back, the symmetry of opposition as right and left, and the hierarchy of organization from head to toe. Likewise the earth, and any other astronomical body, displays asymmetry in three dimensions: rotation as action, opposition as the gradient from equator to two poles, and a vertical distribution of energy, the states of matter, and biological inhabitants.

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self is a material and continuous unit. Interactions are discontinuous and at least binary. Continuity or identity is material / maternal. Every person or system is the daughter of its material self and of the information of the other. The other is the father. p

Carrier of E, land M

». Carrier of E and I

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\ \

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txt

*~—--v ^Mother

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i

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Fig. 9.7 Parental opposites. Each new state of a process (left) or each new entity (center, right) is generated by the interaction of two (or more) entities, one of which contributes matter, and both contribute energy and information. The basic idea is illustrated by Feynman diagrams (right). The electromagnetic field, defined in terms of the force on a charged particle, is regarded as consisting of photons which cause a force on a charged particle by being absorbed by it or simply colliding with it, as in the photo-electric effect. One electron emits a photon and recoils; the second electron absorbs the photon and acquires its momentum. The recoil of the first electron and the impact of the second electron with the photon drive the electrons away from each other, accounting for electric repulsion between like charges.

Structures are co-creations, i.e. tridimensional and relatively stable patterns generated by interactions. Pattern and stability result from complex equilibration of opposite forces. Nonlinear interactions of two (or more) entities create a third in many different ways. Three dimensions are the least necessary to accommodate complementary opposite waves. Logically, an operation that combines two elements generates a third. In catastrophes, the interaction of opposites generates at least one more dimension. Another way in which triadicity emerges is because every entity has at least two aspects and hence two partial opposites. For instance, the complementary opposite of an electron is the proton in common matter, and the positron as a perfect symmetric case. Similarly, innocence (objective and subjective) opposes (subjective) guilt

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with objective innocence (common in depressives) and subjective innocence with objective guilt (characteristic of the self-righteous). The simplest tridimensional structure is a folding. Let us then consider catastrophes as simple instances of generation of tridimensional organization.. The formation of more complex structures may also be governed by control parameters similar to those that govern catastrophes. As discussed in 4.3, energy (which is a positive function of both opposites) functions as a bifurcating control variable, that is to say, linear changes occur at low intensities, and a tridimensional fold occurs at high intensities. In contrast, the relative magnitude of opposite forces provides information regarding the direction of change. When both opposites are of similar intensity, the outcome of is uncertain in the case of catastrophes, while in the case of a bipolar feedback recursion, the outcome is complex bios. Thus catastrophes are governed by an asymmetric factor but complexity emerges from the symmetry of opposites. Linear changes occur in simple interactions between two attractors at the extremes (asymmetry) and non-linear folding obtains at intermediate values. Similarly, in bipolar feedback recursions, linear-like parabiotic patterns are generated when there is marked asymmetry, and more complex biotic patterns appear when the opposites are symmetric. I speculate that the model might apply to physical processes, as the distribution of matter and void is determined by processes of attraction and repulsion that concentrate and separate energy-carrying particles. Simple co-creations as mirror images of catastrophes. A catastrophe is a jump between complementary opposite poles of a linear continuum (asymmetric factor); the trajectory between these poles is nonlinear, folded in a third dimension, when the energy (bifurcating factor) is high. A co-creation is the structure formed by the nonlinear distribution of energy and matter at the fold that occurs when the energy if high and its opposite components are symmetric. This constructs organization, and hence novelty and complexity. The terms catastrophe and co-creation may be appropriate rather than arbitrary. The polarization of opposites often leads to catastrophic consequences, whereas the union of opposites is highly creative.

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9.4 Biotic Co-Creation: Four Generates Bios Let us now consider more specifically the type of co-creation that occurs with bipolar feedback, and that involves at least four factors rather than two competing attractors, as in a catastrophe. Tetrads are universal because oppositions occur in every dimension. Just as three attracting bodies produce structure and chaos, two orthogonal pairs of opposites generate bios and infinitation. A cross of opposites is included in the circularity of the trigonometric functions that generate bios (Fig. 9.8 top left). Bipolar feedback recursions display a prominent period 4 (Fig. 9.8 top right), and a tetradic pattern of rise and fall (Fig.9.8 bottom right) can be demonstrated with methods described in Chapter 4.4. Conversely, biotic like trajectory may be generated by recursions in which the change term is constructed with two orthogonal pairs of opposites display biotic features at very high gain. (Biotic patterns are generated at much lower gain by trigonometric functions that involve an infinite number of pairs of diametric opposites in a plane.) In contrast, when the sine function is replaced by less varied periods, such as period 2 or 3, one does not generate bios. These results, together with the prominence of period 4 in recursions of bipolar (Chapter 3) suggest that four or more attractors are necessary and sufficient to generate biological-like complex trajectories. Four is fundamental because it represents a set of orthogonal pairs of opposites. Co-creation results from the interaction of simple complementary opposites generates novel and complex processes. Just as the interaction of complementary sexes procreates, the interaction of complementary actions generates form, ranging from transient patterns to stable three-dimensional structures to high dimensional life-like organization. We formulated this concept mathematically in the process equation, where the sinusoidal function provides bipolar (positive and negative) feedback. We used it empirically in the diamond of opposites and in complement plots. Causal ("deterministic') interactions between partial (nonlinear) and complementary opposite processes constitute generic processes for the generation of bifurcation, diversity, novelty, and complex (higher dimensional organization) such as tridimensional matter and multidimensional organisms. The formation of matter by positively

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charged massive protons and negatively charged smaller electrons, and sexual procreation are paradigmatic. The generation of complexity by the combination of complementary structures is central to physics and chemistry. Other exemplary cases include the co-evolution of prey and predator species, and cellular differentiation resulting from the interaction among cells. Mutual feedback transforms each interactor. Mutual feedback often occurs between processes within a hierarchical structure.

Fig. 9.8 Bios and tetradic organization. Top. left: the cross of opposites implicit in the circularity of the trigonometric functions that generate bios. Top right: prominent period 4 in the cascade of bifurcations leading to bios. Bottom: proportion of consecutive sequences of rise, fall and repetitions, measured as described in 4.4. X axis: rise, repetition or fall in term t. Y axis: rise, repetition or fall in term t+1. There are few repetitions. Left: 3 classes of change in logistic chaos. Right: 4 classes of change in biotic series.

Both combination and differentiation generate new systems, but, by necessity, bifurcation into opposites is an initial step in the creation of organization, that necessarily precedes chemical combination, dialectic synthesis, system formation, or any other type of creative interaction.

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Both synergic and antagonistic interactions can be creative, and often coexist; this notion is offered as an alternative to both one-sided idealization of competition and struggle as the motor of evolution, history, and economic progress, and one-sided descriptions of systems as integrated, non-conflicrual wholes. Interactions between opposites generate and destroy form, but, by logical necessity, creation must precede destruction. Here I have focused on co-creation by bipolar feedback but this is only one process, albeit generic, for the production of novelty and complexity via interactions. Synthesis, differentiation and semantic combinations are additional sources of creation. As a result, biotic systems such as organisms and societies form organs for the distribution of energy, the processing of information, and the production and reproduction of structure, which have been studied by Miller and others as Living Systems Theory.40 In the process studied here, the interaction of opposites generates bifurcation cascades and thereby complexity. This process is clearly different from the generation of complexity by the combination of opposites (dialectic synthesis) or the assembly of parts into a totality (systems theory), but all these processes create complexity. In contrast to the notions of unidirectional single causality and of random events, the co-creation hypothesis proposes that all causation is interactional. Physiologists such as Heraclitus accounted for natural processes in terms of "justice" (the interaction of two (or more) pairs of opposites) rather than in terms of linear causality. Four traditionally represents justice (e.g. a square deal). Four traditionally also represents justice (e.g. a square deal). Quaternity is an archetype of almost universal occurrence, according to Jung. There are many four-fold symbols of psychological wholeness. It forms the basis for any "whole judgment"; this is illustrated by the American idiom "a square deal". 9.5 Five and Higher Dimensions of Organization Different pairs of opposites lie in orthogonal dimensions; e.g. similaritydifference is orthogonal to harmony-conflict. Similar entities may be 40

Miller, J. G. (1978). Living Systems. McGraw-Hill Book Company. New York.

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allied or compete; different entities may be antagonist or form partnerships. In an N-dimensional process, there will be 2N orthogonal pairs of primary opposites and therefore 2N cascades of bifurcations. Undoubtedly there are processes organized by 5 and more attracting bodies. Five appears as the number of digits, of Platonic bodies, and as a form of symmetry from starfish to mammals (4 limbs and 1 head). Fivefold symmetries are rarely found in non-organic life forms but are uniquely inherent to life, as in the form of the human hand, a starfish, flowers, plants and many other living things. This pattern of five exists even down to a molecular level. Five, therefore, embodies the form and formation of life, the very essence of life. Bios involves at least 5 "pulls": at least two pairs of opposites and time. Eight (23) is another significant numerical pattern, found in a wide range of fields, from the group of eight in particle physics to logical functions and musical octaves. There are eight fundamental colors: three primaries, three complementary secondaries, black, and white. It is interesting that the family of protons, the family of mesons, and the family of gluons, all have eight members, just as the family of fundamental colors. As discovered by Gell-Mann, all known baryons (protons and neutrons that make the atoms' nuclei, as well as particles created artificially in the laboratory) are combinations of three quarks arranged in multiplets that can be described by the eight generators of the Lie group SU(3), and is called the "eight-fold way". One can also see this pattern of eight in the distribution of electrons in the orbitals around the atomic nucleus. The families of chemical elements repeat with the periodicity of eight in Mendeleiev's table of chemical elements. In the Western musical scale, notes of the same pitch repeat over octaves. Curiously, g = 8 generates infinitation in bipolar feedback recursions (Chapter 3). Sixteen (24) is the number of elementary particles in the standard model. These observations suggest a cascade of bifurcations in numerical archetypes. Multiple attractors will produce higher forms of complexity. Infinite represents randomness to the statistician, divinity to the metaphysician, and the attractor of evolution to the physician (Chapter 12).

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9.6 Color: Opposition and Triads Six is a generic form. The benzene ring of aromatic compounds makes biomolecules; hexadic cells appear in many systems because they pack easily, there are six mechanical dimensions (position and velocity vectors); 60-faced structures are important, as illustrated by C-60 fullerene and by Poincare's topological dodecahedron detected in cosmic background radiation (Chapter 6). The importance of the group 60 was already intuited by Babylonian and Chinese arithmetic (Chapter 2). Period 6 is prominent in logistic and biotic recursions. As discussed in Chapter 3.6, the period 6 of the series generated by the time-reversed distinction At+i = At - At_i has a "color" configuration41 (Fig. 9.9 right), meaning that it is composed of three pairs of complementary opposites in which the sum of two complementary opposites produces an identity element (red + green = white), and the sum of two primary colors equals the complement of the third (blue + yellow = green). Many natural processes show a "color configuration". Allow me then to take a detour through an elementary introduction to color.42

Fig. 9.9 Elementary vector forms (left) and the color organization (right) presented as a lattice. 41

Sabelli, H. (1989). Union of Opposites. Lawrenceville, VA: Brunswick Publishing; Sabelli, H. and Carlson-Sabelli, L. (1996). As Simple as One, Two, Three. Arithmetic: a Simple, Powerful, Natural and Dynamic Logic. Proceedings of the International Systems Society. Edited by M. L. W. Hall, pp 543-554. 42 I shall not attempt to deal here with color vision in detail, a subject of incredible complexity think for instance of the fact that colored surfaces retain their daylight appearance in spite of wide changes in the intensity and wavelength composition of the incident illumination.

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Colors are "nothing more" than the way in which the eye sees light waves of different frequency. From the physical perspective, there are no colors, hence the notion that colors are "just an illusion created by our senses", from which some philosophers extracted the idea that there is no objective reality, only subjective interpretation. Taking this idea to its ultimate consequences, life is not real, only thought is.

Fig. 9.10 The Visual pathway illustrates the expansion in the number of opposites with complexity.

The retina has three kinds of receptors for color, the cones. These cells contain substances ("pigments") that selectively absorb light of different frequencies. The sensitivity of these pigments overlap considerably, so many light frequencies are perceived by two different types of cone. This biological partition contrasts with the mutuallyexclusive categories of traditional logic, but conform with the coexistence of opposites that we have encountered in al natural processes. Considering their range of maximum sensitivity, it is evident that the three primary colors detected by the retina correspond to orange, green and violet, the three colors considered as secondary by the artists. This trifurcation of the continuum of light wave frequencies into three colors in the retina marks the passage from physical oneness to biological diversity. I regard this three-way split light into primary colors as the transition from energy to life. I propose that such a trifurcation reveals the cosmic form of creation.

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A different pattern of organization emerges at the neural level: the three-color information that obtains in the retina is processed by the lateral geniculate nucleus as a double opposition, red versus green, yellow versus blue. Neurons respond selectively to colors with either excitation or inhibition; on-and- off discharges cancel each other, thus showing to be mutually antagonistic. A given cell responds to either yellow or blue according to the relative intensity of the excitatory and the inhibitory inputs. Likewise green and red are opponent processes in other cell types. Thus, at the neural level there are 4 primary neural colors, organized as two sets of opposites: red versus green, and yellow versus blue. At the visual cortex level, we perceive, recognize and differentiate the three primary colors, red, yellow and blue, the three secondary colors formed by their combination, all the intermediate cases found in the color wheel, and in addition, black and white, the lowest and the highest element in the lattice formed by them. This organization thus has the properties of opposition and order, thereby resembling group and lattice, two fundamental mathematical structures (Chapter 10). From these elements, the mind constructs an infinite multiplicity of colors. We learn to differentiate colors. Thus some languages name only a few colors: red is almost always labeled, blue or green are also almost always included, but brown is often absent (as in classic Greek). Color perceptions become innumerable, some will contend, potentially infinite. Visual education allows artists to differentiate more colors. Visual color illustrates the creativity of trifurcations and points to their relation with tetrads and infinitating complexity. The number of color distinctions increases with the complexity of the level, from 0 colors in physics, 3 in the retina, 4 in the lower levels of the nervous system, many in language, hundreds of thousands, perhaps even millions, as distinct sensory perceptions in the brain cortex. Most important, we perceive brown. Brown is the one and only common color not present in the solar spectrum. In studies of color recognition, browns are ambiguous.43 Browns are colors created by the

43

A key member of our research club, Arthur Sugerman has conducted an interesting study on the perception of color at Northwestern Hospital (Chicago). Art claims to know colors better than most people because not only he has studied color perception methodically, but also because he is not

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combination of three primaries. Such complexity would explain why there are so many different colors called brown. Browns not only have the distinction of being the most ambiguous color category: they also are the colors of wood and of flesh. Browns are the colors of life. Is there a relation between the complexity of brown as a mixture of three basic colors and the complexity of living organisms? Although colors are not physical facts, they are biological facts created by the interaction of light waves and complex eyes, such as those of primates, certain birds, reptiles and insects. The fact is that many animals do see colors. Color vision also exists in tropical fish —as one would expect from their colorfulness. Considering the complexity of insect eyes, and the richness of color in flowers, as products of long periods of co-evolution makes evident one biological function of color.44 Color thus arises from biological processes. Dismissing color because it is not a physical fact but only chemical, biological, social, and psychological, illustrates how reductionism prevents one from seeing reality. In particular, focusing on the simple physical level, it prevents us from recognizing evolution. Psychologically, it exemplifies a rather arrogant narcissism. Before correcting nature for having invented nonphysically based color vision, perhaps it would be wiser to learn from her. Matter, life and mind are not separate realms: as we learn about life by studying its material composition, we may learn about matter by examining its biological manifestation. Physical law does not end in the retina, but it reveals its power and beauty in this passage into biological complexity. Here we are interested in "color" as an abstract form present also in physical processes. Quarks combine as triplets to make protons and neutrons, and as pairs to make mesons. There are quarks and anti-quarks, and each set has three "colors", while all observable particles are "white", which, as in the case of light, can be produced either by adding confused by the illusions that most people suffer. He is immune to them because he is totally colorblind. From his study, Art has concluded that browns exist only in our minds. 44 Another important function of color vision is to perceive tridimensional space better. Color vision is most developed in flying animals, including insects, birds, and of course humans, who use their brains rather than wings to fly. In humans, depth perception is much worsened by lack of color perception. Perhaps this function of color, to perceive tridimensional space, explains why there are three primary colors.

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three primary colors, or mixing a primary color and its complementary anti-color. This mathematical analogy between visual and quantum "colors" may reflect a natural homology, i.e. the result of a common origin in a natural pattern of organization. A similar triadic organization also applies to a quark's flavor. The logical configuration of color also fits human ideas and feelings, so colors acquire symbolic meanings (emotional, political, religious). For instance, red anger, yellow cowardice and blue depression portray the relation between the three basic emotions of conflict (Section 4.3) and the three primary colors. For his reason I use colors in psychotherapy as a way to go beyond black and white thinking (Chapter 18). In my view, color organization is so fundamental because it involves opposition and triadicity. In triadic systems such as color structures, the opposite of the union of two primary components generates the third; e.g. the sum of blue and yellow produces green, the complementary of which is the third primary color, red. In the field of ideas, one may create third alternatives by considering the opposite of finding what is common to the opposites. 9.7 Dimensiogenesis: Quantity and Quality We may consider creation as the generation of dimensions.45 Dimensions are directions: one direction of time, two directions of information (positive or negative sign), three directions of space (Fig. 9.8 left). Generators create new and complex processes just as genes serve to develop organisms, and innate psychobiological action patterns serve to generate more complex behavior. We may consider the following hypotheses and conjectures: Quantity is universal. Quantity is universal because action, information, and matter are quantic, that is, they are multiples of discrete units. Actions are quantities. At every level of organization, processes and structures are composed of units (e.g. Planck quanta, heat phonons, elementary particles, atoms, molecules, synaptic vesicles, cells, cardiac 45

The multiple mathematical concepts of dimension abstract separately various aspects of natural dimensions.

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beats, words, individual lives, stars). Information is encoded and transmitted by action units or by material tokens, pointing to the use of integers in measurement. Quality is universal because oppositions are qualities. Opposition is the minimum of quality. Quality is information; complexity relates to the number of qualities. Quality is a property that determines interactions, not a class. This is important in logic, where a logic of sets does not describe the logic of attributes (Chapter 18), but it is likewise important in sociology where an individual may belong to more than one class (Chapter 16). Universal qualities are categories, that is to say archetypes, both objective and conceptual. The abstract study of categories has been pursued from philosophical,46 mathematical,47 and semantic48 perspectives. As expected from the universality of small integers, categories develop in pairs and triads.49 Sequential order is a third member of the triad that includes quantity and quality.50 Quantity and its changes establish quality in a nonlinear fashion. There is a close relation between quality and scale (Galileo). Scale constrains the range of possible organization. Changes in quantity produce nonlinear changes in quality as illustrated by changes in time (age), size (an increase in population changes a village into a city), or intensity (appetite and hunger). Varying degrees of sweetness are perceived as pleasant or unpleasant. This is the law of dialectics enunciated by Frederic Engels that he attributed to Hegel.51 The changes are nonlinear, and often include sharp critical points (e.g. water freezes at 0°), thresholds, and shifts, although large quantitative changes may produce gradual qualitative transitions. Action rate as a function of temperature: within limits, chemical processes accelerate with physical temperature -excessive temperature is inconsistent with the very 46

In modern times, Thomism and dialectic materialism follow Aristotle's focus on categories. Mac Lane, S. (1986). Mathematics Form and Function. New York: Springer-Verlag. 48 Lakoff, G. (1987). Women, Fire, and Dangerous Things. The University of Chicago Press. 49 This is no idle comment. Consider for instance that The Encyclopedia of Philosophy (Ed. Paul Edwards, Macmillan Publ. Co, New York, 1967) contains an article about simplicity but not one on complexity, while some nonlinear dynamicists focus on complexity without pairing it with simplicity. 50 This is consistent with the notion of number as quantity, order and form (Chapter 10) and at variance with Hegel's dialectic. 51 Engels, F. (1940). Dialectics of Nature. New York: International Publishers. 47

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existence of molecules. Biological processes manifest a non-linear relation between temperature and rate. Statisticians52 calculate a correlation of .25 (p = .004) for body temperature and heart rate, but heart rate is accelerated by both heat and cold. In catastrophes, linear changes obtain at low energy, and non-linear change at high energy. In mathematical recursions, the interaction of complementary opposites generates different patterns according to their intensity: equilibrium, periodic cycling, chaos and bios. Complex processes display scale-free fractal organization (Mandelbrot). Fractality is a fundamental characteristic of chaos and bios. The organization of natural processes into levels becomes fractal in several different ways (see later).

Quantity and Quality: Galileo Galilei and Frederic Engels.

Complexity is associated with moderate values of temperature, energy, duration, mass, volume, and phase space dimension. For instance, complexity increases from the 3°K background radiation to attain its known maximum in the biosphere, and then decreases as temperatures increase further towards the extremes found in star cores. The maximum of known complexity occurs at 37°C in mammalian brain, and relatively minor changes such as fever disrupt dramatically and even irreversible mental function. 52

Shoemaker, A. (1996). What's Normal? - Temperature, Gender, and Heart Rate. Journal of Statistics Education v.4, n.2.

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Changes in quality involve changes in quantity. Bifurcations are discontinuities but are also quantitative phenomena. For instance, in biotic and logistic recursions, the greater the intensity of the gain, the larger the separation of the opposite outcomes; moreover, increasing intensity increases the number of bifurcations. Orders of magnitude are changes in quality. Complexity is a monotonic function of energy flow density. The free energy flow density increases monotonically with complexity from galactic space to stars (e.g., it is 2 ergs sec-1 g-1 for the sun) to planets to living organisms, to the human brain (150,000 ergs sec-1 g-1).53 Biotic hypothesis: Creative phenomena involve growth such as the physical expansion of intergalactic space, ecological spreading out of species, the growth of young organisms, the progressive nucleation of social systems into larger units (tribe, nation, federation or empire), and the expansion of chaos into bios. Biotic expansion appears to be present even in homeostatic biological systems (Chapter 5). Dimensionality defines complexity. Complexity is the quantity of quality, i.e. the number of dimensions. A complex system is qualitatively larger than a simpler one. Complexity of function depends on complexity of form (Lamarck). Psychological function requires a complex brain. Biological activity requires protein structure. Electrons cannot have consciousness or make "choices". Atomic composition, molecular structure and anatomical organization of living organisms are not arbitrary fruits of happenstance. As illustrated by genetics, computers, and telecommunication, information can be encoded in many but not just any structure. In contrast, the credo of Artificial Life proposes that form and function are separate processes, and that patterns of information could be encoded by any structure. Evolution is dimensiogenesis. Evolution consists in the creation of complex forms of organization from simpler ones. Interactions produce processes with at least one more dimension than the interacting processes. Two-dimensional opposition can generate tridimensional structure; interactions among structures can generate higher dimensional 53

Chaisson, E. (1987). The Life Era. New York: Atlantic Monthly Press.

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organization. In this way, evolution proceeds by bootstrapping. Evolution generates complexity in stages of increasing dimensionality: 0 D Flux-^ 1 D Action -> 2 D Opposition -> 3D Material Objects -> Multimensional Organisms -> High-dimensional Persons -> Infinitely Dimensional Attractor. Evolution generates major discontinuities in complexity: levels of organization. Each level of organization represents the occurrence of a new set of fundamental units, oppositions, structures and creative tetrads. 9.8 Priority and Supremacy: Biotic Feedback The priority of action and the supremacy of creation: Evolution necessarily predominates and exceeds decay. First, action can produce equilibrium, but equilibrium cannot produce action. Further, creation must precede and exceed destruction because it is not possible to destroy what does not exist. Thus, evolution may tend towards an infinitely complex attractor (Chapter 12), but not towards entropic decay (Chapter 11). Priority of the simple and supremacy of the complex:54 Simple processes are universal and generate, constitute and surround complex processes; they predominate via their temporal priority and their greater extension, duration, and energy. Complex processes are short-lived, local, and control the simpler processes that constitute them via their greater informational content, greater energy flow density, and greater creativity. As evolution generates new dimensions, there are major, discontinuous, qualitative changes in complexity, thereby generating a hierarchy of levels of organization in nature. Processes are thus

54

The concepts of priority and supremacy originate with our research (Carlson-SabelH, L. and Sabelli, H.C. (1984). Reality, Perception and the Role Reversal. J Group Psychotherapy Psychodrama and Sociometry 36:162-174. Sabelli, H., and Carlson-Sabelli, L. (1989). Biological Priority and Psychological Supremacy, a New Integrative Paradigm Derived from Process Theory. American Journal of Psychiatry 146 1541-1551. Sabelli, H. (1989). Union of Opposites). The term "supremacy" can be understood in its common sense, as the power of force, as the complementary opposite to the power of priority of the simple. The term supremacy is also used here in a technical sense, meaning the feedback of the complex on the simpler. The same term is used in both cases to convey the notion that these two meanings describe the same phenomenon.

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hierarchically organized in levels: mathematical < physical
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Evolution generates major, discontinuous, qualitative changes in complexity also in brain structures: spinal, bulbar, mesencephalic, diencephalic, cortical, as discussed in Chapter 2, and in psychological functions.57 Evolution also nucleates structures, generating a hierarchy of systems: atom < molecule < cell < organism < society < planet < solar system. Thus traditional systems view arrange levels according to their size each containing the others as Chinese boxes or Russian dolls.58 Process and systems hierarchies do not overlap. Levels of organization in processes represent phases in the evolutionary sequence that created them. They also represent a clear order of complexity. The hierarchy of systems does not portray evolutionary sequence, and describes a different aspect of complexity. The systems perspective divides the physical level into the atomic and the galactic. The same physical laws govern the motion of particles and stars (Newton), but the range of physical forces is vastly different, so gravitation dominates macrophysics and nuclear forces dominate subatomic processes. Process and systems perspective are thus complementary regarding physical processes. Process and systems viewpoints are also complementary regarding human processes. The systems view does not separate the biological and the psychological levels, and assigns greater complexity to the social level than to the psychological. In the process view, the social level is considered as prior and simpler than the psychological level. Social processes precede the development of personal individuality in the history of the species (e.g. social behavior of insects), of the human species (consensus communities preceded individual freedom), of each person (we are male or female, of a particular race, and even of a certain 57

Maslow, A. (1970). Motivation and Personality. Harper and Row. New York. The concept of levels of organization is central to systems science, although not regarded as important by some systems theorists. The holographic model (Pribram, K. H. (1981). The neurobiologic paradigm, in Models for Clinical Psychopathology. Edited by Eisdorfer C, Cohen A, et al. New York, Spectrum Publications) places physical, biological and psychological processes at the same hierarchical level. Likewise, according to Capra, physical reality is a web of relationships "somewhat similar to an inkblot in a Rorschach test", so to isolate a pattern in this complex network by drawing a boundary around it and calling it an object, is somewhat arbitrary. Thus it is "arbitrary" to speak of a tree to refer to a network of relationships among leaves, twigs, branches, and a trunk. As the roots of trees are interconnected in a forest, there are no precise boundaries between individual trees. (Capra, F. (1996), The Web of Life. Anchor Books Doubleday, p. 39]. 58

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religion as soon as we are born), and of each relation (we relate to each other as a function of our social role before we know each other as persons). Social and familial processes are simpler and precede the personal (psychological) level; there are many more individual personalities and life histories than the relatively small number of social roles. As a totality, society has greater energy and complexity than individuals (priority), but each individual mind has greater energetic and informational density (supremacy). Socioeconomic processes are predetermined by physical and biological factors, and controlled by cultural and personal creativity (Chapter 16). The social and the psychological levels thus relate in opposite ways as processes and as systems.59 This illustrates the duality of ordering relations. The interaction between these two orthogonal hierarchies of complexity is creative. The society is simpler than the individual it creates. The creativity of individuals increases the complexity of the collective, which may then in turn generate more complex individuals. Systems

Processes

Fig. 9.11 Levels of organization in systems and in processes.

Generational, sexual and class relations, "pecking order" in animal societies, and many other phenomena including levels of organization, have been regarded as hierarchies, i.e. as pyramidal organizations such as 59

Postulating that social and familial processes are simpler and precede the personal (psychological) level; the process perspective is congruent with sociobiological and sociological theories (Marxist as well as non-Marxist). In contrast, traditional systems theories as well as traditional psychoanalysis, consider psychological processes more fundamental and regard social processes as the result of the collective interaction between individuals.

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army and church in which each component is subordinate to those above it. Twentieth century system theories stressed that in most organizations, relations are dynamic and include competing centers of power, stressing a progressive decrease in hierarchical order.60 Hierarchies certainly are conflictual and changeable, but hierarchical order is real. Natural and human hierarchies have a two-way order, from top to bottom and from bottom to top. There is a hierarchy of levels, but the interactions within the hierarchy are bi-directional. This hierarchical and bi-directional relation is modeled mathematically by lattices. Duality is a theorem of lattice theory: every lattice has a dual. The order relation R is asymmetric and dual: a < b if and only if it is not true that b < a, but by necessity there is another order relation let us say > such that b > a. Lattice order is hierarchical and dual. The concept of lattice duality replaces the notion of unidirectional hierarchy. A major applications of these principles is the notion of biological priority and psychological supremacy in medicine and psychiatry (Chapter 16). Clinically, many psychiatric disorders require pharmacological treatment, and conversely, emotions modify metabolism and contribute significantly to medical illness. These concepts underlie the bio-socio-psychological approach to diagnosis and treatment (Chapter 16) as contrasted to the bio-psycho-social model based on standard systems theory.61 Socioeconomic processes are predetermined by physical and biological factors, and controlled by cultural and personal creativity. The notion of biological priority and psychological supremacy also applies to sociology (Chapter 16). Other significant cases are the priority of the objective and supremacy of the subjective in clinical, social and epistemological insight (Chapter 18), mathematical priority and psychological supremacy regarding scientific methodology (Chapter 18), and social relations. The notions of parental priority and 60 Warren McCulloch has proposed the concept of heterarchy as a form of organization resembling a network. While standard sociology defines political economy as a societal condition principally affected by the requests and demands of an elite, the concept of social heterarchy focuses on the complicated and less predictable set of interdependencies manifest within and between members of a group. In a social heterarchy, authority is determined by knowledge and function. Heterarchical organizations appear to be more creative than hierarchical ones. Networking may constitute a new form of governance more appropriate for contemporary societies, but one should not confuse desires with reality. 61 Engels, F. (1940). Dialectics of Nature. New York: International Publishers.

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supremacy of the offspring,62 female priority and male supremacy,63 privileged and disadvantaged classes,64 and empire and peripheral nations65 are sketched in Chapter 16. The priority of the simple and the supremacy of the complex is a general notion regarding reality, knowledge, and clinical and social practice that differentiates Creation Theory from other systems views, idealistic process philosophies, dialectic materialism, and nonlinear dynamic views that reduce biological and psychological processes to physical chaos.66 Priority and supremacy are two different forms of relating. The hierarchy thus constitutes an asymmetric feedback that propagates and increases complexity. This is biotic feedback. Such feedback is not only bipolar and mutual but also ever-present and hierarchical. Further, it involves several steps, as every level of organization relates to one simpler and one more complex. Biotic feedback is particularly important because processes often include multiple components of different power and complexity. Heart and brain,67 spinal cord and brain cortex, brain and psyche, sexuality and meaning, social solidarity and personal creativity, all illustrate creative feedback relations that are both mutual and hierarchical. We speak of bipolar feedback, but these processes are not mechanical, and there is great heterogeneity among them. Simple and complex levels can overlap extensionally in one process; for instance, economic and cultural processes overlap; there are other cases in which 62

Sabelli, H., Carlson-Sabelli, L., Patel, M., and Sugerman, A. (1997). Dynamics and psychodynamics. Process Foundations of Psychology. J. Mind and Behavior 18: 305-334. 63 Sabelli, H. C. and Synnestvedt, J. (1991). Personalization: A New Vision for the Millennium. Chicago, IL: Society for the Advancement of Clinical Philosophy (SACP). 64 Sabelli, H. and Carlson-Sabelli, L. (1995). Sociodynamics: the application of process methods to the social sciences. Chaos Theory and Society (A. Albert, editor). I.O.S.Press, Amsterdam, Holland, and Les Presses de l'Universite du Quebec, Sainte-Foy, Canada. 65 Sabelli, H. C., Plaza, V., Vazquez, A., Abraira, C , and Martinez, I. (1991). Caos Argentino. Chicago, IL: Society for the Advancement of Clinical Philosophy (SACP). 66 Materialism and idealism give absolute primacy to either matter or ideas. Either the simpler material processes are considered fundamental (e.g., social problems have an economic origin, psychiatric dysfunctions are biological illnesses), or the higher psychosocial processes are recognized as having primacy (e.g. war, poverty, crime, are due to moral or ideological deficits, emotional dysfunctions result from character defects, disruptions of interpersonal communication, or defective cognitive/affective structures). 67 The heart supplies blood to the brain and the innervation of the heart by the brain generates biotic patterns.

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simple and complex levels they do not; for instance, social and neural levels do not overlap. There is also an essential difference between dyadic relations between opposites and triadic and multilevel hierarchies. One may conceive some of these informational relations in linguistic and in computational terms: Structures at the lower level are the alphabet that constructs the more complex level. The higher level is a program that shapes the lower level. Physics is the "hardware" of all other levels of organization. Chemistry is a program for physical entities. Life is a program for chemistry. Biological organization is software regarding chemical entities, and hardware regarding psychological processes. The hardware and software levels are clearly distinct, one precedes and creates the other, and then they interact through different types of forces. Yet the two levels have the same composition. The metaphor has many limits. To start with, computer software is relatively independent of the hardware. The same is not true for the mind. The brain contains multiple built-in programs. Further, biological processes generate psychological changes, as illustrated by mania, depression and drug intoxications; conversely, psychological function alters physiological metabolism and even anatomical structure.68 9.9 Generators The central concept of Creation Theory is the production of diversity, novelty and complexity by the interaction of simple generators. Just as embryological development is initiated by a structurally encoded information (genes) and creates unique individuals, physical evolution starts from a set of relatively simple mathematical forms (generators) embodied in elementary physical processes that function as a "cosmic genome".69 These generators may be attractors in the physical sense of the term (Section 3.5) and are portrayed by the attractors found in the 68

For instance, learning fosters neuronal development even after maturity, while trauma at age two, common among depressed persons, may interfere with the development of neuronal pathways involved in the regulation of mood, facts that have practical clinical application. 69 Sabelli, H., and Carlson-Sabelli, L. (1996). A cosmic gene? A biological model of complex systems. In honor to James Miller. Proc. International Systems Society. 40th meeting, Edited by M. L.W. Hall. Pp. 531-542.

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process trajectory. A theory of processes focuses on change (kinematics) rather than forces (dynamics) and therefore regards attractors as generators of action rather than as stable patterns. In mathematics, a higher dimension is generated by dragging a geometric object in another dimension (e.g. dragging a point generates a line, dragging a line generates a plane). Similarly, in physical processes, each action propels flux in one direction, generating one asymmetry or dimension. One attractor generates unidirectional action, not equilibrium (point attractor). Two generators create an opposition, which may be linear (equilibrium) or nonlinear (catastrophe or bifurcation), and thereby create information; their repetitive operation produces catastrophic developments (Chapter 2). Three attractors produce chaos (Poincare). Four or more attractors appear necessary and sufficient to produce bios and infinitations. In the same manner, we speculate, multiple attractors may generate more complex processes, such as physical, chemical and biological. Matter, I speculate, is the tridimensional equilibrium of (at least three pairs of) opposite attractors. Natural processes appear to involve triads and tetrads of generators that create chaos, bios, and thereby physical processes and structures. The number of generators establishes a hierarchy of patterns of organization from simple and linear to complex and fractal. Complexity is a function of the number of interacting generators. Number archetypes are generators. One may thus regard generators from several (non-identical) perspectives, including numerical (Section 9.10), algebraic (Chapter 10) and physical: 0-directional energy flux, unidirectional action [energy and time], bi-directional communication, which is the minimum of information, and tridimensional space. Generators appear as qualities, and qualities may be regarded as dimensions. Processes are generators, and qualities are aspects of a process, not passive properties, but components of its generator. We may thus regard them as forces, either unipolar or bipolar. Among the latter, we need to consider convergent or divergent cases. Convergence increases energy, information and mass, while divergence reduces them. The coexistence of convergence and divergence produces the concentric spheroid shape of systems, such as cosmological systems centered on

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black holes, constituted by mutually attracting galaxies, and separating from more distant galaxies. Each body consists of a material core, a surrounding energy field of energetic interactions, and radiating field of information. Notably, black holes, defined by their swallowing up energy, information and mass, have been shown by Stephen Hawking to radiate energy: opposites are inseparable. Table 9. 1 Generic Processes Dimensions Levels of organization

0OD D

1_D ID

2D D

3D . Structuration

Flux

Action

Information

Defining process

_ Continually . reversing change of energy

. Directed . change of energy and time

Co-creating by . pairing (matching) or bifurcating . (diverging)

Examples

Vacuum state, heat, normally distributed distributed ,, .. populations populations

Physical and biomolecular molecular asymmetry asymmetry (Pasteur) (Pasteur)

„ • Representative samples

, OT i Shuffled copy

• Time series

Bourbaki's mother structures of mathematics

Set theory and probability

. Lattice theory

Transiently stabilizing, conserving, Creating nucleating and expanding Matter and . energy fields; Spin, radiation primary colors; waves, Systems and quantum harmonies, organisms harmonies, organisms chromochromopolarities polarities dynamics; dynamics; .. atomic atomic orbital; orbital; Series of Series of >T N-dimensiona. repetition aiiierences differences vectors and differences of or differences 4 dimensional ,. . bios, 3 dimensional Group theory . and higher topologies . dimensional , . topologies topologies

S t a t i C

Measures Measures

Prototypic change

(mean, Auto(mean, Autodeviation, correlation, deviation, correlation, etc.) consecutive etc.) consecutive and and process process recurrence recurrence statistics statistics Ordered Ordered sequence Variability „ . of units (chance) (mertial causality)

ManyD Many D Organization

XT

•• ,-„ jj ,-„ Rise, Rise, fall, fall,. and and Proportion, . Proportion, consecutive consecutive rise-fall sequenc rise-fall sequenc repetition repetition

Externally , . , determined ,,. ,. „ (linear causality)

„ ,, . , Stable triads

1^

Novelty, A A nonrandom nonrandom .. complexity, complexity, transient transient complexes, complexes, Autogemc . „ (spontaneity)

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Qualities or dimensions are thus factors or agents in processes of change, which are portrayed as "parameters" in mathematical recursions. Unipolar energy is the bifurcating parameter of catastrophes and the gain parameter g of biotic recursions. Bipolar information is the asymmetric parameter of catastrophes and the biasing parameter q of biotic recursions. Generators are forms that form, producing novelty and complexity as well as simpler attractors. An attractor is the low dimensional (macroscopic) form of a basic generator as portrayed by a low dimensional (macroscopic) portrait of the trajectory formed. Complex processes show greater rate of creation, meaning greater diversification, greater novelty, and greater responsiveness to input. The complex form thus served to promote change. A feedback from the complex to the simple functions as a telic attractor that creates pattern. This is a new concept to be explored. Greater complexity means greater local density of information. Information multiplies the power of action. Further, information represents a form of causation, namely implication, at the mental level; the cyclic engine of mental creation is composed by two complementary opposites: energetic causation and informational implication. 9.10 Numerical Principles Numerical properties are significant properties of generators. Individual numbers are archetypes (principles). The time series of numbers from 1 to oo is an arithmetical model of evolution: small integers have priority and infmitation has supremacy. The generation of the number series portrays an important aspect of the generator of evolution, because actions create quantity. Unidirectional action, two-dimensional opposition, tridimensional structure and five-dimensional bios are universal cosmic forms and psychological archetypes, and their interaction generates variety and complexity of organization. There is no zero. The absence of zero is flux, or energy. One as form is manifested as oneness of composition of physical and mental processes, the discreteness of units, the unidirectionality (asymmetry) of time, sign and

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structure, the uniqueness of each entity, and the universality of time, space, and level of organization. One is many and many is one, said Heraclirus. All reality, both physical and mental, is part of one unidirectional process which both unifies the many, and diversifies each one. One is linked to action, just as twoness is linked to information and threeness to structure. Twoness is another universal numerical form in both physical and psychological space. It is in our body and our brain: we see with two eyes, hear with two ears, walk in two legs, and think with two hemispheres. Physical waves, positive and negative electromagnetic polarities, chromosomal pairing, physiological cycles, bipedal walking, and conjugation in aromatic molecules exemplify the alternation between two opposite states. Difference and change imply twoness. Information is difference; the difference between two equally probable outcomes defines the unit of information. Binary notation suffices to code information in computers. Traditional as well as Boolean mathematical logic use only two values, true and false. Group theory, a second pillar of mathematics according to Bourbaki, studies the relation between opposites (an element and its inverse), and the more complex systems of symmetry they generate. Why is twoness so essential? Because 0 and 1 are idempotent. 0°° is still 0. I00 is still 1. Only two generates something different when repeated. Threeness is a generic form that reoccurs at all levels of organization. Trifurcations are rarer than forkings, but they are fundamental. Physical space has three macroscopic dimensions. Every entity has three aspects, energetic, informational and material. Threeness seems crucial to organization: material structure has three dimensions; the triangle is the only architecturally stable polygon. Mathematically, three bodies produce chaos (Poincare), and Sarkovskii's remarkable theorem demonstrates that period three implies periods of any order, an infinite sequence of marches towards infinity ("infinitations"), and chaos. Ordinary matter is made of three components, quarks, leptons and bosons. Three quarks assemble to make protons and other hadrons.70 70 Patterns in light atomic nuclei can be described from the approximate equivalence of the two particles —the proton and the neutron— that makes them, as described by a group labeled SU(2). Somewhat broader and less evident patterns can be described by considering four nearly equivalent

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Triplets code DNA hereditary information. Many other examples can be presented.71 Each new level of organization starts with the repetition of the simple and universal principles represented by the small integers, and it is characterized by new and higher dimensions. Prime numbers represent novelty in the number series. The power spectrum of the prime numbers contained in the successive intervals of equal length 1=216 =65536 up to N=238 ~ 2.749 x 1011 displays 1/f3 behavior with the exponent |3 ~ 1.64.72 This slope beta does not depend on the length of the sampled intervals, suggesting some kind of self-similarity in the distribution of primes. Notably, the exponent (3 is similar to that observed in mathematical bios. Small integers appear to be universal up to 4; larger integers are common, and larger numbers are rare. There is no actual infinity but complexity and diversity continually increase. Infinity is not actual (Cantor) or potential (Aristotle) but is continually being created. One may thus speak of the priority of small integers and the supremacy of infinitation.

particles --protons and neutrons with spin up or down. However the existence of a great multiplicity of strong interacting particles (baryons and mesons, collectively called hadrons) presented a problem: can there be that many "fundamental" particles? The very idea of "elementary" particles implies that there be few of them. Here enter Gell-Mann and George Zwig who independently proposed the existence of three fundamental quarks, the combination of which generates the multiplicity of hadrons. Quarks are the fundamental building blocks of matter. Quarks are real entities but they do not exist as separate, independent particles in our universe; they only exist in combination. All the heavy subatomic particles (baryons) are combinations of three quarks. The force-carrying mesons are made of two quarks. There are three fundamental properties of quarks "upness", "downnesss" and "strangeness", each of which has an opposite, anti-up, anti-down, and anti-strange. Three types of quarks in various combinations make all the protons and their relatives; for instance, two up quarks and one down quark make up the nucleus of hydrogen, the principal raw material of the universe. Anti-matter is made up of anti-quarks; for instance, an anti-proton is made of two anti-up and one anti-down quark. Mesons are made of the combination of opposites, one quark with one anti-quark. 71 Mother, father and child make the nuclear family. Many models of psychological processes (Freud's id / ego / super-ego; Pierce's I, Thou and It) are tripartite. Philosophical categories are organized in triads for Kant, Schilling, Hegel, and Pierce. Many laws of nature, such as Coulomb's V=I.R and Einstein's E=mc2 relate three variables. Modern constitutions provide for a tripartite division of executive, legislative and judicial powers. Many religions propose a Trinitarian concept of God; in Greek mythology there were 3 Fates, 3 Furies, 3 Graces, and Paris had to choose between 3 Goddesses. There were three Wise men, three musketeers, and three stooges. The conjugation of verbs includes three persons (I, you, them) and three basic tenses (past, present and future). There are three fundamental types of reasoning, induction, deduction and abduction (Eco, U. and T. A. Sebeok. The Sign of Three. Dupin, Holmes Pierce). 72 Wolf, M. (1997). 1/f Noise in the Distribution of Prime Numbers. Physica A , 241:493-499.

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The evolution of a complex system could be understood as a local process of dimensiogenesis, starting from relatively low dimensional physical processes. Biological, social, and psychological processes may represent the emergence of new dimensions portraying information and organization. These additional dimensions may originate in non-linear interactions, just as a tridimensional catastrophe is created by competition between point attractors. Evolution may be regarded as a process of morphogenesis and dimensiogenesis, starting with the universal forms 1, 2, 3, and their consequences 4, 6, it, and growing without bounds. In addition to these integers, we have already discussed irrational and transcendental numerical archetypes that maybe a fundamental source of novelty and complexity in nature (Chapter 10). 9.11 Fractality Creativity implies novelty, but also involves repetition and fractality. A new level of organization emerges with the appearance of new units of organization, new fundamental oppositions, and new processes of creation. Levels of organization are thus fundamentally different, and also are fundamentally similar. First, they are made of the same substance. Second, each level, is formed by, contains, and fractally reproduces lower levels of organization. Generic forms (archetypes) reoccur at each level of organization. Third, as simpler processes are the substance for higher levels of organization, the latter necessarily comply with and reproduce the patterns of simpler levels. Fourth, processes at the more complex level organize the temporal and spatial distribution of actions at the lower level. The simple is the substance that constitutes the complex; for instance, psychological processes are encoded by sequences of action potentials, and organize their temporal and spatial pattern. The simple encodes the complex and the complex organizes the simple; the new forms generated at higher levels become imprinted upon the lower levels insofar as they materially overlap. Accordingly, the lower and the higher levels -such as the timing of the heart and the behavior of the organism -must have each other's form. Physical laws are operational around and within biological organisms, and biological organization is

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imprinted in the physical body of the organism. These fundamental similarities among levels of organization bring about fractal-like organization. In summary, levels of organization are fundamentally similar to each other as well as fundamentally different. Also, basic forms are universal. Each principle contains in itself the others: actions include twoness (energy and time) and occur in tridimensional space; oppositions are actions and display the triadic organization of color. Materialization is the equilibrium of opposite actions, and creation includes its opposite, destruction. Finally, each principle applies to itself: the universality of action implies that actions change themselves (autodynamism); the universality of opposition implies that opposites are similar and different, harmonious and conflictual. 9.12 A Comparison of Theories Process philosophy originates with Heraclitus, as recognized by modern theorists from Hegel and Engels to Thom and Prigogine. Its various formulations ranged from cyclical creation and destruction to progress to decay towards entropic disorder. The discovery of novelty and bios have led us to our current reformulation, Creation Theory (Table 9.2). As information is given by repetitions and differences, a theory is better understood by comparison with other scientific theories of processes philosophies (Table 9.3). This is readily accomplished in the case of dialectic materialism that is formulated as a series of "laws", and for the aristocratic view of nature that celebrates biological (Darwin) and economic (Smith) competition, and in its most extreme forms proclaims that God is dead and celebrates the emergence of superman (Nietzsche), in the same dark mood that announces apocalypse as entropic disorder. The Greek founders of science regarded the universe as alive and creative, and organized by relatively simple mathematical forms -the logos. In the bios model, the universe is alive, and emerged from a mathematical "seed", Bourbaki-Piaget's mother structures of mathematics, as discussed in Chapter 10.

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In summary, the Co-creation hypothesis73 proposes that the universe spontaneously evolves from necessary mathematical relations (lattice order, group inverse, topological continuity) (Chapter 10) embodied as action, opposition, and tridimensional space. They create generic patterns (steady states, periodic cycles, chaos, and bios) at all levels of organization. In a similar manner, they may generate relatively stable structures, such as matter, and evolving higher dimensional organization (chemical, biological, social and psychological), and beyond towards an attractor of infinite complexity. A determined creation of complexity contradicts the notion of unavoidable decay to entropic disorder (Chapter 11). As creation is the spontaneous result of interaction, the universe evolves towards an infinitely complex attractor (Chapter 12). Causation is a process, not a single event, both determined and creative, and including both general patterns and individuation. This is what we call creative development. Co-creation represents an alternative to the notion that conflict drives biological evolution (Darwinism) (Chapter 13), economic progress (standard economics) (Chapter 15), and human history (Marxism) (Chapter 16), beliefs that can undoubtedly foster conflict, but it also contradicts the portrait of systems as integrated and homeostatic (Chapter 14). It offers an alternative to the two main currents of thought in contemporary science, determinism that dominates mechanics, psychoanalysis, economics, and chaos theory, and probabilism that dominates statistical and quantum mechanics as well as biological evolutionism. Socioeconomic as well as psychological development are creative processes, in which branching generates cultural diversification, personal individuation, and pathological bifurcations. There are no iron clad laws of history, or of economics. All development is creative, and human action is also conscious. The future is partially determined, and partially a matter of choice. Each person, and each country, must choose an avenue for evolution, and needs not follow the patterns set by others. Further, development is bipolar, simultaneously generating growth and decline. There is a dark side to progress; economic development frequently means increased exploitation

73

Sabelli, H. (2001). The Co-Creation Hypothesis. In Understanding Complexity. Ed. by G. Ragsdell and J. Wilby. Kluwer Academics/Plenum Publishers. London.

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and misery for many. In contrast, standard models of development postulate a determined linear sequence of stages; "underdevelopment" explains national poverty, and likewise psychopathology results from developmental arrests and regressions. Table 9.2 Greek Physiology, Process Theory and Creation Theory Process Theory

Greek physiology

Creation Theory

^

(2004)

Dynamic monism: fire, river and 3 states of matter

energy, Information and Matter

. . Tension of coexisting opposites

^. , . . Diamond of Opposites Coexistence of synergy . and antagonism _

. Action as denned in quantum physics _ Bipolar feedback Symmetry for bios Non-correlation of opposites Qubit (tetrad)

War as Father and Harmony as Mother

Co-creating opposites

Parental model of causation

Priority of the simple,

Becoming . Enantiodromia Number archetypes Logos „ ,. , .., m ... . God is a child (Herachtus)

Hierarchical feedback

supremacy of the complex Thermodynamic . . enantiodromia Number archetypes Catastrophe and chaos models |

„ , _ _ . God as Supreme Becoming

Thermodynamic enantiodrorma 1, 2N , 3 Attractors /generators Generator equations I

An Infinite and Personal Attractor of Evolution

Let me now consider the union of opposites as a personal and social philosophy, from the perspective of Taoism, which, as Greek physiology and modern science, regards the laws of nature as the best criterion for human behavior. Tao is a name for the laws that govern the universe — the Greek physiologist Heraclitus called it the Logos. Physical laws influence all actions and all thoughts. The laws of nature control existence and evolution, and directly affect the ways in which individuals tend to behave and societies tend to evolve. Thus, understanding these laws gives power (te) to bring harmony into the world.74 Natural law is neither evident nor determined. Thus it is necessary to respect the

74

Rhee, Y.P. (1996). Synthetic Systems Theory: Linkage between Western Theory of Physics and Eastern Thought. 40th annual meeting of the Int. Systems Science Society. Louisville, Kentucky.

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unknown patterns of nature, and to allow for unpredictable events, and for second chances. There is creation everywhere. Thus it is necessary to act. Tao is energy. Although Taoism portrays everything as changing, it paradoxically advises no action. What does "no action" mean in Taoism? If everything is a process, including the self, how can there be "no action"? And how can there be no resistance? How can there be progress, or learning, without resistance? A new idea, particularly a new perception of our personal world, always elicits resistance. Given the paradoxical style in which Taoist ideas are presented, there is room for mistranslation and misunderstanding. "No mind", "no action", "no desire" are paradoxical statements. "No action" means intense concentrated action without allowing unrelated thoughts or ideas interfering with the moment of being. "Desireless" means perceiving the world as it is, rather than through a screen of presuppositions and wishful thinking. This is a goal, but can only be accomplished through the recognition that perceptions are always influenced by our selves and our actions, because perceptions are actions, implying the application of energy for a duration of time. "No action" means to avoid forceful action. Action without reflection is a mere reaction, in which the self loses its protagonist role, its spontaneity. It is unwise to oppose the laws of nature because such resistance fosters the growth of the force it opposes. Excessive force in a particular direction tends to foster the growth of its opposite. An obvious and aggressive attempt to gain power and position can produce an opposite consequence. Evolved individuals, asserts Rhee, act when situations are in their smallest, simplest, most unentrenched, and least reactive state. In contrast, chaos theory supports the notion that change can be more readily influenced when the system is in chaos, the most reactive state. Our clinical experience points to a union of opposites: simpler emotional change is easier to accomplish by affecting the most reactive state, while complex intellectual insight often requires a cool head. Adopting a law of nature as a rule of behavior, in the spirit of Tao, one could say that neither strong action nor no-action are possible, while least action is desirable.

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Bios Table 9.3 A Comparison of Creation Theory with other Process Theories Creation theory Comprehensive theory; mathematical models Action as sole constituent of universe

Standard dynamic views Mathematical models; -no comprehensive theory Energy, information and matter as three components

Opposition: universal, creative, . . 2N attractors synergistic and competitive, evolving (from quantum superposition to local no contradiction to global contradiction)

. . Mathematical dynamics: cyclic attractors _ Physics: Quantum .. . . superposition of opposites . Logic: no-contradiction

Enantiodromia

Evolution or decay as contradictory hypotheses Equilibrium, periodicity, chaos Biological and economic competition

Action, period 2N, 3, chaos, bios Harmonic, conflictual and cocreative opposition Co-creation: bifurcations and Random creation and selection generation of patterns by . . . . , . „ , (Darwinian models) bipolar feedback Numerical archetypes of quantity, , , ,. _. . . , . order and quality. Biotic expansion. Focus on scale-free fractahty Dimensiogenesis Three inseparable aspects of each entity (action, information . . . Physical reductionism, and matter). . . , . , , . . „ . . , . . , „ sociobiological determinism, . . Priority of simple, supremacy of economic determinism complex: Priority of objective, supremacy of subjective Entropic disorder as . , . . T _ . Infinite Attractor end stage of universe , „ , . „ , , (Clausius, Boltzmann) Infinite Attractor and Supreme Agnosticism, Theism, or Becoming as images for Divinity God is dead (Nietzsche)

Dialectic materialism Comprehensive theory; verbal formulation Change is universal and autodynamic* Unity of Opposites: . . . . universal, mainly struggle, ignores superposition, , , ... excludes no-contradiction, . . • , , unity is transient, leads to , . , . synthesis or predominance of one . . Change is mainly progressive Negation of negation** Class struggle leading to abolition of classes Synthesis Transformation of quantity into quality and vice versa _ Philosophical matter (energy-matter) Ontological materialism Historical materialism Epistemological materialism *** No hypothesis regarding evolution of universe Ath e s im

* This is not one of the three laws given by F. Engels. The French philosopher G. Politzer added it. ** Soviet Marxism specifically suppressed this law perhaps because it predicted that after socialism there would be a return to a capitalist-like system. *** Materialism is formulated as ideology added to the laws of dialectics.

Students of Buddhism meditate on the clapping of one hand. The answer to the riddle is simple: to clap one needs two hands. The one-hand

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clapping riddle serves to convey the fact that opposites always coexist. Sexes are paradigmatic of yin and yang. Taoism speaks of yin and yang, but has been coexisting for centuries with the oppression of women. One cannot blame Taoism for social customs, but one cannot help to wonder about its meaning for those who find it compatible with sexism. Sexism is embodied in the description of yin and yang as two classes, thereby associating masculine and feminine with positive and negative traits. Creation Theory highlights that there are multiple, different pairs of opposites, such that their division do not coincide. Some traits may be more commonly associated with men than with women, but they can be greater in particular women more than in most men. Further, opposites are inseparable: masculinity and femininity coexist in every person -just as every object has a right and a left side. Tao is a social philosophy. Power is available to those who align themselves with the current influence of the Tao. Intellectual integration with the laws of nature allows evolved individuals to position themselves effectively in the world, states Rhee, 1996. Inflexibility in belief or behavior leads to failure. Dominance rewards following the Tao. This view glorifies success and thereby emotionally supports and intellectually justifies dominant classes that often are oppressive. Conflict and defeat often reward pioneers who help create a better world. Opposing the Tao makes for a difficult life path. Lao Tzu stressed that social action must be taken in accordance to the laws of nature. John Stuart Mill argued that the maxim "follow nature" fails to provide a guide for social action, as it offers at least as much evil as good. Justice is not natural, but a human creation. Tao is also an emotional serenity. So I ask myself, what is walking with Tao? I want to refer the reader to "Tao of the Mountain", a not well-known, and perhaps even apocryphal, chronicle, written by Lao Tzu, a custodian of the Imperial Archives during the Chou dynasty, as his last gift to men, from whom he was departing, full of disappointment and sorrow. A gatekeeper persuaded him to write down his teachings for posterity, when he rode into the desert to die.75 75

Sabelli, H. (1998). The Union of Opposites: from Taoism to Process Theory. Systems Research 15: 429-441. Republished: The union of opposites: North and South, East and West, Korea and

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The Tao of the Mountain A man came over the mountains that Lao Tzu had crossed when he left the land. He carried with him a few torn pages of what once had been beautiful calligraphy. An old man said it was Lao Tzu's writing. A scholar said that Lao Tzu was only a legend. A child asked: If Lao Tzu was a legend, who wrote Lao Tzu's poem? The man did not know who Lao Tzu was. He only knew of a very old man who sometimes lay for a long time with ache andjoy in his heart, and strife in his soul, before he won sleep. "When I was young ", the man had said, "my life had been a reckless determination to achieve something at any cost, so I climbed a perilous mountain. There were no trails, and there could be no stops. When I reached the top I felt my determination resolve itself into an adventure worthy of all my effort, and keenness of eye, and cunning of reason. I felt no anger, no rush, nor was I spurred by desire or by rivalry, so I sat down and saw the flow of nature that my wise grand-mother called the Tao. The sight of these mountains recall to me the days, not really long past, when I walked into the villages, and spoke of the Tao. In the palace, men who aspired to honor were servants. And then a few more days went by, my lifetime. Men realized I never would achieve distinction. They heard my voice echoed by rocky mountains and muted by deaf men. Ifelt my soul on fire, pregnant with words and images. They saw I was an old man, and still wanting in soundness. They said: You have reached the age of honor.' I made them uncomfortable, I was too intense. When I discovered a new truth, they reminded me of what I have taught before. They said, 'You contradict yourself. 'Do I contradict myself?', I replied, 'So I do contradict myself!' They reminded me of the balance of justice, and wanted to equilibrate my fire with water. 'Do you still love women?', asked me a priest. 'Do I still love women?', I responded, Do you still love roses?' I rode to the mountain to savor in solitude my joy at having touched, even briefly, a truth. My soul was on fire, I could not stop writing. I left some verses with the keeper of the city gate. He thought that I was full of bitterness, that I rode into the desert to die. The desert was kind to me, and what had been a clear resolve to rest and age, turned into an adventure worthy of all my effort and keenness of eye and cunning of reason. Rain made the desert flourish with color and life. Water sustained life, life sustained life, and action raised my spirit. I found myself climbing a mountain again, its gentle slope a challenge to my ageing limbs, a welcome awakening. In the desert I hadfelt the night's loneliness. I lived as an outcast, a lone wolf, by my own choice, yet also longing for the touch of a hand and the sound of a voice, even then, when my life had turned useless, and my soul was filled with strife. Yes, there was some bitterness, my doubts. Had my wisdom been wisdom at all? Had I brought unhappiness to myself and to others by portraying a ruthless heaven and a ruthless earth, where wisdom sprung from lack of action and lack of compassion? My old habit of doubting swept away my quiet once again, but from it evolved a subtle change. Day by day my limbs gained strength. As I climbed higher, the effort seemed to drain away my bitterness. I breathed harder, and each breath renewed my spirit with mountain air. I struggled with a storm, and welcomed the sun when it arrived.

Americain Toward New Paradigm of System Science._P. Y. Rhee editor. Seoul: Seoul National University Press, pp. 251-274.

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The air was colder. One by one my friends, the flowers, then the pines, left me. As in the desert, yet, life grew all around me, moss in the rocks, and small insects, sometimes a lizard. Fresh from the storm I thought that the moss and the lizard were tenacious, having so little to live on, yetfastening to the stone, laboring, grasping, gasping, withstanding, struggling to endure. Then I regained my child's eyes, and I saw that life is easy, springing as soon as a drop of dewfertilizes the stone. Life is easy, but not effortless. This is what I wrote. Take my verses, young man, to the men who lived beyond the mountains and across the desert, tell them it is the Tao I saw in the mountains." "No. He never told me his name," the traveler said. "The Tao, he told me, has infinite names." One The Tao is a story never told, always telling.

free

The wise are ruthless, from compassion. The mother is not ruthless.

One are the heavens and the earth,

The hero is not ruthless.

the heart and the soul,

The sage is not wise.

woman and man, light and darkness, matter and void. Two Two are the heavens, two is the earth, two are mother andfather, in two is divided my soul. The ten thousand things The Tao is one.

The grass lives by bending to the wind and hoof. The arrogant tree struggles helpless against the storm. The sand of the desert yields to the winds, and buries the caravan of men. The mountain elevates its peaks defiant, but wind and water bring it down, inexorable. The wise yields to the wind. Thefools resist the Tao.

One carries two. Two begets three. And three begets the ten thousand things. The ten thousand things carry yin andyang. They create anew.

The tree and the mountain are fools. Mothers arefools. Heroes are fools. Wise men inhabit palaces. The fools die young,

Wisdom The warrior is ruthless. Do not invite the fight. The wise are ruthless. They rule the earth by collecting treasures andpreventing the hungry from stealing, by weakening the desires and confusing the heart, by breaking bones and keeping bellies empty.

and sow the earth. Do not invite the fight. Accept it instead. Mountain The legs of the traveler struggle with the mountain, and ache, but the moss covers the rock, effortless. Blessed be the poor who keep their spirit.

When people lacked knowledge and desire I did not interfere. Nothing was done, all was well. My heart was bitter.

Whatfalls down mustfirstraise. Only the Tao ofHeaven is impartial and stays with good men to the end.

Chapter 10

Mathematical Genesis

Abstract: Bourbaki demonstrated that mathematics can be generated by three "mother structures", lattice, group and topology. Piaget discovered these same generators in the psychological development of children. I1 proposed that lattice order, group opposition and topological transformation are embodied as action, information, and material structure at the physical level. They are also the generators of primordial processes at each level of organization. Quantum flux Is molded and steered by necessary mathematical relations to form action, information and matter

Infinite attractor / Mind f

Algebraic Necessary structures relations

/ Life

Topology

Continuity and bifurcation

Group

Symmetry including apposition (inverse)

Lattice

Asymmetric and transitive order <

Set

Inclusion

I

I

/ Hatter

*s •§.

|

y

/ Information

/

/ Action

Flux

time sequence Revolution) '"

»

•«'

spatial extension and temporal duration

Fig. 10.1 Levels of organization evolve from simple to complex. The simpler levels have larger spatial extension and duration, starting with flux, which is universal, and becoming increasingly more local and transient as they become more complex. The fundamental mathematical structures are defined by simple necessary relations and correspond to simple aspects of physical entities. 1

Sabelli, H. (1989). Union ofOpposites. Lawrenceville, VA: Brunswick. 410

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Mathematics is a natural science that describes the most general forms of processes in nature and mind. Mathematical forms constitute the simplest level of organization because their validity does not require the existence of physical entities. Mathematical relations are logically necessary: 2 plus 2 is always 4, regardless. Being necessary, mathematical relations are universal in time and space. Fluxes in the void as well as all other physical entities necessarily embody the fundamental mathematical forms of set, order, opposition, space, and number. It is proposed that the embodiment of mathematical form by the ever-present flux generates reality. Form distinguishes existence from the void. The interaction of groups of actions generates episodic, diverse, novel, and complex patterns. The small integers and irrational numbers such as e, n, and cp are simple universal archetypes; creation involves the generation of higher dimensions. These hypotheses represent a specific formulation of the concept of generic, archetypal numerical and geometric forms advanced by many thinkers from Pythagoras and Galileo to Godel, Pierce, and Mandelbrot. Archetypes are creative engines. The gene is, in my view, an appropriate metaphor for this concept.2 Cosmic forms serve a "boot-strapping" role to create new and complex processes, just as genes serve to develop organisms, and innate psychobiological action serve to generate more complex behavior. Natural processes and structures display mathematical forms. The logistic equation, fractals, and cellular automata have demonstrated how simple mathematical processes can generate complex and unpredictable outcomes. Biotic recursions show that simple processes involving action, bipolar feedback, and conservation generate creative features such as novelty and complexes. It is thus cogent to ask ourselves how does the mathematical structure of natural processes contribute to their creativity. Such a mathematical model could describe in an abstract manner fundamental processes at all levels of organization. Prima facie, it seems incongruous to consider the possibility that mathematical structure creates reality. Consider, however, the standard model of particle physics that combines quantum mechanics and special 2

Sabelli, H. and Carlson-Sabelli, L. (1996). A cosmic gene? A biological model of complex systems. In honor to James Miller. Proc. International Systems Society. 40th meeting, Louisville, Kentucky, July 14-19. Edited by M. L. W. Hall. pp. 531-542.

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relativity. The model is widely accepted because no significant deviations from it have been observed despite intense experimental testing. The model includes 16 fundamental particles, all of which have been discovered. However, the standard model requires them all to be massless, which is clearly false.3 An additional particle, the Higgs boson is postulated to be responsible for a mechanism by which all other particles acquire mass.4 In a similar manner, a mathematical model that describes fundamental processes at an even more abstract level than the standard model of physics, may acquire physical embodiment. I propose that the ever-present quantum flux provides physical substance to mathematical forms. 10.1 Mathematics as a Natural Science Mathematics is a natural science that describes the most general forms of processes in nature (Galileo) and mind (Piaget). Mathematics deals with reality, postulating axioms believed to be true and confirmed pragmatically by the empirical truth of the theorems derived from them. It distinguishes itself from other natural sciences only in that it obtains very few concepts and relations directly from experience, and infers from them the laws of more complex phenomena by purely deductive means. The idea of securing knowledge by logical deduction from unquestionable principles was explicitly proposed by Aristotle, and succefully applied by Euclid in his Elements and later on by Galileo, Newton and their successors. From its inception in ancient Greece, and again in modern times, science adopted a mathematical interpretation of nature.5 This is not arbitrary, proposes psychologist and mathematician Robin Robertson.6 Einstein wondered how it was possible that mathematics, a product of human thought, so admirably described reality. Mathematical science is "unreasonably effective" in describing 3

Renton, P. (2004). Has the Higgs boson been discovered? Nature 428: 141 - 144. Higgs, P. W. (1964). Broken symmetries, massless particles and gauge fields. Phys. Lett. 12: 132133; Higgs, P. W. (1966). Spontaneous symmetry breaking without massless bosons. Phys. Rev. 145: 1156-1163. 5 Randall, Jr., J. H. (1940). Making of the Modern Mind. Boston: Houghton Mifflin Co. 6 Robertson, R. (1989). The evolution of number. Psychological Perspectives 20: 128-141; Robertson, R. (1995). Jungian Archetypes. York Beach, ME: Nicholas Hays.

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physical reality.7 Mathematical science accounts for, and predicts, natural processes; e.g. calculations almost precisely determine interplanetary travel. We can calculate with surprising accuracy. We can demonstrate with certainty properties of numbers, geometric figures, and abstract algebraic structures, suggesting that these products of our minds also exist objectively. Mathematical science must then describe the mathematical forms of nature; it cannot be just a human invention. Through mathematics, the human mind must undoubtedly come into contact with fundamental physical processes. A very limited period of mathematical development (numbers were invented a few thousand years B.C. at the earliest) has proved sufficient to encapsulate many fundamental laws of nature. Moreover, we can learn this fundamental mathematics in a fraction of our own life span! Undoubtedly our learning abilities must be connected with the fundamental mathematical forms of the cosmos. Mathematical thinking discovers nature. Numbers constitute a universal alphabet. We may speak different languages, hold different beliefs, idealize different heroes, but we all agree when it comes to numbers. Number is a paradigmatic example of the fit between physical reality and psychological processes. In his 1933 Oxford lecture, Einstein highlighted the physical, empirical nature of mathematics by inviting us to consider Euclidean geometry as the science of the possible mutual relations between practically rigid bodies in space -in other words, to treat geometry as a physical science, without abstracting from its original empirical content.8 Without considering geometry as a natural science, Einstein adds, he could have never formulated the theory of relativity. Supporting the view of mathematics as a natural science that describes the logic of nature, mathematics often pre-discovers physical reality. Dirac's equation predicted the positron.9 Mathematical forms are objective forms of natural processes and structures; they are not just mathematical concepts developed in our mind. The objective mathematics of the universe is reproduced in the 7

Wigner, E. (1960). The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Comm. PureAppl. Math. 13:1. 8 Einstein, A. (1954). Ideas and Opinions. New York: Wing Books, p. 272. 9 Farmelo, G. (2002). It Must Be Beautiful: Great Equations of Modern Science. Granta Books.

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"subjective" mathematics discovered by human minds. A "mathematical form" describes in an abstract manner patterns, shapes and structures in the universe. Generic forms ("ideas") have an objective existence as physical properties, shapes, relations, and dimensions. The fact that natural forms are portrayed by abstract mathematical concepts suggested to Pythagoras and Heraclitus, and later to Galileo and modern scientists, that there is a logic to the universe, a rationality, a logos. Human mathematics describes this logic of the universe. 10.2 Mathematical Priority, Psychological Supremacy We discover mathematical structures in nature. Mathematics starts with intuitions regarding number, space, and so on; these intuitions are uniform in many different people not simply because human beings are all approximately equal but because we all deal with the same external world. Fundamental mathematical endeavors, such as finding the relation K between the circumference and its diameter, display a compelling universality and uniqueness that marks them as discoveries. Arithmetic emerged from accounting, and geometry from surveying and astronomy. Mathematicians also invent forms that may or may not exist in reality. Do all of them represent forms actually occurring in nature? Or are there mathematical objects created by the human imagination? Some such mathematical inventions undoubtedly are mental constructions albeit not necessarily only in human minds. The wonderful world of multiple infinite numbers, for instance, seems to me a clear example. The development of non-Euclidean geometries in the 19th century suggested that mathematics consists in the exploration of the logical consequence of axioms regardless of their possible empirical validity.10

10 In his Foundations of Geometry (1899) David Hilbert considers three arbitrary collections of objects, which he calls 'points', 'straight lines' and 'planes', five undefined relations between them, and 20 axioms which are sufficient to characterize the said objects and relations up to isomorphism. This structural equivalence, however, can hold, between different, intuitively disparate, systems of objects. The formalist school of mathematics led by Hilbert, thus attempted to convert mathematics into a purely formal system in which its objects (numbers, points, sets) were to be defined solely by its axioms such that they were totally empty of content and without reference to the objective world. In contrast, the discoverer of non-Euclidean geometry, Lobafevskii, considered that geometrical truth, like other physical laws, can only be verified by experiment. Surprisingly, the universe appears

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The centuries long polemic between Platonists who assume that mathematical laws are discovered in nature and formalists who view mathematics as human invention suggests that both views reflect complementary sides of mathematical science. The concept of priority of the objective and supremacy of the subjective provides a way to understand this dual nature of mathematics: human mathematicians discover natural forms. There are two things that we call mathematics: the mathematical structure of nature that has priority and mathematical science that has supremacy. There are two aspects to mathematical science: discoveries and inventions. The mathematical structure of physical and biological reality has priority in the formulation of mathematical science, while human imagination has supremacy in constructing mathematical concepts that may or may nor correspond to physical reality as well as in deciding which ones we take at this time as true models of reality. The mathematical forms of nature are discovered. They exist before us; they have priority. We also transform them, and create from them new mathematical forms. This does not separate mathematics from other natural sciences. Physics does not cease to be a natural science because accelerators create new chemical elements besides those found in nature. 10.3 Mathematical Certainty and Biological Mediation Mathematical relations are both necessary and certain. They hold true whether or not there are natural entities that realize and actualize them. Two plus two equals four, with total certainty, in both natural processes and human reasoning. Physical processes cannot depart from the laws of mathematics, at any time or place. Necessary mathematical forms and relations are thus materialized in spatial structures and physical processes, and beyond in brain and mind. Mathematical organization has logical and hence temporal priority over the universe. Mathematical form is the simplest level of organization because it does not require the existence of physical entities. It also goes beyond to be Euclidean. This empirical refutation does not diminish the importance of non-Euclidean geometries, showing that mathematics is not only a description of reality.

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physics to include biological and psychological processes that in turn create mathematical science. The priority and universality of mathematics implies that in the physical universe, mathematical certainty is more fundamental than quantum uncertainty. As the necessary form of natural processes, mathematics has logical and temporal priority, informational certainty, and spatial universality. Mathematical forms arise from our bodily experiences; they abstract human actions, not only external forms. Other rational beings could experience differently from us, and thus develop a different set of "metaphors" which could equally well serve to understand certain aspects of nature. Could these reasoning organisms come up with an entirely different mathematics? Could aliens have invented a different geometry? An experiential view of mathematics has been advanced by the leading Swiss psychologist Jean Piaget.11 According to some Kantian philosophers, number, space and time lack objective reality, being mere categories imposed by our minds. This philosophical idealism does not follow from fact. Human experiences are objective: they are interactions with natural objects. Mathematical abstraction, as any other scientific concept, involves both object and human agent. The "subjects" are also objective/material/natural, and their actions are largely congruent with objective reality because they are intended to be efficacious. I thus regard the objectivist and the experimentalist views as complementary. It seems rational to accept that the mathematics of nature are certain, but what provides certainty to a mental process? What makes mathematical science certain? This is not evident. In fact, one should expect that some models would fit reality, however roughly, while others may be quite off the mark. Einstein quibbled that as far as the proposition 11 Chicago mathematician Saunders MacLane also proposes that mathematical ideas are abstract formal representations of human activities, such as counting (arithmetic), shaping (geometry), estimating (probability theory), proving (logic), grouping (set theory), etc. Berkeley cognitive scientist George Lakoff (Women, Fire, and Dangerous Things. Chicago: University of Chicago Press, pp. 355-361, 1987) also rejects the "objectivist" view of mathematics and replaces it with an experiential one. This experiential viewpoint seamlessly becomes subjectivism. Jungian psychologist Marie Louise von Franz (Jung, C. G., Franz, M. L., Henderson, J. L., Jacobi, i. and Jaffe, A. (1971). Man and His Symbols. Garden City, NY: Doubleday) asserts that in examining nature, "man encounters himself instead of looking for and finding objective qualities" (my underlining).

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of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. Human mathematics do not always fit nature. For instance, theories of infinity clash with intuition, and infinite quantities keep appearing in quantum mechanics and need to be removed by ad hoc mathematical means. Thus Polish logician Jaroslaw Mrozek12 proposes that mathematics is neither mathematical nor nonmathematical, but simply amathematical, to explain both the successes and the failures of applications to the natural sciences. To deprive nature of logic and rationality because we sometimes misinterpret it seems to me an exaggeration. The notion of priority of the objective and supremacy of the subjective resolves the issue of failures in human descriptions of nature. Because all perceptions and concepts are in part generated by our minds, they can be erroneous. But they are for the most part true reconstructions of reality. The explanation is that mind exists in the brain. Biology accounts for the fact that mental mathematics fits the mathematics of nature. American scientist Larry Vandervert13 explains: the human brain portrays the universe realistically because it has developed through evolutionary processes that encapsulate the world as neurological order. Mathematical structure is a most dramatic example of the homology between simple and complex levels of organization. Physical cosmic forms (Platonic ideas) are embodied in the human brain.14 The three dimensions of macroscopic physical space determine that the labyrinth of the ear has three orthogonal semicircular canals, and this in turn makes us perceive space as tridimensional. Perceptions and mathematical intuitions provide us with a reasonably appropriate, albeit certainly not perfect, picture of reality. While this notion is labeled "naive realism" against which one can raise scientific caution and ingenious philosophical arguments, nobody behaves based on contrary assumptions. Instead of arrogantly dismissing natural perception as possibly flawed, it seems prudent to learn from nature. 12

Mrozek. J. Did Einstein Claim That Nature Has Mathematical Structure? [email protected]. Vandervert, L. R. (1993). Neurological Positivism's Evolution of Mathematics. Journal of Mind and Behavior 14: 278; Vandervert, L. R. (1988). Systems thinking and a proposal for a neurological positivism. Systems Research 5: 313-321. 14 For an opposite view, see Davies, P. C. W. (1990). Why is the Universe Knowable? Science and Mathematics, edited by R. Mickens. Singapore: World Scientific. 13

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Numbers must be neurologically coded, no matter how vaguely, because infants15 as well as animals16 can differentiate between small numbers, and adults can perfect their use to extremes of precision, abstraction, and creativity. From these modest biological origins, numbers develop as concepts because we encounter numbers in real life. Counting, ordering and measuring are fundamental human actions, in both everyday life and scientific pursuits. Counting with stones (Latin "calculi") lie at the origin of calculus, just as measuring land is the origin of geo-metry. We learn of solids by touching bodies, of flat surfaces by looking at water, of lines by edges. We develop abstract concepts such as "two" through experience, as illustrated by the many different terms used to name concrete twosomes, such as couple, yoke, duo, pair, etc. The laws of algebra are learned unconsciously while performing ordinary arithmetic.17 Conceptual categories, in part genetically inherited, are subsequently developed as experience confirms, reinforces and elaborates on the simpler inborn patterns. With the progress of physics come new intuitions and hence also new mathematical structures. Intuition is not a mystical process, but a direct apprehension of a natural pattern. As perceptions, intuitions are often fallible, but they are also the source of evidence. The intuition of mathematical relations appears to have double roots in inherited psychological structures and in practical experience. Mathematics is thus capable of revealing truth because its ideal objects and processes aptly model real objects and processes. 10.4 Set Theory For much of recent history, set theory has been regarded as the foundation of mathematics. Set theory largely originates with a set of articles by Georg Cantor, published between 1879 and 1884, although 15

Wynn, K. (1998). Psychological foundations of number: numerical competence in human infants. Trends in Cognitive Sciences 2: 296303; Xu, F. and Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition 74(1):B1-B11. For an opposite view, see Feigenson, L., Carey, S., Spelke, E. S. (2002). Infants' discrimination of number vs. continuous extent. Cognitive Psychology 44:33-66. 16 Brannon, E. M. and H. S. Terrace. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science: 746-749. 17 Spencer-Brown, G. (1969, reprinted 1979). Laws of Form. New York: E. P. Dutton.

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Bernard Bolzano had already proposed the notion of set as the idea that we conceive when we regard the arrangement of its parts as a matter of indifference. This is contradictory to the notion of process. It may be possible to develop a different foundation for mathematics from a process perspective. Just as objects are modeled by sets, processes must be modeled by series, which are open ended in time, and hence varying in content. A theory of series is the process equivalent to the logic of sets. We thus view numbers as series, rather than as sets. Thus 0 is a flux, not an emptiness. Likewise, one should consider processes of infinitating but not infinite as an achieved set; infmitations may be regarded as multiple, insofar as they have different initial points -for instance, in bipolar feedback recursions, infinitations have multiple origins and are presumably directed towards different "endings". Although set theory is considered as the foundation of mathematics, it is flawed by paradoxes. Cesare Burali-Forti18 found contradiction in the fact that the ordinal number of the set of all ordinals must be an ordinal. Cantor discovered the paradox implicit in asking what is the cardinal number of the set of all sets. Russell and Zermello independently discovered "Russell's paradox." Yet in spite of its paradoxes, most mathematicians accepted set theory as an intuitive foundation for all of mathematics. In my view, the set theory paradoxes point to the need for new concepts. The paradoxes may disappear adopting a process rather than a static perspective in regarding infinity. 10.5 Bourbaki's Mother Structures of Mathematics Nicolas Bourbaki reorganized mathematics in a way that exerted considerable influence on researchers and educators all over the world for the ensuing decades.19 He created a logically ordered totality based

18 Burali-Forti, C. (1967). A Question on Transfinite Numbers. In From Frege to Godel: A Sourcebook in Mathematical Logic, 1897-1931, edited by J. Heijenoort. Lincoln, NE: toExcel, 104112. 19 While adopting the Bourbakian notion of three mother structures, many mathematicians and physicists recommend major departures. The Bourbaki program minimized both the heterogeneity of mathematics and its empirical roots. Many areas of mathematics originate with empirical science. Mathematics as we know it at any given time does not appear to be a hierarchy of increasingly more

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on a single foundation, set theory.20 To signal this unity, he called his series of six books Elements de Mathematique, dropping the 's' from mathematiques. The Bourbaki books present mathematics axiomatically, going from the general to the particular.21 The spirit is Euclidean. In a well-known article,22 Bourbaki proposed that all mathematics evolve from three mother structures: ordering (e.g. lattices, the study of order < that is asymmetric and transitive), algebra (e.g. groups, the study of closed sets in which every member has an opposite or inverse), and topology (the study of continuous transformations in space). All mathematics can be generated by internal differentiation of these structures, or by combinations of them. Mathematics is the study of structure. Where the superficial observer sees only multiple theories apparently very different from each other, the mathematician using the axiomatic method finds profound reasons and common ideas. There is no way to infer a priori how many basic structures there are, but in order to discover them and to reduce them to the least possible number, one may compare the existing theories in an inductive and systematic way. Note, Bourbaki points out, that there is nothing definitive about the number of structures; we detect them through a posteriori analysis that reveals isomorphism, moving in an opposite direction to the progressive construction of mathematical structures through compartmentalization. Lattice, group and topology are not abstract static structures; they are generators necessary and sufficient to create the entire edifice of mathematics. Mathematical forms constitute a set of rules that creates novelty and complexity. They are living forms, states Bourbaki and underlines Piaget.23

complex subjects. Further, theorems derived in o n e system of axioms quite easily m a y be extraordinary hard to derive in another and vice versa. 20 Bourbaki, N . (1970). Theorie des Ensembles, in the series Elements de Mathematique. Paris: Hermann. 21 Originally Bourbaki eliminated all "secondary mathematics" that "did not lead to anything of proved importance", herein including most number theory, trigonometric series, most general topology, most of group theory, and, of course, ajl applied mathematics. Notably, logic w a s also minimally treated. 22 Bourbaki, N. (1948). L'architecture des mathematiques. In Les grands courants de la pensee mathematique, edited by F. Le Lionnais, Cahiers du Sud, 1948. Blanchard, 1962. Beth, E. W. and Piaget, J. (1961). Epistemologie mathematique et psychologie. Paris: Presses Universitaires de France.

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The Bourbaki portrait of the edifice of mathematics has to be augmented in view of the development of the notion of category, a mathematical structure consisting of two classes: objects such as sets of elements taken together, and morphisms or arrows between a source object and a target object, such as the set of all functions defined on them.24 Categories are algebraic structures with many different complementary aspects: geometric, logical,25 and combinatorial. Category abstracts a fundamental concept akin to similarity, or more properly biological (but not mathematical) homology. The study of categories builds upon rather than nullifies Bourbaki's search for "mother structures". Category may provide a foundation for all mathematics, bypassing set theory.26 This revises a standard assumption held for half a century. At the very least, category provides a unifying and economic mathematical modeling language that lends itself to extracting and generalizing elementary and essential notions and constructions from many mathematical disciplines. It enables one to "transport" problems from one field to another, where the solution may be easier to find. Category is also applied in computation. A category is really a generalization of a group. A topos is a category which also possess a rich logical structure, rich enough to develop most of "ordinary mathematics". Category

Lattice

Group

Topology

Setoftheory Fig. 10.2 A lattice model the structure of mathematics.

Connecting all other components of mathematics, category theory actually continues and enhances Bourbaki's notion of fundamental Eilenberg, S. & Mac Lane, S. (1942). Group Extensions and Homology. Annals of Mathematics 43:757-831, 1942. Mac Lane, S. (1986). Mathematics, Form and Function. New York: Springer. 25 Bunge, M. (1984). Toposes in Logic and Logic in Toposes. Topoi 3(1): 13-22. 26 Lawvere, F. W. (1963). Functorial semantics of algebraic theories. Proceedings, National Academy of Sciences, U.S.A. 50:869-872. Ph.D. Thesis, Columbia University. 24

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mathematical structures. I thus proposed27 to conceive mathematics as a lattice in which sets are the foundation and category is the pinnacle that connects the three "mother structures" (Fig. 10.2). As every lattice has a dual, this scheme may explain why either set or category theory can provide a foundation for mathematics.

Bourbaki congress 1951. From http://planetmath.org/encyclopedia/lSii_>jla!-BLiuibaki.hlml

It is meaningful to consider the psychological atmosphere of the Bourbaki enterprise. "Nicolas Bourbaki" was actually a group of young mathematicians, primarily French alumni from Ecole Normale Superieure who began meeting in the 1930s with the purpose of developing and writing a thorough unified account of all mathematics.28 27

Sabelli, H. (2003). Mathematical Development: A Theory of Natural Creation. Kybernetes 32: 752-766. 28 The Bourbakis (PlanetMath.org. http://planetmath.org/encyclopedia/NicolasBourbaki.html. R. DeCamps: Qui e s t Nicolas Bourbaki?, at http://faq.maths.free.fr; Weil, A . (1992). The Apprenticeship of a Mathematician. Birkhauser: Verlag, pp. 93-122) saw themselves as isolated from modern mathematics because they had no young teachers, as many French scientists and mathematicians had died during the war. One of the Bourbakis explains, "I am not saying that they (the older professors) did not teach us excellent mathematics ... But it is indubitable that a 50 year old mathematician knows the mathematics he learned at 20 or 30, but has only notions, often rather

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As a member of a "Philosophy Club" that has been meeting weekly for twenty-five years, I know that a collective attempt to rethink the world also involves a degree of alienation from the dominant elite. 10.6 The Homology of Mathematical and Psychological Generators Empirical studies of children by the Swiss biologist and psychologist Jean Piaget (1896-1980) demonstrated three mental structures similar to the three mother structures of mathematics.29 Concepts of sedation (lattice ordering), group combination, and topological continuity develop early in the child and thereafter direct cognitive development. Piaget studied empirically and largely naturalistically the development of intellectual abilities from infanthood to adulthood. Central to his theory, genetic epistemology, is the concept of cognitive structures -patterns of physical or mental action that underlie specific acts of intelligence. One type of structure has to do with relations, and hence with order and vague, of the mathematics of his epoch, i.e. the period of time when he is 50."[Dieudonne, J. (1970). The work of Nicholas Bourbaki. American Mathematics Monthly 77: 134-145.] The Bourbakis established one their first and only rules: obligatory retirement at age 50, a common case of the young discriminating against the older and in so doing, they developed a negative image of aging for themselves. One of the practical functions of regarding natural and human processes as creative rather than determined is that we can promote rather than discourage creativity in old age. The young men chose the collective name of Nicolas Bourbaki and kept their organization and its membership quasi secret. They intended to create a work that would be an essential tool for all mathematicians. They intended to completely rethink mathematics and to do so through the publication of a great number of books. The Bourbakis met three times a year (twice for one week and once for two weeks) for twenty years, discussing each mathematical proof critically. The first Chapter of their book took them four years to complete; most others required ten to twelve years. Typically, the first draft written by one of the members following the collective instructions of all others would be thoroughly reduced to pieces in the next meeting, another member would take the task of writing up a second draft that would also be torn apart, continuing the same process some ten times before it would finally be approved for publication. This is another psychological peculiarity of the group, its collective function. No one was the "owner" of their work. There is something unusual in their ability to maintain their collective work going for twenty years. Seen from a psychological perspective, it is significant that the Bourbakis saw themselves as orphans who had lost their rightful teachers (parents) in the war, and rejected older professors belonging to the grandparent generation (the dominant generation at the time of the war). They chose the name of a general defeated by the Germans in the Franco-Prussian war, incorporated German mathematics, and brought into their work a Germanic style obsessed with axiomatic order, rejecting the free flowing mathematical intuition highlighted by Henri Poincare. Notwithstanding, they recreated French mathematics -still today, we hear grumbles regarding the fact that, while other sciences have adopted English as its lingua franca, French mathematicians still do mathematics in French. 29 Piaget, J. (1950). Introduction a I'epistemologie genetique (3 Vols.). Paris: Presses Universitaires de France.

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reciprocity. Other structures refer to classes and show reversibility, as in inversion, and thus relates to algebraic structures such as group. Other structures hinge on the continuum, such as spatial structures. Here topology precedes geometry: squares, triangles and circles are all represented by a closed curve in the drawings of small children. Table 10.1 Relation between fundamental categories. _ . General concept 1 2 3

Relation, order Classification Space

Mathematical structures Lattice Algebra (group) Topology

_. . , Physical Action Information Matter

Swiss psychologist Jean Piaget (1896-1980)

Piaget learned about Bourbaki's work in a conference on "Mathematical and mental structures" that took place in Melun, near Paris, in 1952. Listening to J . Dieudonne, he learned, to his amazement, that Bourbaki's fundamental structures corresponded to his mental structures. Piaget explored extensively the correspondence between Bourbaki's mathematical structures and his own mental structures in a book written in collaboration with leading logician E. W. Beth.30 These 30

Beth, E. W. and Piaget, J. (1961). Epistemologie mathematique etpsychologic Universitaires de France.

Paris: Presses

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structures are natural in the sense that they are observed through the analysis of actions that reveal mental processes, not because they are conscious. Nobody knows what a lattice, a group or a topological homoeomorphism is until he studies mathematics. Bourbaki's mathematical structures M and Piaget's mental genetic structures G are similar but not isomorphic.31 The laws of composition of mental genetic structures G are essentially the same as the relations among mathematical structures M, although the person is not explicitly aware of them. G and M structures are homologous in the biological sense of the term, as in an evolutionary descent such as the relationship among leg, hand, fin and wing. Mental structures are more particular, adapted to our immediate reality; for instance, instead of the N-dimensional space of topology, body and mind focus on the tridimensional space of physical structures and processes. Notwithstanding, the mental structures G are also enormously general, referring to extremely diverse elements. Mathematical structures M result from mathematical reflection. Mental genetic structures G do not. The mathematical structures M descend from the genetic structures G. Mathematical objects amplify the elements of natural thinking. The structures of mathematical science elaborate natural mental forms. The mathematician rediscovers structures already built in the mind. Piaget advanced the view that mathematical formalism emerges from natural mental activity. According to Piaget, "the mother structures of the Bourbaki", the set theoretic foundations of mathematics, "correspond to coordinations that are necessary to all intellectual activity".32 He connected the predicate calculus (logic) and the processes of "natural" reasoning, claiming that the "algebra of logic" provides "a precise method of specifying the structures which emerge in the analysis of the operational mechanisms of thought".33 Piaget regarded the

31

Beth, E. W. and Piaget, J. (1961). Epistemologie mathematique et psychologie. Paris: Presses Universitaires de France. 32 Piaget J. (1970). Structuralism. New York: Basic Books. Trans, by C. Maschler. French original, 1968; Piaget, J. and Inhelder, B. (1969). The Psychology of the Child. New York: Basic Books. Trans, by H. Weaver. French original, 1966. 33 Piaget, J. (1953). Logic and Psychology. Manchester: Manchester University Press; Piaget, J. (1970). Structuralism. New York: Basic Books. Trans, by C. Maschler. French original, 1968. Piaget, J. and Inhelder, B. (1969). The Psychology of the Child. New York: Basic Books. Trans, by H. Weaver. French original, 1966.

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development of human intellectual abilities from infancy to adulthood as a dialectic unfolding of preexisting and determined structures. Starting from a process perspective, and having observed children's development, I depart from the determinism implicit in the Piagetan phases of development. (Most contemporary psychologists doubt that cognitive development is as stage-like as described by Piaget, and consider that he underestimated the capabilities of infants and children.) In Piaget's theory, the child builds cognitive structures i.e. mental "maps" or networks of concepts, and experiences his or her environment using them. If the experience fits, it is assimilated into the existing cognitive structure, so that he or she maintains mental "equilibrium". If the experience is different or new, the child loses equilibrium, and alters his or her cognitive structure to accommodate the new conditions, thereby erecting more and more adequate cognitive structures. Updating these notions in terms of nonequilibrium dynamics, I regard BourbakiPiaget's structures as generators that process environmental feedback, continuously creating a flow of consciousness. This feedback is largely social. Recognition of the role of the social environment on the child's own personal cognitive development emerged from the work of the Soviet developmental psychologist Lev Vygotsky, a literature teacher who attempted to place Marxist interpretation on then-current theories of child development, language and communication. His work became available to western readers only in the 1960s, at which point it was recognized by Piaget and also exerted great influence on our views of child development. The Piagetan view, according to which preexisting determined mathematical structures are the seed rather than the attractor of intellectual development, represents a foundation for the theory of creative development presented here. 10.7 Mathematical Development as a Theory of Natural Creation The fact that the same fundamental structures generate all of mathematics and guide mental development suggested to me that lattice, group, and topology also generate physical and biological evolution.

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Being logically necessary, mathematical relations operate at all levels of organization. Further, I propose that the universe itself is the necessary consequence of the embodiment of these forms by the ever-present flux in the void. Spontaneous fluctuations are present at all levels of integration. Tryon34 suggested that the universe arose from a random quantum fluctuation. Slutzsky proposed that order in nature could be produced by lawful operations on totally random fluctuations.35 Coles and Chiang proposed that galaxies have been generated by gravitational forces acting upon randomly distributed matter (Chapter 6). Instead, I36 have proposed that necessary mathematical relations mold the ever-present flux into organized processes and structures including energy, information and matter, as well as basic processes at higher levels of organization. Specifically, I have proposed that the creative mathematical forms are: (1) Mathematical order (lattice theory) is materialized by the temporal flow of energy (action). (2) Group symmetry (which includes 2 N oppositions) is embodied in groups of physical entities (such as 24 elementary particles) and alphabets of information. (3) Topological formation and transformation are materialized by tridimensional energymatter fields. These three forms, together, constitute a "cosmic genome" that organizes processes at all levels of integration. The interaction of groups of actions generates episodic, diverse, novel, and complex patterns. Development means the unfolding of a generator. "Mother structure" thus is an appropriate name. From a process perspective, lattices describe temporal sequence, groups focus on opposition, topology deals with transformation of form and dimension, and category theory describes evolutionary homologies. From a static perspective, lattices portray hierarchical order, groups

34

Tryon, P. (1973). Nature 246: 396-397. Gottman, J. M. (1981). Time Series Analysis. Cambridge University Press. 36 Sabelli, H. (1989). Union of Opposites; Sabelli, H. (1999). Process theory: mathematical formulation, experimental method, and clinical and social application. Toward a New Paradigm of System Science. P. Y. Rhee editor. Seoul: Seoul National University Press, pp 159-201. Sabelli, H. (2000). The Co-Creation Hypothesis. In Understanding Complexity. G. Ragsdell and Wilby, J. editors. London: Kluwer Academics/Plenum Publishing. Sabelli, H. (2003). Mathematical development: A theory of natural creation. Kybernetes 32: 752-766. 35

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describe symmetry, topology deals with continuity of form, and category describes isomorphism between structures. MOLDS

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Fig. 10.3 Flux becomes locally organized by mathematical forms generating net action, informational feedback, and tridimensional structure. It is assumed that the most elementary entities are asymmetric. Sets of asymmetric elements are organized sequentially (lattice), cyclically (group) or opposing each other and thereby generating stable continuity (topology).

A mathematical view of creation is consistent with a long scientific tradition that regards mathematics as the account of nature. It seems unlikely that the universe emerges simply from the molding of flux by three mathematical forms as here described, but who dares to assert that it evolves independently from, or at variance with, mathematical form? Yet, I also remember those medieval monks who, having found an early Platonic manuscript, prayed equations in the hope of creating matter. The transition from mathematical form to physical existence is a gap wider than from physics to life, and from life to mind. It is cogent to consider the similar situation regarding the relation between mathematical form and physical mass that exists in the case of the standard model as noted in the second paragraph of this Chapter. But I would also add that it is form and transformation that determine existence, as energy is contained in both void and matter. Form underlies existence. Absolute uniformity is

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perceived as void. Perception requires difference between figure and background. The void needs not be emptier than matter. The view that simple mathematics generates (in an as yet not understood manner) the physical universe is advanced by current studies on the physics of information and complexity. A number of explorations in this direction are reviewed by Ilachinski.37 A

1 =°

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The three mother structures of mathematics are manifested in different ways in mathematical and physical processes. Bipolar feedback 37 Feynman noted that ultimate physics must have extremely simple laws and in a similar manner, Wheeler speculated on the need of a pre-geometry, such as some kind of a lattice structure rather than a space-time continuum; also, Hemion treated space-time as a partial order itself. Several models of this type have been developed, including Akama's derivation of a space-time metric from pairs of opposites. Stonier postulates that information is a basic property of the universe and that energy and matter comprise merely its surface. (Ilachinski, A. Cellular Automata: A Discrete Universe. Singapore: World Scientific.)

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is one of them. Bipolar feedback, the combination of action, opposition, and conservation, creates higher dimensional forms. As bipolar feedback processes operate in all natural and human processes, they may shape material systems. This is only an example of how creative processes may arise. In no way do I want to suggest that bipolar feedback is uniquely important in creative processes. However, it plays a very different role than unipolar feedback. For instance, recursions of the cosine function can produce patterns starting from a 0 initial value (Fig. 10.4). Bipolar feedback allows conservation to be manifested; in logistic models of unipolar feedback, conservation has practically no effect. Thus Creation Theory postulates that the interaction between the two forms present in each entity, linear action and cyclic opposition, cocreate form, and thereby life course-limited entities, novelty, complexity and diversity. The most fundamental interaction is the proportion of linear to cyclic form, namely n, which may be (one of) the numerical expression of Pasteur's cosmic asymmetry, and hence embodied in fundamental processes such as the vibrations of elementary strings, and the development of complex patterns. The process equation explores the creative potential of sinusoidal waving. The success of Mendel's concept of the gene, and its importance in biological evolution, provides a cultural background of the notion of a cosmic gene as a theory of natural creation. A generator must combine action, change, and conservation. The cosmic gene must include action, not only information. As noted before, a ribozyme that catalyzes action and carries information offers a model. Notably, these two functions are differentiated in subsequent evolution, as the bifurcation into catalyzing proteins and information-carrying DNA, which is conserved. Notably, RNA remains as the mediator between DNA and proteins. How does the universe create a human heart? The short answer is behaving mathematically. The physical universe is the embodiment of necessary mathematical forms by ever-present flux. Mathematical relations shape natural and mental processes because physical processes necessarily conform to mathematical necessity. This embodiment of necessary mathematical forms by physical energy creates novelty and complexity. In particular, the interaction of opposites is one of the fundamental creative processes. Thus bios, which is created by the

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interaction of opposites, is a generic process that creates novelty and complexity at all levels of organization. The cardiac Mandala portrays the role of closed group in the generator of evolution. Mathematical models allow us to construct a toy universe, a purely mathematical universe that spontaneously generates complexity from simple and universal forms. This kind of speculation of course should be placed at a very different level than the empirical studies reported in this book. Yet, this model serves as a foundation for the process method of analysis. In summary, the continuity of evolution requires that the same fundamental forms must be expressed at physical, biological, and psychological levels of organization. The fact that the same structures appear in mathematics and psychology thus strongly imply that they also operate at the physical level. We38 thus speculated that creative evolution is the necessary consequence of mathematical laws embodied in action, information, and spatial formation at all levels of organization. These forms function as a cosmic generator present at all levels of organization (self-similarity of the universe). At each level, the generator produces creative development that, as embryological development, is both determined and creative. These three cosmic forms (asymmetry, opposition, and diversification) are necessary and sufficient conditions for evolution. Creative processes result from the interaction of the linear infinitation of action, the circular infinitation of information, and the creation of new dimensions and patterns through their interaction. Bourbaki-Piaget algebraic forms have a correspondence with the small integers: the asymmetry of lattice is unidirectionality, the opposition of group inverse is twoness, and natural space is tridimensional. The sequence of numbers orders the mother structures of mathematics.

38

Sabelli, H. (1989). Union of Opposites. Lawrenceville, VA: Brunswick; Sabelli, H., Kauffman, L., Patel, M., Sugerman, A., Carlson-Sabelli, L., Afton, D. and Konecki, J. (1997). How is the universe, that it creates a human heart? Systems thinking, globalization of knowledge, and communitarian ethics, Y. P. Rhee and K. D. Bailey (Eds). Proc. International Systems Society, Seoul, Korea, pp. 912-923; Sabelli, H. and Kauffman, L. (1999). The process equation: formulating and testing the process theory of systems. Cybernetics and Systems 30: 261-294.

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10.8 Formal Numbers39 Numbers describe forms. A materialistic perspective focuses on the composition of systems, and particularly on the elements that compose them all. Yet, finding true elements has proven illusory. "Elements" are repeatedly shown to be constructed from even smaller units. A process perspective focuses on elementary and universal forms, which exist at all levels of complexity and size, from elementary particles to galaxy clusters. Numerical forms are embodied in the physical elements (e.g. simple harmonic motion in radiation, and tridimensional color structure in the chromodynamics of quarks) and organize the chemical elements in the periodic table. In this sense we may say that mathematical form (such as number) is the most fundamental level of organization in nature. Form is the common ground between the physical world of processes and the mental world of ideas. Numbers represent simple and universal forms that repeat at every level of organization, creating a fractal selfsimilarity, as illustrated by the fit between physical reality and psychological processes. Numbers are embedded as forms and patterns in spatial structures and temporal patterns. Fiveness is a form that exists in flowers with five petals, as well as in the plant's genetic code, and the brain of the maiden who enjoys its perfume. That a flower has five petals is as much part of objective reality as that its color is red (Godel).40 Fiveness exists in the plant's genetic code before and after its physical embodiment in petals. Numbers are embodied physically. Numbers are shapes that repeat in natural processes as the same organ, the leaf, varies to form all the parts of a plant, and as a theme and variations in music. Likewise, variations of the same numerical forms appear at all levels of organization, so the study of numbers provides a general morphology applicable to all fields of scientific inquiry. Not only computers or brains calculate, but also atoms and plants constantly do it. Simple operations such as iteration, 39

Sabelli, H. (1989). Union ofOpposites. Lawrenceville, VA: Brunswick Publishing; Sabelli, H. and Carlson-Sabelli, L. (1996). As simple as one, two, three. Arithmetic: a simple, powerful, natural and dynamic logic. Proc. International Systems Society. 40th meeting, Louisville, Kentucky, July 14-19. Edited by M. L. W. Hall. Sustainable Peace in the World System, and the Next Evolution of Human Consciousness, pp. 543-554. 40 Wang, H. (1988). Reflections on Kurt Godel. Cambridge: MIT Press.

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addition, subtraction, and feedback, may be expected to occur in nature, because action, information, and most other physical entities are quantities, and patterns such as music can be coded with numbers. The concept of number as form has gained new validity as digital coding allows us to portray any form as a sequence of numbers. The idea that numbers are associated with qualities has also been reinforced by the discovery of numbers (Newton, Planck, Boltzmann, Froude, Knudsen, Mach, Reynolds and Feigenbaum numbers) that define dynamic characteristics of mechanical systems such as flow, turbulence, and transition to chaos. Forms or qualities have a numerical aspect, and conversely, there are qualities intrinsically associated with at least some numbers. The small integers 1, 2, 3, and 4, as well as e, n, (p41 and a few other numbers, are generic quasi-universal natural forms. Larger numbers describe progressively less common forms. The book of nature is written in numbers and geometrical figures, proclaimed Galileo. Number has three aspects: ordinal, cardinal and formal. There is an essential unity between ordinal and cardinal numbers.42 The ordinal function of numbers has evolved into the structures of order such as lattices. Cardinal numbers have evolved from integers to rational (fractions) to real (decimal) to imaginary and to transfinite numbers. The importance of numbers as portraits of form has been highlighted by the work of Cantor and of Sarkovskii, but their arithmetic has not been developed yet, and is often disregarded as numerology. From Lao-tzu and Pythagoras to Pierce and Godel, number in general, and the small integers in particular, are regarded as primary patterns of natural processes (cosmic forms or archetypes) and, as a result, they also appear as psychological archetypes.43 Psychological 41

The ratio between successive Fibonacci numbers, cp (1.61803...) is preferred by many human subjects, as illustrated by its use from the Egyptian pyramids and the Parthenon to post cards, so Gustav Fechtner adopted it in his attempts to set esthetics on an experimental psychology basis, (p also represents biological proportions such as the ratio between branches of the bronchial system and spiral growth in invertebrates. 42 Aleksandrov, A. D. (1963). A general View of Mathematics. In Mathematics. Its content, methods and meaning. Edited by A. D. Aleksandrov, A. N. Kolmogorov, and Lavrent'ev, M. A. Russian original Moscow, 1956. Translated by K. Hirsch. Cambridge, MA: M.I.T. Press. Unfortunately, this English edition omits those sections that discuss mathematics within the "philosophical setting of dialectical materialism" 43 Robertson, R. (1995). Jungian Archetypes: Jung, Godel and the History of Archetypes. York Beach, ME: Nicholas-Hays.

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archetypes represent abstractly fundamental physical forms. Because numbers describe fundamental aspects of nature, our ancestors must have acquired, and we have inherited, the ability to recognize number, just as we have acquired the ability to perceive light and sound. Archetypes such as number, space and time, do not exist only in the software of our mind, but also in the hardware of our brain. In nature, numerical forms, it is speculated, shape processes and thereby contribute to create anew; in turn, natural processes create numerical forms. The even numbers 2, 4, 8, 16, which are generated by bifurcation cascades, appear in multiple natural processes; 8 is prominent in Mendeleiev's periodic table of chemical elements, 16 is the number of elementary particles in the standard model. 10.9 Infinity as Process: Infinitation and Dimensiogenesis Small integers may be universal up to 4, very abundant for the next few integers, then numerical forms become less frequent; larger numbers are scarce, and infinity is nowhere actual. The evolution of a complex system could be understood as a local process of dimensiogenesis, starting from relatively low dimensional physical processes. Biological, social, and psychological processes may represent the emergence of new dimensions portraying information and organization. These additional dimensions may originate in non-linear interactions, just as a tridimensional catastrophe is created by competition between point attractors. Evolution may be regarded as a process of morphogenesis and dimensiogenesis, starting with the universal forms 1, 2, 3, and their consequences 4, 6, n, and growing without bounds. The culmination of number series is infinity. A major development in Cantor's set theory was his development of a theory of infinity. Yet, by definition, infinity is unbounded; it cannot be reached. Infinity is a process of infinitation. Aristotle argued in Book 3 of The Physics that infinity cannot actually exist; only potential infinity can exist in the same way as time, which is always coming into existence. Mathematical escapes towards infinity in reality end as the computer or the mathematician runs

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out of time. This Aristotelian concept of infinity is significant regarding transfinite numbers and randomness. In his Dialogue on Two New Sciences, Galileo recognized that the number of even integers is infinite, and yet it can be put in one-to-one correspondence with the number of integers. In this sense, the two sets are of the same size. Galileo found this paradoxical. Following a suggestion from Bolzano, Cantor defined an actual infinite set as one in which its members can be put into one-to-one correspondence with members of one of its own proper subsets. If two infinite classes can be put in one-to-one correspondence, then they have the same number of elements. In this manner, Cantor "proves" that the line and the plane contain the same (infinite) number of points, based on their one-to-one correspondence. This is counterintuitive, as one would expect that the (infinite) number of points of the plane should be the square of the (infinite) number of points in the line. One may then argue that proving a paradoxical conclusion invalidates either the hypothesis or the reasoning. Cantor's theory of infinity, as well as set theory, are beset by formal paradoxes and serious departures from intuition. In my view, paradoxical or absurd conclusions should be regarded as refutations, just as contradiction with fact refutes the hypothesis in the empirical sciences. Cogently, Henri Poincare reminded us that there is no actual infinity, a fact forgotten by the Cantorians. By definition, infinity is not a thing or a state that is or that can be achieved, but one that cannot be achieved. Hence there are no infinite sets. It must be realized that, to regard mathematical infinity as actual, requires replacing ordinary logic with formal systems. In my view, a process is always finite; creative processes can be continually infinitating because it is not actually infinite. There are only infmitation processes that could be studied in terms of pattern, rate and polarity. This would eliminate the Galilean paradox (i.e. that the infinity of numbers is the same as the infinity of odd numbers). It would also dispose of the logical paradoxes that stem from considering infinite sets, such as the set of all sets, as actual infinities. In the physical world, infinity is only a potential attractor; nothing is actually infinite. At any given time, the universe is finite in time and space (see Luminet's model in Chapter 6). As a process, the universe is neither finite nor infinite but

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infinitating. Actual infinity occurs only in mathematics. All this does not diminish the beauty and usefulness of creating a mathematics of infinity. Linear infinity is a sequence of actions; circular infinity is circulation, and their feedback interaction also generates infinitating patterns, as observed with the process equation. The line and the circle illustrate basic forms of infinitation, open and closed, unidimensional and planar. Linear and circular infinitations are not commensurable. A static relation between linear and circular infinity generates transcendental n. An iterative relation between them generates periodicities, chaos, bios and infinitations. Just as iteration of the relation between linear and circular infinitations constructs novel and complex patterns in the process equation, the mutual feedback relation between linear action and circular information maybe a fundamental source of novelty and complexity in nature. Beyond the linear and circular, also the relation between any infinities of different topology may be transcendental and generate novelty and complexity. The process of infinitation must involve infinite complexity, including linear time, bipolarity, and ever-increasing number of dimensions. We can conceive of infinity as composed of a hierarchy of levels. At a fundamental level of organization, there is only one infinity, and it is potential. At a mental level, there is a rich and ever-growing creation of infinities. There are many interesting constructions of transfinite numbers, such as Conway's surreal numbers.44 Infinity, as could be expected, is complex. Mathematicians may thus develop the notion of a multilayered infinity that starts with infinity as a process -an infinitation, never completed. Infinitation implies the possibility to add. In the context of a science of creative processes, theories of infinitation are significant regarding the future of evolution. The studies of Cantor, Conway and others have shown that infinity is not simply an unimaginably large number. It is immensely complex, full of probably infinite qualitative differences. Journeys to infinity may thus be expected to be infinitely diverse, rather than convergence to some static random state. This leads us to our next focus: thermodynamics. 44

Conway, J. H. and Guy, R. K. (1996). Cantor's Ordinal Numbers. In The Book of Numbers. Springer-Verlag.

Chapter 11

Biotic Thermodynamics: Entropy as Diversity

Abstract: The second law of thermodynamics asserts that entropy spontaneously increases. This is true for both creative and destructive processes. A common interpretation of this law, however, is that entropy increases spontaneously only during decay, and that creative, evolutionary processes represent exceptions that need to be accounted for. This interpretation, I propose, is in error. This Chapter presents methods to measure the statistical entropy of evolving time series and simple experiments that demonstrate that entropy measures symmetry and diversity in the data, not disorder, decay, complexity, or uncertainty. A formulation of thermodynamics compatible with spontaneous creation is proposed: 0. Thermal flux generates novelty beyond randomness, as illustrated by the cosmic background radiation. 1. Action involves two asymmetries, energy that is conserved and time that continually increases towards infinity. 2. Action generates opposition (symmetry and bifurcation). Opposite changes coexist, as in the interconversion of heat and work, which, contrary to Clausius, can never be complete in either direction. 3. Opposition generates net complexity. Oppositions create steady states, periodicity, dissipative structures, chaos, bios, and material structures; rarely do they arrest at equilibrium. There is a net conversion of energy into matter. There is a net flow of free energy from simple to complex systems. 4. Equilibration nucleates and disperses energy and matter, generating simplicity and complexity, symmetry and asymmetry, uniformity and diversity, evolution and decay (enantiodromia). 437

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5. Complexity, life and mind are associated with an increase in entropy production density.

Sadi Camot (1796 - 1832), who in the course of his brief life published only once.

Stephen Hawking (1942), a great soul who overcame major chronic illness to become a great scientist, father and grandfather.

Claude Shannon (1916-2001), American engineer.

Ilya Prigogine (1917 - 2003), Russianborn Belgian physicist and system theorist.

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An evolutionary view of thermodynamics asserts that the quantity of energy-matter is conserved, while the quality of energy-matter increases globally. In contrast, standard views on evolution, thermodynamics, and mechanics are mutually contradictory (Chapter 2). Biological science describes an overall evolution from simple to complex. Evolution spontaneously creates complexity. Standard thermodynamics proposes decay towards uniformity. Mechanics postulates time reversibility. Boltzmann attempted to conciliate thermodynamics with mechanics with a probabilistic model -statistical mechanics. Schrodinger and Prigogine attempted to reconcile thermodynamics with biological evolution by proposing that living organisms are pockets where entropy actually decreases; such complex systems may reduce their internal entropy by exporting it to the environment. In our view, conciliation is not the answer, nor should scientific disciplines be kept separate from each other. Rather, each discipline must incorporate the insights of the other. Evolution implies that the standard interpretation of entropy as disorder is wrong. Since both evolution and destruction occur, a new thermodynamics must be developed in which the maximization of entropy produces both complexification and simplification. Both evolution and thermodynamics indicate that mechanics must incorporate time irreversibility. A unified theory of creative processes must comprise evolution, decay, and conservation. In a series of articles, we1 have shown that entropy measures diversity and symmetry, properties that are compatible with either simple or complex organization. I thus propose a biotic thermodynamics in which the maximization of entropy generates complex structure by combination 1 Sabelli, H. C, Carlson-Sabelli, L., Zbilut, J., Patel, M , Messer, J., Walthall, K. and Tom, C. (1994). Cardiac entropy in coronary and schizophrenic patients, and the process concept of entropy as symmetry. Cybernetics and Systems '94 2: 967-974, R. Trappl (Ed.). Singapore: World Scientific; Sabelli, H. C. (1994). Entropy as symmetry: theory and empirical support. New Systems Thinking and Action for a New Century. Proc. International Systems Society 38th Annual Mtg., B. Brady and L. Peeno (Eds.), Pacific Grove, CA, pp. 1483-1496; Sabelli, H,. Patel, M., Carlson Sabelli, L., Sugerman, A. and Messer, J. (1995). Entropy as diversity and organization in living systems. Proc. International Society Systems Sciences, pp 113-124; Carlson-Sabelli, L., Sabelli, H., Messer, J., Patel, M., Sugerman, A., Luecht, R., Walthall, K. (1996). Cardiac entropy is decreased in coronary artery disease: clinical and physical significance. Proc. International Systems Society. 40th meeting, M. L. W. Hall (Ed.), pp 165-176; Sabelli, H., Patel, M., Sugerman, A., Kovacevic, L. and Kauffman, L.. (accepted for publication). Creative Processes in Natural and Human Systems: Part 10. Process Entropy, a Multidimensional Measure of Diversity and Symmetry. Journal ofApplied Systems Studies.

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of simple structures (e.g. atoms into molecules) before, and to a larger degree than decay erodes complexity into uniformity. Further, decay itself can produce fractal complexity rather than uniformity, as illustrated by fracture lines in ice. According to the British physicist Sir Arthur Eddington, a scientist who rejects the second law of thermodynamics has, by this very act, ceased to be a scientist.2 His warning should discourage the writer and reader of this Chapter. Yet such fervor reminds me more of religious faith and orthodoxy than of scientific inquiry. Does such zeal conceal doubt? To understand Eddington's Biblical condemnation of breakers of the thermodynamic commandment one must remember that Planck, Zermelo, and Gibbs were among the challengers. Before and after Eddington, there has been much debate about the meaning of entropy. By the twenty-first century, most physicists have forgotten these heated discussions. Many have replaced in their vocabulary the vague notion of entropy with more concrete concepts such as symmetry. Notwithstanding, measures of entropy have been found useful in many fields, and a number of new entropy measures have been introduced to quantify information (Shannon) and complexity (e.g. Kolmogorov-Sinai entropy). We must then consider two questions: How does one measure the entropy of creative processes? How does one interpret entropy when processes are spontaneously creative? Process implies autodynamic change, that is to say, action. Evolution implies the creation of increasingly complex levels of organization. Entropy must then be considered at multiple levels. Thermodynamics originated and developed within a static, reductionist context. The term thermodynamics itself points to the study of a simple form of energy, heat. The first law of the mutual transformation of different forms of energy is given a static formulation as a law of conservation. Interpreting the second law as unavoidable decay implies that the greatest degree of complexity is physical, namely whatever structure existed at the origin of the universe. To assume a continual decay 2

"The law that entropy always increases—the second law of thermodynamics holds, I think, the supreme position of the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations—then so much the worse for Maxwell's equations. If it is found to be contradicted by observation—well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics, I can give you no hope; there is nothing for it but to collapse in deepest humiliation."

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implies to assume infinite primordial organization. To assume a monotonic increase in entropy together with a constant maximum of entropy implies to assume an infinite primordial range of variation. These assumptions seem acceptable to some physicists. 11.1 Definition of Entropy The term entropy has been given many different and contradictory definitions.3 Currently, some scientists and most laymen use the term to mean disorder, while many other scientists regard entropy as a measure of complexity (e.g. of an ecological community). In the course of its history, the term entropy, meaning transformation in Greek, has been given four distinct meanings: physical, statistical, informational, and philosophical. (1) Physical entropy: The physical concept of entropy emerged in the 19th century from work on the efficiency of steam engines4 and was heated by national rivalry.5 Thermodynamics defines the change AS in entropy S, AS = dQ/T, (ll.l) in which dQ is the flow of heat, and T is the absolute temperature. The second law postulates dS>0, (11.2) where 0 occurs when there is no action. Actions are never at equilibrium (although standard thermodynamics assumes that they can be), and whenever there is a change in heat, there must be a change in temperature (although the definition of entropy asks us to assume that there is none). Note that only changes in entropy can be measured; 3

Bunge, M. (1986). Review of C. Truesdell Rational Thermodynamics. Philosophy of Science 53:305-36; Corning, P. A. and Kline S. (1998). Thermodynamics, Information and Life Revisited, Part I: 'To Be or Entropy'. Systems Research and Behavioral Science 15: 273-295. 4 The modern steam engine was invented by the English military engineer Thomas Savery in 1698; its efficiency was improved by the Scottish engineer James Watts, who made a fortune charging his customers a percentage of the cost of maintaining the number horses necessary to perform the same task (hence the expression "horsepower"). 5 The French military engineer Sadi Carnot, son of a republican revolutionary, linked the Waterloo defeat to the backwardness of French technology, and set himself to investigate how to improve the efficiency of steam engines. An ardent nationalist, the German physicist Rudolf Clausius became entangled in multiple polemics regarding priority with British scientists.

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entropy itself cannot. In fact, the definition strictly applies only to the idealized case in which the change in Q does not produce a change in temperature. This is known as the thermodynamic paradox. Although only changes in thermodynamic entropy can be measured, temporal order is not taken into account in the thermodynamic definition of entropy as a state function, or in standard measurements of statistical entropy. The physical concept of entropy has been extended to include related properties. For instance, a young scientist Jacob Bekenstein, and later Stephen Hawking, defined the entropy of a black hole as its surface area. The physical concept of entropy refers to the uniformity of distribution of values, regardless of the quantities measured. Hawking has more recently developed a concept of gravitational entropy that can be applied in multiple dimensions. (2) Statistical entropy: Statistical mechanics defines entropy H using an equation formulated by the French mathematician Abraham de Moivre: (11.3) H = -EP i log(P i ), in which Pi is a probability or expectation. This equation measures the regularity of a distribution in a histogram: when there is an equal number of data points in each bin, H is maximal. H has no intrinsic dimension. There is an inherent contradiction between mechanics, which describes conservative, time reversible processes, and thermodynamics, which posits irreversible change. To eliminate this contradiction, Boltzmann tried to reduce the second law to a law of probability following from the random collisions of mechanical particles. Inspired by Maxwell's model of gas molecules as colliding billiard balls, Boltzmann argued that with each collision nonequilibrium distributions became increasingly disordered, leading to a final state of macroscopic uniformity and microscopic disorder. Because there are so many more possible disordered states than ordered ones, he concluded, a system will almost always be found either in the state of maximum disorder or moving towards it. According to this model, the thermodynamic entropy is measured by the logarithm of the number of microscopic states that can generate the same macroscopic appearance. The Boltzmann equation H = -kIPiln(Pi) (11.4) adds to the de Moivre equation a constant k that has the dimensions of change in heat over temperature. Boltzmann's attempt to reduce the

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second law to a law of disorder became widely accepted because it models near equilibrium systems, which dominated scientific thinking at the time. In contrast to thermodynamic entropy S, statistical mechanical entropy H is, in principle, measurable. While the expansion of a gas filling a small closed container increases when it is allowed to expand and fill a larger container, the entropy of these two random distributions is the same. This is called the statistical mechanics paradox. This formulation of entropy does not establish a direction in the flow of processes, which is the essential point of the second law. The probabilistic conceptualization of entropy involves a potential for reversibility. In statistical mechanics, irreversibility is accounted for by the low probability of organization emerging out of disorder. Macroscopic order, it is argued, represents a single arrangement of microstates, while disorder represents a great diversity of microstates that are not macroscopically distinguishable; disorder is hence more probable than order. This argument does not hold. One cannot logically base thermodynamics on statistical theory and then exclude the improbable from occurring - a theorem demonstrated by Poincare establishes that any closed system must return eventually to its original state. Gibbs, Planck, Zermelo, and many other leading thinkers, with solid arguments that remain unanswered, have rejected the statistical explanation of thermodynamics accepted by most contemporary physicists. Philosophers such as Engels6 did not accept Clausius' notion of entropy as decay because it contradicted the evolutionary view of the universe. The news that the emperor had no clothes was not acclaimed. Most scientists disregarded such philosophical caution and looked upon equilibrium dynamics as being indisputable. Prigogine7 and coworkers, however, revolutionized thermodynamics with the study of open processes far from resting equilibrium. Such systems had been neglected before because the static bias of classic thermodynamics led to a focus on isolated systems near equilibrium, disregarding change as a transient phenomenon on its way to rest.8 There are now many experiments that show that ordering, far 6

Engels, F. (1876, reprinted 1940). Dialectics ofNature. New York: International Publishers. Prigogine, I. (1980). From Being to Becoming. San Francisco: WH Freeman. 8 Building upon our discussion on a process approach to scientific methodology, note that far-from equilibrium thermodynamics did not originate with experiments that contradicted the old paradigm,

7

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from being impossible, spontaneously emerges with certainty given certain conditions. For instance, a vortex forms when water drains through the plughole in a sink; tornadoes are larger vortices. Another example is the formation of hexagon-shaped Bernard cells when a thin layer of liquid lies between two large parallel plates and the bottom plate is heated beyond a critical temperature. Thus, heating creates structure rather than disorder. The crystallization of a saturated solution and the growth of bacteria in a culture are both irreversible processes that decrease free energy and increase entropy. Each of these processes is vastly more probable than their reverse.9 Boltzmann created a brilliant and successful model to account in mechanical terms for thermodynamic changes in simple physical processes such as gas expansion, but its generalization to the universe at large represents an extreme form of physical reductionism. S and H are equivalent given a number of reasonable assumptions, but it is not obvious that this extends to the entropy of evolving processes. In the static case, neither S nor the number of microstates are measurable. Further, thermodynamic entropy always increases; statistical entropy tends to increase, but it may decrease. There is nothing in the equations of mechanics or probability to account for the tendency to maximize entropy; statistical mechanics explains time-asymmetry and thermodynamic irreversibility as the result of initial conditions, which are both arbitrary and untestable.10 According to statistical mechanics, the universe started as a low entropy (Penrose), more ordered (Feynman) state. Disequilibrium precedes equilibrium, apparently contrary to the notion of successive symmetry-breakings in cosmological evolution. The idea that a model for gases expanding in a closed chamber can be extrapolated to life and universe is strange -to use Prigogine's favorite euphemism. Statistical

as in Kuhn's structuralist reconstruction of scientific progress, but with the rebirth of process philosophy. Prigogine and Stengers explicitly considered Engels' dialectic of nature, Heraclitus' flux theory and Pasteur's asymmetry. 9 Bennett, C. H. (1994). Complexity in the Universe. In Physical Origins of Time Asymmetry, J. Halliwell, J. Perez-Mercader, W.H. Zurek (Eds.), pp. 33-46. 10 Georgescu-Roegen, N. (1971). The Entropy Law and the Economic Process. Cambridge, MA: Harvard University Press; Gal-Or, B. (1972). Entropy, Fallacy, and the Origin of Irreversibility: An Essay on the New Astrophysical Revolutionary School of Thermodynamics. Annals of the New York Academy of Science 196: 307-325.

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thermodynamics fails to explain why evolution occurs -in fact, it postulates decay towards uniformity. (3) Informational entropy: The American engineer Claude Shannon11 adopted the de Moivre equation to measure the probability (or the uncertainty) of the occurrence of a signal as a definition and measure of information. Notwithstanding, many authors, quoting Shannon but adhering to the standard Clausius-Boltzmann interpretation of entropy as disorder, define information as negative entropy.12 Entropy measures only one aspect of information, namely the amount being transmitted, disregarding its meaning, its generation, and other essential aspects of information. This was explicitly stated by Shannon. Information can be lost but it cannot be generated during transmission through wires; the notion that information can be lost but not generated in the universe at large does not follow. To state that Shannon's theorem prohibits the generation of information by biological organisms is an unwarranted overgeneralization. Obviously, a system can increase total information when receiving multiple signals and combining them with previously held information. The term Pj in the equation is usually interpreted as a probability, but it simply measures relative frequency; it is thus possible to measure the entropy of any distribution, whether determined or stochastic. Boltzmann's and Shannon's entropy are also statistical measures of entropy that use the same equation, so whatever we can learn regarding statistical measures of time series necessarily applies also to their notions of entropy. Notwithstanding, the three concepts are clearly distinct: the thermodynamic concept of entropy has units of energy per temperature (Joules/Kelvin), Shannon's entropy has units of bits per symbol, and statistical entropy is a measure of relative frequency. (4) Philosophical entropy: With Clausius, thermodynamics acquired a wide philosophical formulation: the quantity of energy is always conserved, and its quality always decays. As Clausius, Boltzmann 11 Shannon, C. E. and Weaver, W. (1949/1964). The Mathematical Theory of Communication. Urbana: University of Illinois Press. 12 The term negentropy was defined by L. Brillouin (in Science and Information Theory. New York: Academic Press, 1962) as 'negative entropy', N = -S. Supposedly living creatures feed on 'negentropy' from the sun. However, it is impossible for entropy to be negative, so 'negentropy' simply means a decrease in entropy.

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portrayed the maximization of entropy as decay towards equilibrium, rest and disorder. Clausius and Boltzmann extended this notion, based on a closed system model, to the entire universe, announcing its unavoidable heat death. Outside the context of thermodynamics, entropy became a metaphor that has been stretched far beyond its breaking point.13 Entropy has become a popular word implying any type of disorder, disorganization, waste, or uncertainty. Elementary texts appeal to purportedly intuitive examples -e.g. glasses break but they never spontaneously form. This neglects the fact that glasses must be formed before they can be broken. The identification of entropy with disorder is meaningless without an independent definition of order. The term order is used ambiguously, e.g. to mean regular arrangement, nonrandom organization, and either symmetry or asymmetry. In mathematics, order is defined as sequence by the order relation < of lattice theory.14 In nature, temporal sequence is the most fundamental form of order. Modern chemistry textbooks omit reference to disorder in the definition of entropy,15 a few years after some of us have insisted on it. The notion of entropy as decay has been questioned since the nineteenth century up to our times.16 Alternative interpretations include chance, uncertainty, complexity, and diversity.17 Shannon's definition of entropy as information directly contradicts Clausius and Boltzmann's concept of entropy as disorder. Echoing philosophical idealism, leading physicists such as Born and Gell-Mann18 attribute thermodynamic irreversibility to "ignorance." Examples of macroscopic disorganization are often given in textbooks and by leading scientists to illustrate the concept of entropy as disorder. Actually, the thermodynamic entropy of objects moved from one position 13

Cohen, J. and Steward, I. (1994). The Collapse of Chaos. New York: Penguin. Birkhoff, G. (1931). Lattice Theory. Providence, RI: Amer. Math. Soc. Colloquium Publ. For instance, Brady & Senese's Chemistry for science majors used disorder/order 65 times to describe entropy in the 3rd edition, and none in the 2004 4th edition. 16 Gal-Or, B. (1972). Entropy, Fallacy, and the Origin of Irreversibility: An Essay on the New Astrophysical Revolutionary School of Thermodynamics. Annals of the New York Academy of Science 196: 307-325; Georgescu-Roegen, N. (1971). The Entropy Law and the Economic Process. Cambridge, MA: Harvard University Press. 17 Wicken, J. S. (1987). Evolution, Thermodynamics and Information. New York: Oxford Univ. Press; Wicken, J. S. (1989). Evolution and Thermodynamics: The New Paradigm. Systems Research 6: 181186. 18 Gell-Mann, M. (1994). The Quark and the Jaguar. New York: W. H. Freeman. 14 15

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to another by an agent does not change. Only the thermodynamic entropy of the agent increases in the process. Entropy relates to action, which produces heat; entropy does not increase in a passively moved object. A collection of ordinary macroscopic objects does not constitute a thermodynamic system as does a group of microparticles. Macroscopic objects are not ceaselessly colliding and exchanging energy under the thermal dominance of their environment as are microparticles.19 The question, however, is whether the movement of particles accounts for entropy. More important than mixing of atoms and molecules is their combination, which creates complexity. In summary, the term entropy is used to confer many different and mutually contradictory concepts. Statistical mechanical entropy H accounts for thermodynamic entropy S only near equilibrium. Shannon's definition of entropy as information contradicts Clausius' concept of entropy as disorder. This confusion in terminology reflects conceptual uncertainty. One way to resolve this morass of interpretations is to examine the equation that defines entropy and results obtained in empirical measurements of empirical data. Empirical studies of the statistical entropy of mathematical, physiological and economic time series have led us to propose that entropy measures both symmetry and diversity. 11.2 Process Entropy Measuring the entropy of creative processes requires examining change in time and increase in complexity. To consider change, one measures the entropy of time series rather than the entropy of distribution of entities at one instant of time. Further, one examines changes in entropy. In this manner, one investigates temporal order, which is the most fundamental type of order in nature. Temporal order is not taken into account in standard measurements of statistical entropy: a time series and its shuffled copy have the same entropy. Likewise, time does not enter into the thermodynamic definition of entropy as a state function, although it

19 Lambert, Frank L. (1999). Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms - Examples of Entropy Increase? Nonsense! Journal of Chemical Education 76: 1385.

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should, because, as already pointed out, only changes in thermodynamic entropy can be measured. To consider increases in complexity, one must measure both simple and complex components of variation. When only one time series is available, this can be done by examining it in multiple dimensions constructed by differencing and by embedding. In contrast, other methods portray simple and complex components by a single value of entropy. Statistical mechanics, for example, measures the distribution of particles and velocities, but it does not consider complex levels of organization. This is not sufficient to measure the informational content, quality or complexity of a system. In order to understand a message, we combine letters into words, rather than studying the individual letters. In the same manner, to measure the entropy of the time series itself is not sufficient. One must also consider the entropy of the patterns formed by the sequence of terms in the series. Table 11.1 Differences between state and process entropy Process view

Static view

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Overwhelming empirical evidence for increase complexity in evolution.

Tendency to uniformity, rest and decay postulated.

Life is the necessary consequence of the coexistence of action and opposition, and involves an increase in entropy production.

Life is an unaccountable improbable accident dependent on a local decrease in entropy.

Infinitely complex final attractor of evolution that includes both central tendency and organization-generating novelty.

Processes tend to macroscopic equilibrium (static or point attractor) and microscopic disorder.

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The measurement of process entropy thus differs conceptually from the standard notion of entropy: (a) it quantifies change, not a state; (b) it is measurable, whereas the entropy of a state is not; (c) it must be separately measured for the simple and complex components of the process. In this study, we analyze the entropy of time series. Notwithstanding, many of the conclusions derived from such analyses may be expected to apply to physical entropy. We have developed a method to measure the entropy of the time series representing process rather than the entropy of the present state of a system that we call process entropy using the de Moivre equation employed in statistics, statistical mechanics and information theory as the definition of entropy. P; is interpreted as the relative frequency of a given value (not necessarily a probability). Whenever one bin is empty, Pj log2 (P;) is computed as 0. 11.3 Order and Shuffling, Simplicity and Complexity While it is widely held that statistical entropy is a measure of randomness,20 simple experiments show that statistical entropy does not measure disorder. The statistical entropy of a sequence of equally spaced integers (1,2 ...1000) is larger than the entropy of a computer-generated uniform random distribution with the same range (Fig. 11.1); random processes other than shuffling such data are highly unlikely to produce complete uniformity and maximal entropy. This is at variance with the notion that randomness generates maximal entropy. The definition of entropy as disorder, we said, is meaningless without a definition of order. In the case of processes, there is a clear definition of order, namely sequence. The statistical entropy of a time series is not associated with sequential order. The entropy of any series is identical to the entropy of its shuffled copy. Statistical entropy is equally low in random or ordered series of two numbers, and it is equally high for distributions of many values, whether randomly distributed or in any kind of pattern. Thus, statistical entropy does not measure disorder in empirical 20 Ebeling, W., Molgedey, L., Kurths, J., and Schwarz, U. (2002). Entropy, Complexity, Predictability, and Data Analysis of Time Series and Letter Sequences. In The Science of Disasters, A. Bunde, J. Kropp, and H.J. Schellnhuber (Eds.). Berlin: Springer.

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or mathematical series. In a similar manner, the statistical mechanical concept of order omits the simplest and most important order: the linear order of time. The relation between thermodynamic entropy with informational entropy has been much questioned; in our view, the widely accepted identification of thermodynamic entropy with the statistical mechanical formulation must be similarly examined. Entropy and complexity are not directly or inversely related. Comparing progressively more complex series generated by the addition of sine waves shows that entropy can vary nonlinearly as a function of complexity (Fig. 11.2). Trivially, the entropy of absolutely uniform data (1,1,1,..., 1) is zero. Consecutive

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11.4 Entropy Measures Symmetry and Diversity The value of entropy increases with the number of bins used for its calculation (Fig. 11.3), just as the amount of information received depends on the discriminatory power of the receiver. Varying the number of bins (e.g. 2 to 100 bins) allows one to deconstruct entropy into two components: symmetry s and diversity d. Entropy H is, within limits, a linear function of the logarithm of the number of bins: H = s + d*log2n (11.5) in which n is the number of bins used to calculate entropy, diversity d is the slope, and symmetry s is the value at 2 bins (the least number of bins required for the calculation of entropy). Both s and d vary from 0 to 1. 3.5 -,

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The intercept s depends on the symmetry of the data. It is 1 for all symmetric distributions (random, sinusoidal, chaotic, etc.), and varies for economic and physiological data, which manifest various degrees of asymmetry (H < 1 at 2 bins). Asymmetry is also present in biotic series generated by the process equation and in random walks. This is meaningful in view of the asymmetry of time and of other fundamental processes (Pasteur).21 21

Haldane, J. B. S. (1960). Pasteur and Cosmic Asymmetry. Nature 185: 87; Clynes, M. (1969). Cybernetic Implications of Rein Control in Perceptual and Conceptual Organization. Annals New York Academy of Sciences 156: 629-670; Corballis, M.C. and Beale, I. L. (1976). The psychology of left and

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Entropy increases with the number of different values in the data from period 2 to period 3,4, ... to sine waves. The slope d of the entropy/bin curve depends on the diversity of the data. The slope is 0 for numerical series with two equally probable values, regardless of their temporal arrangement (random or periodic) and it is 1 for random, sinusoidal, chaotic and biotic series. Statistical noise (random walks, pink noise), cardiac R-R intervals, and many other empirical time series (Fig. 11.3) have a near 1 slope. We refer to this slope as a measure of "entropic diversity." Entropic diversity may be regarded as a form of symmetry in the sense that multiple values occur equally frequently. Note: entropic diversity is not the same as diversification, as described earlier. In summary, statistical entropy increases with diversity and symmetry. What is true for statistical entropy must also be true for the statistical mechanical formulation of thermodynamic entropy. Thus, the identification of entropy with symmetry and diversity (rather than disorder) should also apply to nature. Evolution may be fueled and directed by a flow from asymmetry to symmetry and from sameness to diversity. Also, the simpler process of expansion increases both symmetry and diversity. Only within a closed chamber, the expansion of gas leads to macroscopic rest, in which multiple microscopic states are undistinguishable from one other. As soon as we open the chamber, the gas spontaneously expands, increasing thermodynamic entropy, diversity and symmetry. This macroscopic rest observed in the closed chamber is due to the resistance of the walls, not to a hypothetical equilibrium. Process entropy is, as far as we know, the only method that demonstrates that entropy measures both symmetry and diversity, and allows one to analyze these two components separately. This distinction indicates different reasons for the decrease in entropy observed in the heartbeat series of cardiac and psychiatric patients. It also shows that CBR series have lower than maximal entropy as the result of both asymmetry and lower diversity (Fig. 11.4), differentiating them from brown noise that is symmetric.

right. Mahwah, NJ: Erlbaum; Sabelli, H. (1989). Union ofOpposites. Lawrenceville, VA: Brusnwick Publishing.

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11.5 Entropy by Epochs: Nonlinear Changes in Entropy The entropy of processes, that is, changes in entropy, is examined by dividing the time series into epochs and calculating the entropy of each epoch. Random or chaotic series do not show variations in entropy (Fig. 11.5). Entropy waxes and wanes for nonstationary series such as heartbeat intervals, galactic distances, DNA base sequences, economic data, stochastic series, and mathematical bios (Fig. 11.5). The entropy of the distribution of galaxies varies in a nonlinear manner in space (right ascension) and time (redshift). Entropy also shows nonlinear fluctuations in cellular automata, and in some of them, it consistently increases with increasing order.22 Apparently, the selection of stationary data solely accounts for the monotonic order postulated by the maximization of thermodynamic entropy. What does this say about the second law? Many thinkers have discussed this empirical data, stating that Prigogine accounts for variation by considering the entropy of an entity as the sum of the endogenous entropy plus the entropy gained (or lost) to its environment. Entropy always increases for the total system, but it may locally decrease. It is, however, cogent to also consider changes related to pattern.

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In the series generated by the logistic equation, entropy increases monotonically: it is lowest for steady state (equilibrium), larger for periodic series, and still larger for chaos. In the series generated by the process equation, entropy initially increases with complexity, then decreases with the expansion of chaos into bios, and finally increases to a maximum with the simple order of infinitation, which is an ordered sequence of equally spaced values, such as the one depicted in Fig. 11.1. The biotic decrease in entropy is readily understandable as chaos is symmetric while bios is not. 11.6 Entropy of Differences Patterned changes in entropy can be studied by measuring the entropy of the differences between successive members of the time series. Together, the entropy of the time series and the entropy of the differences quantify phase portraits, a key tool of non-linear dynamics. The entropy of the differences between successive members is lower than the entropy of the time series for cardiac intervals, for integer biotic series, for random walks generated with a small number of steps, for some types of pink noise, and for periodic and chaotic series. In contrast, the entropy of differences is as high as that of the time series for random numbers, for most statistical noise, and for non-integer mathematical bios. The plot of the entropy of differences versus the number of bins reveals oscillations in many time series, not present for the entropy of the time series itself. Oscillations in difference series are particularly noticeable in some economic data and in heartbeat data from psychotic patients. 11.7 Recurrence Entropy Sequences of consecutive recurrences are arranged in bins according to the length of the sequence, then their statistical entropy is measured. The entropy of the series is compared with, that of shuffled copies. Higher entropy in the series than in its randomized copies indicates order. As expected, recurrence entropy correlates with the number of consecutive recurrences. Recurrence entropy varies in parallel with arrangement in

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aperiodic series, but these two measures vary inversely in periodic data, indicating that recurrence entropy is not a measure of complexity. Random data has no recurrence entropy. Pink noise has the same recurrence entropy as its shuffled copy. Periodic series have high recurrence entropy when the embedding corresponds to the period. Many empirical series, and chaotic, biotic and many stochastic series, have significant recurrence entropy at multiple embeddings, but much lower than in simpler periodic series. Considering the statistical entropy and the recurrence entropy of time series together (Fig. 11.7) allows one to distinguish different types of processes. Random series, which have high statistical entropy, have near zero recurrence entropy; this indicates diversity with no complexity. Periodic series have high recurrence entropy, while their statistical entropy depends on the period, ranging from 1 for period 2 to near maximal for sine waves. Heartbeat series, galaxy distribution series, mathematical bios and stochastic noise have high statistical entropy and much higher recurrence entropy than their shuffled copies. The three measures of entropy, the entropy of the series (HE), the entropy of the differences (HD), and recurrence entropy (HR) portray different levels of complexity in the process. A random sequence of any two numbers (binary random) is low in both HE and HR entropy. Random series of many different values show high statistical entropy HE and low HR. Conversely, binary alternations show high HR and low HE. Sine waves and other periodic data that combine both temporal order and diversity, are high on both entropies. Gaussian distributions, chaotic attractors, and trended sinusoidal series occupied intermediate places between these four extremes. Natural processes, such as physiological and economic series, characteristically show high rather than low statistical entropy, high recurrence entropy, and nonlinear variation in the entropy of differences. 11.8 Illness and Aging Decrease Entropy: Clinical Application and Thermodynamic Implications Entropy measures may be clinically useful. The entropy of heartbeats has been reported to be lower with factors that predispose to cardiovascular

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illness,23 such as lack of physical training. We have found that the entropy of heartbeat intervals is decreased in patients with coronary artery disease (CAD) during episodes of angina.24 Entropy is particularly reduced after myocardial infarction. Such a reduction in entropy has been previously observed by the Soviet cardiologists Khalfen and Temkin.25 Epochs of low entropy were observed in CAD patients particularly during the early morning, but not in healthy persons. In the case of patients with CAD, the decrease in the entropy of heartbeat series is due to a decrease in symmetry, without change in the slope of the bin-entropy regression line. This may result from an imbalance between sympathetic and parasympathetic inputs without reduction in the intensity of neural regulation. The entropy of heartbeats has been reported to be lower in men,26 leading to the provocative speculation that women are more complex than men.27 Other investigators have not found differences between sexes, nor have we. The entropy of differences between consecutive heartbeats is lower in cardiac interval series recorded from psychotic patients than in those from healthy persons; this reduction in entropy is due to a decrease in diversity as measured the slope of the bin-entropy regression line, without change in the intercept. This may result from a reduction in the intensity of neural regulation, which may be simply due to the blockage of both cholinergic and adrenergic receptors by antipsychotic drugs. Consistent with this explanation, the oscillations of entropy as a function of the number of

23

Ryan, S. M., Goldberger, A. L., Pincus , S. M., Mietus, J and Lipsitz, L.A. (1994). Gender- and Agerelated Differences in Heart Rate Dynamics: A r e W o m e n More Complex than M e n ? Journal of American College Cardiology 24: 1700-1707. 24 Sabelli, H . C , Carlson-Sabelli, L., Zbilut, J., Patel, M., Messer, J., Walthall, K. and Tom, C. (1994). Cardiac Entropy in Coronary and Schizophrenic Patients, and the Process Concept of Entropy as Symmetry. Cybernetics and Systems '94 2: 967-974, R. Trappl (Ed.). Singapore: World Scientific. 25 Zbilut, J. P. (1991). Power laws, transients, attractors and entropy: possible implications for cardiovascular dynamics. In H. Haken and H-P Koepchen (Eds), Rhythms in Physiological Systems. Berlin:Springer, p p 139-152. 26 Ryan, S. M., Goldberger, A . L., Pincus , S. M., Mietus, J and Lipsitz, L.A. (1994). Gender- and Agerelated Differences in Heart Rate Dynamics: Are Women More Complex than Men? Journal of American College Cardiology 24: 1700-1707. 27 1 wonder if an article making such a claim would have been published one hundred years ago, and if article making the opposite claim could have been published today. In any case, entropy is not a measure of complexity.

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differences found for cardiac interval series recorded from healthy subjects often are absent in patients with cardiac or psychiatric illness. In our data, the entropy of heartbeat series decreases with age. This observed decrease in entropy with and aging and illness is consistent with a process view: since vitality implies activity and change, aging and illness may be expected to decrease entropy production. Since illness and aging are exemplary forms of decay, these results demonstrate that the entropy of a time series does not measure decay. The recurrence entropy of heartbeat series is higher in cardiac patients (1.05 ± 0.10) than in healthy persons (0.62 + 0.04). Also, heartbeat series of psychotic patients show higher recurrence entropy (1.03 + 0.36). These differences may be due to illness or to pharmacological treatment; this is a topic for future research. Recalling that recurrence entropy is higher in periodically ordered series than in creative processes, which in turn show higher recurrence entropy than random data, these results are at variance with the description of illness as "disorder". 11.9 Conclusions from Entropy Measurements Linear expansion has maximal entropy. This is illustrated by sequences of equally spaced terms that monotonically grow toward infinity. In three dimensions, maximal entropy would obtain for an expanding sphere, as in expanding gases and the expanding universe. Entropy does not depend on temporal order, because it is the same for shuffled copies. Entropy does not reflect uniformity (e.g. all the same value), because absolutely uniformity without diversity has 0 entropy. Entropy does not measure disorder or decay. The interpretation of entropy as disorder is unsupported by empirical observations. Entropy is not a measure of disorder because shuffling data does not change their entropy. Entropy is not a measure of complexity because it is lower in complex biological processes than in series of integers that increase linearly. Entropy decreases, instead of increasing, with aging and illness, which are unambiguous examples of decay. Conversely, entropy does not change linearly with obvious changes in complexity such as the addition of sine waves. The interpretation of entropy should be determined by the

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empirical results obtained with known data. Measurements quantify what they actually measure, not what they are expected to measure. Saying that entropy measures disorder, decay, uncertainty or complexity, does not make it so. This use of the term "entropy" has been determined by history, custom, and authority, but in science, the only valid definitions are those that emerge from operational analysis. Entropy decreases with the generation of bios. In mathematical recursions, statistical entropy increases on the average from steady state equilibrium to periodicity to chaos to infinitation, but a transient decrease occurs in the transition from chaos to bios. A similar process may occur in nature, as the entropy of the distribution of galaxies shows an overall increase in time, as expected from the second law of thermodynamics, but there is a reduction in entropy when the pattern becomes biotic. These results must also apply to thermodynamic entropy, as changes in energy and matter cannot conceivably be independent of each other. The biotic reduction in entropy may contribute to the reduction in entropy proposed to account for biological organization. Entropy rises and falls. Entropy rises and falls in biological and nonbiological processes, including mathematical series and the temporal distribution of galaxies, cases in which it is not evident that one could consider exporting entropy elsewhere as a likely explanation for these deviations from monotonic maximization. Entropy maximization implies greater diversity and symmetry. The analysis of entropy as a function of the number of bins shows that entropy is composed by two factors, symmetry and diversity. According to Yates,28 thermodynamic entropy corresponds to macroscopic symmetry. Others have recognized diversity under different names. As we have seen, symmetry and diversity are two factors that foster the generation of bios in bipolar feedback processes.29 The spontaneous maximization of entropy may thereby promote the generation of novelty and complexity in nature as the necessary consequences of positive and negative interactions. In this

28

Yates, F . E. (1987). General Introduction. Self-Organizing Systems. The Emergence of Order. F. E. Yates (Ed). N e w York: Plenum Press. 29 Sabelli, H . and KaufBnan, L. (1999). The Process Equation: Formulating And Testing The Process Theory Of Systems. Cybernetics and Systems 30: 261-294.

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context, one may speculate, the generation of life and mind are very probable processes, not improbable events. 11.10 Asymmetry and Symmetry Statistical mechanics explains the unidirectionality of spontaneous processes by asymmetric initial conditions, as there is nothing in the mathematics of statistical mechanics to bring it forth. Instead, Pasteur's postulate of cosmic asymmetry can replace the need for arbitrary initial conditions by a testable law. The spontaneous unidirectionality of natural processes would result from the existence of a fundamental asymmetry in the most fundamental physical processes and its reproduction at higher levels of organization rather than as result of the asymmetric macroscopic aggregation of reversible and symmetric microscopic processes (Statistical mechanics). Asymmetry coexists with symmetry in thermodynamics processes. Action displays two asymmetries, time and energy. The asymmetric distribution of energy is manifested by the fact that it is not possible to reach absolute zero temperature, so every system has a finite positive entropy. This asymmetry, described by the third law of thermodynamics, is discussed later. The asymmetric flow of energy, whether mechanical, electrical, social, or psychological, creates resistance and opposition. As a result, processes become more symmetric. For a given level of diversity, entropy is maximal when the process is symmetric, but the maximization of entropy is an asymmetric process. It is the fall or flow of heat from higher to lower temperatures that moves a steam engine. Further, the transformation of work into heat is greater than the transformation of heat into work. There is a significant difference between Carnot's notion of an asymmetric but bi-directional exchange of energy between organized processes (work) and disorganized flux (heat), and Clausius view of unidirectional, monotonic increase in entropy. I have proposed30 that in this respect, Carnot's view offers a better description of actual processes. The asymmetry of energy is conserved even when a process reaches equilibrium. First, equilibrium always is local. A process at equilibrium is 30

Sabelli, H. (1989). Union ofOpposites. Lawrenceville, VA: Brunswick Publishing.

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still at disequilibrium with its environment. When the proverbial spoon comes into equilibrium with the hot soup, it becomes warmer than the air surrounding it, and so on, and thus equilibrium and uniformity never are reached. Second, equilibration is the matching of opposite asymmetries. Asymmetry is thus conserved within symmetry, just as two asymmetric hands make a symmetric totality. Energetic asymmetries do not dissolve in the symmetry of uniformity but endure in the symmetry of structure. The equality of opposite forces in equilibrium is manifested not only in the homogeneous and formless mixtures such as grains of sand on a beach but also in the structure of the Notre Dame cathedral. 11.11 The Formation of Structures If the opposing forces are relatively weak, opposites may neutralize each other. If they are both intense, they co-create qualitative change, bifurcations, chaos, and bios. Strong fluctuations generate dissipative structures.31 Bound energy creates and maintains structure. In the course of cosmological evolution, there is a net formation of material structure (atoms, molecules, stars, galaxies). The energy era led to a matter era.32 This conversion of energy into matter is a major case of a tendency for spontaneous generation of complexity. Chaotic attractors, the formation of dissipative structures, the development of biotic processes, and the generation of stable structures, occur in processes far from equilibrium. Evolution results from the occurrence of multiple local concentrations of energy that create information and structure; some of these structures are catalytic -they selectively accelerate the flow of energy locally. The universe as a totality is cooling, but it also creates local concentrations of energy such as galaxies, stars, etc. These "fires" burn hydrogen to generate more complex atoms, which combine into molecules, which in turn form biological organisms. Thereby, further and more complex "fires" are lighted. Equilibration is universal, but far from equilibrium processes are 31 Prigogine, I. (1980). From Being to Becoming. Time and Complexity in the Physical Sciences. San Francisco: W. H. Freeman. 32 Chaisson, E. (1987). The Life Era. Atlantic Monthly Press.

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specific.33 Simple processes predominate generally; complex processes predominate locally. Heraclitus proposed that all becomes and become from "fire" and "logos", which we can interpret as energy and information. A fire is a local concentration of energy. As described by Chaisson34, evolution from the simple to the complex is associated with an increase in the free energy flux density, from 1 erg per second per gram in our galaxy to 150,000 ergs per second per gram in human brain. The creation of fire (high free energy flux density) is thus connected to the production of logos (complexity of information) in local processes. In Union ofOpposites, I proposed that the creation and destruction of structures by the interaction of high intensity opposites should be regarded as a law in process thermodynamics. 11.12 The Formation of Biological Organization The probabilistic formulation of statistical mechanics allows for spontaneous decreases in entropy. Thus statistical mechanics comes to deny the irreversibility of processes it purports to generalize. Such an improbable fluctuation towards a decrease in entropy is assumed to be responsible for the origin of life, which, consequently, Monod35 portrays as an improbable event unlikely to have occurred more than once in the history of the universe. However the random accumulation of the vast quantity of atoms (about 1068) that constitutes a typical galaxy is also extremely unlikely, and so would be the spontaneous formation of water, ammonia, carbon dioxide, amino acids, nucleotide bases, etc. observed to occur in inorganic processes.36 Are we to assume that they also result from the unlikely but possible violations of the second law allowed by its statistical reformulation? While physicists have proposed to account for biological processes by local reductions in entropy,37 some biological 33

Prigogine, I. (1980). From Being to Becoming. San Francisco: W. H. Freeman, p. 93. Chaisson, E. (1987). The Life Era. Atlantic Monthly Press. 35 Monod, J. (1972). Chance and Necessity. New York: Vintage Books 36 Chaisson, E. (1987). The Life Era. Atlantic Monthly Press. 37 Schrodinger, I. (1945). What is Life? Cambridge Univ. Press; Prigogine, I. (1980). From Being to Becoming. San Francisco: W. H. Freeman; Layzer, D. (1967). In Relativity Theory and Astrophysics, J. Ehlers (Ed.). Providence, RI: Amer. Math. Soc, p. 237. 34

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thinkers38 have proposed that biological evolution results from the increase in entropy. Brooks and Wiley39 regard biological systems as partially closed, far from equilibrium dissipative structures that require energy throughput to maintain their steady state. Their entropy increases as result of their function, but it increases less than expected because of part of the produced entropy is dissipated into the environment. Thus evolution results from this relative reduction in entropy. However, unlike dissipative structures, organisms do not disassemble as soon as the throughput is interrupted. Further, they do not only maintain their internal configuration and external shape, but they continually evolve, and at each stage of their development, they contain continually changing biotic processes. Swenson40 has expanded maximizing principles to propose a law of maximum entropy production that would serve as the foundation for a general theory of evolution. Processes produce order and organization because ordered flow produces entropy faster than disordered flow.41 The process model of entropy is consistent with Swenson's view. However, mathematical recursions also show a reduction in entropy due biotic expansion. It is possible that both a faster production of entropy and a reduction in entropy due to biotic expansion may contribute to the development of complexity. Thermodynamic processes may contribute to biological evolution, but physical laws that are universal cannot account for biological phenomena. Moreover, the maximization of entropy can produce decay as readily as complexity. Organisms are not unique in increasing entropy without reaching its maximum. In physical processes, entropy also increases but is not maximized; it simply augments without bounds as matter expands, 38

Lotka, A. J. (1922). Contribution to the Energetics of Evolution. Proceedings of the National Academy of Sciences 8: 147-155; Black, S. (1978). On the Thermodynamics of Evolution. Pers. Biol. Med. 21: 348-346; Brooks, D. R. and Wiley, E. O.. (1986). Evolution as Entropy. Chicago, IL: University of Chicago Press. 39 Brooks, D. R. and Wiley, E. O. (1986). Evolution as Entropy. Chicago, IL: University of Chicago Press. 40 Swenson, R. (1989). Engineering initial conditions in a self-producing environment. In A Delicate Balance: Technics, Culture and Consequences. M. Rogers & N. Warren (Eds.). Los Angeles: Institute of Electrical and Electronic Engineers, pp 68-73; Swenson, R. (1989.) Emergent attractors and the law of maximum entropy production: foundations to a theory of general evolution. System Research 6: 187-198. 41 Swenson, R. (1997). Thermodynamics, evolution and behavior In Comparative Psychology: A Handbook. G. Greenberg & M. Haraway (Eds.). New York: Garland, pp. 207-218.

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information increases, and form becomes more complex. A throughput of energy is undoubtedly necessary for the development of organization in biological organisms and other complex systems. But there is throughput of energy in all systems, including those that do not become more complex. It is possible to go from one level of higher free energy and low entropy to another of lower free energy and higher entropy in many different ways, including a purely destructive process and a transiently creative one. For instance, we can burn or eat bread. Standard thermodynamics appears to confuse these two processes. An organism is a vehicle for a transformation of energy that would take place anyhow in the environment. The organism accelerates the transformation (thereby accelerating the production of entropy) and uses it to construct itself. It also produces patterned behavior that it exports to the environment, discharging information, not only waste. Organisms "secrete" information, not only "excrete" entropy. Excretions, by the way, are not only waste. What is waste for one, it is food for others -e.g. O2 is waste for plants and food for animals. Finally, living organisms become food. Organisms generate and irradiate information, while alive and after their death. In this manner, complex processes expand within their simpler environment. 11.13 Enantiodromia Schrodinger explained life as a local reduction in entropy, and Prigogine has shown that far-from-equilibrium processes generate complexity, without abandoning the concept of entropy as disorder. Life is still regarded as anti-entropic. However, the creation and evolution of galaxies and atoms shows the same development from simplicity to complexity that allegedly makes biological systems an exception to the entropy law. In my view, it is time to discard the concept of entropy as either disorder or complexity, and to replace it with a thermodynamic concept of enantiodromia. In Union ofOpposites, I advanced the concept of thermodynamic enantiodromia as the spontaneous flow from asymmetry to both simpler and more complex forms of symmetry. Both organization and randomization result from the spontaneous increase in entropy. Equilibria create both simplicity and complexity. Further:

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evolution feeds involution and vice versa. The notion of a natural tendency of processes to evolve from unstable to more stable configurations should be nuanced to include the evolution from stable atoms to short-lived organisms. Work becomes heat more than heat becomes work. But likewise in the course of cosmological evolution, energy has become matter more than matter became energy. Just as anabolism and catabolism necessarily coexist in biological organisms, evolution and decay coexist in nature, and may result from the same fundamental process of entropy maximization. In fact we know not of a process that increases organization separately in time or place from the production of disorder and waste. Entropy is generated by both system formation and system destruction, just as energy is liberated by both atomic fusion and atomic fission. It thus seems likely that the maximization of entropy increases both order and disorder, as postulated from the earliest process theorist, Heraclitus, in his concept of enantiodromia (Greek: enantio = opposite; dromos = race). The consumption of energy may serve to construct or to destroy, as contrasted to views of entropy as either complexity or disorder. Time, like ancient Chronus, engenders and devours his children. In nature, evolution coexists with decay, but decay is also creative. What goes up must come down, asserts Taoism, but creation by necessity has priority: what comes down must first go up. Also, decay often generates more complexity -consider for instance the complex forms generated by fracture, and the generation of 1/f patterns characteristic of many complex processes by exponential decay. As energy and matter encode information,42 information is an ever present component of processes. Nothing can exist without information, even if processes do not conserve information quantitatively. Energetically-coded information decreases with the maximization of entropy. Structural information increases with the conversion of energy into matter (which occurred at least in early phases of the universe's evolution), the evolution of hydrogen to heavier atoms to molecules to organisms to brains, and the combination of sentences in dialogues. 42

Shannon, C. E. and Weaver, J. (Eds.) (1964). The Mathematical Theory of Communication. Urbana, IL: University of Illinois Press.

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Spontaneous evolution is enantiodromic, with a simultaneously decrease in energy-coded information and an increase in structurally-coded information. The entropic loss of asymmetry in flows towards point of equilibrium is compensated only by the multiplication of quality by the creation of novelty, variety and complexity in chaotic attractors, biotic processes and the formation of systems. Information is neither conserved nor only degraded. It is lost in transmission, but it is produced and reproduced in processes and interactions. The rise and fall of biochemical structures exemplifies enantiodromia: catabolism fuels anabolism, and the latter creates and maintains structure although it consists of a network of chemical reactions which individually increase entropy. Anabolism and catabolism are continuous with asymmetric exchanges at the organismic, organ and cellular level. A cell, for instance, has a smaller and better conserved identity and a faster rate of chemical reactions than the surrounding circulating milieu, which is larger, with a constantly changing identity, a rapid rate of physical change, and a slow rate of chemical reactions. These asymmetries exist in the interphase between any two compartments: the hotter, chemically more active, smaller and more complex system always is surrounded by a physically faster, circulating, larger and more variable simpler environment. Biological processes are explained by a cycling of energy between the complex organismic phase exporting entropy and the simpler surrounding medium supplying free energy. But such cycles must occur whenever there is an interphase between simpler and more complex processes: The complex pole has a faster rate of chemical reactions that increase its complexity and give up entropy. The simpler system is has a faster rate of physical reactions and gives off free energy. Free energy-rich matter (food, raw materials) flows from the simple environment to the complex organism, while entropy-rich matter (waste) flows from the complex to the simple. Heat flows in both directions, because the wider range of temperature of simple processes allows them to function as both the hot source and the cold sink of energy required by the second law. There is a universal exchange of free energy for entropy in every asymmetry, difference or partition between unequal phases. The growth of complexity appears to be associated with a decrease in the range of temperature and

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other energetic parameters, suggesting why homeothermia and homeostasis play a fundamental role in evolution. Biological organisms are not unique in taking in highly organized, information-rich, free energy- full materials, and discharging entropy as waste. So do fires burning firewood to ashes. There is nothing unique in exporting entropy to the environment. As living processes, fires also spread, and they create structures as they "fire" clay. This is not a play on words but perhaps another example of the collective wisdom embodied in language. A fire is as much a patterned, energy dissipating, selfmaintaining structure as a brain, even if they differ in intensity, stability and complexity. 11.14 Flux and the Third Law of Thermodynamics Thermodynamics is about energy, flux and temperature, not about order or information. Analyses of statistical entropy are nevertheless relevant because, as formulated by Maxwell, Boltzmann and Gibbs, temperature is the average or global flux of the motions of the microscopic particles that make up a system. This motion is assumed random. It is not. Space is filled with non-uniform energy, including as its simplest and oldest component the cosmic background radiation (CBR). The CBR, born in the remote past, pervades the universe here and now. There is a minimum of temperature, approximately 2.7° K. Entropy analysis using the bin variation method shows that CBR data are asymmetric and have less diversity than a perfectly uniform distribution (Fig. 11.4). As described before, recurrence analysis of the CBR shows novelty, that is to say variation greater than random, with no consecutive recurrence. Further, Luminet and co-workers demonstrated a dodecahedral topology. Thus, global flux is asymmetric, positive, non-uniform, novel, noncausal but topologically organized at its simplest and oldest level. An absolute void would represent a maximum of uniformity. As such, it would correspond to a maximum of entropy. However, the vacuum state displays a minimum of entropy. The third law of thermodynamics ("Nernst theorem", after the German physicist Walther Nernst who formulated it) asserts that the entropy S of a system goes to zero (or a "universal

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constant") as its temperature goes to absolute zero. In practical terms, this theorem implies the impossibility of attaining absolute zero, since as a system approaches absolute zero, further extracting of energy from that system becomes more and more difficult; absolute zero itself cannot be reached. Even at absolute zero, there is fluctuation (zero point motion). The quantum system is described by its wave function that has the lowest possible energy, which is called the ground state or the vacuum state. If there is only one unique state available (as in crystal lattices), then S=0. S is nonzero in the case for a system with multiple vacuum states. There are several other violations of the law.43 Within the context of quantum mechanics, flux in the vacuum state is often regarded as a random system. This is paradoxical, because randomness has (near) maximal entropy and the vacuum state has minimum entropy. In any case, space is filled with non-uniform radiation, including the CBR. This is significant. Every generator that is extremely sensitive to initial values, such as chaotic and biotic generators, will magnify the differences among multiple initial values. Also, gravitation amplifies non-uniformities. 11.15 The Concentration and Dispersion of Energy and Matter A formulation of thermodynamics becoming popular in modern textbooks44 portrays entropy as a measure of the dispersal of energy in a process (as a function of temperature). A hot pan spontaneously disperses some of its energy to the cooler air of the room. The sun warms the planets. However, for suns to radiate energy, energy must have first become concentrated. Energy must have been more or less uniformly distributed in the early universe. Spontaneously, galaxies, stars, and atoms formed. Heavier atoms assembled in the core of stars, and 43

At zero temperature, a boson (or fermion) gas confined to a circular string violates Nernst theorem. Also, rotating black holes fail to satisfy the analog of the Nernst theorem, breaking the otherwise perfect analogy between the ordinary laws of thermodynamics and the laws of black hole mechanics. Wald, R. M. (1997). The "Nernst Theorem" and Black Hole Thermodynamics. Phys.Rev. D56: 6467-6474; Bezerra, V.B., Klimchitskaya, G.L., Mostepanenko, V.M., Romero, C. (2004). Violation of the Nernst heat theorem in the theory of thermal Casimir force between Drude metals. Phys. Rev. A 69, N2: 022119-( 1-9). 44 Lambert, F. L. http://www.entropysite.com/

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molecules in cooler bodies. On earth, and presumably in other planets, molecules formed organisms, that concentrate energy from their surroundings. Unicellular organisms associate, form multicellular organisms, that in turn form societies. Human populations increase in size from bands to villages to towns to cities to capitals. There is a net migration from countryside to cities. There is a net flow of human population, raw material, and money from peripheral to central countries. At all levels of organization, we observe the spontaneous formation of systems. Processes spontaneously transform energy into matter, nucleate matter, and transfer energy from simple to complex systems. Empirical evidence thus suggests that the tridimensional nucleation of energy and matter must also be a fundamental law of thermodynamics. If radiation disperses energy, matter conserves it and black holes take it in. In turn, black holes provide energy through the Hawking radiation. Although it is dangerous for a physician to risk such a hypothesis, I might as well state it clearly: the maximization of entropy produces both concentration and dispersal. And further, the attractor of natural processes is infinite complexity, not entropic disorder (Chapter 12). uk

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Chapter 12

The Infinite Attractor of Evolution

Abstract: Evolution is creative and ongoing. Creative evolution has already created consciousness and conscience; humans have a spirit. Biotic development illustrates how evolution may be expected to continue creating an attractor of infinite complexity rather than tending to equilibrium. This provides a mathematical metaphor for God compatible with contemporary science and with mental health principles. Evolution is creative. Creation is evolutionary, gradual, continuing, progressing. Creative evolution has already created to consciousness and conscience, in other words, the human spirit.1 Physical evolution, we surmised in Chapter 11, does not end in entropic decay and random uniformity but creates infinite complexity. The concept of an Infinite Attractor corresponds to God. It is cogent to address this implication in a scientific book, following a long tradition from classic philosophers to Cantor,2 Einstein,3 Feynman4, and Prigogine.5 The book of nature has been recognized as part of God's revelation by educated theologians. Religions must take into account what we know about evolution.

1

Throughout this book, the term spirit is used to encompass the concepts of soul, psyche, and mind. Hedman, B. A. (1993) Cantor's Concept of Infinity: Implications of Infinity for Contingence. Perspectives on Science and Christian Faith 46: 8-16. 3 "I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element; I want to know his thoughts; the rest are details." (A. Einstein) 4 "What is the pattern, or the meaning, or the why? It does not harm to the mystery to know a little about it. For far more marvelous is the truth that any artist of the past imagined!" (R. Feynman) 5 "God is no more an archivist unfolding a infinite sequence he had designed once and forever. He continues the labor of creation throughout time", proposes I. Prigogine (The Rediscovery of Time, in Science and Complexity, Sara Nash editor, Science Reviews, Northwood, Great Britain, 1985). 2

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Without such knowledge, "creation science" is a travesty.6 By refusing to accept Copernicus, Galileo, and Darwin, religions often excluded themselves from the intellectual discourse of modern society. The Nobel Prize-winning Belgian Catholic biologist Christian de Duve offers a scientific discussion of theological questions, stating that respect for truth must take precedence over the regard one may have for the opinions of others.7 He explains: "Religions must revise their scripts and bring them in line with modern science." And adds: "Something positive must be proposed that can eventually replace the myths propagated by religions, while trying not to destroy the many beneficial structures religions have built on these myths."% Science, religion and society need a science of creation. Physicists often write about God and otherwise about demons.9 6

"Often a non-Christian knows something about the earth, the heavens, and the other parts of the world, about the motions and orbits of the stars and even their sizes and distances, and this knowledge he holds with certainty from reason and experience. It is thus offensive and disgraceful for an unbeliever to hear a Christian talk nonsense about such things, claiming that what he is saying is based in Scripture. We should do all that we can to avoid such an embarrassing situation, which people see as ignorance in the Christian and laugh to scorn. " Augustine of Hippo, De Genesi ad litteram libri duodecim (The Literal Meaning of Genesis) 7 Christian de Duve offers a scientific discussion of theological questions, stating that respect for truth must take precedence over the regard one may have for the opinions of others. De Duve ends with an apology to most of his readers for discussing matters that belong to Catholic universities of fifty years ago, but adds "Perhaps my tale may strike a responsive chord in American readers. Whereas the world I depict has virtually disappeared from the European scene, the United States still harbors many fundamentalist institutions of so called higher learning, in comparison with which even the Louvain of my youth would appear magnificently liberal." [De Duve, C. Life Evolving. Oxford University Press, 2002.] The argument must be thought of carefully. People cannot be told that there is no God because this may undermine the sole basis for their morality, claim many at least since ancient Greece. Yet religion has been undermined by the contradictions between religion and morality. It was not the contradictions between religion and science that undermined the Christian Church. It was the denunciation of the immorality of Rome by Huss and by Luther that split Christianity. 8 The argument must be thought of carefully. People cannot be told that there is no God because this may undermine the sole basis for their morality, claim many at least since ancient Greece. Yet religion has been undermined by the contradictions between religion and morality. It was not the contradictions between religion and science that undermined the Christian Church. It was the denunciation of the immorality of Rome by Huss and by Luther that split Christianity. 9 James Clerk Maxwell, the nineteenth century author of the theory of electricity and magnetism, imagined a demon who sits at the gate between two closed chambers, and watches the molecules wandering back and forth. He lets only those molecules that move faster than some limit pass from the right chamber into the left chamber, and he only those moving slower go from the left to the right. As a result, the left chamber heats up and the right chamber cools down. The unlikely figure of a demon capable of decreasing entropy has fascinated physicists since then. Studies have been devoted to prove that it must fail to do its task. It is intriguing that physicists have been fascinated by the demon, and that they became preoccupied with its ability to violate the second law. Assuming that the demon could open and close the gate without spending energy already violates the first law. Also, it has been proven that the demon cannot violate the second law. And yet, Maxwell's demon has appeared in almost every popularization on the subject both before and after such proofs have

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Instead of fighting creationism for being unscientific or science for undermining traditional beliefs, it seems healthier to formulate a scientific theory of creation. If it is cogent to address the spirit from a scientific perspective, it is essential to do so from a clinical and educational perspective. Religions must be informed by science also because they have enormous repercussions regarding scientific freedom and social policies. Conceptions of God can be psychotherapeutic or psychopathogenic (as already discussed by America's first psychiatrist, Benjamin Rush). They may lead to peace or war, social solidarity or racism, sexism, classism, and child abuse.10 The psychotherapeutic or psychopathogenic implications of visions of God are even more evident at the personal level. In fact, one of the great surprises we encounter in clinical practice is the many different, often unique, views that each person has of God. This diversity is masked by a common name and religious denomination. A relation with God can only exist from the perspective of a person. A relation with God must be personal. I have come to believe that every person must create a God for him/herself, not just mechanically adhere to what one learns as a member of a social group, because we must be personally responsible for truth and goodness. I have thus developed a personal concept of God as the Infinite Attractor of evolution, as a scientific concept11 and as a psychotherapeutic metaphor.12 It is based on been acknowledged. Why the continuing interest on Maxwell's demon? Because we know that the universe must have a Maxwellian demon. At some unconscious level, even physicists know that the formulation of the second law as unavoidable decay is counterintuitive. In the physical universe of modern science, Maxwell's demon performs the task of God, to create organization. The existence of organization in the universe is one of the traditional proofs of the existence of God. A psychologically minded observer is struck with the remarkable transformation of God into a demon. Why has modern science change the sign of the Creator? Is it an attempt to remain within the realm of science? Does the name change reflect a change in our perception of the universe? In our times of war, AIDS, environmental destruction and economic exploitation, it may be difficult to see the world as organized by God. Yet, even highly religious authors argued the existence of God based on the manifest order of the universe, never on His manifest benevolence, as natural catastrophes, illness and death always raise Job's questions. 10 The mistranslation of the Biblical "Do not spare the rod" has meant the physical abuse of children including present generations. The expression means that the child should be guided, just as the shepherd guides the sheep by raising the rod. The modern World Wide Web carries a polemic between religious supporters of spanking children and mental health professionals opposing it. 11 Sabelli, H. (1989). Union of Opposites; Sabelli, H. (1992). God the Attractor: A Scientific Concept and a Psychotherapeutic Metaphor. Proc. Internal. Soc. for the Systems Sciences. Edited by L. Peeno. Pp. 1241-1251.

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the notion of creative processes evolving from simple mathematical form to unbounded complexity, and the recognition that the human mind attests to the creation of spirit in the universe. Thus human portraits speak of God in this Chapter. For the same reason, how do we portray God is vital. The Trinity portrays the family, Father, Mother and Child, in all religions, but in current patriarchal interpretations the Mother, who has a feminine name in the Old Testament, is called the Holy Ghost13 and addressed as a man, and likewise the Child is male. If four is the justice of opposites, we need to also recognize the Daughter.

German mathematician Georg Cantor

English mathematician Alfred Whitehead

French paleontologist Pierre Teilhard de Chardin

12.1 Logos, Bios and Telos

"At the beginning was the logos" and "the Logos was God" proclaimed John in the first verse of his Gospel, having learned Heraclitus' philosophy during the many years he lived in Ephesus. The universe is rational, i.e. mathematical, but not static. An evolving universe suggests an evolving divinity. We may conceive God as the Supreme Becoming. The Aristotelian concept of an immutable Supreme Being, the watchmaker, corresponds to a vision of the universe as a mechanism ticking in the same fashion since the original act of creation. Traditional views in theology were static because science pictured a static world. For 12 Sabelli, H. (1992). Maria/ Mary. Bilingual play (Espanol- English) with historical notes Chicago, IL: SACP. 13 This is discussed and referenced in Maria/ Mary.

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modern science, all evolves; there is not being separate from becoming. Correspondingly, the divine must also evolve. Theologians delight in using simple numerical portraits of God -God is one, God is a union of opposites (Nicholas of Cusa), God is a Trinity. The origin of evolution may be a simple mathematical form, but its Attractor is not because we already are life and spirit. God is the Infinite Attractor of evolution. This concept follows a long tradition identifying infinity with God. Cantor felt that his theory of infinity provided a scientific theory of God, and offered it to Christian theologians. Three centuries before, Giordano Bruno, the greatest Renaissance philosopher, regarded both God and nature as infinite. The infinitude of the universe and the infinitude of God show that the two must be indivisible. The Inquisition burned him alive. Also Nicholas of Cusa, philosopher, mathematician, and astronomer, but also Cardinal, considered that the universe, being infinite, participates in an attribute of divinity. He regarded the universe as infinite in a potential sense, and the present universe as finite, corresponding to the notion of infinitation (Chapter 10). The notion of a "mathematical theology" is currently espoused by several theologians and scientists. Systems scientist Hershey14 portrays the creation of the universe as emerging from infinity and moving towards a universal attractor -maximal entropy or randomness. A journey from God to meaningless randomness does not seem reasonable. Consideration of evolution suggests the alternative notion of a simpler mathematical Creator and a meaningful Infinite Attractor. Early religions conceived the spiritual world of God and soul as made up of a very light, invisible substance, very much like air. The spirit was literally thought of as air because the cessation of respiration signals death: we give up our ghost with our last breath. Hence the idea of the soul as the breath of life and the Creator breathing life into inanimate matter. We no longer speak of air, but still, for most philosophers, God and the soul are made of a specific substance, the "spirit". This is crude materialism. Mind cannot be a thing, a substance, however ethereal and different from normal matter. Feeling and thinking are processes, as made evident by the "stream of consciousness", in the felicitous 14

Hershey, D. The Emergence of the Universe out of Infinity. Basal Books.

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expression William James coined by adopting Heraclitus' metaphor. We can thus think of mind as information contained in the pattern of brain processes. Forms are no less real than substances. The human spirit is a pattern of energy originating within a highly organized matter, the brain. This does not mean that the spirit is a special kind of energy, such as electricity or gravity. Rather, psychological activity results from patterned organization of electrical and chemical processes in the brain cortex. As the mind is an organization of information processed within, but not identical with, the structure of the brain, one may conceive of God as the informational aspect of the Universe. In more poetic terms, God is the soul of the universe. This notion of spirit as form may better satisfy the notion of divinity than the conception of spirit as substance. Regarding the universe as alive with energy and information, one can imagine how spirit can emerge from matter. This excludes pseudoscientific speculations that posit God, as "pure spirit", injecting information into various places in the universe in need of his intervention without injecting energy. Evolutionary concepts of God originate with the British mathematician and philosopher Alfred Whitehead15 and the French geologist/paleontologist, Pierre Teilhard de Chardin.16 For Whitehead, God contains the universe and therefore God is changed by the actions that take place in it over the course of time. God is not omnipotent. Individuals do not enjoy a personal immortality, but they do have an objective immortality in that their experiences live on forever in God, who contains all that was. These process concepts have points in common with mine, but there also are radical differences. For Whitehead, the universe is a process in which free willing agents carry 15 Whitehead, A. Process and Reality. (Gifford Lectures Delivered in the University of Edinburgh During the Session 1927-28). Free Press, 1979. 16 Chardin's scientific goal was the development of a general theory of ongoing evolutionary processes (biological, historical and psychological) from which one could draw conclusions as to the future of human evolution as a continuation of universal evolution. He regarded evolution as a transcendental connection that provides meaning of human existence. He affirms "the belief that there is an absolute direction of growth, to which both our duty and our happiness demand that we should conform. It is his [the human] function to complete cosmic evolution." The Church authorities deprived him of his teaching position and prohibited the publication of his ideas. He obeyed. His work was published posthumously after Vatican II. Both Chardin and Whitehead were inspired by Henri Bergson, the French Nobel prize in literature who proposed a philosophy of creation radically different from what I regard as a scientific theory of creation.

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out change. Everything in the universe, not only human beings, have free will, at variance with the fact that complexity of function requires complexity of structure, as it is known since Lamarck. Teilhard pioneered the concept of supremacy of the complex: just as the biological evolution of higher animals is directed by their brain, humankind provides a directing head to the evolutionary process. Teilhard proposed that evolution creates a noosphere,17 that some have compared to the World Wide Web, and converges to an omega point, impersonal18 and distinct from God. The notion of a Cosmic Attractor echoes Whitehead and Chardin but add something fundamentally different: the universe is creating God. For Heraclitus, "God is a Child", still growing.19 This solves the question of evil. Creationism would have us believe that a perfect God created this imperfect, painful and unjust universe, thus proposing a one-sided involution from high to low. A conception of God as the Cosmic Attractor proposes evolution in the opposite direction: from radiation to matter to God; from physical organization that includes explosions, to biological evolution that includes predation, to spirituality that overcomes evil. Regarding divinity as the Attractor of evolution is in line with the central place of attractors in nonlinear dynamics. But, as discussed in Section 3.5, an attractor is actually a generator.20 In this context, the 17 The noosphere is the sphere of knowledge, a concept develop by analogy with the atmosphere and the biosphere (Chapter 14). Echoing Hegel, Teilhard de Chardin says "Man discovers that he is nothing else than evolution becoming conscious of itself." "And here I am thinking of those astonishing electronic machines (the starting-point and hope of the young science of cybernetics), by which our mental capacity to calculate and combine is reinforced and multiplied by the process and to a degree that herald as astonishing advances in this direction as those that optical science has already produced for our power of vision." ls "We are faced with a harmonized collectivity of consciousnesses to a sort of superconciousness. The earth not only becoming covered by myriads of grains of thought, but becoming enclosed in a single thinking envelope, a single unanimous reflection. " (1961, pp. 251-2) Yet such a unanimity of consciousness implies a condition that humans generally reject, depersonalization. Indeed, the conclusion seems inevitable: "So that at the world's Omega, as at its Alpha, lies the Impersonal. " " As I write this article, two images of God the Child surround me, a Renaissance painting of Madonna with Child -and a kneeling Child Buddha that serves to remind me that the conception of God as Child permeates also Eastern traditions. 20 Biotic dynamics exemplifies the creation of new complexity by the interaction of simple origins and their environment. The attractors generated by recursions manifest the form contained in the mathematical generator. The simple forms revealed by mathematical analysis of empirical time series portray their origins (causes), not endpoints (final causes). In a similar manner, the phenotypes generated by biological development represent actualizations of the information contained in the

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Attractor of evolution is its Creator. But Creator does not imply only origin. Creation continues. Creation portrays the Creator. The evolution of nature portrays the evolution of its Creator. 12.2 Science and Religion The origin of life, as the origin of mind and the very existence of the universe remain mysteries that fill us with awe. The claim of some religious thinkers to already know seems presumptuous to most scientists. Knowing is the opposite of awe, it lacks true reverence for the sacred. Also, the poetry of myth fares poorly as scientific hypothesis. As science advances, supernatural processes are understood as natural. "God", my father wrote, "is that part of the world we do not know". Religions have had a dark history regarding science. Pathogenic religious concepts lead to the suppression of science and of scientists remember the murder of Hypatia, Bruno and Severe 21 A theory of two separate truths -science and religion- emerged as a way to protect scientists from the inquisitorial fires. This was a necessary artifice to allow natural philosophy (science) to evolve without challenging the static theology of "Christian" churches that burned alive those scientists who thought something "heretic". The idea has been revamped in our times to protect religion.22 Surprisingly, Gould23 proposes a respectful noninterference as a principle of "Non-Overlapping Magisteria". This is not desirable, because it separates science form philosophy and from general education. Separating science from religion would not enlighten those who become dangerous to others in the name of God. It is the right

genome in interaction with the environment. In all cases, there is creation -there is no determined trajectory; there even is a multiplicity of trajectories with diverse overall forms. 21 The Alexandrian mathematician, astronomer, and philosopher Hypatia was beat to death in 415 A.D. by a Christian mob inspired by the bishop Saint (!) Cyril. "Reserve your right to think, for even to think wrongly is better than not to think at air, stated Hypatia, and added "To teach superstitions as truth is a most terrible thing. " The Italian philosopher Bruno was burned alive by the Inquisition. Galileo almost suffered the same fate. The Spanish physiologist and historian Miguel Severo, who discovered the pulmonary circulation, was burned alive by John Calvin and his followers. 22 Karen Armstrong (The Battle for God. HarperCollins, 2000) in her criticism of creation "science", proposes that genesis is mythos, evolution is logos, and the two must be kept separate. 23 Gould, S. J. Rocks of Ages. Science and Religion in the Fullness of Life. Ballantine Publ. New York, 1999.

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and the duty of science to consider all aspects of reality. It is cogent to explore the larger meaning of scientific concepts. Intellectual activity stagnates when new ideas are not spelled out for fear of offending or seeking the approval of many. Cultural progress cannot take place without the compelling nature of a larger vision.

Three martyrs of science. Hypatia of Alexandria (d -415), mathematician, astronomer, philosopher, and

director of the

Museum, the

Italian Renaissance philosopher

Giordano Bruno (1548-1600) and the Spanish historian and physiologist Miguel Severe (Servetus) (1511-1553).

Leading religious thinkers did not shrink from science. Saint Augustine of Hippo supported scientific education and rejected the literal reading of Scriptures.24 Thomas Aquinas advocated that the book of nature be read as scripture. Honesty demands considering one's beliefs in the light of all available knowledge. Regarding one's beliefs, one can be either critical or hypocritical. It is a sign of weak faith to fear the truth as magnificently explained by the Reverend Thomas, an Anglican clergyman who was the chaplain of King William the Third and a friend of Newton, in his Sacred Story.

24 For instance, he regarded the six days of creation as metaphorical - Newton, more literally minded, thought that the explanation lay on the fact that the earth rotated more slowly at the beginning of time. This is one of the many examples of the decay in rational thinking that outlasted the Middle Ages. Newton apparently also predicted the world would end in the year 2060. Repeating an obvious yet often forgotten fact, what matters in science, as in any other process, is not position but direction. Newton was far closer to the Middle Ages than we are used to think. That Newton was in so many ways involved in arcane medieval infatuations with alchemy, Egyptian pyramids, Solomon's temple, Biblical interpretations,24 and millennial prophesies is not so important as the fact that he discovered the laws of mechanics and invented calculus. Before Newton, the physics of the heavens was far from the natural physics of the planet. After Newton, they were one. The God of Abraham had become a geometer.

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Setting Holy Scriptures in opposition to scientific truth damages science and society. Modern science began with Polish astronomy, Italian physics and Iberic geography. Under the Inquisition, Southern Europe lost its scientific leadership to northern Europe. Spanish science did not recover until Ramon y Cajal. Opposing Scriptures to scientific truth undermines confidence in religious beliefs. This happened in Galileo's time and it reoccurred in the USA when Kansas politicians of a creationist creed introduced it into the school curriculum. Religions evolve. The same Catholic Church that burned Bruno and imprisoned Galileo, apologized -four centuries later!- and shortly afterwards adopted the Big Bang hypothesis as proof of supernatural creation. This was perhaps premature given previous mistakes regarding physics. Religions evolve, or perish. Scientific education is essential for survival in industrial societies, so the future of anti-scientific religionism is predictable, but the damage that it can produce in its death throes may be considerable. It is cogent to pave a way for a smooth transition. Persons as well as groups wish to maintain their belief systems and their loyalty to family, country and church. As discussed by Unamuno,25 a person may change much, but only within continuity. Traditions embody identification with our parents and culture. Loyalties, kept as ideas, can be seamlessly transformed even when they are totally changed.26 12.3 Clinical Psychology and Religion Rumanian-American psychiatrist Jacob Moreno regarded Christianity as the "greatest and most ingenious psycho-therapeutic procedure man has ever invented compared with which medical psycho-therapy has been of practically negligible effect. " The goal of Christianity is, from the very beginning, the treatment of the whole of mankind. This, to Moreno, was

25

Unamuno, M. de. Del sentimiento tragico de la vida en los hombres y en los pueblos (On the Tragic Sense of Life in Men and in Nations), 1913. For instance, without repudiating the hideous idea of stoning a woman, one may demand that only who is free of all sin must throw the first stone. A scientific meditation on theology should be catholic with small c, i.e. ecumenical, but in keeping with my own national tradition, the examples and quotes tend to be Catholic. 26

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the aim of all worthwhile psychotherapy.27 Another great physician, Viktor Frankl, described the psychiatrist as a doctor of the soul.28

Rumanian-American psychiatrist Jakob Moreno. Courtesy of Zerka Moreno.

Though the physical scientist may be satisfied to stop at a place where facts and theory end, and only faith or speculation speak, as clinicians we often need to address the spiritual issues that affect our patients. Existential and spiritual issues touch many patients, particularly those affected by terminal or disabling illnesses, emotional dysfunction, or family conflicts. Even those who profess faith under normal circumstances may walk about angry with a God who allows painful and/or disabling illness, childhood abuse, or the premature death of children. However, most clinicians avoid dealing with religious matters "out of respect for people's beliefs". Actually, respect for unwarranted beliefs that lead to unhealthy behavior implies disrespect for our fellow humans, and disregard for the sacred. "Those who believe absurdities can commit atrocities", pointed out Voltaire. There is nothing intrinsically moral about religion. It depends on what is being taught and Moreno, J. L. Who Shall Survive? Beacon, NY: Beacon House, 1978. Frankl, V. (1946, reprinted 1963). Man's Search for Meaning, Washington Square Press, Simon and Schuster. 27

28

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York:

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practiced. One can assist patients from a position of tolerance and even ambiguity that serves to help any one regardless of religious identity. Helping persons know their own religion almost always helps them to develop healthier concepts of God. Likewise one can help atheists to see the spiritual and the sacred. Different cultures, different persons, and different circumstances require different notions, and it is never up to the clinician to challenge them. My notion of co-creating the divine will not satisfy the need for a parental figure to quench our fears. The inner religion of most people, their unconscious beliefs, are those taught in childhood, not the subtleties of mature theologians. Many inner Gods are punitive. Children who have been taught that God will punish with eternal torture those who disagree with our views on religion are likely, as adults, to retain, at least unconsciously, some of this hate, and some of this fear, and/or escape from religion as an ideology that destroys human solidarity. Believing that God tortures his much weaker subjects for eternity as punishment for disobedience cannot but make it easier for inquisitors and policemen to torture their prisoners. Many persons have rejected the idea of spirituality and divinity for emotional, educational, and/or moral reasons. The Spanish-Jewish physician Moses Maimonides wrote in his "Guide for the Perplexed" (1194) that educated men should not be deprived of religion because they are unable to accept simple, outdated, metaphorical explanations of nature. Similarly, moral persons should not be deprived of religion because they cannot accept God as a cruel tyrant that condemns sinners to eternal flames,29 or children to the horror of war and illness. The Italian scientist Primo Levi, a survivor of the holocaust, concluded that "if there is an Auschwitz, then there cannot be a God." A serious notion 29

In the imagination of most Christians, heaven and hell are real places. However, Christian philosophers, back to Thomas Aquinas in the 13th century, have speculated on the metaphorical quality of heaven, and in 1999, Pope John Paul II, reconfigured Catholic images of heaven and hell as poetic imagery —not actually existing sites of divine or satanic reality. Just like the story of Adam and Eve, heaven and hell are metaphors — or, at most, states of mind. Heaven is the human being's meeting with God. "Metaphorically speaking, heaven is understood as the dwelling place of God." In the same manner, hell, according to Pope John Paul II, is not a punishment imposed by God but "the pain, frustration and emptiness of life without God." The images of hell in scripture should not be taken literally. However, these sane reflections have not reached most Christians. Actually, priests and ministers have depicted hell as a world of fire controlled by devils with pitchforks for centuries, and these images have justified similar behaviors among men.

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of God must confront the issue of evil. Regarding divinity as the Attractor rather than the Creator eliminates the paradox of evil. If God only achieves infinite wisdom, goodness and power as the Infinite Attractor of evolution, it is not difficult to understand how death, suffering, illness, evil, occur as part of the evolution of the universe. God becomes their overcoming. Theology has dealt for centuries with the "question of evil" because its existence is at variance with our notion of an All-Benevolent and Almighty Divinity. Yet, belief has often promoted evil. No war is more cruel than holy war. No enemy can be so ill-treated as the heathen. No pity can be elicited by those who God Himself would condemn to eternal burning in Hell.30 However, religion has also served to create human alternatives and civilized societies. It is sufficient to mention the role of Moses as liberator of his people, the role of Christianity as a resistance and control of Roman imperialism and slavery, the creation of a new civilization by Islam, and the hope brought to Latin America by liberation theology. An essential role of religion is that faith gives us strength and fortitude. One may foster co-creation by pointing to reciprocity as a collective norm - a person gets what he gives out. The justice of the universe, however, is so slow that often does not reach our generation. Another great role of religion is to make us aware of our failings and to enable us to overcome them. Contemporary Unitarian churches and movements that developed historically from John Calvin's tradition hold the memory of Severo in special honor.31 This is true religion. It is superation, meaning a change to a superior opposite.

30 Modern secular societies, nazi, communism or democratic, have matched most of the atrocities performed by religions. Further, the suppression of religious faith in communist societies became a weapon of repression, a symbol of oppression, and a weakness that contributed to their downfall. 31 We can condemn Calvin for burning Servetus. Yet, today, for the sake of Western Civilization, we slaughter tens of thousands, and starve millions." Dr. Richard Boeke, Secretary of the World Congress of Faiths, Servetus, Science and the Breath of God. Honoring Servetus in 2003, the 450th Anniversary of his Martyrdom. Unitarian Universalist Church of Berkeley. December 28, 2003. Sermon Archive.

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Vikto^rankl(190MW)^^^^^^Primo^i(1919-1987)

12.4 Co-Creation: A Question of Science and a Question of Meaning

The notion of God as a Supreme Becoming continues the long tradition in process philosophy and science;32 it overlaps the Aristotelian concept of God as the Final Cause of the universe; and it is compatible with many religious denominations. However, it is unique in implying a personal responsibility in God's creation. Co-creation represents a conception of spirituality and divinity that is compatible with evolutionary science, 32 Griffin, D. R. (1986). Physics and the Ultimate Significance of Time. Albany: State University of New York.

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provides a meaningful explanation for the existence of evil, promotes social and personal moral behavior, and offers hope regarding the meaningfulness of individual life. Creation, determinism and chance are both scientific and moral questions. Determinism, in fact, originates in religion, where it is called fatalism when spelled in Arabic and receives a different name when proclaimed by the New Testament.33 Classic science viewed the universe as rigidly determined by mathematical laws because "the laws of nature" were indeed laws dictated by a master designer. Determinism allows one to believe that salvation means to have been chosen, which may be a recognition of grace or luck but which often implies self-serving pride and the exclusion of the other. Determinism is false innocence. As some blame the devil for their behaviors ("the devil made me do it"), others want to believe that "God made me do it" -that they follow God's will, which determines that they shall be rich and that others are kept poor. We should accept this state of affairs, because it is God's will. The poor will be rewarded in heaven. A more generous mind would think that one must work for the salvation of others to earn your own. One cannot pretend to be spiritual and devote his life to the pursuit of profit. The first duty of a good person is to do good -not well. Traditional economics the management of the household -was under the providential hand of God. The theoretician of capitalism, Adam Smith, replaced the providential hand of God with the invisible hand of the market. God is goods.34 The pursuit of profit first leads to breaking each commandment.35 Industrial science has created ecological disaster by looking at nature as a soul-less field to be dominated, rather than as a parent full of mysterious patterns. Clinical psychotherapy promotes a selfish view of human nature in which Cain's refusal to become his 33

According to Apocalypse, only a small group of Jews, all male, and virgin, will be saved. Predestination was later on proclaimed by Calvin to apply to Christians only. Locke, often regarded as progressive, maintained that the saved could be recognized because God had also given them wealth. This notion is still operative among many contemporary persons. 34 The God of Americans is goods, punned the American humorist H. L. Mencken. The same year that Smith proclaimed the new creed, the American Republic of the brave and the free was founded. Under the invisible hand, the brave new world boasts of one in twelve women with enough mercury in her bloodstream to cause fetal damage. 35 Working on the Sabbath, killing, and neglecting older parents, are examples. Money, property, and capital are graven images that replace God.

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brother's keeper is taken as a model of mental health. On the contrary, mental health is working with and for others, seeking the justice of opposites in mutual and bipolar feedback. In standard materialism, randomness is offered as an alternative to God as the origin of matter, life and consciousness. Probability arguments dismiss randomness as an explanation for natural organization, supporting the classic argument for the existence of God, namely the existence of order in the universe. This discussion is obsolete in the context of creative organization instead of static order. Probability theory also argues for accepting the existence of God on different grounds: personal gain. Throughout history, many have reasoned: if I accept God, society looks upon me as a good man, and treats me accordingly. If I do not accept God, I am placed together with drunkards, eccentrics and communists. "There is no God", James Mill confided to his son John Stuart, "but this is a family secret". Such secrets are kept not only in 19th century England. The religious faith of the French mathematician and philosopher Blaise Pascal was shaken by his research, which contradicted the official physics of the Church, and the religious wars and persecution that made him question religion on moral grounds. Pascal himself was member of a jury that condemned an older woman to burn alive as a witch. He thus proposed a wager to fortify his faith.36 To be an unbeliever is taking an infinitely unreasonable risk. Pascal assumed that there are only two alternative bets, to be Catholic (as interpreted by the political authorities) or not. His choice made him an accomplice to judicial murder. Pascal's wager was not only distastefully calculating. It was immoral. When one chooses to believe, one becomes morally responsible for what one believes in. I thus made my own wager in Union of Opposites: To believe that we co-create. If we can do it, and I do not, I make my life shallow and empty without reason; whereas if we cannot create, but I believe we can, at least I have made my life meaningful in my own eyes. 36

He reasoned: "If there is a God, He is infinitely incomprehensible, since, having, neither parts nor limits, He has no affinity to us. We are then incapable of knowing either what He is or if He is ... you must wager. It is not optional. You are embarked. Which will you choose then? Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager then without hesitation that he is."

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With less faith in the future than the Victorians, current materialist scientists regard historical contingency as meaninglessness. Sacredness has been lost in a portrait of the universe as a meaningless machine, in which life and consciousness are contingent, unpredictable, and accidental.37 "The science in creation science is not science at all, but is the moral anguish so foolish? Or should creationism be viewed rather more sympathetically -misguided to be sure, but part of a broader quest to reinvent the sacred in our secular world?" asks Stuart Kauffman in At Home in the Universe?* I feel quite at home in the universe. Life does not seem to me farcical, nor does the universe seem unfeeling. The notion of evolution does not drain life of meaning. On the contrary, the fact that creation has not ended places us in its midst, so we can be active participants in its course. The mere existence of God would not provide meaning to life.39 But if we live in an evolving universe that, starting from a purposeless and meaningless physical origin creates life, consciousness and the search for meaning, then our role, however small, in creation is indeed meaningful, vast, magnificent, and wonderful. God is the longing for God, said the 12th century Persian poet Rumi. We need to learn to dream again, proclaimed Moreno. I have a dream, said Martin Luther King. Religion exists only when it creates souls and it creates saints. The twentieth century has produced great saints: Gandhi,40 King, and Archbishop Romero. The fundamental issue is not belief in God but co-creating with God. Martin Luther King, the American saint, went beyond Martin Luther and proclaimed the notion that the man of faith must co-create with God. Salvation in this world requires work. We 37 Physicist S. Weinberg describes human life as "just a more-or-less farcical outcome of a chain of accidents reaching back to the first three minutes" meaning early processes after the hypothetical big bang. The French Nobel laureate Jacques Monod concludes Chance and Necessity stating that "Man knows at last that he is alone in the Universe's unfeeling immensity, out of which he emerged only by chance." Yet Monod was a great humanitarian; ontological materialism does not imply moral materialism. 38 Kauffman, S. At Home in the Universe New York: Oxford University Press, 1995. 39 Mere immortality does not "save" my soul. Only I can give meaning to my life. The American philosopher Robert Nozick (Philosophical Explanations. Belknap Press of Harvard University Press. Cambridge, Mass. 1981) argues cogently that the existence of a God who has designed each piece of the universe for a specific purpose fails to satisfy our needs for meaning. What if the purpose for our existence is to breathe and thereby provide carbon dioxide to the plants? 40 "/ am told that religion and politics are different spheres of life. But I would say without a moment's hesitation and yet in all modesty that those who claim this do not know what religion is." Gandhi.

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need faith and work. Faith must become personal and social action. Salvation by faith alone may be theologically correct but it is unsatisfactory from a mental health perspective. It also allows for hypocrisy. I do not want to enter into theological discussions that brought so much blood in the history of Christian Europe and of the Muslim world. From the viewpoint of mental health, we need work, not only faith. In fact we need less faith and more critical thinking. We need love more than faith.41 A notion of co-creation restores to life the sense of sacredness through real, personal and present action. Save the other.

Marlin Luiiicr King, llic A-iiiorican Saint.

41

"Now abideth faith, hope, charity, these three; but the greatest of these is charity." Paul.

Chapter 13

Biotic Evolution

Jean-Baptiste Lamarck 1744-1829

Charles Darwin 1809-1882

Peter Kropotkin 1842-1921

Abstract: Biological evolution is a creative development that proceeds from simple to complex as a result of system formation and biotic (bipolar, mutual and bi-hierarchical) feedback. Evolution results from: (1) Bipolar feedback: synergistic processes such as aggregation, endosymbiosis, pluricellularity, sexuality and sociality, as well as antagonistic interactions such as predation and competition. Synergistic mutual selection is as important as competition. (2) Priority of the simple: simple materials combine to form complex systems (molecules form biomolecules that form cells) and the production of materials by simple organisms propels the creation of higher species. (3) Supremacy of the complex: evolution creates complex processes such as photosynthesis, sexuality and brain function that redirect natural selection and evolution itself. The evolutionary changes generated by the production of oxygen by living organisms are paradigmatic of creative biotic feedback. Heterotrophy embodies both an antagonistic interaction more important than competition and the incorporation of simpler components to generate complex systems. 488

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Biological evolution is a fact,1 but its mechanisms are theory. Natural selection accounts for many evolutionary processes,2 but there are other processes that contribute to evolution.3 Here I advance the hypothesis that biological creation results from biotic processes and the synthesis of systems from preformed materials. As a biotic process, evolution involves causal action (not random change), bipolar and mutual feedback (synergy and antagonism) that generates bifurcation cascades, and the conservation of matter (genes). Preformed materials combine to form complex systems. Synergy and antagonism, bifurcation and synthesis, the priority of simpler processes and systems and the supremacy of complex ones, are three sets of complementary opposites that co-create evolution. Standard evolutionary theory postulates that biological variation results from accidental events (such as random mutations and giant meteorite crashes), and that evolution results from selection of these variations by competition for survival. In contrast, creation theory regards most variations as causal and self-generated, highlights the equal importance of synergistic and antagonistic feedback, and points to the role of complex processes for selection beyond survival. Bipolar and mutual feedback generate greater than random novelty, diversity, complexity, and extreme sensitivity to external inputs and past events. Simple and complex processes are also connected in feedback processes: The physical and chemical processes and products of abiotic evolution initiate and modulate biological evolution (priority of the simple). The complex processes generated by evolution, such as photosynthesis, sexuality and behavior, feedback upon evolution itself (supremacy of the 1 All over the world, evolution is recognized by the educated regardless of their religious beliefs. Pope John Paul II recognized evolution as a fact in 1996. Yet, it is questioned by a large number of educated Americans who misinterpret the term "theory" to mean mere speculation and regard religious metaphors as fact. "Science teaching worldwide treats evolution as routine. The United States is the exception. This controversy is not really about science but about religion and politics," states a recent report (Lerner, L. L. Good and bad science in US schools. Nature 407: 287 - 290, 2000). 2 Smith, M. J., and Szathmary, E. The Major Transitions in Evolution. Oxford: Freeman Press, 1995. Gould, S. The Structure of Evolutionary Theory. Cambridge, MA: The Belknap Press of Harvard University Press, 2003. 3 Crutchfield, J. P. and Schuster, P. (2003). Evolutionary Dynamics. Oxford University Press. Margulis, L. and Sagan, D. (2002). Acquiring Genomes. A Theory of the Origins of Species. Basic Books.

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complex). The generation of materials such as oxygen and carbohydrates by simpler organisms provides necessary components to propel the creation of higher species. This is the material hypothesis of evolution that I proposed in Union ofOpposites. 13.1 Biotic Patterns in Evolutionary Processes Evolutionary trajectories are consistent with biotic patterns generated by bipolar feedback, showing five major characteristics: (1) long periods of gradual change; (2) the coexistence of progressive and involutional processes; (3) novelty, diversification and complexification; (4) repeated cases of functional or material convergence; (5) irreversibility. Evolutionary dynamic models such as those of Bergman and Feldman4, Crutchfield,5 and Schuster6 display patterns that strongly resemble bios: periods of noise-like rough aperiodic variation with significant leaps. Biotic feedback represents a specific formulation of the kind of "stochastic determinism" that these researchers have considered in their models. In mathematical recursions, biotic feedback generates fractal trajectories interspersed with leaps, consistent with the pattern of punctuated equilibria described by Eldredge and Gould in which speciation events are separated by long periods of relative equilibrium.7 13.2 Biotic Feedback as a Cyclic Engine of Evolution In standard accounts of evolution, the planet changes and organisms adapt. Actually, organisms are active participants generating change. Animals choose where they live, how they construct their nest, and what they feed on. Through their behavior, organisms select the forces that 4

Bergman, A. and Feldman, M. W. (2003). On the Population Genetics of Punctuation. In Crutchfield, J.P. and Schuster, P. Evolutionary Dynamics. Oxford University Press. 5 Crutchfield, J. P. (2003). When Evolution is Revolution- Origins of Innovation. In Crutchfield, J.P. and Schuster, P. Evolutionary Dynamics. Oxford University Press. 6 Schuster, P. (2003). Molecular Insights into Evolution of Phenotypes. In Crutchfield, J.P. and Schuster, P. Evolutionary Dynamics. Oxford University Press. 7 Eldredge, N. The Sloshing Bucket: How the Physical Realm Controls Evolution. In Crutchfield, J. P. and Schuster, P. (2003). Evolutionary Dynamics. Oxford University Press. Gould, S. (2003). The Structure of Evolutionary Theory. Cambridge, MA: The Belknap Press of Harvard University Press.

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select them. Organisms actively change their immediate environment or niche. Climate and living organisms co-evolve.8 Climate changes organisms and organisms change climate. "Natural selection" is a bidirectional, mutual feedback. Interactions are both synergistic and antagonistic. This bipolar feedback process serves as a cyclic engine of evolution. Feedback also carries across generations, as each new organism lives in an environment generated by its ancestors and enacts behavior gained from them. A noteworthy example is how lactose tolerance increased in human populations that domesticated cattle.9 The production of physical materials is an important component of this creative feedback. Living organisms modify themselves through the alteration of the composition of the environment. The early atmosphere was primarily composed of nitrogen and contained methane and ammonia. These compounds created a reducing environment that allowed for the spontaneous evolution of organic molecules (see later). Oxygen, which is extremely toxic for many organisms, was not present in the air. This atmosphere was fundamentally changed by biological photosynthesis.10 Early Cyanobacteria began breaking down water and releasing oxygen. As oxygen began to dominate the atmosphere, the biological population of the planet changed to include respiring organisms that utilize oxygen and produce carbon dioxide. Photosynthesis and respiration depend on the products of the other. This process exemplifies co-creation by the cyclic interaction of opposites.11 Organisms are not passively selected by their environment; instead, changes in the environment, sometimes produced by the organisms 8 Schneider, S. and Londer, R. (1984). The Coevolution of Climate and Life. San Francisco: Sierra Club Books. 9 Odling-Smee, F. J., Laland, K. N., and Feldman, M. W. (2003). Niche construction: the neglected process in evolution. Princeton University Press. 10 Photosynthesis is the process that uses sunlight energy to form carbohydrates from atmospheric CO2, carried out by organisms that contain chlorophyll or related pigments. Electrons for this reduction reaction ultimately come from water, releasing oxygen. Cyanobacteria and their relatives are responsible for a major part of photosynthesis in the oceans. 11 Alternative conceptualizations include cyclic and dialectic models. The static view of planetary cycles as homeokinetic processes fails to explain a most fundamental event in evolution, the "oxygen revolution". In the Hegelian terminology of dialectics, the production of oxygen by photosynthetic organisms led to their "negation", namely respiring organisms. But photosynthetic organisms have not been replaced by respiring ones. On the contrary, both coexist in new and more complex systems, and respiration and photosynthesis coexist in every plant.

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inhabiting it, cause changes in their metabolism and behavior. Photosynthetic organisms created a new cyclic engine for creation. The generation of new molecules not previously available in the environment is a component of the creative feedback processes through which living organisms modify themselves. Bacteria and plants provide animals with organic compounds, including carbohydrates, vitamins, and other essential components that higher organisms cannot synthesize. The creation of new and more complex organisms as a result of the previous formation of materials by other organisms is the materialist theory of evolution, meaning, the production of complexity by the assembly of preexisting materials.12 Pre-formed materials sometimes perform only a "permissive action", to borrow an expression used in endocrinology. That is to say, they passively enable active processes to generate complex organisms. In other cases, pre-formed materials drive and direct change, as in genome transfers. 13.3 Co-Creation Genetic exchange is co-creation. Organisms can supply each other with genes and even complete genomes.13 Bacteria regularly transfer genes to other bacteria that can use the accessory DNA to perform additional functions.14 The American biologist Lynn Margulis of the University of Massachusetts has proposed that all bacteria have access to a single gene pool, which is to say, transfers are so extensive that the existence of separate species of bacteria is to be questioned. In higher organisms, such horizontal transfers are more limited, so species can be differentiated. Thus, species differentiate from the initial biomass of gene-transferring bacteria. The collective precedes the individual. This is in agreement with the creation theory view that individuals differentiate within pre-existing systems as contrasted to the standard view that systems form by the aggregation of pre-existing individuals.

12

Sabelli, H. (1989). Union ofOpposites. Syvaken, M. and Kado, C. I. (2002). Horizontal Gene Transfer. Academic Press. 14 Sonea, S. and Mathieu, L. Prokaryotology. Montreal, Canada: Les Presses de l'Universite de Montreal. 13

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Margulis proposes that similar transfers of complete genomes may be responsible for evolutionary processes in higher species. One of the main conclusions presented by the International Human Genome Sequencing Consortium is that "hundreds of genes appear to have resulted from horizontal gene transfer from bacteria at some point in the vertebrate lineage."15 The horizontal transfer of genes explains the development of complex functions; single mutations can hardly be expected to have created a complex organ such as the eye. Horizontal gene transfer may also explain the development of new species. Hybridization can produce speciation in yeast.16 Up to now, the formation of new species was thought to be gradual and require isolation. In Margulis' view, evolution may be punctuated and driven forward by bacterial mergers. Genomic sequence analyses have shown that horizontal gene transfer occurred during the origin of eukaryotes as a consequence of symbiosis, the bodily association of two organisms. Endosymbiosis co-creates complex systems. Living organisms promote their own evolution by assembly. Margulis has advanced the serial endosymbiotic theory that posits the origin of cellular organelles by hereditary symbiosis,17 now supported by scientific evidence. Margulis' symbiogenesis theory states that species arise from the merger of independent organisms through symbiosis. Cyanobacteria (or a closely related prokaryote) entered into symbiotic relationships with large eukaryotic, non-photosynthetic cells, becoming engulfed inside them (phagocytosis) and thereby forming an intracellular organelle, the chloroplast. In this mutually beneficial relationship (endosymbiosis), the photosynthetic organism shares the carbohydrates it produces with the host, and the host provides the photosynthetic bacterium with other compounds as well as protection. The formation of chloroplasts by endosymbiosis has not been the result of a single "chance" event, but has apparently occurred multiple times, indicating a necessary process.

15

International Human Genome Sequencing Consortium. Nature 409: 860-921, 2001. Greig, D., Louis, E. J., Borts, R. H., and Travisano, M. (2002).Hybrid speciation in experimental populations of yeast. Science 298: 773-774. 17 Margulis, L. and Sagan, D. (2002). Acquiring Genomes. A Theory of the Origin of Species. New York: Basic Books. 16

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Similarly, mitochondria, the intracellular organdies responsible for respiration, appear to have originated from the phagocytosis of aerobic bacteria by larger eukaryotic cells. Mitochondria provide oxygen-derived energy and waste disposal in return for food and shelter. Endosymbiogenesis, the merging of organisms into new collectives, is a major source of evolutionary change on Earth. The very origin of eukaryotes may have been a cellular fusion between bacteria and archea.18 Far from leaving microorganisms behind on an evolutionary ladder, we more complex creatures are both surrounded by them and composed of them. Growing knowledge of biology alters our view of evolution as a chronic, bloody competition among individuals and species. Life did not take over the planet by combat, but by networking. Life forms multiplied and grew more complex by incorporating others. Symbiogenesis represents synergy. Such synergy is so vital that eukaryotes without endosymbionts have become extinct.19 Further, endosymbiosis allows pluricellularity. There are no multicellular organisms composed of prokaryotic cells. Endosymbiosis and pluricellularity highlight the role of synergy in evolution. Exosymbiosis co-creates complex systems. The importance of synergistic processes for life and its evolution is well known20 although surprisingly absent from neo-Darwinist discussions. Co-evolution must necessarily be the rule rather than the exception. Animals and plants live symbiotically with microorganisms. We are all inhabited by intestinal flora, harmless microorganisms that are essential for nutrition.21 Also, symbiotic microorganisms can make colonization by pathogenic bacteria more difficult. Destroying these symbiotic organisms endangers not only the hosts but also other organisms. Some of the microorganisms that inhabit us die (depriving us of their services) and 18

Gupta, R. S. and Golding, G. B.. The origin of the eukaryotic cell. Trends Biochem. Sci. 21: 166171,1996. 19 De Duve, C. (2002). Life Evolving. Oxford University Press. 20 One quarter of all documented fungi are lichenized, that is to say, they live photosynthetically with green algal or cyanobacterial partners. Trees need fungi to develop. Ants have cultivated fungi for over 50 million years. Beyond symbiotic twosomes, threesomes have evolved several times. 21 The bacteria obtain nutrients from the host and supply nutrients that the host cannot synthesize itself or obtain from its food. Humans depend on their intestinal flora for essential nutrients. Ruminants also depend on their intestinal flora for digestion.

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others mutate, developing resistance to antibiotics that they can transmit to other pathogenic microorganisms. It is for this reason that antibiotics should not be prescribed unless needed. In a similar manner, antibiotics in farm animal feed cause changes in the intestinal bacterial flora of farmers2 , in their neighbors, and in consumers. Symbiosis shows that synergistic processes are fundamental in evolution. On the other hand, synergistic relations do not exclude conflict. Some microorganisms that live harmlessly in most of us can cause infections in immunodeficient persons. Long-term symbiosis may be a major engine of evolution (symbiogenesis).23 Sexuality is another process of co-creation. It is often questioned why biological organisms developed sexuality. A most obvious reason (not necessarily the only one) is that sexuality produces diversity. Meiosis and recombination work far faster than mutation to generate variety. Diversification is adaptative. The offspring of closely related organisms are often less healthy than the offspring of more distantly related organisms. Genetic diversity enables a species to overcome environmental changes by relatively fast adaptive change.24 At all levels of organization, synergistic relations are essential for the maintenance and evolution of life. Bacteria associate in colonies when stressed. Eukaryotic cells associate permanently to form pluricellular organisms; pluricellularity allows for specialization of cells into tissues and the formation of organs and systems. Animals form societies without which they cannot exist. Mind develops in the brain of humans and other higher animals through the interaction of individuals. These examples illustrate the importance of co-creative processes in evolution. 22

Levy, S.B., FitzGerald, G. B., and Macone, A. B. (1976). Changes in intestinal flora of farm personnel after introduction of a tetracycline-supplemented feed on a farm. New England J Med. 295:583-8. 23 This concept was developed in the nineteenth century by a number of European biologists, particularly in Russia, and later championed in America by I. E. Wallin and more recently by Margulis who generously acknowledges her precursors. 24 Supporting the view that sexual reproduction promotes diversity, individuals and populations of the crustacean Darwinula stevensoni, which has been reproducing asexually for at least 20 million years, vary very little from one another genetically; the genetic distance between individuals is approximately one quarter than that of closely related species that reproduce sexually. This observation contradicts an alternative explanation for the prevalence of sexual reproduction, namely that shifting DNA would help to get rid of mutations, which are mostly harmful. Most random mutations may be harmful, but sexual diversification is useful.

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Lynn Margulis

Stephen Jay Gould

Synergy allows and promotes the differentiation of cells into tissues. In contrast, cancer cells do not differentiate; they compete with other cells, killing the organism and thereby themselves. Two obvious but not trivial facts: There is no life other than as individual organisms, and individual organisms do not thrive for long without interacting with others of their species. This indicates that selection must occur at both the individual and group level. In the name of parsimony, some ecologists25 have argued that group selection should never be invoked except in cases when individual selection has been demonstrated to be inadequate. This is clearly ideological. One could argue instead that individual selection should never be invoked except in cases when group selection has been shown inadequate. Assumptions determine conclusions. 13.4 Competition, the "Negative" Component of Bipolar Feedback In their first report on evolution,26 Wallace portrays the struggle for existence as hard work27 while Darwin declares that war governs 25

Williams, G. C. (1996). Adaptation and Natural Selection. Princeton: Princeton University Press, p.159. 26 When Darwin received his setting out an outline of the theory of natural selection in June 1858, he promptly arranged a meeting of the Linnaean Society for July 1, at which two papers by Darwin were read first and then Wallace's letter. Competition was not only a theory of evolution but a reality of science. 27 "The life of wild animals is a struggle for existence. The full exertion of all their faculties and all their energies is required to preserve their own existence and provide for that of their infant

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nature.28 In the Origin, Darwin explained his idea of struggle as a metaphor, but in the context of the Victorian British Empire, his view of nature encouraged an ethos of conquest and unbridled competition that acquired the name of Social Darwinism. In the context of Darwinism, Tennyson's metaphor of "nature red in tooth and claw"29 became "science." "From the point of view of the moralist the animal world is about on a level of a gladiator's show. The creatures are fairly well treated, and set to fight- whereby the strongest, the swiftest, and the cunningest live to fight another day. The spectator has no need to turn his thumbs down, as no quarter is given," wrote T. S. Huxley in The Struggle for Existence in Human Society. According to standard evolutionary theory, competition for scarce resources selects among individuals of the same species as well as among species. Darwin adopted this focus on scarcity from the exponential model for population growth developed by Malthus (Chapter 3). Scarcity undoubtedly plays an imperative role under certain conditions, yet just as important is the ease with which life emerges as soon as a minimal set of conditions make it possible. Archaeans live in thermal vents or hypersaline water. Lichens grow in bare rocks. Life emerges and evolves also because there are natural resources. Abundance is as significant as scarcity; the feedback is bipolar. 13.5 Predation The feedback is also bipolar because living organisms are the "natural resources" that feed others. Death nourishes life. Far from going from dust to dust, we go from dust to food. Organisms that are unable to synthesize energy-rich organic compounds through photosynthesis must offspring." (A. R. Wallace. Letter to Darwin communicating the theory of evolution by natural selection, read at the Linnean Society, 1 July 1858). 28 "De Candolle, in an eloquent passage, has declared that all nature is at war, one organism with another, or with external nature. Seeing the contented face of nature, this may at first be well doubted; but reflection will inevitably prove it to be true. The war, however, is not constant, but recurrent in a slight degree at short periods, and more severely at occasional more distant periods; and hence its effects are easily overlooked." (C. Darwin, Linnean Society July 1, 1858). 29 Who trusted God was love indeed / And love Creation's final law —/ Tho' Nature, red in tooth and claw /With ravine, shriek'd against his creed — Alfred Tennyson, In Memoriam (1850).

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obtain organic compounds from other organisms (heterotrophy), primarily through ingestion. Heterotrophy takes many forms: predation, scavenging, infection, parasitism, the consumption of dead bodies by worms, as well as human hunting, fishing, agriculture and cattle raising. Predation makes it possible for one species to benefit from the metabolic creations of another. In a significant union of opposites, predation represents both an antagonistic interaction much more important than competition, and the incorporation of simpler components to generate complex systems. This explains the predominance of heterotrophy among complex organisms. Predation is not just an antagonistic interaction; it has synergistic aspects as well. It is often favorable to the organism to be useful prey. Thus, trees produce edible fruit. In the same manner, agriculture and animal domestication have increased the number of individuals in domesticated species. Like inorganic evolution, biological evolution also depends on the assembly of systems. Systems are assembled and destroyed, but their destruction is never complete. The molecular fragments of organisms thus provide the material for the formation of more complex ones. Humans, for instance, require some twenty amino acids, carbohydrates, lipids, and multiple vitamins, all of which are formed by other organisms. Heterotrophy is a major process in the creation of complexity. This may appear obvious, but it is not trivial. It demonstrates the materialist theory of evolution. 13.6 Fitness The concept of fitness is used to mean adaptation and survival (Darwin), superiority, or greater reproductive ability. These three concepts do not overlap. Darwin specifically excluded superiority in his notion of fitness,30 and did not define fitness retrospectively by observed survival, but insisted that fitter organisms could be, in principle, identified before 30 Paraphrasing Ecclesiastes, Darwin observes in the first edition of the Origin of Species,, "It is not the strongest of the species that survive, nor the most intelligent, but the ones most responsive to change."

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any environmental test by features of biological or ecological advantage.31 If "fitness" is defined as reproductive ability, bacteria, insects and rats are fitter than humans, and the concept of survival of the fittest is a mere tautology.32 Who survives? The fittest. Who are the fittest? Those who survive. Selection can exclude the unfit but cannot pick the "fittest" unless the environment would remain static for infinite time.33 The concept of "survival of the fittest" had been proclaimed before Darwin as a political thesis, and has become the ideological underpinning of sexism, racism,34 and imperialism. It has also served to justify forced sterilization and other "eugenetic" measures. The acquisition of a new capacity by an individual may confer advantages such that it becomes a generic characteristic of the species, but an imperfection may have the same effect. For instance, zoologist Ernst Haeckel, in his Natural History of Creation, supposes that a swarm of winged insects on an oceanic island is blown to the sea by a storm and destroyed. The only survivors are those insects that, by a normally undesirable mutation, have been born wingless. In this manner, a deformity is selected. Selection can favor the predominance of the inferior. Recently, human interventions have realized the promotion of the "unfit" among animal populations. Hunting for rams with the largest and most beautiful horns has promoted the predominance of animals with smaller horns;35 fishing larger fish has promoted the predominance of 31

Gould, S. (2003). The Structure of Evolutionary Theory. Cambridge, MA: The Belknap Press of Harvard University Press. 32 Smart, J. J. (1963). Philosophy and Scientific Realism. London: Routledge and Kegan-Paul. The same was argued by Popper and others. 33 Natural selection could determine the best genotype if all possible mutations could be sampled, but this requires a population that is extremely large, an infinite population. It is not possible to sample all possible mutations in actual populations. For this reason what will be the "best genotype" achieved in one population may be quite different from what is the "best genotype" achieved in another. There never is sufficient time for the "best possible genetic configuration" to emerge because evolution occurs in steps. 34 As a Jew, Einstein would have been eliminated as unfit in the Germany of his time. Would have he been fit to survive in prehistoric Africa, competing with our most primitive ancestors? Actually, the relatively mild conditions of the African forests allowed the survival of the early Einsteins that discovered fire and tools. Abundance, not scarcity, probably drove early evolution. In the same manner, we see greater scientific and artistic productivity in wealthy societies. 35 Coltman, D. W., Festa-Bianchet, M., Jorgenson, J. T. and Strobeck, C. Undesirable evolutionary consequences of trophy hunting. Nature 426, 655 - 658, 2003.

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smaller specimens. Similarly, human societies can favor the predominance of the aggressive or the greedy. Evolution is often mediated by the survival of the "unfit". Strains of microorganisms resistant to antibiotics descend from less common variants. New species of animals capable of overcoming climatic changes or taking advantage of new niches evolve from deviant individuals. Physically weaker persons often drive scientific and social progress. Salieri was more successful and lived longer than Mozart. Music appreciation in humans confers no known advantage for survival. 13.7 Synergy Synergic interactions within and among species are as important as competition. Solidarity within a species is one of the complex factors that drive and direct biological evolution. Sociality evolved in all higher species, and in fact is a major trait of the dominant species, humankind. The Russian biologist and social philosopher Prince Peter Kropotkin (1842-1921) developed a theory of evolution as resulting from cooperation among individual organisms, particularly those of the same species. Based on these concepts, he also believed in cooperative, rather than hierarchical and competitive, human relationships, and in devolving the power of the central state to local communities.3 In opposition to standard "gladiatorial" Darwinism, Kropotkin proposed cooperation, not competition, as the predominant way in which species achieve success. Kropotkin's biological views grew from his scientific experience as a naturalist studying the geology and zoology of eastern Russia. During this period, he observed that living things coped with the harsh Siberian environment primarily through cooperative behavior.37 36 This anarchist communism differs radically from both terrorist anarchism and dictatorial communism. 37 In a series of articles written as a rebuttal to Huxley's essay and printed in the same publication, Kropotkin stated: "Two aspects of animal life impressed me most during the journeys which I made in my youth in Eastern Siberia and Northern Manchuria. One of them was the extreme severity of the struggle for existence which most species of animals have to carry on against an inclement Nature; the enormous destruction of life which periodically results from natural agencies; and the consequent paucity of life over the vast territory which fell under my observation. And the other was, that even in those few spots where animal life teemed in abundance, I failed to find -although I was eagerly looking for it- that bitter struggle for the means of existence among animals belonging

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In Kropotkin's theory, synergistic interactions are central, competition plays a lesser role, and 38 mutual aid gives evolutionary advantage to living beings.39 The notion of synergy as a factor in evolution has been more recently developed by Haken40 and Corning,41 among others. Russian nonlinear dynamicists prefer the term synergetics to chaos theory. The concept of bipolar feedback also highlights the importance of synergic interactions in evolution and the overall progress towards complexity. Yet it does not advance synergy as an alternative to conflict as a motor of evolution because bipolar feedback also includes antagonism, struggle, competition and predation on equal footing. 13.8 Harmony and Conflict, Bipolar Feedback I have described Kropotkin's views more extensively than Darwin's because I expect most readers to be familiar with the latter. In my view, both synergistic and antagonistic interactions enter into the multiple feedback processes that shape evolution, as the two indispensable and inseparable components of bipolar feedback. Each of these two components predominates under different circumstances. Darwin's competition occurs when the environment is

to the same species, which was considered by most Darwinists (though not always by Darwin himself) as the dominant characteristic of struggle for life, and the main factor of evolution." 38 "Nature avoids competition in various ways: by separating species geographically into differing habitats; by sorting species into unique niches within habits; by spatial division according to gradations of environmental factors, such as oxygen content at different levels of a body of water; b y territorial demarcations, as when cats mark out with their scent the space which is theirs; and by establishing dominance hierarchies within social groupings of animals." 39 "In the animal world w e have seen that the vast majority of species live in societies, and that they find in association the best arms for the struggle for life; understood, of course, in its wide Darwinian sense - n o t as a struggle for the sheer means of existence, but as a struggle against all natural conditions unfavourable to the species. The animal species, in which individual struggle has been reduced to its narrowest limits, and the practice of mutual aid has attained the greatest development, are invariably the most numerous, the most prosperous, and the most open to further progress. The mutual protection which is obtained in this case, the possibility of attaining old age and of accumulating experience, the higher intellectual development, and the further growth of sociable habits, secure the maintenance of the species, its extension, and its further progressive evolution. The unsociable species, on the contrary, are doomed to decay." 40 Haken, H. (1977). Synergetics, An Introduction. Nonequilibrium Phase-Transitions and SelfOrganization in Physics, Chemistry and Biology. Springer. 41 Corning, P. A. (1983). The Synergism Hypothesis: A Theory of Progressive Evolution. New York: McGraw-Hill.

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plentiful and so is life. If populations stand at carrying capacity, one organism or species can increase only at the expense of others, as is more likely to occur in the tropics. In contrast to Darwin's and Wallace's observations in tropical climates, Kropotkin experienced their polar opposite. The disparity of their observations suggests that competition is greater in the midst of abundance, and cooperation is greater in the midst of scarcity.42 However, tropical abundance is so great that it always allows great diversity in the population. The unfit is excluded, but there is a great diversity among the fit. Darwin and Kropotkin are emblematic of two opposite and complementary views of selection; the concept of bipolar feedback exceeds their combination. Endosymbiosis (rather than mutual aid) is the most important form of synergism, and predation (rather than competition) is the most important form of conflict. Further, as predation shows, synergism and antagonism can coexist in a single process. The coexistence of positive and negative interactions is evident. These interactions constitute feedback because they involve the generation of change by each of the agents, and in part reactions to the action of the other. Selection is an active process. Evolution does not result only from external changes but also from autogenic action. 13.9 The "Unit" of Evolution Darwin focused on individual organisms as the "unit of evolution." Darwinism has narrowed the focus to reproducing individuals. It is argued that genetic traits that confer greater reproductive capabilities are transmitted even if they prove deleterious to the health and survival of the individual. Actually, sexually reproducing individuals are not the only significant ones regarding evolution. It is obvious that animals that contribute to the welfare of the group to which they belong enhance its survival. Thus, individuals who do not reproduce for reasons of age, mate availability, or sexual preference, still can contribute significantly 42

In a similar manner, stress aggregates bacteria into colonies and films that make them antibiotic resistant, mourning unites families, and the 9-11 tragedy increased solidarity among New Yorkers, a phenomenon still observable today.

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to evolution by means of enhancing the survival of the group. Worker bees are exemplary. As discussed earlier, no organism lives in isolation of others, so selection cannot occur at the level of the individual without also involving other organisms that stand in relation of mutual feedback. Major evolutionary events such as the transformation of the atmosphere by photosynthesis are obviously global phenomena. Experimental data demonstrates that biological evolution occurs at the level of the biosphere as a totality. Consider for instance the distribution of species' lifetimes. Currently dominant neo-Darwinian assumptions imply that there is some average lifetime per species and that the lifetimes of different species are independent of one another. This entails an exponential decline. The observed statistics for marine species show instead a power-law decay. This measurement falsifies the notion that species' lifetimes are randomly distributed. It also falsifies models of stochastic diffusion in a double-well landscape. Notably, the observed power-law decay has a p = -1.7 + 0.3.43 This is a value found with biotic series generated by biotic feedback. It thus seems evident that biological evolution occurs at multiple levels: the individual, the species, the community, and the biosphere. Yet, the "unit of evolution" has been extensively debated. For some reason, this debate has often attained religious ferocity, and has at times led to peculiar notions such as "selfish genes."44 13.10 The War of the Ants An instructive example regarding harmonic and conflictual interactions among species is the current war of the ants. It also illustrates that evolution occurs at the global level. Ants are widely spread over the planet in many different habitats; they are the ecologically dominant animals in tropical rain forests. The tiny dark-brown and black Argentine 43

Bomholt, S. (2003). The Dynamics of Large Biological Systems: A Statistical Physics View of Macroevolution. In Crutchfield, J. P. and Schuster, P. Evolutionary Dynamics. Oxford University Press, pp.81-100. 44 Dawkins, R. (1976). The Selfish Gene. Oxford: Oxford University Press. Dawkins, R. (1986). The Blind Watchmaker. New York: W. W. Norton & Company.

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ants, Linepithema humile, have arrived to Europe, the United States, and Australia aboard ships. They thrive in all three continents, displacing native ants, many of which are 10 times larger in size. In Europe, the Argentine ants have developed the largest supercolony ever recorded. It stretches 6,000 kilometers - from northern Italy, through the south of France to the Atlantic coast of Spain - with billions of related ants occupying millions of nests. While European ants from rival nests normally fight each other to the death, Argentine ants from the supercolony have the ability to recognize each other and cooperate even if they come from nests at opposite ends of the colony's range. Their success has resulted from the predominance of cooperative behavior over aggression. Professor Laurent Keller of the University of Lausanne, one of the scientists to have identified the supercolony, considers it "the greatest cooperative unit ever discovered" and hopes that that the supercolony will be destroyed by the reappearance of "healthy Darwinian aggression". The psychiatrist in me evaluates this clinically.

Fig. 13.1 Left: The infamous Argentine ant (Linepithema humile) that insidiously becomes the fittest by displaying unseemingly synergistic behavior instead of Darwinian aggressiveness. Picture from an Australian news article entitled Landcare Research scientists have found the infamous Argentine ant established around the port in Nelson. Right: A cartoon of the same ants from another Australian publication. www.viacorp.com/flybook/ fullgifs.html

The success of the Argentine ants has set off a human offensive against them, which includes not only understandable pest-reducing campaigns but also as an extensive literature characterized by ferocious rhetoric. I first learned about the Argentine ant colonization of foreign shores in articles in Science and Nature that denounced the invasion. A

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web search in 2002 revealed 2760 entries on the Argentine ants. In 2003 the number is 10600, many of them also proclaiming in strong terms that we must defend our native ants against foreign invaders. Granting that ants can be a pest, the rhetoric is excessive - only a diminished sense of humor can prevent Darwinist biologists to be scandalized by the success of the fittest. An Australian cartoon (Fig. 13.1) caricaturizes the fear of the Latin immigrant ants as a projection of an unconscious fear of immigrants. As a psychiatrist, I agree. 13.11 Psychological and Cultural Dynamics of Evolutionary Theories As all ideas, evolutionary theories are the product of subjective human minds and social culture, so they speak as much about them as they do about biological reality. For this reason, it is cogent to examine evolutionary theories from a psychological viewpoint. Darwinism and neo-Darwinism have made speculative forays into sociology, economics, psychology, and education that require critical examination. Many psychosocial issues emerge in evolutionary science: the denial of evolution by a large segment of the educated population in America, the directionality of evolution (progressive or neutral?), the focus on random mechanisms, the stress on conflict and scarcity, and the strange concept of "selfish genes." Evolution seems like a figure in a Rorschach test onto which everyone projects his own ideas and feelings. Dawkins' idea of selfish genes portrays current economic ideology rather than scientific fact. Sociologists, psychologists and psychiatrists often are surprised to learn that such hypothesis is even entertained. Other sociobiologists speculate that rape is a natural behavior,45 or that adult males "try to avoid providing assistance to non-relatives."46 In less pathological fantasies, sociobiologists regarded male promiscuity and female faithfulness as the normal consequences of selection for increased reproduction. Genetic markers demonstrating female promiscuity in 45

Thornhill, C. T. and Palmer, C. T. (2000). A Natural History of Rape: Biological Bases of Sexual Coercion. Cambridge, Mass: MIT Press. 46 Sherman, P. W. and Neff, B. D. (2003). Father knows best. Nature 425: 136 -137.

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many animal species, including birds,47 have regrettably further shattered these masculine expectations. Adopting again my psychiatrist's role, I diagnose many of the notions built around the selfish gene hypothesis as psychological projections; they undoubtedly are influenced by social factors, but most males fail to commit rape or even avoid assisting strangers. Why do scientists accept the unlikely idea that genes have a self? Undoubtedly because the notion of natural selfishness is congruent with the materialist individualism that dominates our culture -what Lasch has called the culture of narcissism.48 Biologists may find it inappropriate that we interpret their theories on psychological terms, just as they object to be linked with particular philosophies. Scientists may deny that they have any (conscious) philosophy, but can hardly claim that they do not have a mind. Social, cultural and psychological facts also find mirror images in the view of natural selection as struggle. Given that so many biological processes are synergistic rather than conflictual, it is notable, at least from the perspective of a psychiatrist, that these are not even considered in many discussion of evolution. Instead, there is a focus in competition, which as we have seen, may be a lesser mechanism. Specialists such as Margulis reject the use of anthropomorphic terms such as cooperation or competition in biology. It is nevertheless cogent to speak of synergy and antagonism, positive and negative feedback. Systems scientists49 regard a reformulation of evolutionary theory away from competition and conflict as instrumental in promoting healthy human behavior. In the same spirit, and perhaps guided by his Marxian philosophy, Gould rejected the gladiator interpretation of Darwinian theory. According to Gould, nature is amoral, sometimes favoring cooperation and sometimes favoring struggle. Peacefulness, equality and kindness are as biological as violence or sexism; nature offers no guide for human behavior. Gould thus regarded evolution as directionless, i.e. it does not promote evolution from simple to complex. Yet, he also 47

Simple arithmetic undermines similar beliefs regarding humans, as one to one intercourse requires an equal number of women and men. 48 Lasch, C. (1978). The Culture of Narcissism. W. W. Norton, New York. 49 Loye, D. and co-workers. The Great Adventure: Toward a Fully Human Theory of Evolution, State University of New York Press, in press.

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considered it his personal responsibility as a scientist to promote education and oppose war. Gould interpreted evolution to include both positive and negative interactions because he thought dialectically. From a different perspective, the cybernetic concept of biotic, bipolar feedback also indicates the coexistence of cooperative and conflictual aspects in nature, but regards their coexistence as necessary and creative. Nature does not simply allow the coexistence of cooperative and conflictual behavior. Natural processes always include both, and their interaction creates novelty, diversity and complexity. 13.12 Social Implications of Darwinism Social Darwinism consists of three related concepts (1) the idea of the "survival of the fittest," (2) classical economics with its preference for laissez-faire, and (3) the Protestant Ethic with its focus on hard work, thrift and economic individualism, postulating a causal relationship between moral virtue and economic success, and sin and failure.50 Spencer even championed the view that the State should not provide public education. The "gladiatorial view of evolution" also found expression in eugenics (promoting forced sterilizations), sexism, classism, Nazism, dictatorial Communism, imperialism and racism. The link between Darwin's natural selection and racism is not surprising given the intellectual climate of the British empire.51 Three centuries after the Pope declared that Native Americans were human, the issue was being debated in England, and Colonel Amherst (honored with the name of cities, universities and colleges) inaugurated biological warfare by providing infected clothing as gifts to the Indians. Darwin proposed that human races were subspecies, and entitled his book On the origin of species by means of natural selection or the preservation of favored races in the struggle for life. More specifically, Darwin extended the 50 Hofstadter, R. (1959). Social Darwinism in American Thought. New York: George Braziller. First published in 1944. 51 Locke was a slave-owner, Hume supported racism, and Hobbes coined the infamous notion of man as man's wolf, which is unsubstantiated by the intense and cooperative social behavior of wolves. Intraspecies violence is inhibited in animal species that have built-in weapons (fangs, antlers, claws) strong enough to do serious harm.

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view of survival of the fittest to national conflicts. He writes: "The more civilised so-called Caucasian races have beaten the Turks hollow in the struggle for existence. Looking at the world at no very distant date, what an endless number of lower races will have been eliminated by the higher civilised races throughout the world."52 Darwinism, as all "isms", is an ideology. Darwinism followed a line of thought stretching from Hobbes, Smith and Malthus, and continues to be a dominant ideology. Natural selection is explained in terms of Malthusian scarcity, purportedly supporting with biological evidence the economic ideologies that actually inspired the interpretation of the biological data. By extending Malthusianism to biology, Darwinism provides a justification to policies that address the pressure of growing populations for a share of wealth with the privatization of water, air, land, energy, education and medicine, bringing forth war and famine. A chapter celebrating war as an evolutionary tool appears in Wilson's Sociobiology, albeit it was decorously omitted in the paperback edition. Darwinism acquired instant success because it supports the claim that success rewards merit, so dear to those with power to acquire wealth by at the expense of others. It justifies competition as the motor of progress. Yet, the subjection of education, science and art to competition forces persons to stray their efforts to the pursuit of less valuable goals. Competition can promote progress, but it is also a motor for destruction, wars being the simplest example. Darwinism's stress on winning is no more than the self-idealization of the powerful, and the carrot they offer others in order to encourage fidelity to the system. Darwinian competition is considered to justify free competition in the market, but it also promoted struggle against capitalism. Marx greatly admired Darwin's theory because he idealized class struggle as a liberating force. Not surprisingly, T. S. Huxley explicitly regarded the rejection of nature's struggle as the basis of civilization.53 In contrast, the mutual aid view of Kropotkin regards nature as a guide for human behavior. 52

Letter to W. Graham. 3 July 1881, quoted by C. Davis Darwin Use of Language. http://www.idlex.freeserve.co.uk/idle/evolution/malthus/darwinswar.html 53 In Evolution and Ethics, 1893, T. S. Huxley proposes "not so much to the survival of the fittest, as to the fitting of as many as possible to survive. (...) the ethical progress of society depends, not on imitating the cosmic process, still less in running away from it, but in combating it."

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Kropotkin's ideas on evolution contrasted sharply with those of British Darwinists, perhaps in part due to their opposite feelings regarding their respective empires - prince Kropotkin left Russia while most of his British colleagues regarded empire as "white man's burden".54 Like Kropotkin, I regard observations of natural processes as a guide for human action because the continuity between animal and human life and behavior seems to me an essential fact. Like Darwin, I regard selection as including both synergistic and antagonistic components. This has quite different social implications: progress is fostered by enhancing social synergies and also by competitive processes, but one without the other produces stagnation or destruction. In this sense, creation theory departs from the conflictual theses of sociobiological, economic and political materialism. Summarizing, evolutionary processes include both synergistic and antagonistic interactions - positive and negative feedback. Cooperative interactions include not only symbiosis and sociality, but also pluricellularity, endosymbiosis, and the transformation of the environment. Conflictual interactions include not only competition for food and sex but also the universal phenomenon of predation that underlies the supply of ready-made components and thereby contributes to conservation and the formation of complex systems. 13.13 The Creative Evolution of Charles Darwin From the Origin to the Descent of Man, Darwin's ideas evolved. In Origin, the emphasis was on struggle, competition and survival. In the Origin, Darwin used the term "kill" twenty-one times, "race" 132 times, "selection" 440 times, "exterminate" 58, "destruction" 77; by contrast, there is no mention of cooperation, collaboration, community, or symbiosis.55 In Descent, David Loye56 notes, Darwin writes 95 times of 54 An expression coined by R. Kipling in a poem subtitled "The United States and the Philippine Islands" promoting a war of conquest in which over a quarter million Filipinos and 4200 American soldiers died. 55 Caldwell, D. E. (1999). Post-modern ecology- is the environment the organism? Environmental Microbiology 1: 279-281. 56 Loye, D. (2000). Darwin's Lost Theory of Love. Universe.

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love, 92 times of moral sensitivity, 61 times of sympathy, and 200 times of brain and mind as prime drivers for evolution at our species level, while he writes only twice of "survival of the fittest" and nine times about competition. Darwin's ideas evolved from an exclusive focus on Malthusian struggle to also include Kropotkin's solidarity. Darwin thus saw the two sides of bipolar feedback. A bipolar feedback model of evolution is Darwinian, as opposed to the Darwinist stress on struggle and competition. Darwin's view stands in sharp contrast to current "Darwinism", with its emphasis on conflict that dominates sociobiological publications, evolutionary teaching at all levels, and the commercial media. Darwinism misinterprets Darwin. The fact that Darwin's ideas changed so drastically points to the personal and creative nature of his thinking. Darwin's theory has often been portrayed as a projection of Victorian class warfare and imperialism. Undoubtedly national culture, sex and class are important perspectives that influence the development of ideas, but they do not determine them. Scientific ideas, as all others, are beyond social, personal psychological processes. The fact that "Darwinism" distorted so drastically Darwin's ideas illustrates that ideas are not transmittable gene-like structures, as envisioned by another product of the sociobiological imagination - "memes". Ideas are evolving processes, not conserved structures. It is not surprising that Darwin's ideas became richer, sharper and truer upon further reflection. It is to be noted, however, that this evolution took place as Darwin aged. Darwin did not only grow old; he also grew up. In contrast, present culture asserts that age decreases intelligence and stops creativity; this is one aspect of the oppression of older adults (see Chapter 16). 13.14 The Genetic Theory of Evolution: Discreteness and Conservation According to the mathematical biotic model, creation requires discrete elements and conservation. Evolution requires genes. Although the Catholic monk Gregor Mendel had discovered genetic processes as early

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as 1866, during Darwin's active life, his work was ignored until its rediscovery by Hugo de Vries near the turn of the twentieth century. During the initial development of genetics, some regarded it as the opposite of evolution, and Darwinian theory was rejected in the same way as Lamarck's contributions are ignored today. Genetic research has also ruled out that function creates its organ in a direct fashion as envisioned by Lamarck,57 but acquired characters may be inherited through indirect mechanisms, including selection among others.58 Following the Swedish botanist Carl Linnaeus who had described the sexual role of flowers (and for this reason known as a "botanical pornographer"), Mendel entertained the notion that hybridization is the source of biological variation. Today we recognize that variation, sexual recombination, and mutation are major sources of variation. Further sources of variation, such as endosymbiosis and genetic transfer, also result from genetic combination. Medical and agricultural genetics are the practical application of Mendelian theory. As other opposites, genetics and evolution are complementary. Mendelian genetics came to fill two major gaps in Darwin's theory. One was the lack of an explanation for heredity, of which Darwin was aware. The other one was the necessity for discrete transmission of hereditary characters that the engineer Fleeming Jenkin and others had pointed out to him. If the characteristics of the parents were blended in the offspring, as Darwin proposed, a single fortunate variation within a population could not spread through the species. It would be blended out, just as a single drop of white paint would be in a gallon of black. These issues were solved in the "new synthesis" developed by combining Darwinian selection with Mendelian genetics. While current evolutionary theory is often labeled as Darwinian, it is actually largely Mendelian.

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August Weismann proposed that the soma and the germline are irremediably separated and therefore genetic variation arising during the course of ontogeny cannot be inherited. In 1958, Crick updated this view, postulating that transfers from protein to R N A or D N A do not exist, and gave it the unfortunate name of "central dogma". 58 Lamarck never proposed that acquired habits produce genetic mutations —genes and mutations were not yet discovered. Darwin's theory also included the notion that all living beings carry "gemmules" that accumulate experience during the life of their bearers and transmit them to the next generation. This is scarcely different from Lamarck's hypothesis.

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Gregor Mendel (1822-1884)

J.B.S. Haldane (1892-1964)

13.15 The Statistical and Dialectic Synthesis The synthesis of Mendelian and Darwinian theories involved major contributions by several scientists59 and included a groundbreaking element: statistics. The Causes of Evolution (1932) by the British geneticist J. B. S. Haldane reestablished natural selection as a fundamental mechanism of evolution by explaining it in terms of the mathematical consequences of Mendelian genetics. Thus Haldane, along with Ronald Fischer and Sewall Wright, founded population genetics. Haldane went farther: he also incorporated Claude Bernard's theory of the constant internal milieu, Frederick Engels' dialectic of nature, and Louis Pasteur's cosmic asymmetry. The son of J. S. Haldane, who was both an eminent physiologist and a philosopher, J . B. S. Haldane understood the need for a comprehensive philosophical perspective in science. He first adopted a Kantian perspective and later dialectic materialism, which he understood, after Engels, as the "science of the

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The modern synthesis was advanced in the early 20th century by the British geneticist J . B. S. Haldane, the American geneticist Sewall Wright, the British mathematician Sir Ronald Fisher, the Russian-born American geneticist Theodosius Dobzhansky; the British biologist Sir Julian Huxley; the German-born American biologist Ernst Mayr, the American paleontologist George Gaylord Simpson, and the American botanist G. Ledyard Stebbins.

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most general laws of change in nature, society, and thought".60 But Haldane's evolutionary dialectic - Darwinian, Mendelian, Pasteurian, quantum mechanical, and statistical - was radically different from Soviet Marxism that was Lamarckian and anti-Mendelian, excluded quantum theory, and did not use mathematical methods. Haldane regarded the three principles of dialectics as general physical and biological hypotheses. For instance, he regarded the union of opposites as embodied in quantum complementarity of particle and wave. More importantly, philosophy did not come as a reflection after empirical or mathematical research, but served to guide research by suggesting general methods and concrete hypotheses. For instance, the law of quality and quantity relates to Haldane's principle that size very often defines what bodily equipment an animal must have; insects, being small, can absorb oxygen through simple diffusion, but larger organisms require more complex respiratory systems. Empowered by natural philosophy, Haldane also pioneered the study of the origin of life. 13.16 Dialectic Conflict The use of natural philosophy as a tool to develop methodology and concrete hypotheses showed its dark side in the Soviet Union. Marx and Engels were Darwinists, viewing the struggle of species as a dialectic conflict. In the 1920s, biologists all over the world debated the conflicting claims of Mendelian genetics, Darwinism and Lamarckism. In the Soviet Union, the debate was derailed by militants demanding that science be reconstructed on the basis of proletarian dialectical materialism, rejecting theories that were foreign and therefore bourgeois. This opened an avenue for T. D. Lysenko, a non-scientific agronomist, to seize power. He became famous for discovering (actually, rediscovering) an agricultural technique that allowed winter crops to be obtained from summer planting, thus improving production. He made excessive claims that were accepted, and he was promoted to positions of power from which he not only disseminated a pseudo-Lamarckist theory of evolution, 60 Sheehan, H. (1985). Marxism and the Philosophy of Science. A Critical History. Humanities Press International.

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but also destroyed the careers and lives of competitors. In 1948, he denounced Mendelian thought as "reactionary and decadent" and declared such thinkers to be "enemies of the Soviet people".61 Through his efforts, many real scientists were sent to labor camps or simply disappeared.62 The Lysenko affair was not an isolated case. Quantum mechanics and psychoanalysis were also discarded in the Soviet Union as bourgeois ideologies. In my view, this is not a result of the distortion of dialectic materialism but an unavoidable consequence of the idealization of conflict by Marxism, its focus on material issues, and the vague, non-mathematical formulation of its principles. 13.17 Priority of the Simple: the Abiotic Origin of Life That living processes are physical is the single most important principle in biology. It follows that there is a necessary continuity between inorganic and organic evolution. Regarding both inorganic processes as fundamentally creative allows one to consider biological evolution as driven and directed by the same general laws that energize and direct physical processes. The biotic feedback model specifically connects abiotic and biotic processes. Current research63 indicates that metabolically sophisticated life had arisen before 3.83 ± 0.01 billion years. As the age of the Solar System and the Earth is estimated to be 4.54 billion years, it seems that life emerges as soon as a minimal set of conditions make it possible. This suggests that biotic evolution follows directly from abiotic evolution.

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Gardner, M. (1957). Lysenkoism. In Fads and Fallacies in the Name of Science. New York: Dover Books. 62 Leading the defense of genetic science was Nikolai Vavilov, the director of the Institute of Genetics of the Academy of Sciences. Remembering Bruno, he wrote: "We shall go the pyre, we shall burn, but we shall not retreat from our convictions. I tell you, in all frankness, that I believed and still believe and insist on what I think is right.... This is a fact, and to retreat from it simply because some occupying high posts desire it is impossible." In 1940, Vavilov was arrested, stood trial and was found guilty of sabotage in agriculture, belonging to a rightist conspiracy, and spying for England. He was sentenced to death. After spending several months in a death cell, Vavilov's sentence was commuted, but he died in prison in 1943 of malnutrition. 63 Mojzsis, S. J. and Ryder, G. (2001). Extraterrestrial accretion to the Earth and Moon ca. 3.85 Ga, In: Accretion of Extraterrestrial Matter Throughout Earth History, edited by B. PeucknerEhrenbrink and B. Schmitz. Kluwer, pp. 423-446.

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This continuity is an essential piece of all natural philosophy. From the time of the ancient Greeks until the late nineteenth century, it was generally accepted that life forms arose spontaneously from non-living matter. Early scientific research on the origin of life (e.g. Redi, Needham, Spallanzani, Pasteur) was devoted to prove that life did not spontaneously appear. They were inspired at least in part for the desire of demonstrating that the intervention of God was necessary. The first experiments devoted to investigate how life could be created naturally were performed by Haldane and the Soviet biochemist Alexander Oparin64 in the 1920s. Haldane's and Oparin's investigations, which proceeded independently from each other, were both fostered by dialectic materialism.65 Mechanistic materialism provided no guidance for such research, and religious philosophy generated animosity against Oparin's theory. Even as late as 1955, "his exposition struck me as laughable, if not suspect of sinister, Marxist connotations," tells us Catholic Christian de Duve on his book on the origin and evolution of life.66 Let us consider this relation between science and philosophy in creative thinking, which is one of the goals of our research project. These oppressive effects of philosophy, be it Catholic Aristotelism, Marxist materialism, or religious fundamentalism, have promoted the idea of non-philosophical science. However, natural philosophy gave birth to science and is still fertile witness the inspiration provided by Christian philosophy to Pasteur, and dialectic materialism to Haldane and Oparin. Rejecting the wider and critical perspective of philosophy does not liberate science from philosophy. Rejecting philosophy is also an ideology, namely positivism. In the name of philosophical neutrality, Darwinism fails to consider critically its own assumptions, and thereby allows the development of scientifically dubious notions that play a negative role in social and personal life. Evolutionism has often led to inhuman behavior, promoting eugenics67 and forced sterilization, which is still practiced at the time of writing this book.68

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Oparin, A. I. (1936). The Origin of Life on Earth. (English edition in 1938). Sheehan, H. (1985). Marxism and the Philosophy of Science. Humanities Press International. 66 De Duve, C. (2002). Life Evolving. Oxford University Press. 67 A pseudoscientific endeavor "for improving the human race" invented by Sir Francis Galton, a cousin of Charles Darwin, who proposed to sterilize the "mentally deficient" including alcoholics, 65

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Positivism also failed to promote the scientific study of the creation of life by abiotic processes. It began in the USA with the work of the Chicago researchers Harold Urey and Stanley Miller in the 1950s. In 1961, the Spanish-American biochemist Juan Oro of the University of Houston showed that amino acids and adenine could be made from hydrogen cyanide and ammonia in an aqueous solution. Adenine is particularly significant because it is one of the four bases in RNA and DNA and also a component of adenosine triphosphate (ATP), which is the major energy-releasing molecule in cells. Many of the compounds synthesized in these experiments have been found in meteorites, and are thus known to be naturally produced in space by abiotic processes. Proteins and nucleotides are both necessary for life as we know it. This presents a paradox. Protein synthesis requires genetic instructions (RNA and DNA), while proteins such as DNA polymerase are required to read these instructions. Several models have been proposed in order to solve this problem, such as the hypercycles discussed by Manfred Eigen and Peter Schuster.69 An alternative is suggested by the work of Nobelprize laureates Sidney Altman and Thomas Cech70 who independently showed that RNA can both store genetic information and act as an enzyme; such RNA is called a ribozyme. Life may have started in an "RNA World". The ribozyme offers a biological model for the notion that action and information must be associated to generate a creative process. Notably, more complex forms of life emerged from a bifurcation / differentiation in which the information is conserved by DNA while enzymatic actions are performed by proteins. Evolution proceeds by bifurcation as well as by the synthesis of systems. In these models, the prebiotic development of a genetic system capable of evolution is epileptics, deaf, dumb, and blind persons. This program was most actively pursued by Hitler, but was also practiced in the USA, and many European countries. 68 Women subjected to forced sterilization include Romani women in Slovakia, indigenous women in Peru during the last decade, Native American women during the 1970s (3,406 according to the General Accounting Office, between 1973 and 1976; 60,000 and 70,000 over the decade according to Sally Torpy, Endangered Species: Native American Women's Struggle for Their Reproductive Rights and Racial Identity, 1970s-1990s, Master Thesis, University of Nebraska at Omaha, 1998. Also, 10 per cent of Native men were sterilized during the decade. 69 Eigen, M . and Schuster, P. (1977). The hypercycle. A principle of natural self-organization. Part A: Emergence of the hypercycle. Naturwissenschaften 64:541-565. 70 Gesteland, R., Cech, T., and Atkins, J. F. (eds). The RNA World. Cold Spring Harbor Monograph Series.

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regarded as the initial step, followed by the evolution of metabolism and then autotrophy. Among alternative hypotheses, Wachtershauser71 has proposed an autotrophic origin in the deep ocean floor near hydrothermal vents. The success of experiments demonstrating prebiotic synthesis of biomolecules and the early appearance of life on the planet indicate not only the continuity of physical and biological processes, but also that life does not result from a haphazard random and rare event, as proposed by leading biologists.72 Certain molecular combinations occur naturally because they conform to specific patterns. Biological evolution thus involves processes that are pre-adapted to the external world because they are made up of the same materials and the same patterns as the external world. The emergence of life by chance is highly improbable, but the creation of life by causal processes seems to be probable, even necessary. This implies that life has probably originated multiple times. 13.18 Biotic Evolution beyond Static Population Dynamics Antagonistic interactions are mutual feedback processes. The coevolution between plants and their natural enemies - including viruses, fungi, bacteria, nematodes, insects and mammals - may have generated much of the Earth's biological diversity.73 A plant develops a new form of resistance that reduces the survival or virulence of its natural enemies; its enemy then develops a counter-resistance. A process analogous to co-evolution occurs in agricultural systems, in which natural enemies adapt to crop resistance introduced by breeding or genetic engineering. For this reason, the cost effectiveness of crops genetically engineered to be resistant to pests is questionable, considering that research and development costs are enormous compared to conventional breeding.

71

Wachtershauser, G. (2000). Origin of Life: Life as We Don't Know It. Science 289: 1307-1308. Monod, J. (1970). Le Hasard et la necessite Chance and Necessity, translated by A. Wainhouse. Vintage, 1971. 73 Thompson, J. N. (1994). The Revolutionary Process. Chicago: Univ. of Chicago Press. 72

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Antagonistic interactions can initiate speciation.74 Interacting populations of prey and their predators have revealed similar dynamics (Fig. 13.2), regardless of the specific species under study. When compared over many generations, the sizes of the predator and prey populations may oscillate in a fairly regular manner. Increases in the prey population will cause the predator population to rise, and increases in the predator population cause the prey death rate to rise. These oscillations are out of phase; while one increases, the other tends to decline, and vice-versa (Fig. 13.2). Alfred Lotka75 and Vito Volterra76 (working independently) modeled these interactions as a set of coupled differential equations. The prey-predator relation is a mutual feedback. This is a special case of bipolar feedback: growth in the prey population increases its consecutive rate of growth but also its rate of death as a result of predation, while growth in the predator population decreases its consecutive rate of growth as a result of prey depletion. This cycle is regarded as a model for a cyclic attractor. An abundance of prey leads to a higher predatory population after a reproductive time lag. This pattern has been observed in experiments in which planktonic rotifers consume one genetic variety of algae. In contrast to such static models, a study77 of population dynamics in which the algae population included two or more phenotypically different clones, the predator-prey cycles were nearly exactly out of phase: predators peaked when prey were at a minimum and vice versa. This pattern can be explained by the ability of algae to rapidly evolve in response to intense predation; the prey population becomes dominated by clones that are resistant to predators. Thus, ecological and evolutionary dynamics can occur on similar timescales. Rapid evolution can modify 74 For instance, infection with cytoplasmically inherited bacteria cause a number of reproductive alterations in insects that serve as a barrier to gene exchange. There are reported instances of Rickettsia species that affect host reproduction. One causes female-biased sex ratio in mites, and a second causes male killing in ladybird beetles. (Cort, L., Anderson, C. L. and T. L Karr. Wolbachia: Evolutionary novelty in a rickettsial bacteria. BMC Evolutionary Biology 1:10, 2001.) 75 Lotka, A. J. (1925). Elements of Physical Biology. New York: Dover Publications. 76 Volterra, V. (1926). Fluctuations in the Abundance of a Species Considered Mathematically. Nature 188: 558-560. 77 Yoshida, T., Jones, L. E., Ellner, S. P. Fussman, G. F. and N. G. Hairston Jr. (2003). Rapid evolution drives ecological dynamics in a predator-prey system. Nature 424: 303-306.

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population cycles and transform them into creative processes. Similarly, in a numerical bifurcation analysis of the Rosenzweig-MacArthur preypredator model, a rich evolutionary dynamic was found.78

Fig. 13.2 In the standard predator-prey cycle, peaks in prey are followed by predator peaks by one-quarter of a cycle.

One may thus regard the prey-predator relation as a cyclic engine of evolution rather than as a static cyclic attractor. Illustrating this point, the cyclic dynamics of lemmings and their predators exhibit at times periodic fluctuations and at others, no clear pattern.79 Notably, a perfect cyclic pattern with the peak in predator numbers lagging behind that of its prey by one-quarter of a cycle occurs when there is a multiplicity of nonspecialized predators that stabilize the prey density at critical times, 78 Dercole, F. Irisson, J-O, and S. Rinaldi . (2003). Bifurcation Analysis of a Prey-Predator Coevolution Model. SIAMJ. of Applied Math. 63: 1378-1391. 79 Hudson, P. J. and Bjornstad, O. N. (2003). Vole stranglers and lemming cycles. Science 30: 797798.

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allowing the specialist predator to catch up.80 The cyclic pattern requires more than two participants; this is not a simple case of mutual feedback. This contradicts elementary descriptions of nonlinear dynamics in which the prey-predator cycle is presented as a closed system. Actually, predation always occurs in the context of a food chain in which each predator is also prey and every prey is also a predator (Fig. 13.3).

Three types of evolutionary relations

T

soiidarit

(Jy* 4.

[ symbiosis

+

y

+ * ( ) + competition 1 prey-predator

+

j

Fig. 13.3 A biological web involves multiple forms of relation among organisms Circles and squares represent individual organisms. Arrows represent interactions, positive (+) or negative (—>). Organisms at the same level both cooperate and compete with each other -one form of bipolar feedback. Organisms at different levels have prey-predator relations. Every organism exists as a prey of some and predator of others. Also, there are mutually beneficial symbiotic relations.

Biological communities are not just food chains, and food chains are not simple hierarchies. While we may regard ourselves at the top of the food chain, we are eaten by infectious organisms during life and by many others after death. Prey-predator interactions occur in a bi-directional 80 Gilg, O., Hanski, I. and Sittler, B. (2003). Cyclic dynamics in a simple predator-prey community. Science 302: 866-868.

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hierarchy in which organisms located higher in the food chain may serve as food for lower organisms. In such a web, there are two orthogonal cyclic engines that provide bipolar mutual feedback: prey-predator interactions between levels in the food chain, and solidarity-competitive relation between similar organisms at the same level in the chain (Fig. 13.3). 13.19 Co-Creation, an Alternative to Individualistic Game Theory Currently, game theory is employed as a framework to explore coevolution. Game theory is the study of conflict between thoughtful and potentially deceitful opponents, intended as a mathematical foundation for capitalism by its creator, the French politician Emile Borel. It was later developed for economic and military purposes by Von Neumann (who advocated an immediate unprovoked nuclear attack on the Soviet Union). 81 These models are full of military metaphors such as "strategy", "hawks and doves", "unbeatable strategies", and "playing chicken". The paradigmatic game is the Prisoners' Dilemma. 82 An enormous proportion of experimental studies on altruism involve the "prisoners' dilemma", a sad commentary on our times, in which the USA competes with China for having the largest prison population. Standard descriptions of the game adopt the viewpoint of the police interrogating two suspects in a crime, but it is crucial to imagine the dilemma also from the perspective of political prisoners being held for interrogation by Hitler's or Pinochet's police: the prisoners' dilemma is not a game. The so-called prisoners dilemma is no dilemma: one would not harm a partner no matter what. The two suspects are held for investigation by the police in separate rooms. Each is offered better treatment if he confesses. 83 Each knows that he might be better off if he gives the police 81

Pundstone, W. (1993). Prisoner's Dilemma. Doubleday, N e w York. These games were devised in the 1950s as part of the Rand Corporation's investigations into game theory regarding global nuclear strategy. 83 Lacking sufficient evidence for conviction, an astute policeman makes the following offer to each. " Y o u may choose to confess or remain silent. If you confess and your accomplice remains silent, I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, he will g o free while you go to jail." 82

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the information they seek, while this will work against his partner. The fear is that the other will talk and he remains silent. Their best outcome is for both to remain silent, particularly as there is no guarantee that the police will keep their promise (two always implies a third). If both confess, both lose. Remaining silent offers the best outcome. Solidarity is both ethical and efficacious. If a prisoner cannot count on the other, he is better off confessing than remaining silent; this results in a Nash equilibrium in which both suspects confess. The result is worse than if both had remained silent, showing that the Nash equilibrium does not necessarily yield the best outcome. The concept of optimal strategy and Nash equilibrium is applied to evolution84 under the assumption that survival will belong to those individuals in the population who display "rational" economic behavior - rational defined as selfish, as per standard economics.85 In reality, individuals live in groups, and participate in bipolar feedback processes. Consider animals sharing a fixed food supply. If all animals eat the necessary, they may all survive. If some animals gorge, however, the food supply will not be sufficient. What is a rational behavior for the individual? To gorge or not to gorge? If A does not gorge and others do, he will not survive. It is thus rational to gorge, and thus the group will necessarily self-destroy. Thus, evolution would eliminate a population formed by individuals who practice "rational" economic behavior. For this reason, "selfish genes" would be eliminated in the course of evolution. Truly rational organisms "calculate" the future. Self-preserving genes create solidarity. Gorging may have a short-term positive effect, but it receives a more powerful negative feedback from the reaction of other members of the group or from the inexorable hand of nature that wipes out populations of anti-social organisms. This negative feedback may be slow in humans, as gorgers who become very powerful may cause vast environmental destruction and enormous public deficits during their lifetime. Apres moi, le deluge (after me, the flood), said Louis XIV. As soon as one introduces time and 84 Kauffman, S. (1995). At Home in the Universe: The Search for the Laws of Self-Organization. Oxford: Oxford University Press. 85 In standard economics, rational behavior means that individuals maximize some objective utility function under the constraints they face.

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repetition, the situation changes radically. In a tournament of Prisoner's Dilemma run by political scientist Robert Axelrod,86 programs played repeated games. The best strategy that emerged was "tit for tat," advanced by Anatol Rapoport. Each player cooperates unless the other defects, in which case the confession is retaliated in the next game and then cooperation resumes. Equally effective is the "always defect" strategy. But this would not apply to actual populations.87 Game models assume that each individual lives by himself and has occasional random encounters. This is fantasy. In reality, cooperators preferentially interact with other cooperators, and shun defectors. Individual behavior elicits bipolar social feedback. Groups with a high proportion of cooperators will have higher fitness.88 Selection occurs not only within groups but also between groups. Further, solidarity is not only the result of such benefits. It is a most basic instinct.89 Game theory is the mathematical toolbox for explaining and shaping social behavior on the actions and needs of individual agents. Its application to biology derives from the political ideology of 'homo economicus' and "selfish genes",90 and their usefulness is limited by the ambiguity of the experimental evidence. For instance, it is not clear from observation what the motivation of female lions establishing a territory is; do they play "chicken" or "prisoners dilemma"? These mathematical models for evolution are accepted only within their field; their terminology imposes on their practitioners an ideological manner of thinking that isolates them from insights from other fields. Specialization allows the formulation of concepts that are obviously flawed when evaluated from the perspective of other disciplines. Let us then embed 86

Axelrod, R. (1984). The Evolution of Cooperation. New York: Basic Books. A clinical example will illustrate the point. I use the "tit for tat" story to teach patients how to interact effectively with family or workmates (Sabelli, Union of Opposites, 1989). The strategy involves being nice, provocable, forgiving, and clear, explains Axelrod. "Nice": do well for the other. "Provocable": retaliate if the other misbehaves. "Forgiving": retaliate only once, and then return to good behavior. "Clear": let the other know that is how you will behave. This strategy is both healthy and extremely useful, while the equally effective "always defect" strategy is neither. 88 Sober, E. and Wilson, D. S. (1998). Unto Others: The Evolution and Psychology of Unselfish Behavior. Harvard University Press. Cambridge Mass. 89 Adler, A. (1968). The Practice and Theory of Individual Psychology. Totowa, NJ: Littlefield, Adams. 90 Nowak, M. A. and Sigmund, K. (2004). Evolutionary Dynamics of Biological games. Science 303: 793-799. 87

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our discussion of evolution in the framework of a general theory of creative processes. 13.20 Evolution and Creation Theory The general theory of creative processes advances the following concepts relevant to biotic evolution: (0) flux, ever present change; (1) action (autogenic change, causal, transmitted, conserved and contingent); (2) information, as contrasted to randomness, which includes mathematical archetypical forms but it is also created by bipolar feedback and other novelty generating processes; (3) matter, and the assembly of preformed material modules into systems; (4) creative development in which the action of simple forms (genes, mathematical archetypes) generates complex processes that spearhead further evolution (priority of the simple and supremacy of the complex); and (5) overall increase in complexity with involutionary epochs. Corresponding to the generic categories of action, opposition and form, evolution consists of actions, not simply change; synergistic and antagonistic interactions, not only predation and competition; and involves the production of form and complexity - morphogenesis and dimensiogenesis - rather than changes in composition. 13.20.1 Flux Just as the simplest physical level is in continuous flux, change is ever present in biological processes. Organisms and species change without necessarily evolving or adapting. According to Kimura's neutral theory of molecular evolution,91 mutations and random drift account for variations at the level of DNA and amino acids. The vast majority of single-nucleotide differences are selectively "neutral", i.e. they do not influence the fitness of either the species or the individual. Random flux and random walk account for much diversity. Competition and selection cannot possibly account for the enormous biochemical and biological 91

Kimura, M. (1994). Population Genetics, Molecular Evolution, and the Neutral Theory: Selected Papers. University of Chicago Press.

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complexity observed because they impose a heavy cost: as a number of individuals with suboptimal fitness die in each generation, the remaining members of the population must reproduce at a higher rate or the population could become extinct. 13.20.2 Action and information That living processes are physical is the single most important principle in biology. It follows that there is a necessary continuity between inorganic and organic evolution. Regarding both processes as fundamentally creative allows one to consider biological evolution as driven and directed by the same general laws that energize and direct physical processes. Action is the common constituent of inorganic and organic matter. Asymmetry is one of the essential characteristics of action and of biomolecules, as discussed in earlier Chapters. Action implies causation rather than randomness. A process is a sequence of actions; a mathematical recursion is a sequence of iterations; life is a sequence of generations. Reproduction involves change at each generation. The offspring resemble the parents but are not identical to them. Such change is autogenetic - the spontaneous and causal result of the biological processes themselves rather than the passive and accidental consequence of external events. Biological change is action, not random change. Yet, random mutations are often described as the sole source of innovation in biological processes. They are regarded as "errors" and as largely harmful. Actually, many mutations are adaptative rather than random.92 This refutes standard neo-Darwinism. 92 For instance, mutations increase with certain stimuli, such as radiation, in many different species, including humans. The literature is immense; see for instance Nelson, S., K. Parks and Grosovsky, A. Ionizing radiation signature mutations in human cell mutants induced by low dose exposures. Mutagenesis 11:275-279, 1996. Wu, L-J., Randers-Pehrson, G., Xu, A., Waldren, C. A., Geard, C. R., Yu, Z. L. & Hei, T. K. Proc. Natl. Acad Set USA 96, 4959-4964, 1999. The increase in mutation rate with radiation may constitute a determined mechanism of defense rather than random occurrence. Genetic mutation rates accelerate in microorganisms subjected to stressful circumstances. Adaptative mutations in direct response to environmental stress have been found in bacteria. (Cairns, J, Overbaugh, J, and Miller, S.. The origin of mutants. Nature 335: 142-145, 1988.) Some of these directed variations require the simultaneous mutation of two genes, a highly unlikely event that cannot be explained by random change. In a recent study (Bjedov, I., Tenaillon, O., Gerard, B., Souza, V., Denamur, E., Radman, M., Taddei, F., and Matic, I. Stress-induced

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Action is transmitted, and thereby causes subsequent events. Changes are conserved as relatively stable patterns and also become imprinted in material (biochemical, anatomical and botanical) structures. The structures already built in the organisms direct subsequent evolution, creating avenues that otherwise would not emerge, and excluding others that in principle could be more appropriate. This places limits on general principles of form and optimality. (In fact, the imperfection of biological forms was one of the arguments employed by Darwin to refute the notion of supernatural design). Every new action is contingent on the previous ones. Evolution is historical. Action carries information. Change is not an isolated event. It is the start of a new lineage. Change produces bifurcation. Bifurcation rather than error is responsible for many evolutionary changes. Gene duplication is an important source of evolutionary novelty. Most cases of duplication involve a single gene, but there is evidence for duplication of entire genomes. At this time, it appears that the evolutionary tree may have originated with a trifurcation. In the late 1970s, Carl Woese and his colleagues at the University of Illinois identified the Archaea as a group distinct from bacteria and eukaryotes. Thus life is divided into three domains: Archaea, Bacteria and Eucaria. This trifurcation is usually interpreted as the result of two successive bifurcations, because the notion of trifurcation is not readily contemplated. As noted in Chapters 4 and 9, trifurcation may be an important natural form.

mutagenesis in bacteria. Science 300(5624): 1404-9, 2003) most of 787 different strains of bacteria from all over the world demonstrated the accelerated mutation effect when subjected to stress. The mechanism by which E. coli accelerates the rate of mutation when starved is now known. The bacteria quadruple their expression of DNA Polymerase IV, an enzyme that is notoriously bad at copying DNA accurately. (Foster, P. and J. Layton. Error-prone DNA polymerase IV is controlled by the stress-response sigma factor, RpoS, in Escherichia coli. Molecular Microbiology 50: 549-561, 2003.) These examples illustrate a growing literature on adaptative evolution. (Barrier, M., R. H. Robichaux, and M. D. Purugganan. 2001. Accelerated regulatory gene evolution in an adaptive radiation. Proceedings of the National Academy of Sciences USA 98:10208-10213. Bush, R. M. 2001. Predicting adaptive evolution. Nature Reviews Genetics 2: 387-392. Lewontin, R. C. 1957. The adaptations of populations to varying environments. Cold Spring Harbor Symposium on Quantitative Biology; 22: 395-408.) 93 Wolfe, K. H. and Shields, D. C. (1997). Molecular evidence for an ancient duplication of the entire yeast genome. Nature 387: 708 - 713.

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Although evolutionary processes are historical, i.e. contingent on previous events, there are many examples of convergence in which two or more lineages independently evolve similar structures and functions, i.e. they display similar phenotypic manifestations in spite of differences in genetic mechanism. For instance, multicellularity, warm-bloodedness, eyes, complex social systems, intelligence, and even penile tumescence, have evolved repeatedly or may be explained by natural selection or on functional bases.94 Convergences also occur as result of the exchange and recombination of genomes. Evolution is not a tree, but a lattice. 13.20.3 Living matter and its conservation Organisms are material systems. Life is not only process; it is "living matter".95 Reproduction conserves genes, and the cytoplasm and the endosymbions of the maternal egg. Evolution requires not only change but also conservation. The reader will remember that bios requires both change and conservation, in contrast to chaos that involves only change. "Living matter" is a morphologically complex form of matter. Chemistry pre-determines life. Life cannot be "programmed" in any arbitrary chemical substance. Organic matter is made of carbon. Carbon plays such special role because of its tetravalence enables it to form macromolecules. In the early 1960s, Pullman and Pullman96 observed that a small number of organic molecules are used repeatedly for many diverse biological functions. For instance, adenine is used in DNA, RNA, as a neuromodulator of sleep97, in the chemical messenger cyclic AMP (adenosine monophosphate), in the energy-releasing molecule ATP (adenosine triphosphate), and in many other functions. They explained this phenomenon by the particular electronic distributions of these biologically ubiquitous substances. A related phenomenon is the repeated use of the same pigments in many different and independent emergences

94

Conway, M. S. (2003). Life's Solution: Inevitable Humans in a Lonely Universe. The expression was coined by the Russian biologist Vladimir Vernadsky to stress the continuity of abiotic and biotic processes. 96 Pullman, B. and Pullman, A. (1963). Quantum Biochemistry. New York: Interscience. 97 Radulovacki, M. (1995). Pharmacology of the adenosine system. In A. Kales (ed.), The Pharmacology of Sleep, Handbook of Experimental Pharmacology. Berlin-Heidelberg: Springer-Verlag, pp. 307-322. 95

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of vision. The chemistry of life is not arbitrary; organization at higher biological level depends on organization at the simpler chemical level. 'Artificial Life' attempts to synthesize and study life-like behaviors in man-made systems within computers or other "alternative" media. Beyond the carbon-chain-based life that has evolved on Earth, Artificial Life attempts to locate "life-as-we-know-it" within the larger context of "life-as-it-could-be", in any of its possible physical incarnations. 98 Computer simulations thus replace actual molecular structures with symbols and actual chemical reactions with algorithms. Without denying interest to these explorations, one should recognize the need for realistic assumptions. The specific chemical requirements of living processes limit the usefulness of computer models that simulate living organisms while ignoring their chemical composition. 13.21 Mathematical Archetypes of Biological Form and Evolution The Scottish biologist D'Arcy Thompson" pioneered the concept that the structures formed and transformed in biological evolution are largely determined by universal laws: ".. .heredity is not the sole determinant of morphology; it is one of the great factors in biology, but we cannot neglect physical and mechanical modes of causation." Living structures must obey engineering principles and display mathematical archetypes. For example, some parts of whales look like seals but that does not mean they are related by ancestry; they are related by their common function. Thus unrelated animals would develop the same characteristics due to a common environmental need. These concepts suggest the possibility of developing a mathematical, ahistorical theory of life forms after the fashion of physics rather than as history. What are the mathematical relations significant in biological evolution? When speaking of mathematical forms, Thompson referred to simple and regular archetypes such as the spiral form of the Nautilus. Since Mandelbrot, we have become intensely aware of rough geometrical 98

Langton, C. G. (1988). Artificial Life. In Artificial Life, edited by C. G. Langton, SFI Studies in the Sciences of Complexity, Addison-Wesley. 99 D'Arcy Thompson. (1917). On Growth and Form. Reprinted, Cambridge University Press, 1942.

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forms. Many biological structures have fractal dichotomous branching100 that greatly amplifies the surface area of tissue, be it for absorption (e.g. lung, intestine, leaf mesophyll), distribution and collection (blood vessels, bile ducts, bronchial tubes, vascular tissue in leaves) or information processing (nerves).

D'Arcy Thompson (1860-1948)

The archetypal form of the Nautilus.

Fractal organization is created by relatively simple processes, as illustrated by the generation of chaos and bios by nonlinear recursions. Underlying evolutionary increases in the size, complexity and diversity of living organisms is their modular construction from reiterated parts. Reiteration produces fractal geometry. The form of plants appears to be constructed by fractal processes.101 Thus individual plants have unique individual form, largely determined by their environment. On the other

100 Deering, W. and West, B. J. (1992). Fractal physiology. IEEE Engin. Med. Biol. 11: 40-46. Goldberger, A. L., Rigney, D. G. and West, B. J. (1990). Chaos and fractals in human physiology. Sci. Am. 262(2):42-49. Glenny, R. W., Robertson, H. T., Yamashiro, S., and Bassingthwaighte, J. B. (1991). Applications of fractal analysis to physiology. J. Appl. Physiol. 70: 2351-2367. West, B. J. and Goldberger, A. L. (1987). Physiology in fractal dimensions. Am. Sci. 75: 354-365. Bittner, H. R. (1991). Modeling of fractal vessel systems. Fractals in the Fundamental and Applied Sciences (ed. by H. O. Peitgen, J. M. Henriques, & L. F. Penedo), Elsevier, Amsterdam, 47-68. Van Beek, J. H. G. M., Roger, S. A. & Bassingthwaighte, J . B. (1989). Regional myocardial flow heterogeneity explained with fractal networks. Am. J. Physiol. 251: HI 670-H1680. 101 Aristid Lindenmayer, a plant biologist, created a system of notation in 1968 as a formal model of plant growth.

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hand, animal forms are largely self-determined, smooth and much less variable. Notwithstanding, they also include fractal components. Among nonlinear generators, particularly important are those that produce patterns that obey power laws. Power law relations are widespread in biology; they were originally described as allometric relations in biology by Julian Huxley. Allometry is the study of the change in proportion of various parts of an organism as a consequence of growth. Many allometric relations have the form Y = k*Mb where the dependent variable Y, such as metabolic rate, is a function of an independent variable M, such as body mass, k is a constant and the exponent b ^ 1. These relations may reflect the fact that biological rates and times are limited by the rates at which energy and materials can be distributed to the tissues where they are used.102 This model predicts a fractal-like structure for distribution networks.

Fig. 13.4 Fractal dichotomous branching in cardiac Purkinje fibers, neuron, and bronchi.

The fact that both synergistic and antagonistic interactions occur in biological processes leads me to consider bipolar, mutual and hierarchical feedback as one of the generic mathematical generators of biological evolution. This model provides a hypothesis regarding the morphogenesis of both smooth periodic and rough fractal anatomical structures. It may also explain that the time course of biological 102

Brown, J. H and Eest, G. B. (2000). Scaling in Biology. Oxford University Press.

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organisms involves relative steady state103 as well as speciation leaps. Naturafacit saltum (nature makes leaps), and bios models them. Diversification, novelty, and nonrandom complexity are obviously present in evolutionary processes. As biotic trajectories and leaps are exquisitely sensitive to inputs, the biotic feedback model conserves our understanding of evolution as a historical process in which specific events can drastically alter the trajectory, so the effective mutations are interdependent. This sensitivity to inputs represents nonrandom historical contingency. Other, more specific, but still generic processes that determine the form and evolution of biological organisms, are functional needs. Living systems thus differentiate into subsystems that process mainly energy, information or matter, although, as discussed before, all of these aspects of reality are inseparable. Twenty generic subsystems have been identified and studied in detail by psychiatrist James Miller in his Living Systems Theory.104 Living systems provide a model for nature because the continuity of evolution requires that the same fundamental forms be expressed at all levels of organization. Biological processes portray generic forms or archetypes present at multiple levels of organization. Expanding Thompson's views, the fundamental archetypes are not only geometric but also physiological. The essence of Miller's living systems theory is, in my view, that systems of biological organisms must have subsystems and functions required by individual living organisms. These archetypes do not determine or constrain subsequent development. They create it. Archetypes are not "forms." They are generators. They are not blueprints that specify the adult form; archetypes contain only a limited amount of information, yet sufficient to generate a diversity of trajectories. Structuralism regards good designs generated by dynamic laws as sufficient to generate biological forms. Nonlinear dynamists advance the view that spontaneous selforganization is the crucial ingredient for evolution. Dissipative 103 Eldredge, N. (2003). The Sloshing Bucket: How the Physical Realm Controls Evolution. In Crutchfield, J. P. and Schuster, P. Evolutionary Dynamics. Oxford University Press. 104 Miller, J. G. (1978). Living Systems. N e w York: McGraw-Hill. Miller J. G. General Living Systems Theory. In H. I Kaplan, A. M. Freedman and B. J. Sadock. Comprehensive Textbook of Psychiatry. Baltimore: Williams and Wilkins, 1980.

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structures, self-criticality, and the edge between order and chaos are offered as models. Expanding Thompson's idea that evolutionary variation is constrained by structural laws, modern structuralist approaches place emphasis on principles of order. Stuart Kauffman105 advanced the concept of "order for free," implying that biological form may be generated by dynamic laws. This notion is embodied also in the notion of cosmic forms central to the biotic model. The biotic model, however, adopts a process (as contrasted to structural) perspective in which action is the basic mathematical archetype, and hence highlights historical contingency. Biological form is an organization resulting from a creative and contingent process initiated by simple forms, not a static order already implicit in general and simple laws of form. The landscape metaphor106 assumes some solid ground when actually the entire biota collectively constitutes the landscape, which is therefore continually evolving.107 Also, the landscape model assumes that a heritable trait that confers higher fitness will spread within the population. But evolution is not necessarily progressive. It includes involution and extinction. Changes in the collective biotic landscape can lead to extinction even when the traits that are spread within a population increase its fitness to previous landscapes. 13.22 Evolution is a Creative Development The main thesis of this book is that natural processes are creative developments -neither random fluctuations, nor determined processes. Simple mechanisms generate novelty, diversity and complexity. Creation is an ongoing process, not a single act of origin in the remote past. These concepts apply to biological evolution. The term "evolution", meaning "unfolding", describes development, the predetermined growth and maturation of a complex from a simpler origin. Evolution is a creative 105 Kauffman, S. (1995). At Home in the Universe: The Search for the Laws of Self-Organization. Oxford: Oxford University Press. 106 Kauffman, S. (1995). At Home in the Universe: The Search for the Laws of Self-Organization. Oxford: Oxford University Press. 107 Nowak, M. A. and Sigmund, K. (2004). Evolutionary Dynamics of Biological games. Science 303: 793-799.

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development because it starts from and is driven by simple causal mechanisms, but it generates diversity, novelty and complexity, the beginning of life, the origin and diversification of multiple species, and the development of consciousness. Evolution is a historical process in which past events produce the subsequence course, at variance with the determinism advocated by structuralism. Evolution is creation. Creation is not a single and supernatural event. It is a process, originating in the past, operative in the present, and continuing in the future. The simple processes that generate evolution include the generic "cosmic genome" (the numerical and algebraic archetypes); the "physical genome" (such as the mechanical forms proposed by D'Arcy Thompson and the fractal forms of nonlinear dynamics, including fractal chaos and bios); the chemical genome of atoms and molecules; and functional forms such as Miller's subsystems that include specific mechanisms that produce diversity, such as adaptative mutation, crossover, and sexuality. 13.23 Biotic Development: Complexification and Enantiodromia A currently popular view of evolution is one we see reflected in advertisements that show a line of figures walking from left to right first an ape walking on all fours, then a semi-erect humanoid perhaps carrying a stick, and finally a consumer displaying his latest acquisition. Actually evolution includes not only the emergence and development of new species, but also their decay and extinction - probably more than 99% of the species that ever lived have become extinct. A meaningful theory of evolution must then consider both progress and involution. Evolution may generate simplicity. During the course of adapting to their host, parasites often lose structures and functions that were essential for their free-living ancestors; for instance, tapeworms have no eyes, no digestive tract, and only vestigial nervous, excretory, and muscular systems. In the same manner, Mycobacterium leprae, an intracellular parasite in Schwann cells, has a genome that is 25% smaller than that of its cousin M. tuberculosis. 108 Clearly evolution includes its very opposite - Heraclitus' notion of enantiodromia. 108

Cole, S. T. et al. (2001). Nature 22 February.

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Yet evolution has undoubtedly resulted in the generation of more complex species. Empirically, biologic evolution has increased overall complexity. Biological organisms evolve from simpler microorganisms, which are ancestors of all higher forms of life, its components, and its environment. Simple life forms have priority. Although neo-Darwinists dispute that natural selection produces evolutionary progress, none of them could argue that evolution began with complex organisms. Evolution does not necessarily produce progress, but it must start at simple levels. Darwinist biologists deny that evolution produce overall complexity. Gould argues that the fact that most forms of life increase in size (Cope's law, after 19th century paleontologist Edward D. Cope) and complexity is an "artifact" resulting from the circumstance that life begun at the extreme of smallness and simplicity. However, a simple origin is not an artifact. How else could life have begun? Since life could not have started large and complex, doesn't this fact reflect the basic logic of the universe? Evolutionary progress may be explained as an obligatory sequence: Creation must necessarily precede destruction. Simplicity must necessarily precede complexity. Evolution is creation rather than adaptation. Simple organisms are as adapted as complex ones. Creativity favors adaptation and adaptation is necessary for survival and may facilitate creativity. Adaptation favors cooperation. Creation and adaptation are largely synergistic but may be contradictory. Among humans, adaptation often is a sign of mediocrity, while those who do not adapt foster progress. Complexification rather than selection is the main characteristic of evolution. Evolution also increases diversity. Darwin assumed that the best individuals and species simply crowded out the inferior one. Actually, diversification, rather than selection, is the hallmark of evolution. Selection of the best fit to the current environment is not optimal for the species because it makes it vulnerable to unexpected environmental changes. The multiplication of deviant organisms, "suboptimal" in one environment, enables a species to overcome environmental change when it occurs. Evolution includes trees branching off in many directions that generate an immense diversity of inorganic structures and living organisms, and the uniqueness of individuals - from snowflakes to human persons. Yet, while evolution has increased diversity in many

Biotic Evolution

535

respects within the species, it has reduced metabolic diversity. Animals show only one metabolic mode, respiration; plants also have photosynthesis, while bacteria have more than twenty different types of metabolism.109 The complexification of respirators adds to the total diversity of the biosphere, yet at higher levels of organization there is less diversity of metabolism than at lower levels. Microorganisms can live in a wide range of temperatures, as demonstrated by thermophiles; mind requires a narrow range of temperature. The number of genders is extremely large among mushrooms, while we are limited to two sexes. The simple is more diverse in quality, just as it is more extended in quantity. The diversification of species generates an evolutionary lattice in which, however, the elements are not fixed but evolve gradually in a topological fashion. Periods of punctuated equilibrium involve gradual but not trivial change -consider, for instance, the drastic difference among dog breeds without discontinuity of the species. This pattern of epochs of contiguous change separated by leaps is consistent with a biotic process. Evolution is fundamentally irreversible. For instance, when a beneficial mutation occurs the population cannot go back to an inferior type, and the effective mutations are interdependent. This ratchet-like process introduces the asymmetry of time and effectively erases the purported randomness. Finally, evolution continues. Humans are not the final pinnacle, as we are prone to believe. More significantly, evolution has already created an animal that is conscious, moral, altruistic, artistic, scientific, and spiritual. Evolution has already surpassed the biological stage. 13.24 Supremacy of the Complex Evolution is creation of the complex by the simple, but it also involves the modification of the simple by the complex, a bootstrapping process that creates further complexity. The priority of the simple and the supremacy of the complex do not only describe the direction of 109

Margulis, L. and Sagan, D. (2002). Acquiring Genomes. A Theory of the Origin of Species. New York: Basic Books.

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evolution. They also represent bi-hierarchical feedback, an engine for progress. Complexity is not only the result of evolution but also a major factor in its development. The efficient jaw structures of worker termites and ants are shaped to apply maximum force at a useful distance from the hinge, in compliance with Archimedes' laws of levers. Selection has thus occurred at the level of macromechanical processes, which in turn determine the molecular processes involved in the formation of the anatomical system. This "downward causation"110 illustrates the supremacy of the complex in natural selection. The importance of behavior as a factor in evolution has been recognized since Lamarck, who regarded the evolution of living forms as self-propelled, or "autogenic",111 as contrasted to the later views that attribute evolution to outside forces or to chance mutation. Darwinism highlights survival of the fittest. Lamarck speaks of the species making itself fit. To regard evolution as active and creative encourages the notion that human nature can be improved by education, while Darwinism discourages this notion. The German Zoologist August Weissman "refuted" Lamarck by cutting the tails of mice to show that later generations of mice were not tailless! Obviously passive consequences cannot be considered as acquired characters without a stupendous degree of philosophical naivete. A significant bi-directional hierarchy is the relationship between species. In a food chain, the prey-predator relations determine an order that roughly coincides with a scale of complexity, but the bodies of the higher organisms end up serving as food for microorganisms. More generally, simple organisms have absolute priority because we cannot live without them. Yet as the dominant species, humans largely determine the environment. Migration and commerce are major factors that contribute to the geographical distribution of many species. Urbanization and agriculture are other major causes of evolution. Industrial fishing has destroyed fisheries; loggers and governments 110 Donald, T., and Campbell, D. T. (1974). 'Downward Causation' in Hierarchically Organized Biological Systems. In FJ. Ayala and T. Dobzhansky, eds., Studies in the Philosophy of Biology: Reduction and Related Problems Berkeley and Los Angeles: University of California Press, pp. 179186. 111 Lamarck's term autogenic compares with autodynamic and autopoietic.

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promote deforestation. In our times, we have seen the disappearance of species at a rate comparable to that of the most tragic catastrophes in our planet's history. The rate of extinction of species has increased, it is said, 120,000 fold as result of human activity. Man, as Julian Huxley denounced, has become the cancer of the earth. Humans use energy faster than all other species, hence they increase entropy more than all others. In the same manner, dominant countries and dominant classes use energy and increase entropy more than all others. Another bi-directional hierarchy concerns the complexity of evolutionary processes. Simple factors have absolute priority in evolution. Survival is indispensable, but selection is not determined solely by survival. The generation of complexity introduces new factors in evolution, ranging from sexual selection to conscious behavior. To attribute evolution or even selection solely to survival is unacceptable reductionism. Other goals have supremacy. Reproduction obviously does, so evolutionary trends are more affected by organisms that reproduce more, even if they live less. This is of course included in the technical redefinition of "fitness" as reproductive success. To lump together individual fitness for continued existence and reproductive abilities obscures the bi-directional relation between the priority of survival and the supremacy of reproduction. Complexity of function requires complexity of form (a notion advanced by Lamarck that has escaped quantum mechanicians, who speculated on the "choices" made by electrons, and sociobiologists who speak of "selfish genes"). Consequently, complexity of form enables complexity of function. The development of greater complexity allows for the development of psychological functions. Behavior is a causal factor in selection. Selection by behavior implies supremacy of the brain. Simpler evolution generates brains, and then mind guides evolution. Conscious behavior introduces "artificial" selection of domestic plants and animals, and indirectly also selects non-native species. It cannot fail to also affect the evolution of human beings. Biological evolution and human history are driven by the development of higher functions. In the Descent of Man, Darwin pointed out that brain and mind play an important role in our evolution. Whether or not the Baldwin effect

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actually exists is open to question. Waddington112 proposed that animals may select, out of the range open to them, the particular environments in which they will pass their lives, and thus to have an influence on the type of natural selective pressure to which they will be subjected. The control of the simple by the complex is a feedback that propagates and increases complexity. The supremacy of the complex in biological evolution is illustrated by its most recent chapter, synthetic biology -the human engineering of metabolic pathways. The supremacy of brain (and other higher functions) accounts for the apparent purposive pattern of some physiological and evolutionary processes.113 This subject is not developed here in all its due importance simply because it is far beyond the research in which I have been directly involved. Table 13.1 Biotic recursion and evolutionary change Mathematical recursions Iteration Conservation Trigonometric feedback Bions „ . . Co-creative systems of equations

Biological evolution Generation Genetic inheritance Synergistic and antagonistic feedbacks Development Biological webs with prey-predator and .f. . . . . solidarity-competitive interactions Systems and modules Macromolecules and components Living systems Organisms and biotas Intelligent, learning, heuristic systems Organisms with neuropsychological functions Bios: power-law decay with p = -1.7 Species extinction: p — -1.7

112 Waddington, C. H. (1975). The Evolution of an Evolutionist. Edinburgh: Edinburgh University Press. 113 Nature, as art, both resemble purposive agents but pursue no external goal, remarked Kant.

Chapter 14

Biotic Earth, Biotic Climate

Abstract: Meteorological changes include biotic patterns in addition to periodic and chaotic ones. As a superorganism, the planet appears to evolve in a biotic fashion rather than be homeostatically regulated. The supremacy of the most complex planetary level, the human, is developing enantiodromically, both destroying biological species and generating a new level of world consciousness. 14.1 Novelty in the Ancient Nile Egypt is, in Herodotus' famous phrasing, the child of the Nile, being totally dependent on its yearly flooding for irrigation. In legendary antiquity, Joseph interpreted pharaoh's dream of seven fat cows followed by seven thin ones as a prediction of seven years of good flood followed by seven of low flood. He had apparently discovered that there was a tendency for a good flood year to be followed by another good flood year, and for a low flood year to be followed by another. We can demonstrate partial autocorrelation (lag 1: 0.83; lag 2 to 5: 0.19 to 0.11). The British engineer H. E. Hurst rediscovered this non-random run in the twentieth century when he conducted a study of 800 years of records of the Nile's flooding (the Roda gauge at the Nile reaches back to the year 622 AD). Hurst1 found significant correlations among fluctuations in Nile river outflows and described these correlations in terms of power laws; Fig. 14.1 shows the 1/f power spectrum and the

1 Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Tr. of the American Society of Civil Engineers 116:770-808.

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corresponding wavelet plot. Mandelbrot and Wallis 2 used the term Joseph effect to refer to such persistence phenomena. Hurst quantified the phenomenon with a measure now known as the Hurst exponent, which turned out to be 0.91 for the annual levels of the Nile, indicating strong persistence. The calculation of this exponent is fraught with problems,3 and involves detrending the data - a transformation that, as discussed previously (Section 4.1), precludes the observation of essential components of creativity. When the data are not detrended, isometry analysis shows marked novelty (Fig. 14.2) and well-delineated complexes without high consecutive recurrence, as also observed in other series with a 1/f power spectrum.

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The study of the weather pioneered by Lorenz brought chaotic processes to the forum.4 Atmospheric flows, for instance, exhibit self-similar fluctuations on all scales of space and time. Evidence of chaos indicates the need to test for bios. Diversification is found in a number of meteorological time series: temperature changes for several Midwest5 (Fig. 14.3) and California locations (Fig. 14.4), water temperatures in the Pacific Ocean (Fig. 14.5), and in paleoclimatic indicators from coral samples.6 Recurrence plots of these series showed distinct episodic complexes, not the stationary patterns observed with chaos. Comparison with shuffled copies indicates novelty with (Fig. 14.6), or without 4

Lorenz, E. N. (1993). The Essence of Chaos. Seattle: University of Washington Press; Fraedrich, K. and Schonwiese, CD. (2002). Space-time Variability of the European Climate. In The Science of Disasters, A. Bunde, J. Kropp, and H. J. Schellnhuber (Eds). Berlin: Springer. 5 Sabelli, H. (2000). In Peoria, the weather is biotic. General Systems Bulletin 29:9-10. 6 Charles, C. D., Hunter, D. E., and Fairbanks, R. G. (1997). Interaction between the ENSO and the Asian monsoon in a coral record of tropical climate. Science 277: 925-928; Charles, C. D., Hunter, D. E., and Fairbanks, R. G. (1997). Seychelles coral dl8O, IGBP PAGES/World Data Center-A for Paleoclimatology Data Contribution Series # 97-032. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA; Sabelli, H., Sugerman, A., Kauffman, L., Kovacevic, L., Carlson-Sabelli, L., Patel, M., Messer, J., Konecki, J., Walthall, K., and K. Kane (in press). Bios Data Analysis. Part 11. Biotic patterns in biological, economic and physical processes. Journal of Applied Systems Studies, special issue edited by H. Sabelli.

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consecutive recurrence (Fig. 14.17). Arrangement is high, indicating nonrandom complexity. Wavelet plots, Lyapunov exponent, dumpiness test, and all other analyses are also compatible with biotic pattern. Temperature variation in several parts of the globe has a clear biotic pattern within its seasonal periodicity.

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chaotic according to each of the above tests. This finding agrees with our intuition that temperature is more predictable than precipitation. Yet, torrential rains and other severe convective weather conditions appear to be predictable7 and may be modeled by "blown-ups".8 Apparently, atmospheric processes include flows, cycles, chaos and bios. Only in mathematical models do we find examples of single processes with unmixed pattern; real processes contain several types of components that not only add but also interact. Midwest air temperature, radius 0.1

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7

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8

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Biotic Earth, Biotic Climate

545

(temperature), flow (wind), asymmetric cycling of opposites (circulation patterns), and adopt a spheroid shape with tridimensional organization (night-day variation in the East West direction, North-South bipolarity, and a vertical hierarchy of pressure). There are seasonal periodicities, and chaotic patterns resulting from interactions with land and sea. But, as the data shows, there are also biotic patterns. 14.3 Biotic Earth: Gaia and Bios The Earth's climate is biotic because the planetary surface is biotic. Seen from space, our planet is green. Even the chemically poor oceans teem with life.10 The biosphere is a thin layer on the surface of the Earth where all organisms live. The atmosphere and the earth's surface are created, maintained and modified by living organisms. Life evolves only at the interphase of water, air and solid matter. Planets without life, like Mars or Venus, have neither water nor soil. It is living organisms that create soil. They have contributed to maintain water on the earth's surface. Without life, there might be no clouds, rain, rivers or oceans. Without water, the tectonic plates responsible for continental movement might not move. The chemical reactions of life (e.g., photosynthesis-respiration, carbonate precipitation, etc.) have determined the chemical composition of the atmosphere. The fact that life is a major geological force illustrates the supremacy of the complex. Just as each of us lives in symbiosis with many species,11 every species lives in conjunction with its entire ecosystem. There is a growing consensus among scientists that the earth should be regarded as a single, self-regulating system.12 The Greek physiologists considered the world as alive. Newton compared the planet to a living organism. The Russian scientist Vladimir Vernadsky developed the modern concept of "biosphere" in the early twentieth century. The biosphere is a thin layer 10 The "microbial ocean" was, surprisingly, discovered only after methods were developed to detect life on Mars. The pelagic bacteria that account for most of the ocean biomass, over 99% of the bacteria in the sea, were first detected in 1977 and viruses were not studied until 1989 [Azam, F. and A. Z. Worden. Microbes, molecules and marine ecosystems. Science 303: 1622-1624, 2004]. 11 About 400 different microorganisms inhabit the human gut, accounting for 1 kg of mass. 12 See, for instance, the Amsterdam Declaration on Global Change (2001), co-signed by more than 1,500 scientists from over 100 countries.

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on the surface of the Earth where all organisms live. The biosphere involves many differentiated ecosystems, but it functions as a more or less integrated system, including significant horizontal genetic transfers. James Lovelock,13 a leading environmentalist, proposed that living organisms regulate the atmosphere (a fact that seems evident) in their own interest (a purposefulness that to me seems rather doubtful). He thus regards the biosphere as a superorganism, named Gaia after the Greek Earth Goddess. The Gaia hypothesis states that the earth, as living organisms, involves a multiplicity of positive and negative feedback processes to maintain homeostasis. The notion of homeostasis needs reformulation regarding individual organisms (Chapter 5). It is not applicable to life as a process that involves the birth and death of individuals and entire species. 14.4 The Drama of Privatization Versus the Tragedy of the Commons According to Lovelock, Gaia is aging. Planetary self-regulation does not imply that nature can tolerate whatever humans do to it. On the contrary, humans are very much part of the system, and can counteract or accelerate its aging. The Gaia hypothesis contradicts the Darwinist view of life. First, synergistic processes take the lead over competition. Second, biological organisms co-determine the evolution of the planet (supremacy of the complex) rather than serve as the passive recipients of climatic changes. The Gaia model has great scientific and social value, as it has stimulated research and environmental protection. However, homeostatic models tend to ignore essential change. An instructive and significant example is the story of the hole in the ozone layer.14 Living organisms 13

Lovelock, J. (2000). The Ages of Gaia. Oxford University Press. During the 20th century, industrial sources released enormous amounts of chlorofluorocarbons (CFCs) into the atmosphere. These compounds were regarded as indestructible (i.e., unreactive). A process view indicates that nothing is indestructible. Based on this assumption, Mexican post doctoral fellow Mario Molina and University of California Sherry Rowland explored the potential consequences of CFCs reacting in the upper atmosphere and found that this could lead to the depletion of ozone in the atmosphere. The other piece of relevant philosophy that entered into their investigation was the environmental consciousness created by the 1960s generation. Molina and 14

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create the planetary cortex. We are now witnessing its radical change by the action of the top member of the biosphere -our species. Just as actual homeostasis, planetary homeostasis is neither a point nor a cyclic attractor dynamical system. Self-regulation is accompanied by temporal evolution. This combination of homeostatic features with nonstationarity (Lovelock's "aging") is found in homeobios but not in stochastic noise, chaotic attractors, or random systems. Thus Gaia must be a biotic, or more precisely, homeobiotic system. This is consistent with the coexistence of positive and negative feedback processes described by Lovelock. As expected from bipolar feedback, the well-known planetary cycles (water, oxygen, carbon, nitrogen) show biotic trajectories. They do not maintain equilibrium as in the homeostatic and homeokinetic models, but create anew. Physical and chemical biotic cycles are engines for evolution. Biotic processes involve not only creation but also destruction. The biosphere is not aging. It is literally being killed. Industrial progress and commercial interests are responsible for one of the most severe extinctions of animals and plants in planetary history. For instance, fisheries are declining as a result of their overexploitation, mostly during the twentieth century; from 1900 to 1999, biomass has decreased by a factor often or more.15 This accompanies human self-destruction by war. Determinism and creative choice provide different portraits of our current environmental crises and indicate opposite courses of action. In a much quoted 1968 Science article, recently celebrated on the cover of the same leading scientific journal, Garret Hardin defined the current environmental crises as a Tragedy of the Commons, for which there are Rowland made their results known to the public in 1974. The industry mounted a powerful campaign to continue its practice, alleging that there was no scientific evidence for deleterious effects on the ozone layer. Here entered a third piece of sound philosophy: the precautionary principle according to which one need not await proof that something has already caused damage if there is evidence that it could. Against the massive opposition of the industry, the use of CFCs was discontinued. A. Irwin's An Environmental Fairy Tale (In It Must Be Beautiful, G. Farmelo (ed). London: Granta Books, 2002.) beautifully narrates a further chapter of the story, in which a wrong philosophy delays scientific insight. British scientists recorded low ozone readings in Antarctica,14 but refrained from publishing for three years because a NASA satellite that was in much better condition to observe the ozone layer had reported no significant changes. The NASA satellite had also recorded the reduction in ozone, but its scientists had given instructions to the computer to ignore low recordings as probable errors! This illustrates the consequences of discarding extreme values as outliers. 15 Pauly, D. and Maclean, J. (2003). In a Perfect Ocean. Island Press.

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only two solutions -centralized government and private property. The term 'commons' refers to pasture areas communally owned and used by English villagers. Used efficiently for centuries, they were ruined by overutilization as a result of the transformation from feudal to capitalist modes of production. The destruction of the commons was the consequence of the privatization of ownership. In Hardin's speculation, each herdsman tries to keep as many cattle as possible on the commons to maximize his own gain, and as this strategy is employed by each and every herdsman, depletion of the resource follows unavoidably. The British commons were not destroyed in this fashion. When individual persons belong to their community, they protect it as their own. But the entrepreneur who lives elsewhere does not belong to the community and is alienated from it. While Hardin and others consider the behavior of alienated individuals as normal and rational, the psychiatrist remembers that alienation means insanity. The term Tragedy of the Commons is an ideological misnomer that obscures scientific discussion. It is not tragedy and it is not produced by public ownership. It is not tragedy because the term refers to unavoidable catastrophes resulting from the very essence of the protagonist, the hero's 'fatal flaw' in Aristotle's words. The Tragedy of the Commons is drama, that is to say, it involves struggle between opposite parties. It is not the consequence of human nature. The misnomer Tragedy of the Commons distracts our attention from the true problem: the drama of privatization and statization. Privatization allows the destruction of what should be used and protected in common by private greed. Statization places control of what should be used and protected in common in the hands of governments that often promote privateers, a name originating under English law that encouraged pirates to pillage Latin America. Neither privatization nor statization will prevent environmental destruction. In fact corporations seeking profit and governments seeking economic development and military power are responsible for polluting air, soil, rivers, and oceans, depleting forests and fisheries, and even altering the global climate.16 Often, corporations and governments are 16 Watson, R. T. (2003). Climate change: The political situation. Science 302: 1925-1926; Houck, O. (2003). Tales from a troubled marriage: Science and law in environmental policy. Science 302: 1926-1929.

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controlled by the same individuals. Thus regulations do not work without continual public monitoring. Regulatory policies are initiated by public pressure. Once the establishment of a regulatory agency provides reassurance to the public, which holds a general but unorganized interest in the commons, the highly organized specific interest groups who wish to make incursions into the commons bring sufficient pressure to bear through other political processes in order to convert the agency to the protection and furthering of their interests. Eventually the government staffs the regulating agency with members of the businesses that it is supposed to regulate. International treaties are likewise ineffective to control pollution by military powers. "Lack of certainty" regarding global warming is the argument used by the USA government to continue polluting the atmosphere. "The scientific debate remains open. Voters believe that there is no consensus about global warming within the scientific community. Should the public come to believe that the scientific issues are settled, their views about global warming will change accordingly. Therefore, you need to continue to make the lack of scientific certainty the primary issue in the debate.. ."17 advises a political strategist. The present chapter in the story of the ozone hole is instructive. As of 2003, the hole in the ozone layer over Antarctica continues to grow18 as the result of the long life of CFCs, one of the earth's many maladies. Yet public understanding of, and interest in, environmental issues has decreased in the US, and is undermined by unsound reporting.19 14.5 A Third Way: Public Action and Human Consciousness Public action thus represents the one and only option to maintain our planet alive. The role of the impartial and ethical scientist is crucial in turning public sentiment around. In examining the role of scientists, 17 Frank Luntz, (2002). Quoted in Houck, O. (2003). Tales from a troubled marriage: Science and law in environmental policy. Science 302: 1926-1929. 18 World Meteorological Organization. (2003). Nature 425: 114. " This is how the 1985 discovery of the ozone hole is described in Nature: "Each Antarctic spring, in the late 1980s and early 1990s, enthusiastic scientists shared the news about the hole with a fascinated and equally enthusiastic public (my underlining)." (Solomon, S. (2003). The hole truth. Nature 427: 289-291).

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Houck20 points out that "scientific management has been trying that for decades and failed, eating up heroic amounts of money, remaining information-starved, featuring shameless manipulation of the data, facing crippling political pressure, and producing little abatement." Bad science is continually being generated by private corporations and even by government agencies. In 1998, the New England Journal of Medicine reported a "significant difference" between the opinions of scientists who received corporate funding and those who did not, on the very same issues. A final caution, says Houck, is the lure of the "safe" life, the apolitical life, free from the application of what scientists know to the issues around them. An increasing number of scientists are being pulled off of studies, sanctioned, and even dismissed for conclusions that contradict the economic interests and/or the ideology of the powerful. A scientist has no obligation to be socially conscious, but it has the moral responsibility of not being an accomplice to antisocial behavior. In fact, scientists all over the world are greatly concerned and active. A recent editorial in Science21 contrasts creative and destructive visions of the future. The 2003 report commissioned by the USA Pentagon22 announces the possibility of abrupt climate changes over the next 20 years that could result in a global catastrophe costing millions of lives in wars and natural disasters, and advised building "defensive fortresses" around the USA to keep massive waves of would-be immigrants away. The recommendation has been followed, and the USA now allocates $450 billions per year to the military, which is half of the world military spending. But climate, epidemics, pollution, cannot be fenced by national frontiers. The 2004 State of the Planet conference23 showed that there are options to combine economic welfare and environmental sustainability. World-wide scientific and moral consciousness and conscience are thus essential for survival.

20 Houck, O. (2003). Tales from a Troubled Marriage: Science and Law in Environmental Policy. Science 302: 1926-1929. 21 Sachs, J. D. Sustainable Development. Science 304: 649, 2004. 22 www.ems.org 23 www.earth.columbia.edu/sop2004

Chapter 15

Biotic Processes in Economics

Abstract: Empirical and theoretical analyses point to biotic pattern and bipolar feedback processes as a new model for economic processes. (1) Many economic time series (commodities, currencies, economic indexes, small business transactions) show biotic patterns. (2) Economic processes are shaped by bipolar feedback opposite forces (abundance and scarcity, supply and demand) rather than by scarcity alone as postulated by current models. (3) Economic growth can be creative or destructive. (4) Economic processes are co-determined by physical and biological processes that have priority, and by social, psychological and technological/scientific processes that have supremacy. A bipolar feedback of abundance and scarcity contests many concepts postulated by standard economics with a paucity of empirical testing to prescribe policies. Economics offer a noteworthy opportunity to study human processes because it combines the availability of numerical data with enormous human significance. The term "economics", meaning "relating to the household", is first and last, "home economics".1 The soundness of economic theory and economic policies can only be judged by their effect on the well-being of persons, our species, and the biosphere. The economic models upon which major decisions that affect

1

Berry, W. (1987). Home Economics. North Point Press: San Francisco.

551

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millions of people are based are nearly devoid of empirical testing.2 Economic theory does not describe; it prescribes. The results are far from satisfactory.3 It is urgent to study empirical economic processes with modern scientific methods. Economic theories are largely biased by political ideology. It is taken for granted that the proper purpose of economic activity is the pursuit of private profit. The study of economic processes, transparently called "Political Economy" in the past, is now evasively called "Economics". Economic theories utilize the general theories that dominate scientific discourse, such as mechanism (Adam Smith), dialectic conflict (Marx), periodicity,4 stochastic change (Bachelier, Mandelbrot)5, and chaos.6 Equilibrium models dominate standard economics, teaching, and the media; in simple terms, economic processes are equilibrium systems determined by global forces because individual actions are averaged out, and variations occur because equilibrium is disturbed by exogenous random change. The notion of social and economic equilibrium as normal, desirable, and healthy is based on a terminological confusion; equilibrium in physics is associated with rest and in thermodynamics with decay; chemical equilibration accompanies death, not living. 2 Hall, A.S. (1990). Sanctioning Resource Depletion: Economic Development and Neo-Classical Economics. The Ecologist 20: 99-104. 3 A few examples should suffice. The Argentine economy, adjusted faithfully to the policies of the World Bank, and judged as successful by the bank's economic analysts, collapsed in 2001. Economic development in Latin America, as advised by current economic theory, has resulted in an increase in the number of people living below the poverty line, from 135.9 millions in 1980 to 200.2 millions in 1990 to 204 millions in 1997. Under the guidance of current economic theory, the "Asian tigers" collapsed, and life expectancy in Russia dropped 10 years as it switched to capitalism. In 2002, the USA ranks in the 34th place among nations regarding infant mortality (Fig. 16.1). 4 Economic cycles with more or less regular periodicity ranging from 40 months to 60 years, have been described by many economists [Kondratieff, N.D. (1984). The Long Wave Cycle. New York]; and rejected by others [McCullock, J. H. (1975). The Monte Carlo cycle in business activity. Economic Inquiry 13: 303-321. "Monte Carlo cycles", i.e. superstitions such as those indulged by casino gamblers. 5 Cootner, P. H. (1964). The Random Character of Stock Market Prices. Cambridge, MA: MIT Press; Mantegna, R.N. (1991). Levy walks and enhances diffusion in Milan stock exchange. Physica A 179; 232-242; Mandelbrot, B.B. (1999) Multifractals and 1/f noise. Springer, New York, p. 69. 6 Ruth, M. (1993). Integrating Economics, Ecology and Thermodynamics. Netherlands: Kluwer; Gabaix, X., Gopikrishan, P., Plerou, V. and Stanley, H. E. (2003). A theory of power-law distributions in financial market flutuations. Nature 41i: 267-270.

Biotic Processes in Economics

553

Economic equilibrium is a point that actual prices cross without stopping. Reflecting mechanism, Smith replaced divine providence with the "invisible hand" of the market. Yet, to the crises of underproduction resulting from crop failures, plagues or wars, the capitalist control of the economy added crises of "overproduction", i.e. deficits in demand. Equilibrium models clearly contradict dynamic models advanced by scientists, and the methods employed by many practicing economists. While the economy is a process that constantly evolves in time, showing perpetually novel behavior and emergent phenomena, conventional economics studies patterns that cause no change in the assumed equilibrium state. General equilibrium theory poses no incentive for change because it investigates what prices, production and consumption rates are consistent with the overall pattern of the market. Arthur7 regards this portrait of the economy as both unrealistic and political. Although equilibrium theories have dominated political economics throughout history, dynamic models and analyses are as old as economics itself,8 as illustrated by the work of Cournot, Marshall, and Marx, who described the economy as a process out of equilibrium, subject to periodic crises, and eventually changing from one system into another. Awareness of all these factors led to the adoption of policies to reduce the severity of crises, such as the Marshall plan following World War II. Today governmental control of the economy is effected via adjustments made by federal regulators to prevent inflation by purposefully maintaining unemployment. This relation between employment and profit has been portrayed by a cyclic predator-prey model: a decrease in the level of employment decreases the workers' wage demands, thereby increasing profit and leading to greater investment, with subsequent increase in employment and wage

7

Arthur, W. B. (1999). Complexity and the Economy. Science 284: 107-109. Puu, T. (1989, 1991, 1993, 1997, 2000). Nonlinear economic dynamics. Lecture Notes in Economics and Mathematical Systems 336, (Springer-Verlag, ISBN 3-540-51438-4), 4th completely revised and enlarged edition, (Springer-Verlag, ISBN 3-540-62768-5). 8

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demands.9 The equilibrium model is no longer accepted by those who make economic decisions or influence them through the media.10 Standard models assume that economic processes equilibrate unless disturbed by external shocks, that changes in prices, being externally generated, are therefore unrelated to one another and randomly distributed, and that, whether deterministic or probabilistic, the laws that govern economic processes are autonomous and unchangeable. In other words, economic science can ignore physical, biological, historical and psychological factors. These models thus include psychologically untenable assumptions. Many assume that economic agents are rationally free,11 fully informed, and react immediately to market changes. In contrast, many practicing economists reasonably assume that prices and economic indicators are to some degree continuous and not instantaneous, that changes result from reactions to previous changes, and that such reactions are biased by prevailing social attitudes, the action of major market players, governmental interventions, and scientific and technological advances. 9

Goodwin, R.M. (1967). Reprinted in Goodwin, R.M. (1982). Essays in Dynamic Economics. London: MacMillan, pp. 165-170; Blatt, J. M. (1983). Dynamic Economic Systems. New York: M. E. Sharpe. 10 For instance, in 1997 New York embraced a policy, promoted by federal funds, to reduce the training of physicians, based on the notion that an oversupply of doctors increases the cost of medicine. Two decades earlier, based on the expectations of the "law of supply and demand", the policy was to increase the number of physicians to decrease the cost of medicine. In either case, the economy was not regarded as self-controlling. '"The hidden hand of the market will never work without a hidden fist -MacDonald's cannot flourish without McDonnell Douglas, the designer of the F-15. And the hidden fist that keeps the world safe for Silicon Valley's technologies is called the United States Army, Air Force, Navy and Marine Corps', states a New York Times headline calling for military enforcement of a "global order'" [Friedman, T. L. (1999). From supercharged financial markets to Osama bin Laden, the emerging global order demands an enforcer. That's America's new burden. New York Times Magazine, March 28] —a statement made stronger by the history associated with the terms "global order" and "White man's burden". 1 ' The concept of "free and rational consumer", presented as fact by many economists during the late twentieth century, uses technical definitions that distort common use of the terms. Overwhelming psychological evidence show that humans are controlled by biological needs and emotional reactions. Humans are both rational and irrational, and advertising prospers on make the most of this fact. In 2004, Americans are not free to purchase chicken without antibiotics, produce without genetic transformations, and cheaper Canadian Pharmaceuticals. Poor people all over the world are not free to satisfy their most elementary needs, and have no access to clean air and water.

Biotic Processes in Economics

555

Innovations result from creative human acts, with major roles for individuals and industrial, educational and governmental institutions. Technological innovations, production and marketing, buying and selling, are reactions to many events, including changes in price, demand, expectations, offers, and many other factors that are complex and diverse, but not random. 15.1 Biotic Patterns of Economic Processes We have explored the applicability of bios as a mathematical model for monetary economic processes in a series of studies devoted primarily to time series analysis.12 The identification of pattern can serve specific, practical business purposes13 and has implications regarding what mechanisms may be involved. Monetary phenomena are sensitive quantitative indicators of social processes, and conversely cause social change. Hence, significant economic processes are portrayed in the pattern 12 Sabelli, H. and Carlson-Sabelli, L. (1995). Sociodynamics: the application of process methods to the social sciences. Chaos Theory and Society, edited by A. Albert. Amsterdam: I.O.S. Press, and Sainte-Foy, Canada: Les Presses de l'Universite du Quebec; Sabelli, H. (2003). Bios, creative organization in economic, biological, and meteorological data. International Conference on Advances in Internet, Processing, Systems, and Interdisciplinary Research. Electronic Publication IPSI-2003; Sugerman, A., Sabelli, H., and Patel, M. (1999). Biotic patterns of economic processes: beyond equilibrium, chaos, and determinism. Proc. 43rd Annual Meeting of the International Society for the Systems Sciences, edited by J. K. Allen, M. L. Hall and J. Wilby; Sabelli, H et. al. (in press). Creative Processes in Natural and Human Systems: Part 11: Biotic Patterns in Biological, Economic and Physical Processes, Journal of Applied Systems Studies, special issue edited by H. Sabelli. Sabelli, H. and Kauffman, L. (1999). The Process Equation: Formulating And Testing The Process Theory Of Systems. Cybernetics and Systems 30: 261-294; Sabelli, H. (2001). Novelty, a Measure of Creative Organization in Natural and Mathematical Time Series. Nonlinear Dynamics, Psychology, and Life Sciences 5: 89-113; Sabelli, H. (2001). Arrangement, a measure of nonrandom complexity. Systems Analysis Modelling Simulation 42: 395-403; Sabelli, H. and Abouzeid, A. (2003). Definition and Empirical Characterization of Creative Processes. Nonlinear Dynamics, Psychology and the Life Sciences 7(1): 35-47; Sugerman, A. and Sabelli, H. (2003). Novelty, Diversification and Nonrandom Complexity Define Creative Processes. Kybernetes 32: 829-836. Levy-Carciente, S., Sabelli, H. and Jaffe, K. (2004). Complex Patterns in the Oil Market. Intersciencia 29: 320-323. 13 When Mandelbrot became a staff mathematician at IBM's Thomas J. Watson Research Center, he was able to halt a useless multimillion dollar research project aimed at eliminating "noise in signal transmission" by recognizing it for what it actually was, chaos, a pattern he had already found in the yearly evolution of cotton prices. [Oliver, D. (1992). Fractal Vision. Carmel, Indiana: SAMS Publishing, p. 53].

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of time series. We have thus considered currency exchange rates, economic indexes such as the Dow Jones Industrial Average (DJIA) and Standard and Poor's Composite Index of 500 stocks (S&P), commodities,14 time series of purchases, and small business inventories. Statistical, frequency and dynamic analysis of financial time series show biotic features (broad spectrum, non-normal distribution, asymmetry, non-stationarity, diversity, diversification, complexes, novelty, non-random complexity, and low dimensional consecutive recurrence indicating nonrandom causation). The statistical distributions of financial data are often multimodal and characteristically have skewed statistical distributions, as observed with statistical noise and biotic and parabiotic series, in contrast to the symmetric distribution of random, periodic and chaotic series. Dynamic skewness15 is positive for some economic data. Economic series characteristically have high entropy and a high coefficient of variation, denoting diversity. Most economic series show global diversification (Fig. 15.1). Many series show local diversification (DJIA, crude oil, 1 month Treasury bills, gold, silver Eurodollar, yen, Dutch Mark, British pound, business accounts), but others, such as the S&P, show convergence. Power spectrum analysis (Table 15.1) shows p exponents between 1.5 and -2, as observed in biotic series, different from chaos and from white, pink or brown noise. Series of differences between consecutive terms show positive P exponents compatible with bios or chaos but not randomness. Wavelet plots often show complex patterns similar to those produced by 1/f noise and biotic time series. (In contrast, the S&P shows a simple random-like pattern.) A comparison of wavelet plots portraying 14 A commodity is a fixed physical substance that investors buy or sell, usually via future contracts. A commodity future contract is a commitment to buy or sell a specified quantity of a commodity at a specified price in a stipulated future date. A future commodity market serves to guarantee producers the price of a good or raw material used in production, while it also provides an opportunity for others, even philosophers (Chapter 2), to make a profit. 15 Vectors of 30, 40, 50...200 terms starting with each term of the series are constructed, and their skewness is measured. The average skewness for all vectors of the same length is calculated, and plotted against the vector length (embedding).

557

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DJIA series and parabiotic series generated with the process equation show remarkable similarities (Fig. 15.11). 400

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Recurrence plots of most economic series (Fig. 15.10) show "complexes", separated by brief recurrence-free epochs. In very significant cases, economic series are trended as well as biotic ("parabiotic"), so the complexes are small and lie along the central diagonal of the recurrence plot. Month-long patterns are similar in form to extended years-long patterns, showing self-similar fractal organization. In contrast, the recurrence plots of the S&P are simple in pattern and uniform in time, like periodic or chaotic series. ^

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Biotic Processes in Economics

559

Economic series exhibit low recurrence and novelty, including the S&P.16 In most series of stock and currencies, a high proportion of recurrence isometry is consecutive, particularly at low dimensions (except the S&P, which shows no consecutive recurrence). Reduction in the percent of consecutive recurrences by shuffling demonstrates causation, and measures of recurrence entropy indicate nonrandom causation. This is surprising in view of measurements of statistical correlation suggesting random price increments. As it is well known, successive terms of economic series are highly correlated (Pearson's correlation r > 0.9),17 while the differences between them are not.18 These results have been regarded as evidence for the hypothesis that stock price series are random walks -a reasonable inference but no proof. Trading occurs simultaneously in different parts of the world. Buyers and sellers may not know the immediately preceding transactions, or may ignore them as unrepresentative of the actual state of affairs. The price they agree upon likely reflects previous changes rather than the immediately preceding transactions. Lack of correlation between consecutive terms may also reflect the composite character of the data. For instance, the Pearson's r is near 0 for the DJIA and differs markedly from 0 for a single commodity. Moreover, differences between successive terms in biotic series show a wide range of correlations according to the gain. Thus, lack of correlation between successive differences may also be observed in deterministic processes. That price increments show low or no correlation in most cases is not surprising. Low isometry and high consecutive recurrence result in high arrangement. 16 In agreement with these findings, we also found innovation by measuring the Hurst exponent of stock and currency exchange series using the CD A. We found a Hurst exponent equal or smaller. In contrast, Mandelbrot noted higher than 0.5 Hurst exponents, denoting long term memory. As noted in Chapter 14, the estimation of the Hurst exponent is complex and fraught with problems. Other authors also have not found persistence in economic data. [Mandelbrot, B.B. (1999). Multifractals and 1/f noise. New York: Springer, p. 69; Lo, A. W. and A. Craig MacKinlay. (1999). A NonRandom Walk Down Wall Street. Princeton: Princeton University Press]. 17 There are exceptions, such as the S&P (r = 0.12) and daily accounts for small business (r = 0.28). 18 Also in this case we have found exceptions such as small positive correlations for differences between successive corn prices (r = 0.12), and significant negative correlations for S&P (-0.45) and business accounts (-0.43).

560

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The median embedding dimension (MED differs widely among economic series (Table 15.2). Corn prices (MED = 40) compare to biotic series, the DJIA (MED = 6) to parabiotic series, and the S&P (MED = 300) to random data and chaotic series. Table 15.2 Arrangement at the Median Embedding Dimension (M.E.D.) Dow Jones Industrial Average Corn Random (uniform) 1/f pink noise Logistic chaos Process chaos g = 4.3 Bios g = 4.65

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Biotic Processes in Economics

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Fig. 15.4 Autocorrelation in oil series. Both oil volume and price index show extended autocorrelation as observed with bios, and shorter than observed with Brownian noise. Long autocorrelation between successive terms are not found in most chaotic series.

Fig. 15.5 Autocorrelation in series of differences between consecutive term of oil series. The autocorrelation is small, but different from the 0 autocorrelation found in the random series of differences between consecutive terms of a random walk. The autocorrelation between successive changes is negative, as observed with mathematical bios at some gains.

We inferred that the observed biotic patterns may be generated by a co-creative process, so we then considered two measures of an economic process, the relation between the future prices (oil price index) and volumes of crude oil sold in the London International Exchange (see

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Figs. 15.3-15.14).19 Both series are parabiotic and increase together in a highly correlated manner (r =0.81). This correlation indicates that opposites such as supply, demand and price form circuits rather than equilibrium. Oil price

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19 International Petroleum Exchange (IPE) of London: the daily average for the 15 day-future price of Brent crude oil (IPE Brent Oil Index) and the volume of Brent crude oil exchanged everyday from June 1988 to September 2002. A preliminary study employing standard statistical and non-linear analytic techniques showed only that variations in the price index and volume of oil exchanged are not random and are markedly different from each other [Levy-Carciente, S, Sabelli, H and Jaffe, K.. Complex Patterns in the Oil Market. Intersciencia 29: 320-323, 2004]. The price index values showed short periods of stability, suggesting strong historic constrains for prices.

563

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Plotting production and price in orthogonal axes in a phase plane demonstrates a direct relation for the volume of oil production and the 15-day future price: the higher the price, the greater the production. Higher prices provide greater incentive for production, contradicting equilibrium model predictions. The data shows expansion accompanied by diversification, novelty and complexity, as to be expected from diverse and bipolar feedback. I "000 i 250000

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Fig. 15.10 Recurrence time graphs of oil series: oil price index (left), oil volume (right). Delay 1. Embedding 10. Cutoff radius = mean distance. Time series (top row). In both cases, there are well-defined clusters of recurrences (complexes) indicating the existence of high dimensional, non-periodic organization. Note the temporal correspondence of the complexes in the two series. After shuffling the data, the plot is uniform, and the number of recurrences is increased, indicating novelty. Series of differences (middle row), and their randomized copies (bottom row). In the series of differences, there are complexes but they are not separated by interruptions of pattern. The pattern is uniform after shuffling.

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The shift from the statistical to biotic models may help to dispel socially meaningful errors regarding energy policy. The commonly used statistical model20 assumes that production follows the "central limit theorem," which states that the sum of a large number of erratic variables follows a bellshaped curve. It follows that production grows to a peak after which it 20 Hubbert, K, M. (1956) Nuclear Energy and the fossil fuels. In Practice series. American Petroleum Institute, Washington, D.C.

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declines at the same rate at which it initially grew. Unavoidably, the country and the world will run out of oil, a prediction made for the USA in 1919, and more recently triggered the "energy crisis" of 1973, followed shortly thereafter by the "oil glut" of 1986. Actually, the production of oil over the years follows an irregular curve that appears either biotic or stochastic. Though fears of oil depletion are unjustified, they moved the British to invade the Middle East in 1914, points out a well-known corporate strategist in Science?1 \

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Maugeri, L. (2004). Oil: Never Cry Wolf-Why the Petroleum Age Is Far from over. Science 304: 1114-1115.

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15.2 Bipolar Feedback: Abundance and Scarcity We have seen that the pattern of economic processes is biotic. Such pattern cannot be generated by a stable equilibrium with fluctuations due to random inputs. Biotic patterns observed in economic processes cannot be generated by unipolar feedback, such as the logistic equation, so they cannot result solely from the tendency for supply to grow (or decrease) as a function of demand. Biotic patterns are generated by bipolar feedback, pointing to abundance as the necessary complement to scarcity. The central place of scarcity in economics stems from the harsh theological speculations22 of Parson Thomas Malthus. Scarcity plays a role in biological growth which is limited by whatever resource is in least supply,23 but abundance is just as important. Life exists because nature's supplies are abundant. Natural supplies obviously precede human production. Scarcity often represents the inefficient use of resources. The oil depletion crisis of the 1970s was followed shortly by an oil glut, and the energy conservation laws passed thereafter could lead to a self-sufficient USA were it more energy conscious. Likewise, the "coming crisis" of water scarcity is in many ways avoidable.24 We so ill distribute nature's supplies that we increase the population of humans, rats, cockroaches, bacteria and viruses, and decrease gazelles, chimps, and whales. Serious economic theory must start with the recognition that resources necessarily precede scarcity. On the contrary, economists advocate policies that promote scarcity, such as those suggested or 22

Malthus' ideas departed from religious notions of "God's abundance" and "wealth in the kingdom of God". 23 This fact was discovered by the German agronomist Carl Sprengel (1787-1859) but it is often attributed to the German chemist Justus von Liebig (1803-1873). He is credited with being the "Father of the Fertilizer Industry" for his Law of the Minimum according to which yield is proportional to the amount of the most limiting nutrient. The law of the minimum has been extended to include other factors beyond nutrients such as moisture, temperature, insect control, and light. 24 Gleick, P.H. Making every drop count; Gleick, P.H. Safeguarding our water; Martindale, D. and P.H. Gleick. How we can do it; Postel, S. Growing more food with less water. Scientific American, February 2001.

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imposed on less powerful nations by world financial institutions. Economic plans of austerity are like bleeding as medical treatment. 15.3 Bipolar Feedback: Demand Creates Supply (Keynes) and Supply Creates Demand (Say) The traditional "law" of supply and demand, postulated to generate economic equilibrium, rhetorically justifies the underpayment of labor. Economic data never show that demand and supply neutralize each other in equilibrium. Offer decreases demand in the obvious way of satisfying it. But offer also increases demand by reducing price, by increasing wants, by creating needs for products that complement those we already get and/or are essential for economic competition, and in many other different ways. In the same manner, demand increases supply by offering a market and decreases supply by consuming it. As demand fosters supply and supply fosters demand, one would then expect an increase in both, rather than equilibrium. Not surprisingly, this is exactly what we see in many economic series, as in the oil market. Given that oil plays a major economic role, consistent with the fundamental role of energy in physical processes, the simultaneous increase in oil production and profits has a wide social significance. The increase in both supply and demand for oil, however, does not produce a simple linear rise; rather, the pattern is clearly biotic. The complexity of pattern probably results in part from the asynchrony of production and consumption. Consumption has a clear historical and current priority over production, and in turn production acquires supremacy over the historical course of the process as well as contemporaneously. The priority of consumption is evident. Animals, children, the elderly, the sick and the disabled, the wealthy, the military, and many others, consume but do not produce. Consumption has priority over production; demand has priority over supply. Demand is complex. In any society, there are those who die because they cannot satisfy their most elementary needs for food (in poor countries) or medical care (in

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poor countries and in the USA (Fig. 16.1), those who satisfy elementary needs only, a wide spectrum of those who satisfy some wants and can be made to have more needs and wants, and those who could satisfy all their needs and often spend unnecessarily, conspicuously, and unsatisfactorily. Supply affects demand very differently in these groups, and affects aggregate demand, even in opposite ways, depending on the proportion of the population belonging to each class. In natural environments, physical power determines predation, and predation is the one and only effective demand. In human societies, in our times, money often determines "effective demand". Without money, needs become "noneffective demand". In turn, political relations, feelings and ideas determine how we balance the powers of demand and supply. Whether we choose to feed the hungry or to feed the lions is a political decision, not an economic process. Production is a natural process, not uniquely human, though our mode is radically different. In the course of history, gathering, hunting and mining have become a first step in the transformation of natural supplies into manufactured products. Thus, production acquired supremacy over consumption. The generation of supply by demand was postulated by Keynes.25 The generation of demand by supply is called "Say's law".26 Offer and 25 The British economist John Maynard Keynes (1883-1946) in his General Theory posited that aggregate output and employment were determined by aggregate demand. Oversimplifying Keynes, changes in supply result from changes in demand. He proposed the concept of a demand-determined equilibrium, which includes the possibility of unemployment, the ineffectiveness of price flexibility to cure unemployment, and the possibility of using government fiscal and monetary policy to help eliminate recessions and control economic booms. The success of American policies to prevent the depression expected to occur after WWII attests to the effectiveness of the Keynesian approach, as does the downward spiral of the standard of living after the Keynesian policies were abandoned. 26 The notion that "supply creates demand" is attributed to the French economist Jean Baptiste Say (1767-1832); this expression, however, does not appear in Say's writings. "Say's law" was developed by later economists in attempting to understand the economic crises of overproduction, euphemistically called "recessions", typical of our economic system. Their purpose was to show that crises could not possibly be due to underconsumption. In recent years, this purported economic principle has been highlighted as a justification for "supply-side economics". "Law", such a poor metaphor in describing the regularities of nature, may however be more appropriate to characterize economic processes, as they indeed are dictated by law, the law of the state or the law of the mighty, seldom if ever to be distinguished. Say's law, at least in its present embodiment as a justification for supply-side economics, fits well this description.

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demand stimulate and inhibit each other, thereby generating bipolar feedback. We proposed that demand creates supply and supply creates demand, and that their interaction generates bios, not equilibrium.27 Obviously, present demand implies future demand, as populations survive, reproduce, and often grow. Equally obvious: present production, both natural and human, implies future production, as natural and human processes for the most part continue to operate. Say wrote "products are paid for with products", which is generally true.28 In a barter world, buying and selling are one and the same act, and Say's law is trivially true. It is not true in nature, where organisms predate upon each other. It can be only partially true in contemporary societies, in which there is unemployment, unsold goods, recessions, and depressions. Supply side economists claim that production is the source of demand.29 One's ability to demand goods and services derives from our income, and our income is purportedly produced by one's own acts of production. This description excludes the expropriation of others, such as by military conquest, thievery, and fraud as sources of income. Not all assets derive from labor, certainly not from the labor of the person who controls the assets. Also, Say's claim that unemployment would not be possible is simply false. In contemporary societies, money mediates supply and demand. The demand for current goods and services will not precisely match the value of what has been produced, as some money remains in someone's possession (most frequently a non-producer). Demand can become insufficient because producers are not paid enough. Thus, given the existence and use of property, Say's law does not 27

Sabelli, H. (2003). Bios, creative organization in economic, biological, and meteorological data. VIP Forum of the IPSI-2003, Montenegro. 28 "It is worth while to remark, that a product is no sooner created, than it, from that instant, affords a market for other products to the full extent of its own value. When the producer has put the finishing hand to his product, he is most anxious to sell it immediately, lest its value should diminish in his hands. Nor is he less anxious to dispose of the money he may get for it; for the value of money is also perishable. But the only way of getting rid of money is in the purchase of some product or other. Thus the mere circumstance of creation of one product immediately opens a vent for other products." (Say, I B . (1803). Traite d'economie politique, ou simple exposition de la mcmiere dont seforment, se distribuent, et se composent les richesses.) 29 W. H. Hurt. (1975). A Rehabilitation of Say's Law. Athens, OH: Ohio University Press.

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exclude the possibility that aggregate demand is insufficient to purchase what has been supplied. Keynes' and Say's notions appear to be only partially valid from strictly economic considerations. This fact, together with the apparent applicability of the bipolar model of mutually implying opposites in other fields, suggests the desirability of developing an economic theory that integrates both. In an exchange, supply and demand complement each other exactly, so each decreases the other simultaneously and to the same extent in the short run. In the long run, supply and demand can increase each other. Supply reduces demand insofar as it satisfies current needs and wants, and increases demand insofar as it creates new possibilities, needs and wants. Changes in demand and supply are correlated but not synchronic (it may take more, or less, time, for production to increase than for demand to resume). As illustrated by recursions with delay (Chapter 3), these types of asynchronous relations can generate complex patterns. Nonperiodic business cycles may be expected from the very nature of bipolar feedback. One factor is technological creativity and the corresponding lag in the development of social institutions. As a result, unemployment increases. The accumulation of wealth in few hands decreases effective demand. Only the many make up a sufficient aggregate demand. No matter how profligate, a small privileged class cannot consume enough, nor do they invest enough. It follows that a rational economic policy that provides for the welfare of many, without preventing reasonable privilege, must foster both demand and supply. The one-sided pursuit of one at the expense of the other is a short-term policy that may obtain wealth or popularity, but will certainly fail -by the certainty of mathematical law, stronger than the law of governments. We need a demand and supply economics. A bipolar feedback captures the rational aspect of equilibrium theory in the sense that it involves the interaction of multiple agents seeking their own goal.

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15.4 Biotic Creation: Historical Slow Waves and Managed Markets A wave pattern of alternating price-change and relative price stationarity was discovered in the 18th century, and has been investigated by European economists in the 1930s, and more recently by Fischer30 in the USA. Long biotic series generated by the kinetic process equation in which the gain increases to large values show biotic epochs separated by major shifts in mean. There is a striking similarity between these patterns and the long aperiodic waves in time series of prices from the 13th to the 20th century31 (Fig. 15.15). Each of these leaps follow an increase in population, resulting from increased fertility due to rising expectations, rather than decreased mortality. These examples illustrate that biological factors (in this case population) have priority while psychological causes (expectations) have supremacy regarding economic processes. These empirical and mathematical results point to a process model of development as a diversification resulting from the interaction of complementary opposites. The bios model suggests methods to monitor economic processes, as here illustrated, and potentially to transform them. Economic processes are open to choice. There is no justification for inhumane economic policies. There is no need to artificially stop economic expansion.32 Economic downturns are not unavoidable

30

Dornbusch, R. and Fischer, S. (1978). Macroeconomics. New York. Fischer, D. H. (1996). The Great Wave. Oxford University Press. New York. Nor is there any need to artificially stop economic expansion. Alan Blinder, of Princeton University, and formerly of the Federal Reserve, in an article published in the New York Times August 24, 1999, recognizes that "macroeconomic folklore laws hold that expansions don't die of old age; they die because the Federal reserve kills them. (...) almost every American recession since World War II has been preceded by tighter monetary policy -that is, higher interests rates." But then he proceeds to explain the long duration of the economic expansion during the Clinton administration to "fortuitous series of what economists call favorable supply shocks". These "random events" include cheaper imports, falling raw material prices, the rapid expansion of science and industry, including a rapid growth of computation, the reduction of salaries for workers and of income for health care professionals, and many other predictable and purposefully generated consequences of the American dominance in the international arena, and of corporations in both the national and international arena. These are not random and isolated events. 31

32

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consequences of determined laws. There are always alternatives.33 Annual Price Index (1451-75=100) 10000

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Economic processes are so highly intertwined with physical, social and cultural processes, that the models offered by economists must add "external shocks", such as ever-present technological developments and sociopolitical changes, to account for observations. "Shocks" are major changes not modeled by random walk models. The influence of "exogenous" shocks may be expected to be greater in deterministic processes that are extremely sensitive to external inputs ("initial conditions") that in stochastic noise that are not. Purely economic models of economic processes are unrealistic. Political factors often are decisive, as demonstrated by currency exchange rates, which are always 33 TINA, meaning "there is no alternative", was the nickname of well known politician whose name I do not wish to remember.

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determined by the powerful, as illustrated by the fact that at times they are maintained at a given value by government. Economic processes, in summary, display biotic patterns, indicating that they are created rather than determined by the impersonal forces of the market. This is not to imply a conspiracy of financial and industrial magnates to expand their egos by insane accumulation beyond any possible need (would a half billionaire have less to spend than a full billionaire?), although recent financial scandals may so suggest. This is the consequence of the fact that the economy is managed, explains Harvard economist John Galbraith34 in The Economics of Innocent Fraud. In recognition of the supremacy of ideas, Galbraith devotes much of this book to recount the renaming of the current economic system. "Capitalism" is seldom used by articulate defenders of the system because it has acquired strongly negative implications in most thinking persons as a result of monopolies and the great depression of the 1930s. Thus followed a determined search for benign alternatives to the name, such as "social democracy" in Europe and "free enterprise" in the USA. These names did not succeed because socialism was not wanted by the capitalists and "free enterprise", which is limited to few, is not reassuring to the many. Then came the "market system", which its connotation of impersonality and control by the consumer. Such control is, as Galbraith stresses, false, as needs, wants and, most importantly, scarcities are created. A more appropriate designation will be "corporate system", he states, but sensitive friends and beneficiaries of the system do not want to identify who is in authority. Economic processes are created because the economy is managed. It is managed by a class, which I have called the administrative class35 to point out the similarity among corporate executives, public officials, communist party officials, and military and church administrators. No longer owners such as stockholders control the economy, stresses 34

Galbraith, J. K. (2004). The Economics of Innocent Fraud. Houghton Mifflin Co. Boston. Sabelli, H. C. and Synnestvedt, J. (1991). Personalization: A New Vision for the Millennium. Chicago, IL: Society for the Advancement of Clinical Philosophy (SACP).

35

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Galbraith. It does not matter that communist officials did not have the ownership of the capital, I pointed out then. What matters is control. According to Galbraith, the same economic system exists all over the world, except in North Korea, Cuba and, in principle, China. It is meaningful that no other countries are excluded. This is not the economic system of the successful countries. It is also the economic system of those who suffer famine, epidemics, and civil war, who lack water and medicines, and who suffer military dictatorships shored up by our business. To learn about capitalism, one should not look at it in the metropolis, where it dons clothes, but in the colonies where it goes naked, pointed out Marx. As for the exceptions made by Galbraith, I beg to disagree. Managers also control the economy in China, Cuba and North Korea, and they controlled it in the Soviet Union with the disastrous effects that are now highlighted. This implies a dire prediction for our managed economy, one already made clear by pollution, diminishing services, decline in the standard of living, and tragically, by war. Galbraith denounces war, death, random cruelty, and suspension of civilized values as human failure and regards them as inescapable. This is the determinism that, happily, the biotic nature of the data contradicts. As for innocence, this is a long held belief in America to which psychotherapists contribute by regarding guilt and shame as symptoms rather than as danger signals. "Shameless and guiltless" does not amount to honorable and dutiful, but may rather imply lack of conscience. Persons have conscience. Governments and corporations do not, because they are institutions, not persons. They are innocent only because they cannot be guilty. This is the core problem: we need an economy managed by persons, not institutions.

Chapter 16

Biological Priority, Psychological Supremacy

Abstract: The concepts of continual creation, mutual feedback and biological priority and psychological supremacy offer concrete strategies for salutary interventions in clinical and educational practice. It also affords an approach to collective health, which is the most important scientific concern of our times, as increasing violence demands a change from conflictual thinking to co-creation, and from hierarchical states and corporations to personalized systems co-created by bi-directional relations of mutual and bipolar feedback. Biotic dynamics (conservation plus bipolar, mutual and hierarchical feedback) provides new foundations for new theory in medicine, sociology, and psychology. Our group is pursuing their development. Some ideas regarding clinical1 and social2 applications have been explored in previous publications. 1

Sabelli, H. and Carlson-Sabelli, L. (1989). Biological Priority and Psychological Supremacy, a New Integrative Paradigm Derived from Process Theory. American Journal of Psychiatry 146 15411551. Sabelli H. C , Carlson-Sabelli L., Javaid J. I. (1990). The Thermodynamics of Bipolarity: A Bifurcation Model of Bipolar Illness and Bipolar Character and Its Psychotherapeutic Applications. Psychiatry: Interpersonal and Biological Processes. 53:346-367; Sabelli, H. C. and Carlson-Sabelli, L. (1991). Process Theory as a Framework for Comprehensive Psychodynamic Formulations. Genetic, Social, and General Psychology Monographs. 117:5-27. Sabelli, H., Carlson-Sabelli, L. and Messer, J. (1994). The Process Method of Comprehensive Patient Evaluation Based on the Emerging Science of Complex Dynamical Systems. Theoretical and Applied Chaos and Nursing. 1: 33-41. Sabelli, H. C , Carlson-Sabelli, L., Patel, M., Zbilut, J., Messer, J., and Walthall, K. (1995). Psychocardiological portraits: A clinical application of process theory. In Chaos theory in Psychology. F. D. Abraham and A. R. Gilgen (Eds). Greenwood Publishing Group, Inc., Westport, CT. pp 107-125. Sabelli, H., Carlson-Sabelli, L., Patel, M and Sugerman, A. (1997). Dynamics and psychodynamics. Process Foundations of Psychology. J. Mind and Behavior 18: 305-334. 2 Sabelli, H. C. and Synnestvedt, J. (1991). Personalization: A New Vision for the Millennium. Chicago, IL: Society for the Advancement of Clinical Philosophy (SACP). Sabelli, H. C , Plaza, V., Vazquez, A., Abraira, C , and Martinez, I. (1991). Caos Argentina: Diagnostico y Enfoque Clinico.

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16.1 Biological Priority and Psychological Supremacy in Medicine Cardiovascular illness exemplifies hierarchical and bi-directional feedback among biological, social and psychological processes. A case study is outlined elsewhere.3 Beyond medication, current practice focuses on exercise and diet, which are largely determined by social and psychological processes that are not addressed. Competition, anger, and rushing contribute significantly to coronary artery disease; cardiological care seldom attends to these aspects, and most studies focus on the personality of the cardiac patient to the exclusion of the patient's social context. Yet, we live in a society that enforces, promotes and even celebrates competition, in the midst of social conflicts that propagate anger and an economic environment that imposes rushing to increase profits. Personality differences may make some individuals more susceptible than others, but the social environment affects us all. Acknowledging the predominantly social and cultural origin of emotional processes in cardiac illness is scientifically honest and will help to change cultural traits that promote illness. Focusing on individual psychology blames the victim and does not solve the problem. Learning about social influences may help individuals avoid them, for instance, by changing jobs. Individuals should not be forced to wait until social issues are solved to protect their own life, and in fact their individual action may contribute to social change (see section 16.8).

Chicago, IL: SACP. Sabelli, H. and Carlson-Sabelli, L. (1995). From social atoms to multinational processes. Must Cinderella live among the ashes? Systems thinking, Government Policy and Decision Making. Proc. International Systems Society Edited by B. Bergvall-Kareborn pp. 815-826. 114. Sabelli, H. and Carlson-Sabelli, L. (1995). How can Cinderella have her prince? Choosing to diversify social power^Proc. International Systems Society p 827-838. Sabelli, H. and Sugerman, A. (2002). Life-Long Creation in the Prevention Of Premature Aging. Kybemetes. 32: 778-787, 2003. Sabelli, H., Patel, M., Carlson-Sabelli, L., Konecki, J., Nagib, J., and Sugerman, A. (2003). Aging and Social Systems Kybemetes. 32: 767-777; Sabelli, H. (2003). Hipotesis y propuestas para un desarrollo creativo. In E. Herrscher. Pensamiento Sistemico. 3 Sabelli, H., Carlson-Sabelli, L. and Messer, J. (1994). The Process Method of Comprehensive Patient Evaluation Based on the Emerging Science of Complex Dynamical Systems. Theoretical and Applied Chaos and Nursing 1: 33-41; Carlson-Sabelli, L., Sabelli, H. C , Patel, M., Messer, J., Zbilut, J., Sugerman, A., Walthall, K., Tom, C. and Zdanovics, O. (1995). Electropsychocardiography. Illustrating the Application of Process Methods and Chaos Theory to the Comprehensive Evaluation of Coronary Patients. Complexity and Chaos in Nursing 2: 16-24.

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A dramatic example is the abandonment of breast-feeding in the rich countries (on the advice of their pediatricians) and in poor countries (as advertised by employees of corporations disguised as nurses4). The concept of biological priority and psychological supremacy5 provides a bio-socio-psychological method for psychosomatic medicine and a strategy for a systemic approach to medicine and psychiatry.6 The hierarchy is dynamic. For instance, restoring breathing always has absolute priority, but once life is not threatened, taking care of the patient's emotional well-being may become more important than treating a respiratory difficulty. Conversely, attending to the psychological welfare of a dying patient has absolute supremacy. Whether in medicine or psychiatry, insight into biological issues has priority. A patient who denies the meaning of pain will not seek the needed treatment; likewise, a patient suffering from a genetically determined affective disorder cannot be adequately treated unless he or she is aware that it is a medical illness. Therapists who promote "insight" into hypothetical unconscious reasons, childhood traumas or current 4

Two of the world's largest producers of powdered baby milk, are currently breaking a World Health Organisation Code on the marketing of breast milk substitutes. Nestle and Wyeth provide free milk to maternity hospitals in the Third World so that newborn babies are routinely bottle-fed and do not learn to suckle well. The baby is then dependent on artificial milk. When the mother and baby leave hospital, the milk is no longer free. At home parents are forced to buy more milk, which can cost 50% of the family income. Because the milk is so expensive the child is not fed enough. This leads to malnutrition. The water mixed with the formula is often contaminated. This leads to diarrhea, malnutrition and often death. James Grant, Executive Officer of UNICEF, has said: Every day some 3,000 to 4,000 infants die because they are denied access to adequate breast milk. 1.5 million babies die every year from unsafe bottle feeding. Breast feeding is free and safe and protects against infection - but companies want to do business. 5 Sabelli, H. C. and Carlson-Sabelli, L. (1989). Biological Priority and Psychological Supremacy, a New Integrative Paradigm Derived from Process Theory. American Journal of Psychiatry 146(12):1541-1551. 6 Psychosomatic medicine pioneered the integration of biological and psychological care but ignored the social aspects of health, and it was biased by psychoanalytic interpretations. Systems theory went further [Grinker, R.R.(1975). The relevance of general systems theory to psychiatry. In American Handbook of Psychiatry, 2nd ed., vol 6, S. Arieti (Ed). New York: Basic Books, Inc; Marmor, J. (1983). Systems thinking in psychiatry: Some theoretical and clinical implications. American Journal of Psychiatry 140:833-838; Engel, G. L. (1980). The clinical application of the biopsychosocial model. American Journal of Psychiatry 137:535-544; Pribram, K. H. (1981). The neurobiologic paradigm. In Models for Clinical Psychopathology, C. Eisdorfer (Ed). New York: Spectrum Publications] but it does not provide guidelines regarding the sequence in which problems are to be treated On the basis of systems theory, Engel proposed a sequential bio-psycho-social approach, while Pribram advocated that treatment can start at any point, since to change any part is to change the whole [Abroms, E. M. (1983). Beyond eclecticism. American Journal of Psychiatry 140:740-745].

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family conflicts, while denying the importance of biological causes, prevent insight. Biological insight must be complemented with social and psychological insight. In clinical practice, we increasingly witness patients with the emotional consequences of unemployment, job insecurity, marital conflict, or childhood abuse being treated with antidepressants. Family therapy should be employed frequently in recognition of mutual feedback among family members. Social causes should be given great weight in all medicine in general. Conversely, biological issues should be given priority in social matters. Infant mortality measures the health of a society, and the values of its members. The facts presented in Fig. 16.1 speak for themselves. The problem is that children are a large constituency, even a majority, but not an effective majority. (The same phenomenon occurs regarding classes; the middle class, rather than the workers, may be the effective majority.)

Fig. 16.1 Infant mortality rank in 2002 [(horizontal axis: from highest (left) to lowest (right) mortality], and average reduction since 1990 (vertical axis: decrease mortality upward, increase mortality downward). Note that these data precede the Iraq war.

16.2 Bipolar Feedback, Roles, Systems and Individuals Social and psychological processes are driven by multiple systems of mutual feedback. A person has multiple roles (e.g. worker, father, reader, patient), which are first social and then personal. Social roles are not

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external. The self is the sum of these roles.7 Thus the self is co-created by each person and by the others that constitute her/his world. A lady is not a lady because of the way she behaves, but because of the way she is treated, noted George Bernard Shaw. A person performs not only multiple roles but also contradictory ones. Consider for instance the class role of a poor woman married to a rich man, or the national feelings of immigrants. This is an important issue regarding social issues.8 Persons are interchangeable modules regarding social roles. Social roles embody numerical archetypes, as age stages are experienced by everyone, sexes are two, classes invariably include three strata, and further differentiations, including personal uniqueness, are created. Social roles occur in pairs, in which the meaning of each member depends on its complementary opposite (woman and man, parent and child, teacher and student). Social processes precede the development of personal individuality in the history of the species, of the human species, of each person, and of each relation. Social and familial processes are simpler and precede the personal (psychological) level; there are many more individual personalities and life histories than the relatively small number of social roles. As a totality, society has greater energy and complexity than individuals (priority), but each individual mind has greater energetic and informational density (supremacy). The social and the psychological levels thus relate in opposite ways as processes and as systems.9 This illustrates the duality of lattice order. The interaction between these two orthogonal hierarchies of complexity is creative. The society is simpler than the individual it creates. The creativity of individuals increases the complexity of the collective, which may then in turn generate more complex individuals. The most fundamental roles are biological -age and sex—but other social roles are also assigned to us before we develop as individuals. 7

Moreno, J. L. (1978). Who Shall Survive? Beacon, NY: Beacon House. A social theory based on role rather than class has not been developed as yet, but some ideas are sketched in Union ofOpposites. ' Postulating that social and familial processes are simpler and precede the personal (psychological) level; the process perspective is congruent with sociobiological and sociological theories (Marxist as well as non-Marxist). In contrast, systems theories and psychoanalysis consider psychological processes more fundamental and regard social processes as the result of the collective interaction between individuals. 8

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Likewise, before knowing each other as individuals, persons face each other as a function of their respective roles; different persons may replace one another regarding social roles (generation, sex, profession, etc). We are members of society before we are individuals. In biological evolution, social species (ants, birds) antedate psychologically-minded humans. Humans began their history as animals with a rich social behavior.10 Only later does a psychological self emerge. Biological and social roles have priority, but personal processes eventually gain supremacy, for it is in the development of personal uniqueness that creativity comes into being. Psyche creates culture. It seems absurd to have to say it, but creativeness can even be demonstrated through the mathematical analysis of patterns (Fig. 16.4). Psyche exceeds culture: institutions develop their own culture, but do not develop consciousness or conscience. Consider, for instant, breast-feeding as discussed in section 16.1. Feedback is diverse, not limited to opposition. The coexistence of two pairs of opposites (e.g. age and sex) implies four classes, and each pair always implies a third and sometimes a fourth; e.g. son and daughter vis a vis mother and father; enabler vis a vis abused and abuser. Every individual further interacts with many others. The system has priority over the individual. The biosphere precedes the species, the species precedes society, society precedes family, and family begets the individual. Systems create individuals, not vice versa. This fact has two important implications. First, we cannot understand human psychology without attending to social organization, roles and ideologies. For instance, one cannot understand human psychology without attending to economics; since economics is ignored by all major psychological theories, it is necessary to develop entirely new psychodynamic theory. Second, the individual is more complex than the system. This indicates that social progress may be expected from the personalization of society rather than from the socialization of individuals, albeit both processes occur in parallel. Personalization and socialization constitute a bipolar feedback process, in which each reinforces and reduces the other. 10 Lack of social solidarity is not psychological independence of mind. It is sociopathy. Illustrating the frequent rise of sociopathic individuals to positions of power, a well-known twentieth century female prime minister stated that there is no society, only individuals.

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It is cogent to distinguish the notions of role, class, personal world, and system. Nations are systems. Classes are categories of persons with similar roles; rarely do they function as systems. Personal worlds are "networks". Family and personal "networks" are not systems separated by boundaries,11 but overlapping nets of interactions centered on one person. Each person, like a solar system (Chapter 9), has a material core (person), a wider "planetary" field of energetic relations (family, friends, coworkers, community), and an even wider domain of persons with whom he or she communicates, a social communication network that exceeds his life tenure. Family and personal "networks" are not systems separated by boundaries, but overlapping nets of interaction centering in each person. Personal systems, such as families, do not have boundaries that separate them from others, but they constantly evolve through marriage, births and deaths. Instead of boundaries, there are fields of interaction, and mutual feedback. Thus replacing the concept of "family system" has many psychotherapeutic implications;12 while the system's concept of family homeostasis implies that improvement of one member will be compensated by the deterioration of another, the process notion of similarity of opposites implies parallel improvement. 16.3 Bipolar Feedback in Psychological Development The biotic model of psychological development is based on and opposed to the dialectic model advanced by psychoanalyst Erik Erikson.13 Erikson proposed that humans develop in predetermined stages, each consisting of a contradiction of opposites that is eventually resolved in dialectic 11 The distinction has practical implications. The systems' concept of family homeostasis implies that improvement of one family member will be compensated by the deterioration of another; the notions of co-creation and similarity of opposites implies parallel improvement. (Sabelli, H. (1989). Union of Opposites. Lawrenceville, VA: Brunswick; Sabelli, H.C. and Carlson-Sabelli, L. (1991). Process Theory as a Framework for Comprehensive Psychodynamic Formulations. Genetic, Social, and General Psychology Monographs 117:5-27) 12 Sabelli, H. (1989). Union of Opposites. Lawrenceville, VA: Brunswick Publishing; Sabelli, H. C , and Carlson-Sabelli, L. (1991). Process Theory as a Framework for Comprehensive Psychodynamic Formulations. Genetic, Social, and General Psychology Monographs. 117: 5-27; Carlson-Sabelli, L., Sabelli, H. C , Patel, M., Holm, K. (1992). The Union of Opposites in Sociometry: An Empirical Application of Process Theory. The Journal of Group Psychotherapy, Psychodrama and Sociometry. 44(4):147-171 13 Erikson, E. H. (1982). The Life Cycle Completed. New York: W. W. Norton.

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synthesis, allowing the development of a new phase characterized by a new opposition. As in other dialectic models, development is viewed as a linear sequence. The first psychosocial stage, experienced in the first year of life, deals with trust and mistrust. Integrity versus despair is the final developmental stage, which individuals experience during late adulthood. Erikson regards one side of each dichotomy as positive. The co-creation model regards psychological oppositions as bipolar feedback processes that create diversification, novelty, and complexity within the context of linear growth and subsequent decay. Each bifurcation generates new oppositions. Development is a tree, not a linear sequence. Each differentiation of opposites is a forking in a cascade of bifurcations. Each distinction provides a two-dimensional framework for making decisions that evolves throughout life. Development is heuristic: multiple paths are possible, as differentiations are compounded, thereby generating multiple dimensions of complexity (one per opposition). Predetermined developmental stages are constantly modified by personal creativity and co-determined by social and personal interactions. Development is driven by the continuing interaction of opposites, both personal and interpersonal. The contradiction of internal, psychological opposites is never resolved. Each dichotomy has a positive and a negative side; healthy functioning involves the adequate assignment of one or the other, or a mixture of both, to each situation. Consider, for instance, trust and distrust. Rational behavior requires a proper mixture of both; persons who do not know when to distrust often suffer negative consequences, and as a result they become mildly paranoid. Teaching them how to distrust is thus therapeutic, and allows the therapist to go along with the person's feelings rather than struggle against his resistance. This illustrates the practical significance of the difference between co-creation and Erikson's dialectic model. The concept of cocreation offers an even more drastic departure regarding ageing. Instead of the dichotomy of integrity versus despair, which hinges primarily on past life events, co-creation involves continually growing up as we grow old (enantiodromia).

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16.4 Age and Generation14 Congruent with the notion of action and process, life is a series of deeds, not just a series of changes determined by external circumstances. Health is not a state. Health is a process in which actions have consequences. Health is constructed to a significant extent by our actions. Exercise develops muscles and neurons; inactivity atrophies them. Nor is age a state, but a process of continuous growth and decay beginning prior to birth and continuing throughout life. Children and youngsters must be given freedom and responsibility to develop. Aging involves greater order and rigidity, both physically and mentally (Fig. 16.2), indicating the need for change to maintain function. Emotions, behavior, and intellectual activity markedly influence cardiovascular function, immunological responses, and the growth of synapses in the central nervous system. In turn, social norms and culture set up beliefs, emotions, behavior, and intellectual activity. Cultural attitude influences health by modifying behavior. Expectations influence health behavior. Expecting a short life span reduces self-care. Expecting a decrease in our abilities to be physically and mentally active, to learn and to create, is a self-fulfilling prophecy. Future-oriented thinking traces a plan for personal and clinical care. A process approach points to the process of growing up and growing old as fundamental in social and personal life. A healthy concept of age is a medical, psychotherapeutic and social goal. The relation between generations can best be understood as a bipolar, mutual, and hierarchical feedback. In all societies, adults have supremacy. Yet equally fundamental is the power of the children in the family. Parents provide and serve the children; as adults, they are dominated both physically and socially by their offspring (priority of youth). The hierarchical relations between generations, just as hierarchical relations in mathematical lattices, are dual, or bi-directional. They are also bipolar, not solely positive. Child abuse is prevalent and infant mortality is high. In the same manner, elders are sometimes abused and often excluded, neglected and discriminated against. For this 14 Sabelli, H. and Sugerman, A. (2003). Life-Long Creation in the Prevention of Premature Aging. Kybernetes 32: 778-787; Sabelli, H., Patel, M., Carlson-Sabelli, L., Konecki, J., Nagib, J., and Sugerman, A. (2003). Aging and Social Systems. Kybernetes 32: 767-777.

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reason, they must assert their rights. The rights of elders may become the next focus in human liberation,15 as a complement to efforts for the liberation of children, youngsters, and women. Creation theory also has concrete applications for clinical interventions.16 But first and foremost is desire. Desire is as essential as knowledge in living and creating. Ageing, pessimism, cynicism, are lack of desire. The "cultural conserve" plays an essential role in creativity (Chapter 17). Elders have a significant social role to play: Remember and tell. Part of the discrimination against elders is dismissing the ideas of their generation as obsolete. Recognize enantiodromia, the newer is both better and worse than the past: it is vital to convey what was good to counteract what is worse.17 This is not to deny the existence of decay, which occurs in each individual and also, most important, in each tradition. Every movement and every ideology decays as it is transferred from one generation to another. Christianity, from the Apostles to the Inquisition, clearly illustrates it. For this reason, adherence to tradition often has negative social effects, and there is great

15

Neglected in the past, ageism may become a focus for 21st century emancipatory movements in the wealthier countries. As older adults represent a large, powerful and growing constituency, success could be achieved in relatively short time. The success of one such movement paves the way for further social progress. 16 Allow me to illustrate the practical significance of the bios model with psychoeducational strategies for elders. In applying the concepts of creativity to daily life, aspects of creation can be paired with suggestions to improve quality of life. Diversification suggests variation in how one goes about one's day, rather than becoming mired in routine. The notion of episodic patterning encourages alternating different activities, thereby reducing wear and increasing range of capabilities. Novelty clearly suggests doing new things. We recommend elders try something new every week. Structure and order provide inspiration for actively organizing one's days, rather than letting them go by. Novel organization and structured order are opposite, complementary ways to maintain complexity and to overcome decay. Healthy aging involves continuing physical, social and intellectual activity throughout life —action. Changing cultural perceptions regarding aging is only a first step in this direction. Dynamic monism has further implications for health, as it suggests demanding comprehensive medical care. Biological priority and psychological supremacy advocate attending first to one's personal health and keeping life meaningful. Opposition implies interactions with older and younger persons. Conservation plays both personal and social roles. Transforming isolated memories of apparently separate episodes into an integrated story provides meaning. Telling memories serves to create the story. Elders may be further encouraged to record their memories for future family generations. Talking with others of the same generation may help us see the social context in which we operate. Telling our story to the young connects generations. Elders can foster progress by transmitting to the young their ideals and experiences. " Specifically, the ideals of the 1960s generation that promoted civil rights, women's liberation and sexual freedom, and opposed racism, war and colonialism, are worth transmitting to younger generations dominated by market interests, terror and war.

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advantage in promoting young leaders. Each generation must create anew. Those of us who had good parents are emotionally conservative but it is the tradition of being creative that must be passed from generation to generation. 3.5 T

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16.5 Female Priority and Male Supremacy Among sociobiological classes, unidirectional process connects age classes; sex imprints duality in behavior, social organization, and psychological processes. Woman's greater role in reproduction makes sexes fundamentally different, and probably is, as pointed out by Simone de Beauvoir,18 a major cause for social inequality.19 The larger size of males may have been a biological basis for male supremacy. Power is unequally distributed between women and men. Male supremacy exists, to a greater or lesser degree, in all societies. It is lessening as physical size becomes less important and reproduction is regulated, demonstrating the supremacy of social over biological factors. The dominant role of men is supported by most cultural traditions and religions, and justified by many social and psychological theories. In contrast, such male domination has been denounced as a major, crucial flaw in society 18

de Beauvoir, S. (1949). The Second Sex. Trans. H .M. Parshley. New York: Penguin, 1972. Reproduction has also been used as a pretext for male supremacy. In the early twentieth century, eminent psychologists including G. Stanley Hall, claimed that advanced education would reduce women's reproductive capacity, so, to protect the species from extinction, women must be excluded from colleges and universities. In our times, psychiatrists, pharmacologists and governments employ concepts of race that sociologists regard as racist and biologists as ignorant. 19

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responsible for violence and war. While there is disparity in the value attributed to male domination, few question its existence in every area of human life. Clinical experience, however, presents a different picture including families ruled and/or supported by, the mother; husbands who are emotionally and socially dependent upon their wives; sons who are tied to the present, or past, authority of their mothers; narcissistic wives who enjoy leisure and demand attention, services, and privileges from hard-working husbands. The hierarchy is bi-directional. We are mammals -the term itself expresses the idea that being nurtured by our mother is fundamental. Mothers are the first identification, authority and beloved figure for children. Mother is the first universe we inhabit, the first person we know, our first love, our first source of nutrition, warmth and protection. In almost all human societies, just as in almost all animal species, there is male supremacy, but equally fundamental is the familial power of the women (female priority).20 Such bi-directional asymmetry does not justify the sexual inequities that still persist - Equal Rights are as yet not approved in the USA! Women and men are more similar than different; there is a total overlap in the range of capacities of women and men. Male supremacy, as White supremacy, describes undesirable asymmetries associated with injustice. Notably, it is also associated with negative consequences for men. In our times, women live substantially longer than men.21 16.6 Class, Race and Nation As human processes are creative, they generate differentiations, such as classes and nationalities, beyond those determined sociobiologically (age and sex). Classes result (or create) divisions of labor, so they are, by necessity, feedback processes. Nations also function in mutual feedback 20

Sabelli, H . and Synnestvedt, J. (1991). Personalization: A New Vision for the Millennium. Chicago: Society for the Advancement of Clinical Philosophy (SACP); Sabelli, H., a n d CarlsonSabelli, L. (1995). Sociodynamics: the application of process methods to the social sciences. Chaos Theory and Society, A . Albert (Ed). Amsterdam: I.O.S.Press and Sainte-Foy, C a n a d a : L e s Presses de l'Universite du Quebec. 21 That women live on the average ten years more than m e n is often dismissed as unimportant. Similar differences in life expectancy among other social groups are considered to demonstrate the unfairness of society.

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relations rather than as isolated systems. The most fundamental class relation -slavery, the ultimate in private property- is the product of international war and piracy. Slaves were not people born poor but prisoners obtained by kidnapping.22 Class dominance often derives from the use of force. Thus military classes often become dominant (empires, feudal systems, and 20th century dictatorships), and "races" often are nations submitted by them and kept as underclasses. Other classes that also become dominant are commercial, financial, industrial capitalists, landlords, clerics, and executives. Most modes of social organization involve multiple combinations of co-dominance. The existence of social mobility does not solve equity issues, namely the availability of sanitation, water, medicine, education, and justice for all. Moreover, focusing on individual competition contributes to maintain and increase class differences. Class divisions are not disappearing;23 classes are diversifying. The distribution of wealth and power can become extremely asymmetric, as in the USA. Empires are not disappearing,24 and wars continue unabated. The concept of diversification implies that social differences will multiply, but it does not support the inequities promoted by the ideologies of conflict and selfishness. Sex does not have to imply sexism. Race does not have to imply racism. In the same manner that we try to eliminate sexism and racism, it might be possible to eliminate classism and imperialism. Here again, we need bipolar feedback between nations and economic centers. Power is distributed, albeit unequally, among all classes and all nations. The increase in population in the poorest countries as a result of improved medical care shows that even they benefit from the contradictory progress of history, even if they also suffer its worst consequences in the form of famine, war, dictatorships, and unemployment. Classes co-dominate: the supremacy of the upper classes 22 The consequences of slavery persist in the US, and many refuse to give a chance to children born to their descendants. It is in this context that we must consider sociobiological theories of human behavior (Chapter 13), and their use to account for social differences between races. 23 For a significant number of decades during the twentieth century, people were indoctrinated with the notion that classes were disappearing as result of greater social mobility in the USA or socialism in the USSR. 24 The existence of empire was also denied in the USA and the USSR for a significant number of decades during the twentieth century, but at the beginning of the twenty-first century some call for strengthening and expansion of the American empire. Imperialism has lost its bad name.

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is always in dynamic interaction with the priority of the lower classes, the producers. Classes cooperate insofar as they represent a division of labor necessary for economic production, but they also conflict regarding the distribution of profit. Class cooperation and conflict are complementary component of the bipolar feedback process that is a motor of history, along with scientific and technological progress. Social processes are historical: they do not reproduce themselves in endless repetitions, but evolve with a unique history. Creation is, like a biotic trajectory, uninterrupted, not a sequence of static structures separated by revolutions. Opposite socioeconomic processes co-exist and combine rather than one destroying and replacing its predecessor. The periodically announced demise of capitalism has not taken place, nor has socialism ended. Likewise hunting, gathering, agriculture, commerce, and every other economic process in history, continue to be components of the economic process. Social progress and justice require both cooperation and conflict bipolar feedback. The upper classes often preach social harmony, as the maintenance of the status quo obviously favors them; every theory of social cooperation is hence suspected of favoring oppressors. All processes include oppositions and conflict. To ignore their existence serves to increase inequities. Freedom and justice require conflict. Cocreative behavior cannot be edulcurous harmony, but must contain a significant dose of salty conflict. 25,

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Conflict is one thing, and war is another. Revolutionaries preach class war, as if class hatred is somewhat nobler than racial hatred. Social

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liberation requires reducing class war, not promoting it. Revolutionaries preach class struggle; capitalists practice it all the time, in George Bernard Shaw's accurate diagnosis. The most oppressed classes are deprived of means of economic support. Notably unemployment rate has a biotic pattern at least in the more developed countries (Fig. 16.3), indicating causal and created processes. Class and race war are unabashedly promoted by some academics that blame people's poverty on culture.25 Race war is also promoted by these authors (Section 4.3.4). Social systems present important cases of biotic feedback in the dual relations of power between generations, sexes, classes, and nations. Generational, sexual and class relations, "pecking order" in animal societies, and many other phenomena including levels of organization, have been regarded as hierarchies.26 Twentieth century system theories stressed that in most organizations, relations are dynamic and include competing centers of power, stressing a progressive decrease in hierarchical order.27 Social organizations certainly are conflictual and changeable, but hierarchical order is real. Natural and human hierarchies have a two-way order, from top to bottom (supremacy28) and from bottom to top (priority) and refer also to these opposite and asymmetric relations. The notions of parental priority and supremacy of the offspring,29 female priority and male supremacy,30 privileged and 25

Harrison, L. and Huntington, S. P. (2000). Culture Matters. Basic Books, New York. The term hierarchy originally meant 'sacred power' and referred to a class of priests who mediated between man and God. "Hierarchy" and "insubordination" are favorite concepts in the armies of Latin American dictators. An Irish saying claims that man is for God and woman is for man. Given these implications, one should also be suspicious of the concept of hierarchy in physics and biology, and reluctant to take it as natural in zoology and sociology. 27 Warren McCulloch has proposed the concept of heterarchy as a form of organization resembling a network. While standard sociology defines political economy as a societal condition principally affected by the requests and demands of an elite, the concept of social heterarchy focuses on the complicated and less predictable set of interdependencies manifest within and between members of a group. In a social heterarchy, authority is determined by knowledge and function. Heterarchical organizations appear to be more creative than hierarchical ones. Networking may constitute a new form of governance more appropriate for contemporary societies. 28 The choice of the term supremacy is made to evoke ideologies such as male and white supremacy that are here opposed by the priority of the other. The implication is the existence and desirability of co-dominance. 29 Sabelli, H., Carlson-Sabelli, L., Patel, M and Sugerman, A. (1997). Dynamics and psychodynamics. Process Foundations of Psychology. /. Mind and Behavior 18: 305-334. 30 Sabelli, H. C. and Synnestvedt, J. (1991). Personalization: A New Vision for the Millennium. Chicago, IL: Society for the Advancement of Clinical Philosophy (SACP). 26

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disadvantaged classes,31 and empire and peripheral nations32 have been sketched in earlier publications. In brief, social relations are dynamic, hierarchical and dual.33 The supremacy of the powerful confronts the greater but often unrecognized power of the weaker. Rendering people conscious of their power may promote equity. Mutual control is absolutely necessary for good relations among individuals, generations, sexes, classes, races, and nations. Without mutual control, the concentration of power, wealth, information, or their distribution, allows exploitation, abuse, and even criminal behavior. Criminals often dominate government.34 Furthermore, no class of individuals is incapable of abuse.35 For thousands of years our forefathers enslaved workers and treated children and women in ways that we now recognize as abusive.36 Regarding economic, social and political hierarchies, it is vital to insure mutual feedback, preventing anybody from assuming control in the name of national security, social justice or divine inspiration. 16.7 Psychodynamics As humans are the product of evolution, psychology must also be based on physics and biology. Freud thus launched psychodynamics with the concept of psychological energy, generational and sexual conflict, and deterministic causation. That mental processes are flows of physical energy explains how biological structures and processes cause mental 31

Sabelli, H. and L. Carlson-Sabelli. (1995). Sociodynamics: the application of process methods to the social sciences. Chaos Theory and Society (A. Albert, editor). I.O.S.Press, Amsterdam, Holland, and Les Presses de l'Universite du Quebec, Sainte-Foy, Canada. 32 Sabelli, H. C , Plaza, V., Vazquez, A., Abraira, C , and I. Martinez. (1991). Caos Argentino. Chicago, IL: Society for the Advancement of Clinical Philosophy (SACP). 33 In two-way interactions, the subordinated elements also rule the dominant ones. The master is the slave of the slave, quipped Hegel. This literary formulation does not make the necessary distinction between the two complementary opposite relations. The master may be the slave of the slave, but he remains the master. 34 It is sufficient to mention the Latin American military dictators. 35 It is sufficient to mention that Thomas Jefferson took as his mistress Sally Hemming, a slave, a child he had himself raised, and half sister to his wife. He also kept his children by her as slaves. 36 Slavery, child abuse, and wife abuse have not been forbidden by the Scriptures of any of the major religions, which nevertheless often list hundreds of specific injunctions regarding how human beings should eat, dress, pray, butcher animals, and many other minor behaviors.

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actions, and in turn mental processes modify biological processes. A creative process model replaces the concept of psychological energy by psychological action, highlights the coexistence of harmony and conflict between multiple pairs of opposites, including social ones, and points to creative phenomena beyond determinism. As proposed by Freud, psychological energy is physical energy; it includes emotional, sexual, mental and interpersonal37 components. Based on closed system thermodynamics, Freud assumed that psychic energy is constant, so subjective changes in energy reflect displacements rather than actual changes; different feelings, such as love and self-love, compete with one another, as one can grow only at the expense of the other. It is now widely recognized that energy can increase or decrease in open systems such as biological organisms. Creation theory highlights the concomitant variation of energy and time as inseparable aspects of action. The notion of psychological action is well illustrated by the conjoint variation of energy and time in affective disorders. Feelings of low energy combine with slowness and even retardation of thinking and behavior in depression, while feelings of increased energy accompany acceleration in mania. I38 thus conceptualize depression as a shortage of psychological action and mania as an overabundance.39 As noted in section 4.3, bipolarity is associated with increased creativity in patients and their relatives. This is in line with computer experiments showing the emergence of creative biotic patterns at relatively high gain and equilibrium, periodicity, and chaos at lower energy levels.

37 Illustrating this concept, Freud regarded psychological energy as libido, meaning that it has a biological basis on sexuality. In my view, attention, which also is both internal and interpersonal, epitomizes psychological energy. (Sabelli, H., Carlson-Sabelli, L., Patel, M., and Sugerman, A. (1997). Dynamics and psychodynamics. Process Foundations of Psychology. J. Mind and Behavior 18: 305-334). 38 Sabelli H., Carlson-Sabelli L., Javaid, J. (1990). T h e Thermodynamics of Bipolarity: A Bifurcation Model o f Bipolar Illness and Bipolar Character and Its Psychotherapeutic Applications. Psychiatry: Interpersonal and Biological Processes 53: 346-367; Sabelli, H.C. and Carlson-Sabelli, L. (1991). Process Theory as a Framework for Comprehensive Psychodynamic Formulations. Genetic, Social, and General Psychology Monographs 117:5-27. 39 Manic persons show increased goal-directed activity, excessive involvement in pleasurable activities, increased sexuality, decreased need for sleep, talkativeness, flight of ideas, distractibility, and inflated self-esteem, as well as increased affection. They also experience greater negative feelings such as anger, anxiety, paranoia, and even depression; in other words, greater energy increases opposite feelings.

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Oppositions play an important role in psychobiology, as illustrated by the paired sympathetic and parasympathetic innervation of internal organs by the nerves, and the existence of the ergotropic system (alerting, activity, sympathetic predominance) and trophotropic system (sleep, nutrition, parasympathetic predominance) in the central nervous system as described by Nobel Laureate Walter Hess. In line with nineteenth century obsession with conflict, these physiological opposites were initially regarded as competing or conflictual. In a similar manner, Freud proposed that libidinal energy conflicts with either nutritive functions or destructive with aggressiveness. We are now beginning to identify the material carriers of psychological energy. Not only are they multiple, including thyroid hormones, sexual hormones, and brain neurohormones of the adrenergic type,40 but also their range of action contradicts the notion of conflictual opposites. Testosterone and phenylethylamine increase both sexual libido and aggressiveness. Both estrogens and testosterone promote female libido, while progesterone promotes maternal behavior. These cases refute the Freudian scheme of opposites. Likewise visceral regulation does not hinge on competition. Vegetative nerves have very different anatomical distribution (the sympathetic is horizontally organized while the parasympathetic is vertically organized), and even when paired and opposed, they are components of a bipolar feedback system, not competing or conflictual entities. Higher nervous functions are constructed upon a multiplicity of specific anatomical and metabolic pathways, not by paired opposites. Emotional life is written in an alphabet of genetically determined patterns of behavior ("instincts") coded by specific brain chemicals, a concept that has guided the development of psychopharmacology in terms of synaptic theory. Affects are multiple, and enhance and inhibit each other in complex ways. Affection is not aim-inhibited sexuality, but a separate drive that can be associated as in the love between spouses, but

40

Among neurohormones of the adrenergic type, the role of norepinephrine and dopamine are well demonstrated; phenylethylamine (PEA), however, may play some of the roles assigned to them [Sabelli, H. (2002). Phenylethylamine deficit and replacement in depressive illness. In D. Mischoulon and J. F. Rosenbaum. Natural Medications for Psychiatric Disorders. Baltimore: Lippincottt Williams and Wilkins. pp. 83-110]).

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that can also be sexually inhibiting as seen in persons raised together in a kibbutz. Conflict triggers three emotional responses (Section 4.3), not two. The coexistence of opposite feelings and ideas is obvious to practicing psychologists who deal with actual persons rather than abstract logical models. Recognition of this fact has led us to propose some guidelines for psychodynamic hypotheses:41 (1) When an emotion or belief is strongly stated, seek how it is being enhanced by its opposite. (2) When a patient attributes an emotion to another, seek how it applies to his or her own self, and vice versa. (3) Pay attention to what is not said; seek what is missing. (4) Given an intrapsychic conflict, seek the interpersonal conflict, and vice versa. (5) Whenever one finds a positive transference, search for the negative transference, and vice versa. In abstract terms, whenever a person denies A, he must have been, by necessity, thinking about A, so no-A implies A. Likewise, asserting A implies in some way no-A. Logicians deny this coexistence of opposites, just as many patients do, but perhaps for better reasons (Chapter 18): if one is to assert that everything implies its opposite, how can we separate true from false? This is in fact why Popper condemned both psychoanalysis and dialectics42 as irrefutable (Chapter 18). In psychoanalysis, pointed out Popper, the analyst's interpretation is regarded as supported by its acceptance by the patient or by its rejection that evidences resistance. This is not Freud, but a later development, a symptom of the decay experienced by every ideology as it moves through generations. As Freud astutely perceived, the psyche has both dyadic43 and triadic structure, id, superego and ego (Freud used simple everyday terms to refer to them, not pretentious Latin.) They correspond to the biological, sociobiological and personal levels of organization -thus the ego is hierarchically above the superego, as contrasted to standard psychoanalytic theory. On the basis of contradictory pattern of dreams, 41 Sabelli, H. C. and Carlson-Sabelli, L. (1991). Process Theory as a Framework for Comprehensive Psychodynamic Formulations. Genetic, Social, and General Psychology Monographs 117: 5-27. 42 Popper regarded Marx theory as scientific because it was predictive. However, when these predictions were not in fact borne out, Marxists modified the theory by the addition of ad hoc hypotheses which made it compatible with the facts. In this way, a theory that was initially scientific degenerated into pseudo-scientific dogma. In my opinion, psychoanalysis also emerged from a genuine scientific effort by Freud, Adler, and others. 43 The dyad, Freud concluded, is Eros and Thanatos, love and death —notably, the opposite of death is love, not life, and Psyche is Eros' lover in Greek mythology.

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Freud viewed the unconscious as a Heraclitean fire fueled by the contradiction between mutually exclusive feelings and wishes. In contrast, he accepted the commonly held belief that consciousness is an Aristotelian logician that keeps opposite ideas and feelings separated. Thus, consciousness and unconsciousness represent a mechanism of separation through which the mind manages to contain opposite and antagonistic ideas, wishes and feelings. The intellectual and affective contents of these two separate parts of the mind are intertwined in mutual struggle. In the co-creation model, conscious and unconscious processes are largely synergistic. Contradictions and antagonisms exist in the mind, just as conflicts and oppositions exist throughout nature, but opposing mental contents coexist also in the conscious realm, not only in the unconscious, where Freud relegated them. In our view,44 also conscious ideas, wishes, and feelings evoke their opposite, and the unconscious contains ideas and feelings similar to conscious ones. Further, to be conscious of coexisting opposites is simply to be aware of the actual complexity of the world. Freud opposed love and self-love as antagonistic opposites in dialectic struggle; self-love as immature "narcissism" that becomes partially transformed into its opposite, love, and thus love and self-love compete with each other for a limited amount of psychological energy. Maturation increases love for others at the expense of primitive narcissism. In contrast, Antonio Sabelli45 advanced the notion of love and self-love as complementary opposites, feeding and mutually reinforcing each other. Affection, sexuality and attention can be selfdirected if and only if they are also other-directed. Conversely, if love for the other conflicts with self-love, love frequently ends. Psychological energy is material and variable; love and self-love usually but not necessarily grow and diminish together; they both reinforce and conflict with each other. Opposites form and transform each other, but opposition is not removed by either struggle or synthesis. Opposition is a creative anvil. The notion of synergism between love and self-love is now widely 44

Sabelli, H. C. and Carlson-Sabelli, L. (1989). Biological Priority and Psychological Supremacy, a New Integrative Paradigm Derived from Process Theory. American Journal of Psychiatry 146(12):1541-1551. 45 Sabelli, A. (1952>. Escritos. Buenos Aires: Private Edition.

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accepted by many psychotherapists.46 The relation between self and other is bipolar, including harmony and conflict; we have our greatest conflicts with those we love the most. Self-love extends to love for our family, friends, community, and country. Clinical psychiatrist Alfred Adler identified solidarity as a fundamental human instinct. Human societies are based on cooperation within large groups, involving a division of labor and the distribution of products, starting with cooperative hunting and food-sharing in prehistory. Duty and honor, the positive feelings they evoke, innocence and pride, and "hunger" for them, guilt and shame, are central components of human conscience. Persons without guilt are sociopaths in non-technical terms, criminals. As a person unable to perceive pain suffers destructive harm because hurting does not warn him, a society of "persons" without guilt destroys itself. The feedback needs be bipolar. Self-love also leads to competition and conflict; social feedback, in being bipolar, more likely to generate a creative result -bios- rather than dynamic equilibrium. Both cooperation and conflict are social behaviors. It is thus strange, to use once more Prigogine's favorite epithet, that sociobiology and standard economics portray us as selfish individuals. These views so dominate current scientific discourse that solidarity is now labeled "altruism" and behaviorists seek explanations for it. Experimental evidence demonstrates altruism.47 Strangers naturally and spontaneously engage in "altruistic" behavior - i.e. behavior that benefits the other while representing a cost oneself -while among animals, altruistic behavior is restricted for the most part to kin groups. Cooperation is enhanced by reciprocity and enhancement of reputation, but human altruism also includes strong reciprocity -meaning rewarding others for cooperating and punishing others for norm violations at our own cost. A number of laboratory experiments show that altruism and self-interest are not mutually exclusive. On the contrary, experimental evidence shows that they can combine to motivate behavior. Experimental studies show that solidarity and self-interest are both instinctual. It is unscientific to describe self-interest as selfishness. It is in 46 It is often attributed to Erikson, who actually did not change the Freudian model that opposes narcissism to love. 47 Fehr, E. and Fischbacher, U. (2003). The nature of human altruism. Nature 425: 785-791.

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fact unintelligent. The best formula to be happy in a marriage, common sense will tell you, is to make your spouse as happy as you can, because then you will be likewise made happy. All relations are in this sense like marriages, including international relations. What made us human is cocreation, not struggle and competition. Competition is extremely important. It is just not what made us human. The implications of these results for social and economic organization are vast and should be obvious. There are also significant implications regarding the current notion that clinical observations, such as Adler's, are worthless in comparison to simplistic behavioral experiment. Many psychological processes display a 1/f power spectrum.48 Behavioral patterns are biotic. This is clearly demonstrated by the empirical evidence of cardiac recordings, since cardiac activity by necessity adjusts to behavior. Yet, the notion of health as equilibrium still dominates medical and psychiatric discourse. Freud postulated that behavior tended to discharge psychological energy and restore equilibrium. In a similar manner, early ethologists portrayed behavioral pathways as linear sequences of appetitive behaviors from a repeller (such as hunger) to an attractor (such as satiety). Instead, we49 proposed that many behavioral pathways, such as sleep, feeding, and sex, are cyclic (appetiteconsummation-relaxation-appetite); only repellers such as pain, hunger, fear, or anger initiate linear pathways toward point attractors. Second, consummatory acts are positive reinforcers, while frustration reduces behavior, even sustainedly (Seligman's learned helplessness50). Consummation creates appetite, as illustrated by cascades of orgasms. Contrary to the notion of cathartic discharge, emotions may actually be increased by their expression. Third, there is a profound similarity between attractors and repellers: sensations and emotions such as bitter or sweet, heat and cold, anger and fear, even pain, are pleasurable at low intensities, and produce suffering at high intensities. This is also illustrated by appetite, 48

Gilden, D. L. (2001). Cognitive Emissions of 1/f Noise. Psychological Reviews 108: 33- 56. Sabelli, H., Carlson-Sabelli, L., Patel, M., and Sugerman, A. (1997). Dynamics and Psychodynamics. Process Foundations of Psychology. Journal of Mind and Behavior 18: 305-334, special issue edited by L. Vandervert. Understanding Tomorrow's Mind: Advances in Chaos Theory, Quantum Theory, and Consciousness in Psychology. 50 Seligman, M . E. P. (1991). Helplessness: On Depression, Development, and Death. Second edition. N e w York: W . H. Freeman. 49

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a pleasure we seek, and hunger, a deprivation we avoid. A change in quantity produces a change in quality. Fourth, positive and negative reinforcers, pleasure and pain, may coexist. The mutual exclusion of opposite reinforcers postulated by conditioning theory fails to account for the pleasurable effect of righteous indignation, theatrical tragedy, horror literature, or sexual masochism. Finally, emotions are patterns of social and interpersonal behavior. They are part of mutual feedback processes, so we share responsibility for one another's well-being, contrary to individualistic psychotherapeutic notions. Behavior is not a self-propelling path toward an attractor; it is co-created in interactions and can be frustrated by lack of external complementary response. External stimuli trigger appetite, sexual arousal, curiosity, and violence. Appetite and consummation are interpersonal acts. This interpersonal notion of emotions has fundamental implications regarding psychological treatment. As discussed in section 4.3, depression, anxiety and anger are three responses to conflict. When a person is depressed, we must ask, who is the depressing other? The conflict theory of anxiety and depression stresses the frequent role of social and familial conflicts in their pathogenesis, and prescribes marital therapy in their treatment. Creative talent cannot be understood in terms of that overrated construct "intelligence" that seems to be most clearly measurable by those who have the least of it. Virtually all definitions of intelligence view it as the ability to adapt to the environment. This biased view simply rationalizes social differences in a purportedly equal opportunity society. Adaptive intelligence is the opposite to creativity, which by necessity departs from accepted views, and clashes, at times violently, with dominant dogma. Further, hard work, intrinsic motivation, and social environment are equally or more important than personal talent, points out Ramon y Cajal. To foster creativity, society must provide favorable conditions to develop talent and motivation, rather than identifying "talented children" as suggested by genetic determinism. This again illustrates the opposite conclusions derived from focusing on fixed biological structures and from process views. The notion of co-creation departs from biological, psychoanalytic, behavioral determinism but still stresses the search of causation. This is

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to promote creativity, but it does not exclude "luck", which is so heartless denied a role in personal life by psychological theories. There obviously are local random intersections, events that are meaningless in their cause but meaningful in their consequences, such as being hit by a brick in the head or being raped. It is here unfeeling to analyze causation. For Aristotle the goal of philosophy was to expand the soul. To be spiritual, it is not sufficient to believe a certain creed, perform certain rituals, or to have received a soul gratis as a supernatural gift. It is necessary to cultivate our soul with action, science, and art.51 The arts also provide the most thorough education for mental health professionals. In Greek tragedy we learn that the hero's greater strength is also his fatal flaw, and that drama is the conflict of good with good, not of good with evil (Hegel). In contrast to the critique of grandiosity that dominates psychoanalysis (gaining psychiatrists the moniker of "shrinks" by association with tribal head-shrinkers), we take Aristotle's idea of greatsoulness as a beacon for our clinical philosophy. The twentieth century saint, Gandhi, was given the name Mahatma, meaning great soul. 16.8 Personalization Personal processes, including rational consciousness thinking and ethical conscience, represent the highest phase in evolution. A person is both a member of the community and an individual. Socialization and personalization are both synergistic and conflictual. Individuation is greater in well-developed societies and families, and depersonalization decreases solidarity. We treat better those others whom we know 51 We give the arts an important place in medical and psychological therapy: Peres, M. (1989). Music, emotions, and hospitalized children. Some theoretical considerations. In Rehabilitation, Music and Human Well-being, edited by M. H. M. Lee, Saint Louis, Missouri: MMB Music. Sabelli, H., Carlson-Sabelli, L., and Seiden, (1990). D. Process theory and Art Therapy. Illinois Art Therapy Association's 11th Annual Conference. Chicago, IL. May 19; Seiden, D and Sabelli H. (1992). CoCreation: A Process Theory of Form in Art and Life. Proc Internal Soc Systems Sciences; CarlsonSabelli, L., and Sabelli, H. C. (1994). The psychotherapeutic myth of the Mother Goddess. A cocreative theatrical performance. Proc. International Systems Society. B. Brady and L. Peeno (Eds.), Pacific Grove, CA, pp. 1589-1600; Carlson-Sabelli, L. and Sabelli, H. Heart Mates, a physiological warm up for sociodynamics Conference on the Creative Therapies and Psychodrama. Lake Geneva, April, 1996. Carlson-Sabelli, L. (1998). Children's puppet theatre for traumatized Children: A process theory approach. International Journal of Action Methods: Psychodrama, Skill Training, and Role Playing. 51, (3), 91-112.

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personally. Hence, the personalization of society functions as a hierarchical feedback that may raise society by its bootstraps. The growth of human systems in size expands solidarity but also creates impersonal relations. Greater ethical and humanitarian attitudes are thus accompanied by the development of nuclear war and sophisticated technologies for genocide and for torture. Our increased ability to communicate and inform grows together with an increased ability to misinform. Worldwide economic development is accompanied by areas of famine which never existed under less developed conditions. In such circumstances, alienation can be healthier than socialization.52 Personal ethics, not social mores, must guide personal development. It is thus vital to human health to transmit the true history of archetypal figures.53 Psychological archetypes evolve; they represent social roles, not static biological forms. The Greek Gods represent social classes, the king, the warrior, and the worker -namely Hephaestus, seldom mentioned in standard psychological discussions but who was the male God of Athens. Social archetypes evolve with the persons who enact the social roles. Governments, institutions, and corporations must be placed under the control of public opinion. Only persons, but not institutions, have desire, consciousness and conscience. Thus governments, corporations and markets do not, and cannot protect our environment (Chapter 14), and they should not be entrusted with our lives. Good governance is destroyed by secrecy that prevents mutual feedback. Secrecy empowers abuse and crime.54 I thus propose personalization as mode of operation beyond representative government. Computers may make this kind of direct democracy possible by allowing public supervision of public and private institutions; otherwise, they can be used for dictatorial 52 "There cannot be a healthy individual within a sick society", explained Emilio Mira y Lopez, the Catalan pioneer of integral medicine and family therapy. Integration into society is often regarded as a sign of mental health. Actually, healthy individuals are alienated from sick societies. 53 See Maria/ Mary Bilingual play (Espanol- English) with historical notes by H. Sabelli. Chicago, IL: SACP, 1992. But this book misrepresents Mary Magdalene. In this regard see Haskin, S. (1993). Mary Magdalene. Myth and Metaphor. Riverhead Books, New York. 54 In the "Tuskegee experiment," more than 600 African-American men suffering from syphilis were left untreated for years in a secret study conducted in Alabama between 1932 and 1972, at which time only eight persons had survived. At this time, producers of pesticides have initiated human experiments in response to 1996 US child protection rules that may force a reduction in pesticide use (Science 303: 1272-1273,2004).

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surveillance of individuals and for electoral fraud. Personalization is also a criterion for choosing between alternative courses of action. We mean to place medicine, education, law, art, economics, and political processes at the service of persons, rather than institutions, higher purposes, or abstract principles of any kind. We envision a society for persons, not for profit, not for the fatherland, not for the "revolution," nor for "God," nor even for "people" as a collective entity. We55 have just begun exploring how this could be accomplished, but one can readily see the need for bidirectional feedback between personal and collective power to protect personal property, including clean air and water. Both statization and privatization often expropriate personal property ("private" is used to mean corporate property, not personal property). Personalization means that persons -not governments, parties, churches or corporations— must control society. In our times, corporations have been declared to be legal persons. But persons without conscience are sociopaths. Corporations are mandated by law to place profit above all other considerations. Regardless of the good intensions of management, corporations must increase gains at all cost, and therefore reduce the quality of their product, create obsolescence (e.g. of genetically engineered seeds!), destroy the environment, underpay the workers, and promote drugs of doubtful value. The legal travesty of declaring corporations persons decreases negative feedback necessary for maintaining healthy social behavior. At this time, corporations "own" human genes. Clinicians have successfully won a fight to overturn patents for breast-cancer genes in Europe but not in the USA.56 A pro-life stance requires terminating with the corporate ownership of life. The standpoint of life should be fundamental to social organization. The best possible social philosophy is a clinical philosophy that

55 Sabelli, H. and Synnestvedt, J. (1991). Personalization: A New Vision for the Millennium. Chicago: Society for the Advancement of Clinical Philosophy (SACP). There are some simple measures that can drastically enhance personalization without departing from our traditions, such as one-person-one vote electoral systems. These systems are rare even in democracies; for instance, the USA Electoral College system gives four times more weight to voters from rural areas than to presumably more educated urbanites. 56 Abbott, A. (2004). Clinicians win a fight to overturn patent for breast-cancer gene. Nature 429329.

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integrates science from mathematics to psychology, stresses methodological doubt, and has a clear therapeutic aim. Personalization involves personal responsibility. Each person, each scientist, each manager, each reporter, and each soldier must hold himself personally responsible for his actions. A scientist becomes personally responsible in his or her practice by choosing what problems to study, what assumptions to make, and what hypotheses to entertain. Science must provide means to effect desirable change. Utopian visions are not enough. Linear progress is not sufficient. Adaptation perpetuates the status quo -progress, remarked Bernard Shaw, is promoted by those who do not fit. Conflict generates conflict. Revolutions may be just cyclic movements, replacing one dominant group by another, pointed out Stravinsky.57 Chaos is too destructive. Increasing violence demands a change from conflictual thinking to co-creation, and from hierarchical states and corporations to personalized systems co-created by bidirectional relations of mutual and bipolar feedback. Co-creation means that issues are modifiable by our actions but also determined by objective realities and by the action of others. The distinction between local and global changes is in this respect essential. Personalization requires to think locally and act globally, complementing the slogan "Think globally, act locally" popular in the 1960s. Both approaches are useful, at different times and in different respects.58 Consider for instance educating persons on the role of competition in coronary artery disease, an issue that few cardiologists bring up. If patients become aware of it, they will pressure doctors to take a more active role as educators, 57 A structuralist perspective regards socioeconomic systems as conserved until replaced by revolution; reform is inconsequential, and only delays revolution. In the process view, systems are continuously evolving, usually gradually (reform) but at times discontinuously (revolution). Real progress does not stem in replacing one class for another in the position of power, but from transforming the relation between classes. Nowhere this is more evident than in the case of sex classes where the beheading of the oppressors cannot be wished even by the oppressed. 58 Acting globally can produce the widest positive results, while acting locally can be punished by the most severe negative retribution. A supervisor can actually or purposefully ignore your defiance of authority in general; he cannot tolerate a direct challenge to his/her authority. A husband can support a woman fighting for the liberation of her sex but not attacks upon himself. When the home is the battleground for a campaign against male behavior, marriage and family suffer, or are destroyed. Unions serve a purpose because they bring the power of workers from other places to come to fight against the local management. This depersonalizes the fight. Blacks and women gained their advances by global changes in society at large. Because the general changes in public opinion, each institution had to change policies. Progress is not a battle done institution by institution.

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educators to stop idealizing competitiveness, and employers to eliminate unnecessary competition. We must take good care of our enemies because we contribute to shape their behavior.59 One should take seriously the idea of mutual and bipolar feedback, and apply it to national, social and economic conflicts. The most important social activity that a person performs often is his or her own work. This is a place to apply principles and values. This long essay illustrates how I took seriously the notion of grounding medical practice in science and philosophy. This notion is even more clearly in educational programs being developed at Rush University (Chapter 17). 2 -,

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59 "The handbook of the strategist has said: /'Do not invite the fight, accept it instead,' /'Better a foot behind than an inch too far ahead,' / Which means: /Look a man straight in the face and make no move/Roll up your sleeve and clench no fist,/Open your hand and show no weapon/Bare your breast and find no foe./But as long as there be a foe, value him,/Respect him, measure him, be humble toward him;/Let him not strip from you, however strong he be/Compassion, the one wealth which can afford him." (Bynner, W. The Way of Life According to Laotzu, Perigee Books, 1986).

Chapter 17

Co-Creation Practice: Education, Nursing and Psychodrama

Abstract: Illustrating the educational andpsychoeducational application of Creation theory, an online program for clinical training and supervision for psychiatric nurses is being developed at a major American medical center.1 Action is not just change, experience, or experiment. Action is foremost practice.2 It is thus cogent to conclude this study of creation with a program created by one of the founding members of our research group3 that incorporates basic principles for promoting creativity derived from our empirical and mathematical study of creative processes. This is an online program designed to educate nurses as primary care psychiatric practitioners,4 and to increase their number in medically underserved 1 Project Aha! Online Clinical Supervision for Psychiatric Mental Health Nurse Practitioners. Rush University Medical Center. This project is supported in part by funds from the Division of Nursing (DN), Bureau of Health Professions (BHPr), Health Resources and Services Administration (HRSA), Department of Health and Human Services (DHHS) under grant number 1D09HP0298701-00 Advanced Education Nursing Grants for $478,739. The information about the grant is supplied by the author and should not be construed as the official position or policy of, nor should be endorsements be inferred by the Division of Nursing, BHPr, DHHS or the U.S. Government. 2 Control experiments often are controlled by those who performed, and there are serious questions regarding the objectivity, reliability and validity of many drug evaluations; for instance, antiarrhythmic agents were eventually demonstrated to increase mortality. Clinical experience, often dismissed as "anecdotal" often is more reliable than controlled experiment because it reflects the actual conditions in which agents are used and are not directly affected by commercial interests. 3 The Peter and Maria McCormick Forum for Clinical Philosophy, Rush University. 4 This program prepares "Psychiatric Mental Health Nurse Practitioners". These professionals are well suited to fill roles as direct care providers, case managers and program developers in the mental health care system (Repta, 1999 Behavioral managed care administrator's view: Traditional clinical nurse specialists employment in the private health care sector. In National Advisory Council on Nurse Education and Practice [Eds.]. Federal support for the preparation of the clinical nurse

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rural and urban areas.5 A critical aspect of developing innovative community-based services is educating mental health professionals who belong to the community, and also are capable of utilizing the resources from governmental and corporate institutions which, being institutions, are inherently unable to have feelings for the community. In this program, the students will perform their clinical practicum and residency specialist workforce through title VIII. pp. 44-45). Washington, DC. :HRSA.). At this time, the number of psychiatrists working in mental health facilities continues to decline in the USA (Manderscheid et al., 2000. Highlights of organized mental health services in 1998 and major national and state trends. In R.W. Manderscheid & M. J. Henderson [Eds.], Mental Health, United States [2000] Chapter 14. Retrieved November 15, 2001, from http://www.mentalhealth.org/publication/allpubs/SMA01-3537chapterl4.asp). Experts agree that at this time, meeting treatment needs in the USA demands new roles for mental health professionals to provide services that are cost effective and accessible (New Freedom Commission on Mental Health, 2003. Achieving the promise: Transforming Mental Health Care in America. Final Report. CHHS Pub. No. SMA-03-3832. Rockville, Maryland.). The aim is to extend patient care, not to reduce costs to foster profits by establishing a two-tiered system of medical care, physicians for the rich and paramedical professionals for the poor. In China, "barefoot doctors" with scant medical training played a major role in improving medical care for the poor in rural areas after the Japanese and civil wars, but the standards are now improving. 5 A large number of Americans suffer from mental illness. Estimates are that 20% of the adult US population (circa 50 million people), are affected by a mental disorder in a given year (Reiger et al., 1993. One-month prevalence of mental disorders in the United States and sociodemographic characteristics: The Epidemiological Catchment's Area program. Acta Psychiatrica Scandinavica, 88, 335-47.). The prevalence rate climbs to 30% with the inclusion of those known to have an addictive disorder (Kessler et al., 1996. The epidemiology of co-occurring addictive and mental disorders: Implications for prevention and service utilization. American Journal of Orthopsychiatry, 66, 21-23.). Only 15% of persons with severe mental illness receive care from a mental health professionals, 40% of persons do not receive treatment at all (Kessler et al, 2001. The prevalence and correlates of untreated serious mental illness. Health Systems Research, 36, 987-1007.), and 70% of persons with a mental disorder do not seek services (Howard et al, 1996. Patterns of mental health service utilization. Archives of General Psychiatry, 53, 696-707.). Meeting the population's mental health needs is impeded by poverty, lack of public health programs, the transformation of health care into a profit-making industry, and geographic maldistribution of providers. Low socioeconomic status is associated with increased risk for mental illness and with under utilization of mental health services (DHHS, 2001. Mental Health : Culture, race and ethnicity. A supplement to mental health: A report of the Surgeon General Retrieved November 15, 2000 from http://www.mentalhealth.org/cre/default.asp). Poverty creates risk factors for mental health, increases stress and reduces access to professional care (Costello, Compton, Keeler and Angold, 2003. Relationships between poverty and psychopathology: A natural experiment. Journal of the American Medical Association, 2023-2029). According to the latest census, the 9.6 percent of the people in non-metro areas and 9.2 percent in metro areas live below the poverty line (Economic Research Service, USDA, 2003. Briefing room: rural income, poverty and welfare. Retrieved from htto://www.ers.usda.gov/Briefing/IncomePovertyWelfare/ruralpoverty/). In Chicago, 1.7 million people live below the poverty line (City of Chicago Department of Public Health, 1999. Community Area Health Inventory, Volume I. Retrieved on November 1, 2001 from http://www.ci.chi.ilus/Health/Publicationnns/Commiinity/AreaHealthInventoryvolume2/CommArea Vol2.html). There is a critical need to improve the geographic availability of mental health services (Surgeon General's report, 2001).

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in their own communities, and the faculty of Rush University of Chicago will provide clinical supervision to students and their preceptors. This led to the choice of online teaching to reach students who live in rural communities.6 Supervision and preceptor mentorship are vital aspects psychiatric clinical education, but are difficult to provide from a distance. An innovative feature is the design of tools for delivering the clinical supervision component online. Also, the online program targets a group of students for whom on-campus participation is not readily available. Online learning is the only manner to reach a significant student population. Our goal is education, not simply training, and this distinction must be stressed in our times, when universities are transmogrified into career avenues, because patient care requires no less than true professionals. 17.1 Online Education, Content and Form Content and form are inseparable (Aristotle) and co-create each other but they do not co-determine each other. The medium is not the message.7 Online learning does not determine what and how we learn and teach. It simply expands the ways in which we can do it, opening horizons and allowing for greater individuality. As any other method, there are advantages and disadvantages.8 Among the latter, social and personal 6

Carlson-Sabelli, L. (2002). Welcome to Online Clinical Reasoning. University of Illinois at Chicago Nursing Institute Central States Workshop for Nurse Educators, Chicago, IL. 7 Marshal McLuhan, coined the phrase "the medium is the message" as a critique of the effects of technology and advertisement on popular culture and human beings relations. Einstein denounced our times as one in which the perfection of means obscures a poverty of goals. Leonardo's masterpieces were created with exceedingly primitive brushes. The Spanish poet Antonio Machado sung: "Dejar quisiera mi verso como deja el capitan su espada, famosa por la mano viril que la blandiera, no por el docto oficio del forjador preciada." (I wish to leave my verse as the captain leaves his sword, famous for the virile hand that brandished it, not for the learned skill of the blacksmith, who crafted it.) Let this also apply to equations and computer programs. 8 Online learning is already opening horizons and changing how we teach traditional courses. As any other method, there are advantages and disadvantages. It is also the only manner to reach a significant student population. Unique characteristics of online education include efficient information access, convenient methods for updating course information, making corrections to instructions, linking resources, the creation of an automatic paper trail of all discussions, increased social distance, and reduction of cues to appearance, race, social status, and physical disabilities, allowing for anonymity. It results in a greater sense of equal participation, and decreases inhibitions. Online learning can thus facilitates the construction of new knowledge by supports social negotiation

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isolation are significant. One of the features of the program being developed is to turn this around by creating a virtual community. Thus the apparent weakness of online teaching becomes its strength. Electronic distance learning methodologies already in use9 are employed to deliver the educational content. The main difference with standard courses is the greater flexibility afforded to the student10 and to the faculty, and the enormous number of resources that are not available in standard lectures. Clinical reasoning is modeled using the narrative perspective.11 Creative interactive activities to engage students in reflecting on their own process are accomplished through composing and analyzing clinical scenarios, dialogues and stories built around therapy interactions. Role playing scenarios provide the student with an imaginary role, allowing the student to try out new behaviors in a "mistakes allowed" atmosphere as well as seeing how others might handle the situation. The teaching methods utilize up-to-date programs, and do not depart from well-known principles already applied in online teaching of nursing: to encourage active learning, cooperation among students, and student-faculty contact, to provide prompt feedback, to emphasize time on task, to communicate high expectations, and to respect diverse talent and ways of learning. Creation Theory serves these goals with a number

of ideas, providing multiple perspectives, facilitating access to vast information, and supporting collaboration and networking in ways that surpass the campus environment. We use WebCT, Campus Edition Courseware for delivering all of the core and specialty courses for academic credit through Rush University. Project Aha! is created as a website that can be accessed by students and preceptors through WebCT, and by graduates and guests, through the Internet. 10 The Aha! Center web site will be a place-oriented site, where students have the feel of "traveling" among rooms in which they do various interactive activities using image map hyperlinks. Discussions to promote reflection will be held in asynchronous chat environment. Faculty and preceptors will have online offices. Real time chat will be available for individual meetings, and clinical supervision. There will be a Resource Center, a Student Lounge and a Presentation area for viewing each other's work. Visitors will be able to tour the "premises" and read materials about the program, "visit" potential clinical sites and learn about the learning activities, documents, completed assignments, evaluation data and other relevant information, will be housed and retrieved from the WebCT electronic databases. Mattingly and Fleming. (1994). Clinical reasoning: Forms of inquiry in a therapeutic practice. Philadelphia, F. A. Davis; Schon. (1983). The reflective practitioner: How professionals think in action. New York: Basic. 9

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of new methods and strategies. Five tools are being developed through collaboration among faculty, students, and computer experts.12 Learning in action involves bringing together clinical practice with theoretical analysis and reflection. Co-creation and bipolar feedback is effected through psychodramatic role reversal as well as through interactions among students, between individual students and their preceptors and advisors, and between them and the faculty. A critical appraisal of the supremacy of the psychological involves considering how the patient's perspective and the student's own perspective affect patient care. Education is personalized: the entire educational process is student-centered -here the flexibility of online programs is evident. Yet there also are group activities, teaching the reality of work situations.

12 The Moment Maps are dramatic portrayals that include selected dialogue of a psychotherapy session (e.g. to highlight a moment of difficulty or of learning). Doing and viewing moment maps alerts students to deep-seated beliefs, and to the potential impact of the student therapists' values on patients. Constructing moment maps from their own therapy with patients allows students to demonstrate how they connect knowledge with action. Automated Clinical Development Scale is a tool that enables students and preceptors to quickly enter clinical evaluation data in a checklist form, and receive a graphic and narrative report of strengths and learning needs. These automated ratings provide a springboard for discussion of clinical performance between student and preceptor. The ratings are based on the "diamond of opposites" method (Chapter 4.3). Tutorial Quiz: Students are asked to create a tutorial quiz depicting essential learning that takes place during clinical time. This tool provides a method for students to demonstrate reasoning skills and to engage in peer teaching, which promotes leaning. An Electronic Portfolio Data Base provides each student with a method for tracking the progress of the "characters" patients they work with through their clinical experience. Sharing Clinical Stories: Faculty, students and preceptors exchange clinical stories in an asynchronous discussion forum. Story telling as a method of sharing learning experiences has been used with great success in education. As one story stimulates another, students become vicariously involved with the experiences of their classmates. Faculty monitors these stories, and intervenes to focus or broaden meaningful topics and themes. Telling one's experience leads the student to bring it to the conscious verbal level that is intrinsically higher than the action level. It forces them to role reverse with the audience that needs to understand the story, and automatically makes one see oneself from the outside, to connect the different parts of the story, to see how one leads to the other, so they can see the power of their action. Electronic Authoring Software to create Role Based Clinical Reasoning Scenarios: This tool will provide faculty and preceptors an authoring method to create "on the spot" customized clinical activities that capture the learning moment (i.e., the faculty member or clinical preceptor will use a standard format to design and present a creative learning activity that meets a specific need of a particular student at a particular time). We envision these activities as methods for students to imagine themselves solving problems related to various clinical competencies. These activities place a student in the center of an imaginative scenario as the responsible care giver. The structure of the activity provides links to web resources and tools helpful in deciding what to do and how to do it. A student enters a scenario, does something, and comes up with a "product" that can be displayed online, demonstrating interventions and their rationale. Each scenario is devised to help the student demonstrate aspects of nationally recognized clinical competencies. The activities are later evaluated, refined and kept to be used for other students.

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Students collaborate and teach each other. The aim is competency, not competition. As an example of how we apply theoretical concepts, learning and evaluation are not separate tasks but an integral unit. Evaluation is a tool for psychoeducation. The student must become competent to perform a vital social task, nursing care. In this system, the student's evaluation is not a matter of competition between students -a psychopathogenic system that teaches competition rather than responsibility and curiosity. At the beginning of their clinical year, students complete a selfassessment of their perceived level of expertise in each area of clinical competency, and then rate themselves on their performance over time. At the same time, preceptors assess their own level of skill on each of the preceptor competencies and also rate their own performance over time. After seeing the data from the other, the student and preceptor discuss how well the ongoing activities are useful for the student in meeting competency standards. What opportunities have the students had, missed, or have not been available? The mutual feedback between student, preceptor, and faculty puts into practice the concept of creative biotic feedback -mutual, bipolar and hierarchical. In any certifying program the student must satisfy the teacher's criteria. Here there is an additional objective, congruence. The student needs to learn to see herself or himself as others see them. This is a component of learning how to take care of a patient, as well as of working with others. More generally, it is a component of empathy that will well serve them in their personal life. We each have strengths and weaknesses, which are perceived by others and by ourselves in different ways. Matching student perception with their preceptor's perceptions serves as useful feedback for both to grow. It teaches us what to expect from others, given the way we are perceived by them. It teaches us who we are. This is Socratic dialectics: Know thyself. It also illustrates Heraclitus' justice of opposites. This matching of opposites -self and other ~ is not an equilibrium point, but may be expected to promote empathic, ethical, and effective behavior. This example, intuitively clear, illuminates the idea, discussed in Chapter 8, that the symmetry of opposites produces bios, not equilibrium. The "justice of opposites" is extended by the grading of the teacher by the students, and further enlarged by the input of faculty, and the interchange

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among students. Students contribute to each other's work. This is the beginning of a virtual community that may serve for psychotherapeutic supervision and, in a way, collective psychotherapy (see later). Because we change and our environment changes, the matching of our subjective impressions of our own selves and the objective view of others is a lifelong creative process. A psychotherapeutic aim is for students (and faculty) to learn that a sine qua non condition to be good is that others regard it as good for them. It serves the student as a student, but it also has positive effects in their professional and personal life and, indirectly, in the life of society.13 17.2 Primary Psychiatric Care We shall be brief. General principles are discussed in Chapter 16; more specific issues are outside the scope of this book. The application of process principles and of nonlinear dynamic methods to nursing practice has been described in published articles.14 Primary Psychiatric Care requires focusing on the fundamentals. The concept of action leads directly to the notion of agency and spontaneity as mental health, and to the self-concept of persons in their patient role. Patients must learn to tolerate being patients and relinquishing control, and yet also avoid becoming passive patients. A person must be an agent as much as (s)he can. To promote both patience and agency requires well-timed and sensitive bipolar feedback. Both the caregiver and the patient must be aware of the fact that we all are in part agents and in part patients, at least we are patients when infant and when sick. Indeed illness can make us vulnerable and passive like children. But it is also important not to infantilize the patient. Everyone who is sick is also healthy in many ways, and everyone who is healthy still has health issues. A person 13 It is easy to convince ourselves that what we want to do is good for others, and if they do not recognize it, it is because they are paranoid or stupid. False innocence is a major sin of powerful. 14 Sabelli, H., Carlson-Sabelli, L. and Messer, J. (1994). The Process Method of Comprehensive Patient Evaluation Based on the Emerging Science of Complex Dynamical Systems. Theoretical and Applied Chaos and Nursing. 1: 33-41; Carlson-Sabelli L., Sabelli, H. C , Patel, M., Messer, J., Zbilut, J., Sugerman, A., Walthall K., Tom, C. and Zdanovics, O. (1995). Electropsychocardiography. Illustrating the Application of Process Methods and Chaos Theory to the Comprehensive Evaluation of Coronary Patients. Complexity and Chaos in Nursing 2: 16-24.

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should not loose status because (s)he is sick. Here enters the ability of the caregiver to role reverse with the patient, and to evaluate his/her performance from the perspective of the other, as discussed before. It is necessary to perceive the patient as (s)he is now, which varies moment to moment, and also to view living as a process in which the patient has a past and hopefully a future. Prevention and therapeutic intervention, in addition to their own intrinsic function, also become vehicles to convey the psychotherapeutic notion of creative determination of the future by the present. Treating the patient as a person requires attending to the individual, to the family, and to their culture. Psychiatric care is particularly culturally sensitive. Our program includes specific measures to recruit, retain, and graduate students from underrepresented minority groups and/or students from disadvantaged or low-income backgrounds, as well as learning experiences to promote an understanding of cultural diversity. For instance, we are creating role-based scenarios that include patients of a variety of cultural backgrounds. We are also developing an ongoing online forum for students and educators to share culturally sensitive experiences about psychiatric and mental health issues. The concept of biological priority and psychological supremacy can be readily translated as health, work, family, and soul.15 Placing health first means focusing on psychobiology. Students must learn to recognize biopsychiatric illnesses such as bipolar disorder, and also to distinguish them from presumably entities that may or may not be real illnesses but that are given names for insurance purposes. Health issues go beyond psychiatry. Primary psychiatric care involves primary medical care and "triaging",16 meaning referral to appropriate medical sources, because the psychiatric professional often becomes a trusted long term care giver. "Nursing" suggests mothering. Indeed patients may need mothering. Among structured exercises for health care education, one is to role reverse with a patient and with a child. Another is to experience mother 15 Consider a young schizophrenic man: First, take your medication. Next, get a job. Third, relate to your family, develop friends, may be a girlfriend. Then, attend to your spirit. (On the contrary, it would be unhealthy to attend to voices with religious instructions before taking antipsychotic medication.) 16 It is of course tempting to point out the occurrence of threeness in triage.

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archetypes.17 A "parental" vision of health care articulates with a "parental" conception of co-creating opposites. 17.3 Co-Creating Community Structure is a springboard for creativity. We are creating a virtual community that includes the university faculty, the students and their preceptors at their local communities.18 (We intend our graduates to become our future preceptors.) Clinical supervision is an essential aspect of education and practice for mental health professionals. It has traditionally been accomplished in personal one-on-one or small group formats, and in many cases is very expensive. Mutual supervision among professionals can thus serve a major role in maintaining and enhancing professional standards. One of the central goals of our program is to create a virtual supervision community of Mental Health Practitioners using sociometric and sociodynamic principles. The plan becomes a sociodynamic experiment in forming a networked community of professionals. The sociometric structure of the virtual supervision community is built around the notion of double dyads and triads - three attractors produce chaos, four produce bios. The structure is engineered on the principle of 1,2,3, 4 and many. The process is student centered. As a student is accepted into the program she/he is assigned a faculty advisor. So we have a natural dyad - advisor and student. We have another natural dyad, the faculty supervisor - advisor pair. As the student enters the clinical portion of their education and is assigned a preceptor in the last year of the program, a triad emerges. This system is based on the notion that pairing, triads and tetrads all are creative entities different from each other, each with advantages and disadvantages (e.g. the well-

17 We include the Goddess as Mother Nature and Mary as the Mother of Jesus. This provides an enormous range for exploring how we conceive caring, particularly when the student observes how others interpret these archetypal figures. 18 Carlson-Sabelli, L. (2002, March 16). Aha! Strategies that encourage student involvement in their own learning in a virtual clinical supervision community. American Association for Higher Learning National Conference. Chicago, IL.

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known phenomenon of "triangulation"19). Building a virtual clinical supervision community is a sociometric experiment that will be documented, in an effort to evaluate creative and destructive dynamic in dyads, triads and tetrads. Some organizations and groupings can be more effective that others in promoting the aims of the virtual supervision community. Here we have a social experiment to be tracked as a study of class relations (faculty, students and preceptors). We make a psychotherapeutic expectation of the outcome, a co-creative system, but we also expect conflicts. How we handle them is also part of the psychoeducational process that conveys (or does not) the concepts of personalization and co-creation, and incorporates (or fails to do so) the scientific methods of sociometry as augmented by nonlinear dynamic techniques. 17.4 Sociometry and Psychodrama as a Clinical Philosophy In the educational program, and particularly in the development of the virtual community, we incorporate sociometric principles and psychodramatic action techniques20 that originate with Jacob and Zerka Moreno,21 and further elaborated by Ann Hale.22 For instance, we use psychodramatic techniques online (soliloquy, doubling, role reversal, surplus reality). We also incorporate sociodramatic techniques in our Cocreative children puppet theatre23 and other forms of Co-creative 19 Virtually all significant relationships, beginning with the nuclear family, include three or more parties. Triangulation describes pathological processes arising in personal triads. For instance, a couple's unable to handle differences and disagreements may triangulation an adolescent, either pushing the child out as a scapegoat or pulling hime/her in as a coalition partner or mediator. 20 Carlson-Sabelli, L. (2001). The use of psychodrama in nursing. In Joyce J. Fitzpatrick (Ed). The Psychiatric Mental Health Nursing Research Digest. New York: Springer. 21 Moreno, J. L. (1978). Who Shall Survive? Beacon, NY: Beacon House; Raaz, N., Carlson-Sabelli, L., and Sabelli, H. C. (1992). Fragmented stories-putting together the pieces: A psychodramatic therapies in the treatment of Multiple model. In Kluft, E. (Ed). Expressive and functional personality, Charles Thomas, Springfield, IL; Carlson-Sabelli, L., Sabelli, H. C , and Hale, A. (1994). Sociometry and Sociodynamics. In Psychodrama since Moreno: Innovations in theory and practice. Karp, Watson and Holmes, Editors. 22 Hale, A. (1987). New Developments in sociometry. Journal of Group Psychotherapy, Psychodrama and Sociometry, 3, 119-1123. 23 Carlson-Sabelli, L. (1998). Children's puppet theatre for traumatized Children: A process theory approach. International Journal of Action Methods: Psychodrama, Skill Training, and Role Playing,

51:91-112.

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theatre.24 As already discussed in earlier Chapters (4.3, 12, and 16), Creation Theory articulates with Moreno's concept of spontaneity, role complementarity, and creativity, which highlights action as therapy, role reversal with others as the process to gain insight, and co-creation and conservation as creative components25 (Table 17.1). Creation Theory updates Moreno's theory as a foundation for psychodrama, sociometry and family therapy.26 The Morenos, in a long tradition that stems from Pythagoras, modeled creative marriage.

Jacob and Zerka Moreno. Courtesy of Zerka Moreno.

Creation Theory, and in particular this virtual community of mental health practitioners, continue Moreno's notion of collective 24 Carlson-Sabelli, L . (1995, Spring). Co-creating Stories: A sociodramatic activity. Psychodrama Network Newst 2-3.Carlson-Sabelli, L . (1995, Winter). Heart Mates: A sociodynamic technique. Psychodrama Network News,, 4-6. Carlson-Sabelli, L, and Sabelli, H. C. The psychotherapeutic myth of the Mother Goddess. A co-creative theatrical performance. Proc. International Systems Society 38th Annual Mtg., B . Brady and L. Peeno (Eds.), Pacific Grove, CA, 1994, pp. 1589-1600. 25 Moreno, J . L. (1978). Who Shall Survive? Beacon, NY: Beacon House; Raaz, N., Carlson-Sabelli, L. and Sabelli, H. C. (1992). Fragmented stories—putting together the pieces: A psychodramatic model. In Kluft, E. (Ed). Expressive and functional therapies in the treatment of Multiple personality, Charles Thomas, Springfield, IL; Carlson-Sabelli, L., Sabelli, H. C, and Hale, A. (1994). Sociometry and Sociodynamics. In Psychodrama since Moreno: Innovations in theory and p r a c t i c e . Karp, Watson and Holmes, Editors . 26 Carlson-Sabelli, L and Sabelli, H. C. (1984). Reality, Perception and the Role Reversal. J Group Psychotherapy Psychodrama and Sociometry 36:162-174. Carlson-Sabelli, L, Sabelli, H. C , Patel, M., Holm, K. (1992). The Union of Opposites in Sociometry: An Empirical Application of Process Theory. The Journal of Group Psychotherapy, Psychodrama and Sociometry 44:147-171. Raaz N, Carlson-Sabelli, L., and Sabelli, H. C. (1992). Fragmented stories-putting together the pieces: A psychodramatic model. In Kluft, E. (Ed). Expressive and functional therapies in the treatment of Multiple personality, Charles Thomas, Springfield, IL. Carlson-Sabelli, L., Sabelli, H. C, and Hale, A. (1994). Sociometry and Sociodynamics. In Psychodrama since Moreno: Innovations in theory and practice^ Karp, Watson and Holmes, Editors.

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psychotherapy. "A truly psycho-therapeutic procedure cannot have less an objective than the whole of mankind', states Jacob Moreno in the opening sentence of his major work. 27 In this spirit we extend our clinical philosophy to all fields. This is the focus of our final Chapter. Table 17.1 Creation Theory as an update of Moreno's Clinical Philosophy Psychodrama and _ . _,, _, . . Creation Theory Sociometry . . , Action principle and action Action therapy . . „ . , _ . - i therapies. Spontaneity and r f_ . : SpontaneityJ rprinciple r asymmetry of action Group therapy with Biotic Dynamics: bipolar, director and other mutual and hierarchical professional roles feedback Role reversal (in Complementary opposites group Psychodrama). Complete role reversal as Complete role reversa main technique in family in family interactions, therapy28 „ .. .... . _ . , Co-creative children puppet Sociodrama . , , theatre. Co-creative theatre.

Online Clinical _ . . _ Supervision Program Learning in action. Thinking, doing, • • • a reflecting in stones. Attention to °. . , „,, . , . sequence of actions and of thinking. Students and preceptors assess self and other, providing mutual, yet hierarchical feedback. Role based interactive scenarios, Role reversal as a clinical supervision technique. Use of psychodramatic techniques online. Moment Maps portraying, reflecting , , • , on and analyzing therapy . . • , • Kf interventions in a dramatic format Sociodynamics (diamond of Building and studying an online Sociometry opposites as nonlinear community. Diamond of opposites in clinical development scale dynamics in sociometry)29 _ .. , Co-creation by and Co-creation as a vision 3 synthesis y Co-creation as goal by biotic feedback for therapy and life. „ , , „ . . . . .. Continual use of research Cultural conserve in Conservation term in biotic . . . . . .. .. . information from internet creativity equation. ,... and library sources. Materiality Psychobiology Priority of simple ^ Wor Role based interactive scenarios, Supremacy of complex ' ° b Concept of religion as Scientific and _ , . .. ,, .. „ , ., . . . Exploring spiritual issues when they collective Psychotherapeutic concept ol ° . . , , ., ^ , . „„ . .. anse in therapy psychotherapy. | God as Attractor of Evolutiorj

27

Moreno, J. L. (1978). Who Shall Survive? Beacon, N Y : Beacon House. While psychodramatic techniques are used in education and in creative group therapy, Moreno actually pioneered family therapy with role reversal between mother and son. 29 Section 4.3. 28

Chapter 18

A Manner of Thinking: Mathematical Priority and Psychological Supremacy

To survive we need a new manner of thinking. A. Einstein. To survive we need to think. Juan Manuel Miguez. Thinking is shared by all. Think for yourself. Heraclitus.

Abstract: This chapter sketches how creation theory could provide foundations for scientific methodology, everyday creative thinking, and a dynamic mathematical and psychological logic. Medicine provides a manner of thinking. Just as the physician must depend on practical experience in order to settle questions of fact in medicine, so the philosopher must depend on the same indispensable source of knowledge in order to settle questions of fact in general. In other words, according to Locke, "the appropriate method of inquiry

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required in philosophy is, implicitly, the very same method required in medicine generalized"} The standpoint of life should also be fundamental to scientific endeavors. Science, said Quine, continues common sense. Einstein pointed out "the critical thinking of the physicist cannot proceed without considering critically a more difficult problem, the problem of analyzing the nature of everyday thinking." Common sense corresponds to the common man. Opposition to common sense, and reliance on experts, has always been the program of aristocratic parties from Plato to our times. Science is a human activity. Culture, ideologies, personal feelings and interests influence its march. Science has a psychodynamics and a sociodynamics. Facts have priority; psychological factors (including social and economic interests) determine their interpretation. For this reason, critical thinking is necessary. For the same reason, critique is not sufficient. Challenging assumptions, prejudices,2 ignorance,3 carelessness,4 errors, and even dishonest distortions of data for profit, is at times crucial, but it often becomes unnecessary.5 It is, in any case, useless to oppose a view unless one can provide an alternative. We need creative thinking. Creative thinking implies action, not just change, and it considers past, present and future; focusing on the present is a static manner of

1 Romanell, P. (1984). John Locke and Medicine. New York: Prometheus Books. It is difficult to list the many physician-philosophers, from Imhotep to Empedocles to Avicenna, Averroes, Maimonides, Copernicus, and many others. A prejudice in favor of circular movement directed Ptolemy to design his cosmological model. It also impeded Copernicus to propose a simpler system, it delayed Kepler's discovery of the elliptical form of planetary orbits for almost twenty years?, and it prevented Galileo to accept Kepler's discovery! [Koyre, A. (1973). Etudes d'histoire de lapensee scientifique. Editions Gallimard] One example should suffice. The founders of sociobiology claim that the female orgasm is a "human invention"; females of other species (including rabbits that only ovulate after coitus) do not experience orgasm (Wenegrat, B. 1984. Sociobiology and Mental Disorder. Menlo Park. CA. Addison-Wesley Publ.) These zoologists must have never had pets. In the early twentieth century, eminent psychologists, including G. Stanley Hall, claimed that advanced education would reduce women's reproductive capacity, so, to protect the species from extinction, women must be excluded from colleges and universities. Even today, psychiatrists, pharmacologists and governments employ concepts of race that sociologists regard as racist and biologists as ignorant. 4 Up to the time in which Watson and Crick discovery of its structure unchained the development of modern genetics, medical textbooks taught us that human cells contained 48 chromosomes, rather than the 46 that actually exists. As time goes by, it becomes increasingly unnecessary to discuss psychoanalysis, Marxism, behaviorism, quantum mechanical speculations denying the existence of matter, and other theories taught as fact no long ago. Time is limited, pointed out my father, why waste it in polemics?

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thinking.6 Second, focuses on bipolar opposition, not just conflict. The twentieth century spawned a most vast and radical historical process, the women's movement, which has made us take seriously not only the equality of the two halves of the human species but also of opposites in all areas of reality. A case in point is the coexistence of information and misinformation. Third, it regards qualities as dimensions that measure different aspects of an entity rather than as separate classes. For instance, we ask ourselves the intensity and domain of introversion (and of extroversion) in each individual persons, rather than classify persons as introversive or extroversive. We ask ourselves to what extent a country is monarchical and republican (in a Platonic fashion) rather than one or the other (in an Aristotelian classificatory mode).7 Fourth, it replaces determinism and probabilism with the notion of creative determination of the future by the present. Finally, creative thinking requires not only interdisciplinary integration, but also critical examination of the tenets of one science from the perspective of others. We are exploring the development of creative thinking in two different contexts, as logic of science and as psychotherapy.8 These two issues are not independent. It is not only important to know how to perfect our thinking, but it is also important to understand why we, and others, fall into distorted ways of reasoning. Reason does not stand alone. It is always paired with irrationality. Recognizing the coexistence of these opposites indicates that logic must be both mathematical and psychological. We must not only design computers and algorithms but also choose what algorithms to design, and for what purpose. For instance, from the perspective of evolutionary science, a focus on invariance and universality to the exclusion of change is irrational. Yet 6

Consider the opposite attitudes fostered in the elderly by living in the past (as often happens), living in the present (as it is often advised) and living in process, aware of past, present and future. Likewise young persons develop healthier attitudes by being aware of all three perspectives. 7 The USA constitution combines republican concepts derived from the Iroquois and the Greek with strongly monarchical traits derived from the British system, and it also allowed for plus slavery. 8 Sabelli, H. Mathematical Dialectics, Scientific Logic and the Psychoanalysis of Thinking. In Hegel and the Sciences, Edited by R. S. Cohen and M. W. Wartofsky. New York: D. Reidel Publishing Co., 1984:349-359; Sabelli, H. Non-linear dynamics as a dialectic logic. Proc. International Systems Society, pp. 101- 112, 1995; Sabelli, H. and Carlson-Sabelli, L. (1996). As simple as one, two, three. Arithmetic: a simple, powerful, natural and dynamic logic. Proc. International Systems Society, pp. 543-554; Sabelli, H. The Union of Opposites: from Taoism to Process Theory. Systems Research 15: 429-441, 1998.

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the entire edifice of standard logic is built on the assumption of permanent entities. This is useful in mathematics, but it contradicts evolutionary science. Standard logic is not independent from the static worldview that prevailed before. Logic is constructed with timeless sets and tenseless propositions, driving our attention away from change and evolution, and thereby from reality itself. A=A is true in mathematics but misleading elsewhere.9 It is disingenuous to pretend that ideas have no consequences. Ideas guide actions. For this reason, it is cogent to attend to the implication of hypotheses, and to be particularly careful with those that have potentially harmful effects - such as those postulating conflict and selfishness as dominant factors in behavior. Prejudices in favor of static concepts still dominate scientific discourse. I must confess to an equal but opposite prejudice that makes me pursue dog headedly a world view in which nature and thought are actions, opposites are similar, processes are creative, and human actions are effective. o

iVv

A

Fig. 18.1 Helicoids. Helicoids are sets with a relation J, satisfying the following postulates: If AJ.B, then it is not true that B|A. If AjB, B|C and CJ.D, then AJ.D. It follows that A
Creation theory provides general guidelines for creative thinking (Table 8.1) that may possibly be firmed up as a biotic logic. A logic involves (1) identity and unidirectional implication, (2) two values (negation) and (3) operations that combine two elements to generate a third. Logical implication (if ... then) is a partial order and hence generates lattices. Dialectic refutation is at once a partial order and a negation, and hence generates two-colored lattices (helicoids). If A implies B and B is false, then A is false. These two types of inference are complementary. It is easier to walk on two feet than on one. Both types 9

Consider, for instance, the simple statement "Chinese are Chinese". A few decades ago, sociologists wrote long essays discussing why the Chinese did not progress, and attributing it to culture and mentality. At this time, China is one of the fastest growing nations in the world.

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of inference occur in helicoids (Fig. 18.1).10 The conceptual similarity between bios and helicoids would not escape the reader. 18.1 Action Ideas are actions. Action calls for spontaneity, integration, and practice. Act, do not react. Take the initiative.11 Practice measures ideas, as illustrated by health measures of democracy (Fig. 16.2). Action implies order and organization. We thus assume that natural processes are patterned rather than random. When a difference between data and random models is not detected, we strive to develop methods that will demonstrate it before abandoning the apparent (a.k.a. evident) pattern as having been definitely demonstrated to be fortuitous. If ideas are actions, logic must become dynamic. Dialectics has been proposed as a dynamic logic12 but it remained purely philosophical. This allowed for political distortions that led many to regard dialectics as the last resort of the scoundrel. The only possible solution, I concluded, is a mathematical formulation. Certainly in our times of mechanical computation, dialectics must become mathematical. Several attempts have been made,13 including group14 and catastrophe15 models. 10 Sabelli, H. C. An Attempt to Formalize Some Aspects of Dialectic Logic. Hegel-Jahrbuch 1970. H.v. Wilhelm R. Beyer, Verlag Anton Hain. Meisenheim am Glan, 1971, pp. 211-213.1 have used helicoids as models to locate the site of action of drugs on neural nets [A Pharmacological Strategy for the Study of Central Modulator Linkages. In Recent Advances in Biological Psychiatry, Edited by J. Wortis. New York: Plenum Press, 1964:6:145-82; Sabelli H. A Pharmacological Approach for Modeling Neuronal Nets. In Biocybernetics, Edited by H. Drischeland P. Dattmar. Jena, Germany: Veb Gustav Fischer Verlag, 1972: IV: 1-9]. 11 Nobelist Bernardo Houssay, my mother's mentor, advised me (and probably many others) to study something new rather than following the mainstream. ("They" have the economic resources, and can publish faster. Create anew, set the trail. Let them read your work and follow you.) 12 Lefevre, H. Logique formelle et logique dialectique. Paris, 1947. 13 1 am not familiar with work from scientists from the Eastern Europe, so I may have missed much of importance. I refer the reader to Theoretical Dialectical Journal: Physics-Mathematics-LogicPhilosophy, http://www.tedial.narod.ru/eni01.htm. Concerning the relationship between dialectics and formal logic, the official Soviet position until the 1960s was that there were two logics, formal logic dealing with simple, abstract relations and dialectical logic devoted to concrete and complex relations. In the hands of political dictators, dialectic contradiction became a justification for inhumane behavior. Later on Soviet Marxists treated dialectics as an epistemology rather than as a logic per se. In other words, these authors abandoned dialectic logic. 14 Giinther, G. (1967). Time, Timeless Logic and Self-Referential Systems. In Annals of the New York Academy of Sciences. Edward M. Weyer. pp: 396-406; Sabelli, H. C. (1970). An attempt to formalize some aspects of dialectic logic. In Hegel-Jahrbuch. pp: 211-213; Gauthier, Y. (1984).

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Bios Table 18.1 Three Forms of Reason Logic Static A=A

Identity

Opposition

Implication y

Matenality 3

Dialectic Dynamic Complementary . ,I n (orthogonal) 2 Two values Quantu Coexisting opposites loca

Biotic Dynamic A t < A1+1 Autonomous (planar) IN i 2 values. Quantum superposition, local no contradiction and global co-existence

. , Linear . (categoncal ,v n . 6 (orthogonal) U _? Two values ,. . _T w Coexisting opposites No-contradiction (contradiction) Formal (if then) of Mutual implication of cause by opposites (ambiguous J , _ .. . consequence definition) Extension portrays . intension: properties , _ ,, are defined by sets

Creation No model Psychobioloeical .T 3 6 . None bases Mathematical _ . , , Boolean model Technological n i , , , A. .. . Standard computation realization | ]

Formal and material

Lattices of classes. „ .. . ,. Qualities as dimensions. „ „ .... Groups of qualities,

_ . . Opposite properties . . , ... coexist in each entity

Synthesis ,T None

Bifurcation and synthesis Cognitive structures, , . , neurophysiology , XT ,. Nonlinear dynamics

,, None .T None

(of

, . consequence by cause)

|

None. Quantum . _ computation?

Logic traditionally is formal and extensional (i.e. material).16 Both traits indicate a static bias. A process logic must define an evolving identity At+i> At that implies continuity and similarity, but not equality. Extension and intention do not show one-to-one correspondence: opposite properties coexist in each entity, in a dialectic fashion, so one must describe them separately. Sign does not determine boundaries. Finally, formal implication of the cause by the demonstration of its

Hegel's Logic from a Logical Point ofView. In Boston Studies in the Philosophy of Science. Robert S. Cohen and Marx W. Wartofsky. 64: 303-310; Kosok, M. (1984). The Dynamics of Hegelian Dialectics, and Non-Linearity in the Sciences. In Boston Studies in the Philosophy of Science. Robert S. Cohen and Marx W. Wartofsky. vol. 64: 311-348. 15 Thom, R. (1970). Topologie et linguistique, in A. Haefliger and R. Narasimhan, eds., Essays on Topology and Related Topics, Springer-Verlag, New York. Rene, T. (1972). Stabilite Structurelle et Morphogenese, W. A. Benjamin, Inc., Reading, Massachusetts. 16 There are of course a number of other logics. A temporal logic has been developed by Rescher and Urquhart, [Rescher, N. and Urquhart, A. (1971). Temporal Logic. Ed. Bunge, M. Springler-Verlag. New York.]. It should be noted that Rescher [Rescher, N. (1996). Process Metaphysics. State University of New York Press] regards process philosophy as a twentieth century, primarily American (meaning USA) creation, and that he does not include in it coexisting opposites.

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consequence must be complemented by the implication of the consequence by the process that creates it. For instance, period 3 implies its antecedents such as bifurcation cascades (Sarkovskii's theorem) because bifurcation cascades generate period 3. From a process perspective, bifurcation cascades imply period 3. 18.2 Opposition Oppositions are so widespread that it is not possible or rational to ignore them whatever issue we consider. Purely quantitative approaches are, in a sense, blind to a fundamental aspect of reality. On the other hand, focusing on opposites also blinds us from seeing similarities and third alternatives. The coexistence of multiple oppositions is also confusing; hence oversimplifying thesis like being with me or against me. It is essential to establish a hierarchy of importance if one is going to fight.17 To gain insight, to create, it is more important to develop a new way of looking at reality, to conceive a new partition, which runs "diagonal" to the existing one. An insight, an "aha", is always a new distinction, a new opposition. Likewise, to create peace and prosperity, it is often to create a "cross partition" that unites the humanists present on both opposing sides of a conflict, and separates them from others on "their" side.18 This is not a call for "harmony" between two good sides that are misrepresented as enemies by prejudice, but a denunciation of both belligerents. Standard logics regard opposites as linear, either two values or poles of a continuum. Corresponding to matter and void, the two components of mechanism, standard logic offers two values, 1 and 0 (existence and absence). Process theories postulate real opposition, and therefore the fundamental values are 1 and - 1 . Dialectic complementarity involves synergy and antagonism, so opposites are orthogonal to each other (1 and i). In the biotic model, opposites are planar, including all possible 17 Mao Zedong advanced the famous notion of "main contradiction". An extensive critique of this viewpoint is developed in Union of Opposites, and a Taoist alternative is developed in Sabelli, H. (1998). The Union of Opposites: from Taoism to Process Theory. Systems Research 15: 429-441. 18 Consider, for instance, the religious wars between Catholic and Protestant Christians that bloodied Europe in the "little Middle Ages" contemporaneous with the birth of science and modernity.

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manners of relating to each other, including linear diametric opposites (1 and -1) and orthogonal complementary opposites (1 and i). In the same manner, the outcome of the combination of two entities may be orthogonal to them, creating a tridimensional structure. Thorn's catastrophe theory is the foundation of a mathematical dialectics because it involves opposites (rather than existence and absence) and further, it relates them in a nonlinear fashion. Bios theory also includes a multiplicity of opposites and of relations between them. Bios data analysis of empirical data and of mathematical bios shows that opposites vary autonomously (lack of linear correlation, Section 4.5) but not independently, in contrast to the linear opposition postulated by logic and the complementary opposition conceived by dialectics. Thus the principle of no contradiction cannot be taken for granted. Nor can we assume a gradient from true to false as in probabilistic or fuzzy logic. There are multiple ways in which partial truth coexists with partial error. Both positive and negative interactions contribute to the creation of novelty and complexity. Confirmation plays a major role in science,19 and so does proof in mathematics. The accepted structure of logical reasoning is a lattice of implications, starting with axioms. This view permeates mathematics from Euclid to Hilbert, Frege and Russell. By considering only deductive certainty, such view fails to portray the exploratory nature and creativity of rational thinking. In reality, the scientific community carries on a continuous dialectic in which refutations are as important as proofs. Opposition is creative in two different ways. First, the most useful way to test a hypothesis is to attempt to refute it; thus the Australian neurophysiologist Sir John Eccles provided the best evidence for chemical synaptic transmission by attempting to refute this hypothesis. Conversely, following ideas to their ultimate consequences serves to 19 Generalizing from repeated observations into a general rule is a common, and common sense, mode of learning. Statistics develops induction into a scientific method. Just as to claim that induction is the one and only scientific method was an over-enthusiastic proclamation, motivated by a justified reaction against medieval philosophy, to deny that induction is a psychological fact of ordinary life as well as a scientific procedure [Popper, Conjectures and refutations. The growth of scientific knowledge] is vastly exaggerated. Even if repeated observations offer no proof, most of us would dismiss the hypothesis that the sun will not rise tomorrow, even as we understand that the sentence is now to be interpreted as planetary rotation.

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refute them. Second, refutations play a creative role by bridging notions that cannot be readily connected linearly. This is the argument of reduction to the absurd that is so useful when the principle of no contradiction can be applied, as in mathematics. The biotic model indicates that multiple opposites are required to create complexity. A biotic logic should then include a multiplicity of informational (truth) values. Just as cascades of bifurcations multiply the number of oppositions in mathematical recursions and in natural processes, the number of truth-values can be multiplied by iterating complementation (a set theoretic model for logical negation) as a process (iterated negation20). Thus two-valued negation becomes 22 valued, beginning with four values: 00 (neither A nor no-A), 01 (no-A), 10 (A), and 11 (both A and no-A). Expanding two-valued Boolean algebra into a 2N-valued logic accommodates coexisting opposites. The qubit includes four values, and in particular distinguishes between +/- and -/+; there are two intermediate values between positive and negative representing directions of change. An application of the concept of multiple opposites is in the formulation of a research strategy. Instead of testing one hypothesis to attempt to confirm it (as it is common) or to refute it (as in Socrates' negative dialectics and in Popper's falsification strategy), or two opposing views (as Protagoras), it is often useful to contrast many, as discussed by Bacon, Chamberlain, and Platt.21 The negation of truth is false but the negation of the false can be false. Negation is asymmetric: there is only one truth, but there are many errors. The multiplicity of opposition ends with the paradoxes generated by two-valued logic. For instance, induction formalizes the common sense notion that given a hypothesis (e.g. "all ravens are black") is supported by finding a case which is true (e.g. a black raven). In twovalued logic, "No no-black entity is a raven" is the same as "all ravens are black", so finding a red herring supports this hypothesis (HempePs

20

Sabelli, H. (1984). Mathematical Dialectics, Scientific Logic and the Psychoanalysis of Thinking. In Hegel and the Sciences, Edited by R. S. Cohen and M. W. Wartofsky. New York: D. Reidel Publishing Co. pp. 349-359. 21 Platt, J. R. (1964). Strong Inference. Science 146: 347-53.

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paradox22 that scientists may dismiss, but logicians take very seriously). To assert P is to make a particular statement; to assert no-P is to refer to an infinite set almost identical to the universe. Inductionism defines confirmation as the finding of the case of a hypothesis. I defined a stronger form of confirmation as the refutation of the refutation of the hypothesis. This can be modeled by helicoids (Fig. 18.1). Chaos theory (as Greek physiology, Taoism and dialectics) indicates to focus on triads. Beyond opposites, there is a third that complements and opposes both. This differs radically from Aristotle's golden middle, Marx struggle, and Thorn's catastrophes. How does one generate such third? Quantitative logics postulate a third between opposites, a "center" that finds favor among vote-seeking politicians. Traditional dialectic regarded the third as the synthesis of opposites. There is of course a third in the undifferentiated state that precedes a distinction. But Aristotle suggested a more interesting third, the open value for the future. One may create a third alternative by considering what is common to both opposites and negating it (just as one primary color is the opposite of the secondary color generated by the combination of the other two primaries). This is the neither/nor case (Shaffer's stroke), a logical function that can by itself generate the entire Boolean logic. For instance, the theory of creative processes emerged from negating both determinism and indeterminism, both of which imply that nothing new and more complex emerges, and that humans have no control. Similarly, the concept of priority / supremacy is not a middle ground between materialism and idealism but a rejection of their shared unidirectional conception of causality. Opposites are also diverse. A fundamental diversity relates to levels of organization; in Chapter 9 we discussed a principle of quantum superposition, local exclusion and global implication of opposites. How this applies to quantum computation is as yet to be explored. Regardless of quantum superposition and dialectic contradiction, the fact is that

22

Hempel, C. G. (1943). A Purely Syntactical Definition of Confirmation. J. Symb. Logic 8, 122143. Hempel, C. G. (1946). A Note on the Paradoxes of Confirmation. Mind 55.

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Schrodinger's famous cat23 is either dead or alive, irrespective of whether or not the box has been opened and an observation has been made. Logic thus denies the coexistence of opposites: if one is to assert that everything implies its opposite, how can we separate true from false? In my view, logic must include both logical refutation by contradiction and the coexistence and separation of opposites, not just one or the other. The notion of local no contradiction leads to investigate quantitative asymmetry: which one predominates when, where, and in what respect? The notion of global contradiction leads us to propose the coexistence of the opposite as a hypothesis to be tested (not a certainty). Atx if and only if Atx- or AfX. The existence of one action implies the existence of its opposite, at a different time t and/or at a different place x. Measurement complements qualitative logic. Some scientists believe that one can replace logic by measurement. Some regard qualitative description as poor quantitative analysis. Actually quantitative thinking alone leads to linear thinking, so it is more primitive than even a simple dialectic of opposites. Yet dialectic opposition does not account for the rich qualitative gamut of reality, and favors conflictual thinking. 18.2.1 Paraconsciousness and black and white thinking Thinking dynamically, considering multiple opposites, and regarding processes as creative, is common sense. Why then logic and dialectics focus on the mutual exclusion or struggle of opposites? Paraconsciousness24 is the distortion of thinking created by living immersed in social conflict, which makes demonize our rivals or enemies and regard ourselves and our allies as faultless angels. Racism, sexism, political and religious fanaticism are clear examples, but patriotism often covers paraconsciousness. The introjection of conflict creates polar, manicheistic, dogmatic, competitive, antagonistic thinking. "You are 23

A cat sits in a box with a radioactive device and a container of poison. A decay could break the container, releasing the poison and killing the cat. Because such quantum events are probabilistic and because we cannot see into the box, we have no way of knowing whether the cat is alive or dead. The Copenhagen interpretation of quantum mechanics would then claim that the cat is neither alive nor dead until we open the cage and observe it. Schr6dinger formulated this metaphor to refute such an interpretation. 24 Sabelli, H. (1989). Union of Opposites.

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either with me or you are against me". Paraconsciousness plays a greater role in social pathology than Freudian unconsciousness and Marxian false consciousness.25 Fear largely explains irrational thinking regarding national and racial conflicts. Logic and dialectics focus on the mutual exclusion and the struggle of opposites because we live immersed in social conflict. Black and white thinking contributes to generate paraconsciousness, and it often is its product. It is characteristic of neurotics,26 depressives,27 and borderline personality disorders,28 and correcting it has been found therapeutic in depression.29 Along the same lines, we teach patients to see the similarity, and inseparability, of opposite motivations, roles, and sides in a conflict, and, further, to analyze conflicts in terms of two different oppositions -four cases rather than two. This serves to expand understanding and tolerance. Thinking in triads promotes creativity.30 Learning to think in gray is psychotherapeutic, but learning to think in color, i.e. learning to see a third alternative that does not lie between the other two, promotes creativeness.31 More generally, I find it useful to think "arithmetically", that is to say to regard every issue from each of these different "numerical" perspectives- its unity, the oppositions and the triads it contains, its multiple dimensions and the creation of further complexity. This "arithmetic" logic has the advantage of being readily taught educationally or psychotherapeutically. Paraconsciousness influences scientific thinking. The cold war, for instance, split not only the human sciences but even the mathematical ones. For instance, Boolean and dialectic logic became separated. Soviet 25

The term false consciousness originates with Marxism, but its conflictual view of history actually is paradigmatic of what I call paraconsciousness. 26 Adler, A. (1954). Understanding Human Nature. Greenwich, CN.1 Fawcett Publishing. 27 Beck, A., Rush, A., and Shaw, B. (1979). Cognitive Therapy of Depression. New York: Guilford Press. 28 Vaillant, G. E. and Perry, J. C. (1980). Personality Disorders. In Comprehensive Textbook of Psychiatry, H. I. Kaplan, A. M. Freedman, and Sadock, B. J. (Eds.). Baltimore, MD: Williams and Wilkins. 29 Beck, A., Rush, A., and Shaw, B. (1979). Cognitive Therapy of Depression. New York: Guilford Press. 30 Torre, C. (1995). Chaos in the triadic theory of psychological competence in the academic setting. In Chaos Theory in Psychology, F. D. Abraham and A. R. Gilgen (Eds). Westport, CN: Prager. 31 Carlson-Sabelli, L. and Sabelli, H. (1996) Promoting creativity in action, while having fun. An experiential exercise. Proc. International Systems Society. 40th meeting, Edited by M. L. W. Hall, pp 177-188

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Marxism opposed dialectics to logic, while Western academia has largely ignored dialectics. In philosophy, materialism was opposed to idealism, and static views to dynamic ones. Structuralism pretends that only one perspective dominates scientific discourse at each time. The American philosopher of science Thomas S. Kuhn describes the history of science as a succession of paradigms in which winner takes all (as in the American electoral system).32 Actually, diverging paradigms coexist in the scientific process.33 Science advances through the interaction of multiple views. Diversity promotes, and consensus delays, scientific progress. Goldstein's "difference questioning" seeks non-consensus by highlighting differences in attitude and perception to foster new ideas.34 False ideas contribute to social and personal pathology. Generalization and black and white thinking foster not only personal depression, but also social depression and war. The implications of inevitability implicit in both determinism and chance render feedback inoperative, and serve to justify inhuman policies. Progress requires bipolar feedback, including the recognition of what is wrong, just as medicine hinges on recognizing symptoms. When Dr. Pangloss reassures us that we live in the best of all possible worlds, what is he condoning? Thus social and psychological analysis can contribute to science by critical appraisal of assumptions, methods, and lines of reasoning. Conversely, science can contribute to human processes by investigating and highlighting creative rather than destructive patterns of thinking.

32 Kuhn rightly perceived that there is a sociological component to what is accepted as scientific truth, and that most scientists are not interested in foundations, but his description of science and scientists is farfetched. Kuhn described "typical scientists" as conservative individuals who accept the existing paradigm, and defend it until the evidence against them becomes overwhelming. In rare moments, the refutation of a major theory brings about a scientific revolution in which an older paradigm is replaced by a new one. The new paradigm does not build on the preceding one; it supplants it. It is "not only incompatible but actually incommensurable with that which has gone before." This is not so. Science develops though interactions of multiple systems and persons. Einstein did not "refute" Newton, but built upon his theory. Scientists are often competitive individuals who continually proclaim their findings as revolutionary new paradigms, particularly after Kuhn popularized the term. In any case, science is driven by the desire of discovering something new, not by the curiosity of individuals who want to learn the truth -you can learn much more in fifteen minutes on the Internet than in one year in your laboratory. 33 Sabelli, H. (1989). Union ofOpposites. Lawrenceville, VA: Brunswick. 34 Goldstein, J. (1994). The Unshackled Organization: Facing the Challenge of Unpredictability through Spontaneous Reorganization.

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Kurt Godel (1906-1978), Austrian-American mathematician.

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Imre Lakatos (1922-1974) Hungarian mathematician and philosopher.

In simple terms, either-or thinking (logic), more-or-less thinking (quantitative) and both-and thinking (complementarity) represent three attitudes that psychotherapists recognize as having significantly different consequences regarding both personal behavior and understanding. It seems likely that these three ways of thinking will also have different implications in scientific reasoning. There is thus reason to go beyond two-valued logic and linear probabilistic and fuzzy logics. Mathematical dynamics35 offers the possibility of developing a scientific logic for bothand thinking. 18.3 Self-Reference, Conservation, and Partial Contradiction Logical self-reference is feedback and therefore it produces change. In a static framework, self-reference generates paradoxes such as Epimenides ("I am lying"). In a timeless logical symbolism, A = -A. We must instead consider reasoning as a process, and therefore replace timeless logic by recursions such as those of mathematical dynamics. The paradox disappears as soon as we introduce time: At+i = - At. We are left with a 35

Grim, P., Mar, G., and St. Denis, P. (1998). The Philosophical Computer. Cambridge, MA: MIT Press; Goldstein, J . (2001) Mathematics of Philosophy or Philosophy of Mathematics? Nonlinear Dynamics, Psychology and Life Sciences 5: 197-204.

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simple period 2, which is ubiquitous in nature (Chapter 9). The liar paradox and Russell's paradox are simple oscillations. Long before, dialectics described this logical period 2 in its law of the negation of the negation. We may expand these views by considering period 2N, aperiodicities such as chaos or bios, and bipolar feedback. It is also useful (and respectful of scientific priorities) to integrate dynamic models in the historical contexts of process theories and dialectic logic. In extensional logic, A and B is the set of properties common to A and B, while A or B is the set of properties displayed by one or the other, but there is no function corresponding to properties displayed by their combination, as necessary for a logic of creative processes. How is this to be accomplished? When Bohr affirmed that "contraries are complementary ", he added "The opposite of a great truth is another great truth." This provides a rule for creative reasoning. Thus dialectics may be incorporated into the scientific method as a heuristic.36 An effective way to develop a new hypothesis is to oppose an accepted truth to get a better one. This is possible because every truth is only an approximation, and therefore there is a sense in which it is wrong. Think how the opposite of what is obvious, evident, accepted, could be true. Systematically consider the opposite of each assumption, belief, and hypothesis as a hypothesis to be tested. This is a guideline for which there is no mechanical performance. To conceive meaningful alternatives requires imagination. The opposition must be partial, as undoubtedly what we accept up to now as true probably incorporates a great deal of truth. To oppose what is obviously false is not very creative. Given the similarity of opposites, the direct opposite of a false idea often is false. In the same manner, the opposite of a great lie often is another great lie, the opposite of terror often is terror, and the opposite of evil often is evil. Watching Montague and Capulet wage war, we may well cry "A plague o' both your houses." To create, it is often necessary to go beyond existing opposites. The goal is not to conciliate or integrate opposites but to create new alternatives. 36

1 use dialectics as a heuristic and as guideline for developing methods, while Marx regarded it as a method of presentation applicable only after a science has been developed. [Meikle, S. Dialectic Contradiction and Necessity, in Issues in Marxist Philosophy. I: 5-33, 1979. edited by J. Mepham and D. Ruben. Harvester Press. Sussex, England.]

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Seeking the synthesis of opposites or the middle ground between them seldom generates new ideas or new movements. Change and conservation are both needed for creation, as illustrated for the mathematical generation of bios (Chapter 8) - hence the historical method for theory development (Chapter 2). Continuity is necessary. A biotic pattern requires continuity (a conservation term in the recursion). A person may be asked to change, and he may change much, but within continuity. To lose one's identity is like committing suicide. Persons as well as groups normally wish to maintain their belief systems and their loyalty to family, country and church. The same occurs with nations.37 To maintain continuity within change is the only manner to change and evolve. As "clinical philosophers", we do not offer Rogerian unconditional psychotherapeutic support nor psychoanalytic critical analysis, but partial contradiction.38 Pure confrontation increases resistance. Nor can we simply agree with our patient, because without a modicum of challenge there can be no change. It is necessary to offer a limited challenge, while being on the main supportive. To cross a river, one must swim diagonally across the current. Partial contradiction also describes fundamental oppositions in nature, and should be useful in social action. The notion of partial contradiction applies also in science. Scientific theories are forever confronted by "an ocean of counterexamples". Lakatos39 showed how mathematicians develop a theorem by incorporating refutations into the original conjecture. We do not prove the truth of a hypothesis by refuting its opposite, but we expand the truth of a hypothesis by incorporating into it its refutations. Creation thus results from implications, refutations, and the overcoming of refutations, a bipolar feedback. These process concepts stand in sharp contradiction with Kuhn's structuralist view of scientific evolution. 18.4 Priority of the Objective, Supremacy of the Subjective40 37

U n a m u n o , M . de. (1913). Del Sentiment Trdgico de la Vida. N e w York: Las Americas Press. Sabelli, H. and Carlson-Sabelli, L. (1989). Biological Priority and Psychological Supremacy, a N e w Integrative Paradigm Derived from Process Theory. American J. of Psychiatry 146: 1541-1551. 39 Lakatos, I. (1976). Proofs and Refutations. Eds. J. Worrall and E. Zahar. Cambridge University Press. 40 Carlson-Sabelli, L. and Sabelli, H . C. (1984). Reality, Perception and the Role Reversal. J. Group Psychotherapy Psychodrama and Sociometry 36:162-174. 38

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Integration requires examining all the relevant levels of organization, including the scientist and the social milieu.41 Consider how the complex may be reduced to simple components, and what complex processes reveal about its simple origins (complexity inference, Chapter 2). Logic is often conceived as a purely formal discipline. The idea is that all other sciences can in principle be reduced to physics, physics can be reduced to mathematics, and mathematics to logic. This last step was blocked by Godel's theorem.42 Creative evolution is of course incompatible with reduction. Congruently, logic must include mathematical developments, continually evolving to give rigor to ever developing intuitions generated by the natural and human sciences (see 17.4). On the contrary, logicians disregard natural intuitions to attain rigor (e.g. the reformulation of logical axioms discussed in Section 2.4). As the science of reasoning, logic must adhere to physical and neurophysiological reality. Logicians dismiss attempts to base logic on actual physiological and psychological processes as "psychologism".43 Physicists may be equally reluctant to submit the scientific method to the "softer" sciences, but both relativity and quantum mechanics highlight the role of the observer. As discussed by Piaget,44 there is no epistemology worth its name that does not include neurophysiology and psychology. There is only one scientific epistemology, one that is experimental, biological, sociological and psychological; in our times, a purely philosophical epistemology is stamp collecting. The role of the 41 As discussed in Chapter 1, we should take each idea to its ultimate consequence. Science began when the rational and practical approach to everyday activities was expanded to a systematic description of reality. Throughout history, this repeatedly conflicted with dominant beliefs -often including those of the scientist. Nor surprisingly, many wish to restrict the realm of science to nature, leaving room for dominant political and religious ideologies. Scientific thinking is currently dominated by an ideology, sometimes called positivism or empiricism, which as a matter of principle refuses to consider the meaning of physical experiments and theories. It considers taking scientific ideas seriously, to their ultimate consequences, as "metaphysics". "Grand principles" are summarily and strongly rejected. In my view, being unprincipled does not fare better in science than in life. Principles cannot entirely account for historically concrete processes but they do initiate them. 42 Godel proved that any logical system that is at least complex enough to include arithmetic contains true statements whose truth or falsity cannot be proved with the system by a self-referential mapping of meta-statements about arithmetic onto arithmetic statements, and arithmetic statements onto numbers. 43 Psychologism is the doctrine, which according to which propositions are thousand rules of inferences are laws of thought. Boole called his book The Laws of Thought. 44 Piaget, J. (1970). L 'epistemologie genetique. Que sais-je? Presses Universitaires de France.

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observer is not restricted to physics, nor is it restricted to kicking electrons. Even more important is the influence of ideology on theory. In particular, the interpretation of Heisenberg's thought experiment as demonstrating indeterminism is ideological rather than physical. Empirical data and mathematical measurement provide objectivity and reliability (reproducibility). Psychological, sociological, and philosophical considerations are required to provide validity. Thinking is a psychological phenomenon. Logic is also psycho-logic. Thinking also is a collective cultural process. Scientific statements are of the general form "according to method M, A is / becomes B". Given the veracity of this statement, we may conclude that A is / becomes B, or that the method M is not reliable. For instance, if a given statistical method cannot demonstrate a difference between a given set of data and a random distribution, must we regard the data as random or conclude that the method is wanting? Either conclusion may be correct, and the decision depends on other methods, other data, theory, and ideology. One should not reduce logic to set theory. We should augment mathematical logic to match the creativity and complexity of human logic - and thereby also enlarge human logic. (In the same manner, we do not analyze complex time series into simple parts that fit already described attractors, but analyze them in multidimensional frameworks to reveal their complexity.) After G6del, a science of mathematical reasoning cannot be simpler than arithmetic. Correspondingly, a mathematical science of reasoning (logic) cannot be simpler than arithmetic. To develop such logic we must attend to the entire hierarchy of levels of organization. Mathematics and physics are the roots and trunk of the tree of science but chemical, biological, social, and psychological processes represent creations of forms not contained in the physical building blocks. One must give as much importance to the treetop as to trunk and roots. What is "supramentaF is as important as what is fundamental. Creation theory must not only be radical -as Marx defined addressing root problems —but also psychological.45 Because the objective laws of nature have priority, brain, perception and reason 45

Practicing this notion, psychology is discussed here along with logic, and in Chapter 16 regarding sociology. Likewise evolution is discussed together with the social implications of the various theories of evolution.

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reflect the forms of nature (Chapter 2). We can trust the evidence of our senses and of our reason; "subjectivity" is fundamentally objective. Yet, cultural perspectives and even the specific psychodynamics of the scientist predetermine observations, reason, and methodology. Objective facts generate perceptions, but cultural and psychological processes interpret them. Subjectivity permeates physics, not only psychology. For instance, a focus on equilibrium, rest, static structures, and stable attractors represents a conservative bias. As brain is the best organ for learning developed by evolutionary processes of adaptation and selection on our planet, perception, intuition, and reasoning should be expected to provide us with a reasonably appropriate, albeit certainly not perfect, picture of the real world.45 We do not perceive space as tridimensional because the labyrinth has three orthogonal semicircular canals, but rather our ear is so constructed because space has three dimensions. We perceive time as flowing forward because actions are changes of in time. The American system scientist Larry Vandervert47 proposes that the preinferential, undebatable basic data and order for all that can be known by any creature are in the algorithms of its neurological order. Brain encapsulates the world as neurological order. As the product of evolution, brain embodies its patterns and it is thereby pre-adapted to portray reality. World, brain and mind are homologous. The organization of the universe is embodied in the central nervous system. Embodiment in the brain is thus evidence for truth. If we define truth pragmatically as biological adaptation to reality, the best criterion for truth must be the patterns of behavior selected by natural processes and embodied in brain function. As the organ of thinking selected by nature, brain must embody in its structure the general patterns (laws) of nature. If rational thinking means biological adaptation to reality (what else would be rational?), then, by examining the logic of brain, we can construct rational hypotheses regarding the logic of nature and thereby rules for logical thinking.

46 Vandervert, L. R. (1988). Systems thinking and a proposal for a neurological positivism. Systems Research, 5, 313-321. Sabelli, H. (1989). Union ofOpposites. 47 Vandervert, L. R. (1993). Neurological Positivism's Evolution of Mathematics, Journal of Mind and Behavior, 14,278.

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18.5 Creative Reason For a theory to be "scientific," it must not only agree with observed facts but must also lead to the discovery of novel ones. Only the successful theoretical prediction of novel facts -such as the return of Halley's comet or the observation of antiparticles- identifies sound scientific theory. Since Kant and Marx, Critical Reason has been regarded as essential. Scientific reason is, and must be, creative, not merely critical. While Francis Bacon, extolled as the founder of modern thinking, opposed Aristotle's logic in his Novum Organum, his physician William Harvey discovered the circulation of the blood by employing Aristotelian empiricism and deductive methods. In our times, while reductionism was criticized on good grounds, genetic reductionism made the greatest scientific advances. Critical Reason itself must be critically analyzed. Critical thinking is necessary. Information always contains misinformation. As opposites tend to become similar, we must be wary of how we oppose our enemies, to avoid becoming like them. Respond, do not react. As scientists, as professionals, our role cannot be limited to describe and criticize our social reality. Critical reasoning is necessary, but not sufficient. Being against is ineffective. It is necessary to conceive alternatives, to seize the initiative, and to promote change gently primun non noscere. I propose a medical manner of thinking. Our research group took heartbeat series as models for creative processes, and unabashedly applied the insights learned there as an alternative to current ideas in a number of fields. In this manner we found bios in many processes, and other forms of novelty. Stepping where angels dare not to tread, I extend these concepts to thinking. In so doing, I practice science from the perspective of a physician. Practicing medicine always involves dealing with issues in which our ignorance exceeds our knowledge. This makes us physicians more daring and more cautious than other professionals. In attempting to integrate multiple disciplines, I endanger making myself a fool, nay, I guarantee it, but I also practice my medicine where it is needed. We need to develop creative ways of thinking because our very survival is threatened by the empowerment of sociopathic ideas by modern technology. My errors and shortcomings in the more basic sciences should not mislead the reader to minimize the

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significance of natural creation as an alternative to equilibrium, chaos, dialectics, stochasticity, entropic decay, and quantum uncertainty. It is often said that the devil is in the details. I beg to disagree. Most often, the devil is in the overall framework. Einstein denounced our age as one in which perfection of detail methodology obscured a poverty of goals. The bitter experiences of the 20th century have made us skeptical of Utopias, yet it is not ideas that are destroying the planet. Faith cannot replace science; markets cannot replace ideas; persons should not be reduced to customers or guided like animals by shepherds. Ideas have brought us health, prosperity, and a modicum of mental health, including sexual equality, and the protection of children against abuse in the hands of parents, teachers and priests. Scientific ideas, like any others, are often wrong, but they have the advantage of being continually questioned. We need to be faithful to ideals, as we update ideas. Rationality must be scientific, creative and therapeutic. We need a new vision, a new set of ideas. The rationality of markets cannot replace ideas; ancient faiths cannot replace scientific reason. Neither of them can release us from the quagmire created by our own technological, industrial, commercial and military powers. In fact, they can make them worst. Ethnic, religious and oil wars plague us. Greed destroys the planet and human health. The bitter experiences of the 20th century have made us skeptical of scientific Utopias, but it is greed, not ideals, that is destroying our planet. Collective mental health is the most important scientific issue of our times, when our energetic and informational powers have developed faster than our emotional health. It is cogent to remember again that in the history of our own civilization, empire and the consequent invasion of the excluded nations destroyed science, technology, civilization, prosperity, and freedom of thinking for over one thousand years. History is enantiodromic, not necessarily progressive. Biotic processes are both creative and destructive. But they are also readily modifiable by small forces, such as personal actions. In our own times, rational thinking and psychological insight have improved our behavior regarding the treatment of children, women, minorities and the mentally ill. Yet science also provides destructive technology and propaganda machines. There is only one reason, but in dire conflict with itself. A reason

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that creates as well as destroys. A reason that elevates us from the animal but that also rationalizes inhumane behavior. Reason does not only oppose animality, irrationality, or superstition. It also opposes itself. We are threatened not only by the struggle between science and ignorance and superstition. We are also endangered by the war between creative solidarity and destructive selfishness. Solidarity, predicted Darwin, will win.48 Yet, in the name of Darwin, as others in the name of Jesus, Mohammed or Marx, a well-articulated ideology provides scientific rationalization to destructive greed. The cant of competition and selection of the fittest have brought more misery than enlightenment. Darwin's view of global solidarity may be too far into the future. Our world may be destroyed beforehand by the very forces of communication, commerce and science that hopefully may brings us together. We are not the first ones to face the destruction of our world. Salman Rushdie, in The Moor's Last Sigh, narrates such a story, and says: "... even if the world's beauty and love were on the edge of destruction, theirs would still be the only side to be on; defeated love would still be love, hate's victory would not make it other than it was. Better, however, to win." Even better is to create anew. A philosopher, said Machado, is a poet who believes in the reality of his own images. In our computer age, a philosopher is a mathematician who believes in the reality of his own equations. Fully aware of the difference between preliminary explorations and scientific discourse, let me state the conclusion I would like to draw from these experiments, namely that the necessary mathematical properties of action sustain a development that, albeit causal, is creative. Such universe does not emerge from, or head towards chaos and entropic disorder. It emerges from action, and heads towards an attractor of infinite complexity. We are part of this evolution, minor but conscious participants. The future is not fully determined, or unpredictable, but co-created. "Caminante, no hay caminos, los caminos se hacen al andar".49 (Antonio Machado). 48

"As man advances in civilization, and small tribes are united into larger communities, the simplest reason would tell each individual he ought to extend his social instincts and sympathies to all members of the same nation, though personally unknown to him. The point being once reached, there is only an artificial barrier to prevent his sympathies extending to the men of all nations and races." 49 Walker, there are no paths; paths are made by walking.

Subject Index

1/f pattern, 23, 118, 127, 144-151, 144-151, 188, 228, 244-252, 318, 322, 352, 353, 400, 452-465 Abundance / Scarcity, 10, 25, 74, 78, 109, 112, 497-503, 507, 78,109,112,497-503,507, 510,521,551,572 510, 521, 551, 572 Action, 43-45, 77, 524-526, 547-554 Action as biotic factor, 324 263, Action pathways, 76, 83, 263, 598, 602 Action, as social / psychotherapeutic intervention, 549, 597, 609, 625 ff Action, as theoretical principle 353-357, 348-409 Action, measurement of, 119, 126 ff, 143 Action, principle of least, 347,356 Action, psychological, 597 Age, Aging, 456, 571, 584-591 584-591 Algebraic forms (see Lattice, Group, Topology, Set, and Category), 431 Alphabet, 177, 261, 310, 372, 413, 598 413,598 Altruism, 312-313, 525, 541, 601 601 Anger and Anxiety (see also Psychogeometry), 169-174, 262-264,582,603 262-264, 582, 603

Archetype (see also Number forms, Algebraic forms, Color organization), 3-6, 12, 38-45, 72,74,85,133,257,294,313, 72, 74, 85, 133, 257, 294, 313, 317,355,372,386,412-420, 317, 355, 372, 386, 412-420, 474, 474, 528 528 ff, ff, 555, 555, 617 617 Archetypes, mathematical, 28, 40, 45,70,98,296,317,349,355, 45, 70, 98, 296, 317, 349, 355, 380, 401-406, 410, 419-425, 429,431,528,538,585 429, 431, 528, 538, 585 Archetypes, psychological, 398, 433, 605 433,605 Arithmetic thinking, 632, 638 Arithmetic, 31, 39-45, 414-418, 432 -229, 239-252, 239-252, Arrangement, 221 221-229, 265-267, 277-287, 301, 307-309, 319, 321, 336, 397, 307-309,319,321,336,397, 419, 443-446, 452-455, 531, 542, 555-560, 567-569, 608 Asymmetry (see (see also also Bias), Bias), 22, 22, Asymmetry 27, 31, 44, 53, 69-71, 77, 85, 27,31,44,53,69-71,77,85, 99-101, 112, 133-135, 139, 161, 168, 175, 259, 281, 293, 293, 310, 310, 320, 327-356, 366-376, 396-398, 430, 437, 444-446, 451, 451,460 460ff,ff, 512, 512,525,535,556, 525, 535, 556, 562,567,592,620,631 562, 567, 592, 620, 631 Asymmetry, cosmic, 45, 69, 281, 356,430,460,515 356,430,460,515 643

644

Attractor of evolution, 27, 348, 350, 380, 448, 472-476, 482 Attractor, 19, 63, 76, 82-84, 138 Attractor, telic, 398, 474 Attractor, universal / cosmic / infinite Attractor of evolution (see also God the Attractor), 19, 469 Bias (parameter of biotic equations), 5, 36, 76, 82, 105, 124, 165, 168,236,318, 124,165,168,236,318, 343-347, 443, 626, 639 Biculturation / Bilingual, 153, 166, 473, 605 Bifurcating personality, 153, 156 Bifurcation, 26, 49, 72, 88-92, 104-110, 176 Bion, 94, 538, 544 Bioperiodicity, 23, 90-95, 207 Bios Hypothesis, 102, 287, 318, 344,347 344, 347 Bios, Biotic pattern, Biotic process, 1-12, 16-28, 179, 247, 255, 260-267, 304-310, 255,260-267,304-310, 318-347, 377 ff, 430, 436,454, 459, 461, 463, 542 ff, 555-562, 567, 572, 577 ff Bios, concept of, 319-324 Bios, mathematical, 74, 87, 88-97 Bios, types of, 99-102 Bio-socio-psychological, 583 Biotic Expansion of the Universe, 271-292 Bipolar illness, 157, 170, 172, 581,597,616 581, 597, 616

Bios

Black and white thinking (see Paraconscious) Cardiac illness, 116, 193, 199, 201, 257, 582 201, Catastrophe, 49, 62, 71-73, 91, 160-170, 344, 347, 368, 376, 401, 404, 396, 401, 404, 434, 434, 550, 550, 625, 625, 628 Category, 46, 58, 61, 155, 169, 326, 382-400, 416-427, 524, 587 Causation, chance, and cause, 18, 24, 51-54, 78, 116, 119, 136, 24,51-54,78, 142, 207-212, 374-379, 556-559, 556-559,567-571,462, 567-571, 462, 484-486, 604 Certainty, 31, 52, 60, 122, 353, 413-416, 444, 471, 549, 576, 628 Chaos theory, 66, 75, 89, 92, 105, 152, 198, 198,204,238,246,319, 204, 238, 246, 319, 333-337, 340, 541, 543, 552, 557 Choice (see also Sociodynamic test, Sociometry), 2, 154, 160-163, 577 577 160-163, Class / classism, 10, 28, 57, 65, 70, 169, 322, 361, 386, 392, 70,169, 406, 472, 509-512, 574-579, 584-587, 592-596, 607, 618 Class, logical, 360 Class, social, 605 Climate, 129, 138, 189, 239, 248, 292, 323, 390, 422, 476, 491, 292,323,390,422,476,491, 504, 507, 539, 541 ff, 612

Subject Index

Clinical Philosophy, 11, 17, 34, 11,17, 394,579,581,592-596, 394, 579, 581, 592-596, 604-609, 618, 620, 640 71, Co-creation, 12, 17, 48, 56, 71, 160-166, 191, 191,313,482,487, 313, 482,487, 491,495,520 491, 495, 520 Co-creation, as social / psychotherapeutic intervention, 581,587-607,613,618-620 581, 587-607, 613, 618-620 Co-creation, as theoretical principle, 323, 347, 357, 365-379, 403, 406 Color organization, 86, 381, 385, 385, 432, 632 Common sense, 35, 43, 46, 56-58, 389, 602, 622, 628-631 389,602,622,628-631 Competition, 17, 73, 163, 361, 361, 379, 401, 406, 434, 488, 489, 379,401,406,434,488,489, 494-502, 506-509, 524, 546, 573, 582, 593, 598, 601, 607, 607, 614,642 614, 642 Complement plot, 3, 83, 114, 190-195, 253-257, 266, 321, 321, 377 Complementary, 45-47, 54, 60, 67, 71, 78, 86, 133,153,171, 133, 153, 171, 67,71,78,86, 176, 189-195, 189-195,205,316,328, 205, 316, 328, 344, 359, 489, 600, 624, 627-630, 635 Complexes, 118, 118,214,541 214, 541 Complexification, 18, 18,21,439, 21,439, 538, 539, 540 Complexity (see also Supremacy of the complex), 5-13, 21, 26, 26, 28,114-119, 28, 114-119, 125, 130-133, 144, 160-176,220-252,314-317, 160-176, 220-252, 314-317,

645

339, 347, 364-403, 429, 438, 440, 448 ff, 524-538 Complexity, nonrandom (see Arrangement) Confirmation, Confirmation, 628, 628, 630 630 Conservation as biotic factor, 333 Conservation as intervention, 619 Conservation, 24, 79, 143, 336, 345, 347, 430, 439, 489, 510, 345,347,430,439,489,510, 527, 538, 581, 634 527,538,581,634 Conserved term, 77, 106, 180, 333-336 Contiguity, 188, 277, 336 Contradiction (see also Logic), 42, 50, 57, 155, 168, 176, 357 ff, 406, 419, 435, 442, 587, 600, 625-636 Contradiction, Local principle of no contradiction, 58 Contradiction, partial, 164, 636 Cooperation, 10, 110, 221, 313, 358,362,502,508,512,527, 358, 362, 502, 508, 512, 527, 539,594,601,612 539, 594, 601, 612 Co-recurrent, 127 Correlation, 22, 95, 97, 119, 127, 136-143, 150, 171, 199-206, 236, 240, 259, 262, 274, 308, 321, 359, 387, 397, 404, 559, 321, 562,628 562, 628 Cosmic Background Radiation, 292-303, 320, 452, 467, 468 Creation theory (see Action, Opposition, Co-creation, Priority, Supremacy, Numerical archetypes, Algebraic archetypes), 348-409

646

Creation, mathematical model 350, 410-436 Creation, random model 297, 350 Creation, supernatural model 303, 350 Creative, 7-10 Creativity (Psychological), 156, 585, 603, 609 585,603, Crime, 65, 75, 169, 171, 239, 253, 263, 394, 525, 596, 601, 605 605 Cultural conserve, 590, 620 Cyclic engine, 63, 84, 367-369, 398, 490, 523, 547 Darwinism, 45-54, 64, 313, 402, 471, 488, 498-518, 530, 471,488,498-518,530, 539-543, 642 Data transformation, 118-128 Decay, 9, 22-29, 36, 49, 55, 57, 69, 81, 95-98, 145, 271, 287, 69,81,95-98,145,271,287, 321, 358, 367, 389, 402-406, 437-448, 458, 463, 465, 470, 472,478,501,503,533,538, 472, 478, 501, 503, 533, 538, 552,580,588-590,599,631, 552, 580, 588-590, 599, 631, 641 Definition, 17-22, 114, 118, 129, 171, 175, 191, 191,209,221-224, 209, 221-224, 230-240, 250, 321, 354, 370, 373, 434, 441-449, 555, 626, 629 Depression (see also Bipolar illness), 75, 157, 169-174, 239, 253, 255, 263, 265, 359,385, 359, 385, 395, 574, 579, 597, 602, 632 Determinism, 10, 14, 17, 24, 26, 35,47,51,119,124,143,212, 35, 47, 51,119, 124, 143, 212, 230, 242, 244, 251, 277, 277, 280, 280,

Bios

286, 288, 296, 321, 324, 353, 363, 403-408, 426, 484,490, 533,547,555, 533, 547, 555, 580, 597, 603, 616, 623, 630, 633 Detrended fluctuation analysis, 126 Development, 1, 9-15, 21-25, 34, 46,54,62,65,71,76,83,87, 46, 54, 62, 65, 71, 76, 83, 87, 98, 98, 103-115, 103-115, 125, 125, 155, 155, 167, 167, 223, 223, 295, 303, 303,312-316, 312-316, 321, 325, 327, 334-339, 345, 349, 369, 390, 395, 403, 414, 421-434, 461-464,470,475,493,501, 461-464, 470, 475, 493,501, 510,515-517,531-538, 510, 515-517, 531-538, 548-552, 576, 581, 585-605, 613, 618-623, 636, 642 Development, creative, 17, 71, 76, 82, 82,120,157,403,426,431, 120, 157, 403,426, 431, 488, 524, 532 Development, economic, social, 404, 581, 605 404,581,605 Development, mathematical, 72, 76,95, 76, 95, 110-113, 110-113,413,427, 413, 427, 637 Development, psychological, 76, 83, 403, 410, 423-426, 587 Dialectics, 6, 28, 36, 45, 55-58, 64-66, 191, 206, 347, 357-361, 64-66,191,206,347,357-361, 368, 386, 393, 406, 443, 491, 512,588,599,614,623-635, 512, 588, 599, 614, 623-635, 641 Diamond of Opposites (see Phase Plane of Opposites) Differentiation, 25, 72, 124, 223, 420, 585, 588 Diffusion, biotic, 102

Subject Index

Diffusion, local, global, 129, 132, 260, 282-287, 542 Dimensiogenesis, 21, 28, 28, 231-237,242,348,350, 231-237, 242, 348, 350, 385-388,401,406,434,528 385-388, 401, 406, 434, 528 Dimensions (see also Complexity, Simplicity), 20, 28,49, 53, 61, 61, 67-71,87, 116-120, 131, 151, 151, 198, 208-212, 222, 230-252, 263, 280, 338, 344, 347-417, 431-436,442,448,458,529, 559, 567, 567,588,623-632, 588, 623-632, 639 Discrete / Continuous, 44, 77, 107, 115, 119, 124, 188,209, 241,310-316,325,351,355, 241, 310-316, 325, 351, 355, 358,371,385,429,510 358, 371, 385, 429, 510 Distinction, 18, 43, 58, 61, 168, 174-176,251,357,362,366, 174-176, 251, 357, 362, 366, 381,384,408,452,587,596, 381, 384, 408, 452, 587, 596, 607,611,627,630 607, 611, 627, 630 Divergence (see Infinitation) Infinitation) Diversification, local, global, 130-132, 256, 260, 282-287, 302,306,541,556,563 302, 306, 541, 556, 563 Drama of Privatization, 546 Dynamics, 59 Education, 47, 165, 169, 312, 337, 383, 387, 447, 477-479, 505SOS508, 536, 591, 593, 604-662 SOS, Electrocardiogram (see also Heart Rate Variation), 116, 118, 146, 190, 215, 225, 225,253-255, 253-255, 263 Electroencephalogram, 130, 147, 150, 189, 189,226,266,269 226, 266, 269 Electropsychocardiography, 215, 253, 263, 263,582 582

647

Embedding methods, 237, 543 Embedding, choice, of, 238, 249 Embedding, Embedding plots, 21, 115-120, 126-134, 146, 148, 208-212, 227-259, 227-259, 265-270, 265-270, 208-212, 277-290, 298-309, 320, 448, 456, 541-544, 556-560, 566-569,608 566-569, 608 Empire, 56, 59, 63, 321, 347, 388, 394, 498, 509, 511, 593, 596, 394,498,509,511,593,596, 641 Enantiodromia, 17, 27, 48, 55, 85, 321, 344, 359, 404, 406, 437, 321,344,359,404,406,437, 464-466, 533, 588, 590 Energy, psychic 158 Entanglement, 60, 143, 357, 363 Entropy (see Thermodynamics) Environment, 5, 8, 50, 67, 79, 82, 174, 254, 312, 321, 365, 369, 426, 439, 447, 453, 461-467, 476,491,500-503,511,534, 476, 491, 500-503, 511, 534, 539-550, 582, 603-606, 611-614 Episodic patterning, 18, 22, 109, 118, 125, 214, 218, 220, 253, 125,214,218,220,253, 277,298,321,336,590 277,298,321,336,590 Epistemology, 39, 423, 625, 637 Equations, arithmetic, 84-87 Equations, biotic, 34, 83, 87, 98, 168, 181, 184, 336-338, 620 168,181,184,336-338,620 Equations, difference, 45, 322 ff Equations, diversifying, 87, 93-95, 326 Equations, logistic, 73, 105-110, 133-137, 147, 181-184, 248, 336,369,411, 455, 572 336,369,411,455,572

648

Equations, logistic, bipolar, 110 Equations, process, 74, 82-101, 107-111, 123, 132-147, 107-111,123,132-147, 179-184, 193-196, 202-207, 226, 243-247, 255, 260, 296, 316,322-349,363,368,377, 316, 322-349, 363, 368, 377, 430,436,451-557,577 430, 436, 451-557, 577 Equilibria, punctuated, 490 Equilibrium / Point attractor / Steady action / Steady state, 9, 19, 27, 29,44, 88-101, 106, 19,27,29,44,88-101,106, 111, 426, 437, 441-448, 452, 111,426,437,441-448,452, 455, 459-466, 490, 522, 535, 597,601 597, 601 Equilibrium, economic models 552 ff, 562, 572-576 Evolution, cosmological, 26, 62, 296-297,321,369,444,461, 296-297, 321, 369, 444, 461, 465 Evolution, creative, 42, 62, 103, 233,271-275,313,431,470, 233, 271-275, 313, 431, 470, 637 Evolution, genetic theory 313 Expansion, 19, 53, 102, 108, 129, 152, 271-277, 282, 287, 297, 321,333-336,345,347,443, 321, 333-336, 345, 347, 443, 452, 455, 458, 463, 468, 563, 565, 577 Expectations, 507, 554, 577, 589, 612 Factor analysis, 119, 171, 262 262 False (see Truth) Falsification (see Refutation) Refutation) Family, 24, 155, 157, 165, 165,319, 319, 360, 380, 400, 473, 479, 485,

Bios

523, 583-590, 601, 607, 616-620, 636 Family, therapy, 584, 605, 619 Feedback, 27, 35, 67, 79-82, 87, 99, 106-116, 147, 181, 213, 260, 99,106-116,147,181,213,260, 315-348,398,426-433, 315-348, 398, 426-433, 496-502,518,530,538,546, 496-502, 518, 530, 538, 546, 586,589,601,606 586, 589, 601, 606 Feedback, biotic, 16, 68, 73, 323, 324, 346, 389, 394, 488, 490, 505,517,536,595,614,620 505, 517, 536, 595, 614, 620 Feedback, bipolar, 1, 6-10, 23-25, 39, 48, 57, 74, 80, 88, 98, 100, 108-112,144,157,168,188, 108-112, 144, 157, 168, 188, 196,214-226,253,311, 196, 214-226, 253, 311, 319-337, 343, 344, 360-380, 394,404-411,419,429,459, 404-411, 419, 429, 459, 394, 485-491,501-512,521-528, 485-491, 501-512, 521-528, 547,551,563,572-588, 593-598, 607-615, 633-636 Feedback, creative, 29, 338, 394, 491 Feedback, harmonic, 297 Feedback, mutual, 79, 338-342, 358, 378, 436, 489, 491, 491, 504, 504, 520-524, 581-596, 603-605, 614 Feedback, unipolar, 74, 181, 336, 430, 572 Fibonacci series, 38, 85, 92, 433 Fitness, biological, 312, 500, 527, 529, 529, 537, 537, 542 542 Flux, 1, 6, 17, 51-54, 75, 120, 127, 129, 303, 320, 351 35 Iff, ff, 389, 396-398, 410-412, 419, 427 ff, 437,444,460, 437, 444, 460, 462, 467, 524

Subject Index

Fractal, 9, 16, 21, 28, 39, 47, 63, 103,115,117,131,145,176, 103, 115, 117, 131, 145, 176, 234-237,241,273-275,291, 234-237, 241, 273-275, 291, 319-324,338,361,366,374, 319-324, 338, 361, 366, 374, 387,396,401,411,432,440, 387, 396, 401, 411, 432, 440, 490, 529, 530, 533, 555, 558 Gaia, 24, 27, 545 Galaxies, 1, 271-292, 297, 303, 344, 427,453, 459 344,427,453, Gene, 9, 20, 22, 39, 66, 222, 304308,311-317,373,385,395, 308, 311-317, 373, 385, 395, 411,430,489,492,505,507, 411, 430, 489, 492, 505, 507, 512,521,526-531,543,606 512, 521, 526-531, 543, 606 Generation, 586-590, 636 Generator, 7, 21, 38, 71, 82-85, 98, 105, 109, 181, 185, 207, 98,105,109, 181,185,207, 232,251,315,318,325,337, 232, 251, 315, 318, 325, 337, 347, 395, 398, 404, 427-431, 347,395,398,404,427-431, 468, 476 Generic, 38, 397 Global sensitivity to initial conditions, 23, 95 God the Attractor, 472 26, 37, 60, 167, 221, God, 12, 12,26,37,60,167,221, 273, 303, 400-406, 470-486, 497,515,572, 595, 605, 620 497, 515,572,595, Group, 411, 420 ff Harmonic feedback, harmonic reiterations, harmonic recursions, harmonic opposition (see Trigonometric model of opposites) Harmonic, 25, 73, 81, 83, 87, 144, 159,186,193,294,297,316, 159, 186, 193, 294, 297, 316, 318,322,357,362,406,432, 503

649

Harmony, 28, 40, 45-49, 74, 107, 153, 156, 361, 379, 404, 501, 594, 597, 601, 627 Health, 172, 264, 615 Heart Rate Variation, 75, 93, 116, 126, 144, 195, 248, 253, 255 Helicoids, 34, 624, 630 Hierarchies, 28, 38, 103, 391-395, 502, 524, 585, 595 Homeobios, 260, 547 Homeostasis, 17, 23, 76, 99-103, 116, 129, 147, 151, 170, 260, 116,129, 147,151,170,260, 265, 338, 347, 388, 403, 403,467, 467, 546, 587 Homology, 87, 122, 369, 385, 417, 421-425, 639 Hurst exponent, 20, 133, 256, 321, 539,559 539, 559 Idea (see Archetype) Identity, 77, 86, 137, 165, 167, 374, 381, 466,481, 516, 374,381,466,481,516, 624-636 Ideology, 17, 22, 24, 36, 61, 65, 109, 230, 361, 406, 481, 505, 109,230,361,406,481,505, 508, 515, 523, 548, 550, 552, 508,515,523,548,550,552, 590, 599, 625, 633, 637, 642 Infant mortality, 552, 584, 589 Inference, 31, 37, 41, 559, 624, 629 Infinitation, 89-97, 325-337, 343-347, 419, 431-436, 343-347,419,431-436, 454-459,490 454-459, 490 Infinite, 10, 414-419, 435, 474 Information, 8, 16, 20, 26, 41, 78, 119, 124, 152-155, 161-164, 119,124, 174-178,191,213,231,235, 174-178, 191,213,231,235,

650

241, 311, 316, 326, 329, 332, 241,311,316,326,329,332, 343-347, 348-379, 410, 424-436, 440, 445 ff, 461-467, 516,525 516, 525 Irreversibility, 18, 23, 29, 95-97, 152, 439, 443-446, 462, 490 Isometry (see Recurrence) Isometry histograms, 213, 571 Lattice, 9, 26,42-46, 70, 78, 84, 99, 119, 218, 261, 356, 381, 99,119,218,261,356,381, 383, 393, 397, 403, 410, 420-431, 446, 527, 535, 420-431,446,527,535, 585,628 Leap (see Infinitation) Infinitation) Levels of Organization, 36, 349, 364, 390 ff Linear personality, 156 Literature, 246, 608 Logic (see also Identity, Negation, Contradiction, Dialectic, Biotic logic), 11, 28, 32, 34, 41,45-49, 55-60, 65-70, 77, 84, 86, 154, 176, 233,357-365, 386, 233, 357-365, 381, 386, 399,406,413-421,425,432, 399, 406, 413-421, 425, 432, 435, 534, 621-640 Logic, biotic, 624, 629 Logon, 73, 106-113 Love, Self-love, 10, 54, 153, 158, 254, 361, 390, 408, 487, 497, 509, 592, 597-601, 642 Lyapunov exponent, 21, 131, 152, 21,131,152, 238,542 238, 542 Mandala, 2-4, 18, 114,190-195, 114, 190-195, 253,257,372, 430 253, 257, 372, Mania (see also Bipolar illness), 157,359,395, 157, 359,395, 597

Bios

Marxism, 36, 47-52, 64, 76, 403, 406, 510, 515-518, 552, 580, 599, 622-642 Material hypothesis of evolution, 490 Materialization, 49, 348, 370, 402, 461, 527 461,527 Median Embedding Dimension, (M.E.D.), 227, 248, 265, 560 Misinformation, 177,365,623,640 Modules, 371,373, 371, 373, 585 Monism, 42-45, 50, 263, 372, 404, 590 Nation / nationality / ethnicity, 55, 70, 165, 321, 347, 388, 394, 479, 552, 572, 587, 592-596, 610, 624, 636, 641 Negation (see Distinction, Logic), 175, 368, 406, 491, 624, 629, 635 Nonstationarity (see Stationarity) Novelty, 1, 5-10, 16-24, 118-120, 125-130, 144, 247-253, 277, 284, 298, 306, 318-321, 336, 284,298,306,318-321,336, 351 ff, 420, 436, 490, 539, 540, 555-559, 563-571, 588 Number / Formal numbers, Number archetypes, Numerical laws, 98, 396 ff, 433 Nursing, 155, 215, 253, 263, 581, 609-618 Objective (see Priority of the objective), 13, 28, 56, 75, 124, 129,310,352, 375, 382, 386, 129,310,352,375,382,386, 406, 413-416, 432, 475, 522, 607, 614, 620, 639

Subject Index

Observation / observer, 55, 61, 61, 111,118, 129, 137, 175, 182, 111,118,129,137,175,182, 206, 210, 219, 225, 274, 274,296, 296, 347, 352, 420, 440, 472, 496, 502,527,540,631,637,640 502, 527, 540, 631, 637, 640 Oil, 565, 573 Opposites, co-creative, 45, 154 Opposition, 3, 9, 18, 28, 39, 45-49,54,67,78,98,272,313, 45-49, 54, 67, 78, 98, 272, 313, 357-374,381-388,411,420, 357-374, 381-388, 411, 420, 427 ff, 437, 460, 500 Opposition, as biotic factor, 327 Opposition, as Information 357 Opposition, as social / psychotherapeutic intervention, 585, 599, 627 ff Opposition, as theoretical principle 357-370 Opposition, measurement of (see Phase Plane of Opposites, Trigonometric analysis of opposites) Order / Organization 18, 356 Parabios, 100, 168, 318, 320, 557 ff, 569 Paraconscious, 385, 631-633 Partial contradiction, 164, 636 Period 2 Chaos, 88, 92, 105, 137, 139, 143,182, 143, 182, 205-207, 226, 249 Period 3, 74, 87, 92, 94, 99, 106-108, 334, 336, 369, 627 Period 4, 74, 89-94, 98, 108-111, 333, 336,377 333,336,377 Period 6, 85-87, 92, 98, 102, 381 Personalization, 11, 11,17, 17, 394, 579,

651

581, 586, 592, 595, 604-607, 581,586,592,595,604-607, 618 Phase Plane of Opposites, 119, 152-168, 377, 404, 613, 620 Pink Noise (see 1/f pattern) Pollution, 18, 547-550, 580 Power law, 529, 538 Power spectrum analysis (see also 1/f pattern), 66, 116, 127, 144-151,293, 144-151, 293, 302, 302, 538, 538, 556 556 ffff Predation, 10, 476, 488, 499, 503, 511, 517-523, 528, 574 511,517-523,528,574 Prime number, 145, 147, 400 Priority of consumption, 573 Priority of the objective, 28, 39, 56, 62, 124, 129, 159, 160-175, 255, 263, 310, 375, 382, 393, 406,414-417, 406, 414-417, 505, 597, 615, 636 Priority of the simple, 10, 27-29, 35, 39, 68, 133, 158, 234, 265, 348, 353, 389, 394, 404, 476, 488, 490, 513, 524, 535, 538, 545 Priority, 8, 25, 28, 33, 39, 51, 61, 231,255,310,323, 67, 77, 223, 231, 255, 310, 323, 368,392,398,400,406,441, 368, 392, 398, 400, 406, 441, 514,534, 465, 489, 514, 534, 537, 539, 551,573,577,581-595,613, 551, 573, 577, 581-595, 613, 630, 634, 639 Priority, biological, 10, 12, 34, 39, 42, 88, 170, 348, 389, 393, 581-583, 590, 600, 616, 636 Priority, female, 394, 591, 595 Priority, mathematical, 66, 393, 414, 621

652

1,116, Process analysis, 1, 116, 253 Process entropy, 309, 310, 448, 449, 452 Process method, 36, 75, 114-253, 263, 296, 394, 431, 555, 555, 592, 592, 596 Process statistics, 43, 114, 127, 129, 397 Process theory (see also Creation theory), 12, 66, 73, 74,75, 99-101, 193, 225, 228,253, 99-101,193,225,228,253, 261, 263, 272, 296, 327, 340, 348, 349, 351, 427, 431, 581, 348,349,351,427,431,581, 604,618 Process, stochastic, 18, 21, 24, 24, 103, 120, 124, 138, 142, 212, 232, 274, 286, 309, 315-324, 232,274,286,309,315-324, 370 Psychodrama, 66, 114, 155, 160-164, 389, 587, 604, 609, 618-620, 636 618-620,636 12, 17, 52, 239, Psychodynamics, 12,17, 254, 266, 394, 581, 595-597, 602, 622, 639 Psychogeometry, 114, 169-173 Psychological energy, 370, 596, 597, 598, 600, 602 Quanta, 41, 44, 55, 151, 354, 385 Quantity and quality, 28, 40, 77, 326, 338, 355-361, 367, 370, 385-389, 398, 406, 439,445, 603,606,623,631 603, 606, 623,631 Quantum conjugation, 52, 356 Quaternity, 2, 6, 10, 48, 54, 74, 93, 108, 122, 146, 157, 167, 174, 184, 186, 198, 220, 264,

Bios

275, 277, 310, 348, 355, 365, 365, 377-379, 384, 396, 399, 415, 423, 441, 450, 456, 473, 479, 519,586,606,617,629,632 519, 586, 606, 617, 629, 632 Race, 48, 55, 70, 85, 391, 465, 509,515,591-595,610,622 509,515,591-595,610,622 Random walk, 19, 75, 122-152, 178-195, 208-220, 237, 244-252,286,310,337,370, 244-252, 286, 310, 337, 370, 451-455,524,559-569,578 451-455, 524, 559-569, 578 Raven paradox, 629 Reciprocity, 191, 423, 482, 601 Recurrence entropy, 240,455-458, 469 Recurrence isometry, 208, 216, 266 Recurrence similarity, 209, 211, 216, 219, 220, 226 Recurrence, 21-24, 83, 93, 106, 115-120,127, 115-120, 127, 146-149, 159, 181,208-220,225-269, 181, 208-220, 225-269, 277-292,298,299,306-310, 277-292, 298, 299, 306-310, 318-321,337,397,448, 318-321, 337, 397, 448, 455-458, 467, 540, 556-559, 566-569, 591, 608 Recurrence, consecutive, 24, 120, 146,149, 159, 160,181, 208-213, 208-213, 220, 220, 226, 226, 232, 232, 240, 240, 244,247,251,253,257,267, 244, 247, 251, 253, 257, 267, 269,291,299,306-310,337, 269, 291, 299, 306-310, 337, 397,455, 467, 540, 542, 556, 559, 567, 569, 591, 608 Recurrence, recurrence plots, 160, Reduction, 637 Refutation, 30 ff, 55-57, 65, 313, 353, 356, 415, 624, 628-633

Subject Index

Reiteration, 108,184, 333 ff, 534 Repetition, Rise and Fall, 114, 119, 174-178, 185,307 119,174-178,185,307 Return maps, 82, 153, 179, 195 Roles, 368, 373, 392, 554, 584-586, 590, 598, 605, 609, 620, 632 Sarkovskii's theorem, 49, 74, 107, 627 Scarcity (see abundance) Self-centered system, 372, 587 Set, 638 Shift (see Infinitation) Infinitation) Simplicity (see also Complexity, and Priority of the simple), 231, 449, 534 449,534 Sine climbing equation (see Process equation) Social Darwinism, 65, 498, 507, 509 Social dynamics / Sociology, 10, 31, 34, 65, 103, 114,128, 31,34,65,103, 114, 128, 153 ff, 160-164, 386, 393, 505,555,581-596,604, 618-622, 638 Sociobiology, 313, 510, 601, 622 Sociodynamic test, 160 Sociological polls, 168 Sociometry (see also Choice), 66, 114, 155, 160-163, 168, 168,389, 389, 587, 618-620, 636 587,618-620, Solidarity, 10, 158, 165, 230, 312, 394, 472,481, 501, 503, 512, 394,472,481,501,503,512, 524, 526, 544, 586, 601, 604, 642

653

Spirit, 10, 222, 229, 350, 405, 408, 420, 470-474, 508, 616, 619 Spontaneity, 22, 397, 405, 615, 619, 625 619,625 Stationarity, 8, 23, 83, 95, Stationary, 116-129, 215, 218, 237,250, 116-129,215,218,237,250, 260, 263, 273-280, 304, 311, 260,263,273-280,304,311, 320-322,453,541,547,556, 320-322,453,541,547,556, 577 Superation, 482 Superposition, 49, 60, 206, 357-365, 406, 626, 630 Supply and demand, 573-576 Supramental, 638 Supremacy (see Priority) Supremacy of production (see Priority of consumption) Supremacy of the complex (see Priority of the simple) Supremacy of the subjective (see Priority of the objective) Supremacy, male (see Priority, female) Supremacy, psychological (see Priority, biological, and Priority, mathematical) Symmetry, 9, 49, 67-71, 91, 133, 164, 164,168,327-330,344-347, 168, 327-330, 344-347, 357 ff, 367, 369, 374, 376, 380, 399, 412, 427, 437, 451 ff, 460 ff Symmetry as biotic factor, 327333, 347 333,347 Symmetry, kinetic, 330, 347

654

System, System formation, 38, 54, 222 ff, 370-378, 391-393, 461 ff, 488, 529, 531, 544-547, 583, 585-587, 595-598 Systems, biotic, 338, 344 ff, ff, Taoism, 35, 46, 49, 206, 347, 359, 361, 404-409, 465, 608, 623, 627, 630 Thermodynamics, 6, 9, 17, 22, 27, 29, 34, 44-52, 62, 69, 115- 120, 170, 174, 197, 223, 240-252, 259, 267, 277-280, 297, 309, 317, 340, 349, 351, 354, 354, 436-552, 556-562, 567, 569,581,597 569, 581, 597 Thinking, critical, creative (see also Common sense, and Clinical Philosophy), 313, 487, 622, 640 Topology, 5, 9, 42, 84, 237, 294, 303,357,371,410,420, 303, 357, 371, 410, 420, 424-428, 436, 467, 626 Tragedy of the Commons (see Drama of Privatization) Transitivity, 45, 136, 143, 281, 356

Bios

Triad, Trifurcation (see also 169,372, Period 3), 49, 87,101, 87, 101, 169, 372, 382, 386, 399, 474, 526, 617, 630, 632 Trifurcating equation, 101, 104, 336 Trigonometric analysis of opposites, 119,190-196 Trigonometric model of opposites, 59, 191, 362-365, 369 196-202 Trigonometric plots, 190, 190,196-202 Truth, false (see also Logic), 31, 37, 42-47, 55-70, 82, 177, 229, 273, 293, 320, 354-358, 363-366, 390-399, 408-418, 432, 437, 452, 470-472, 477-484, 498, 548, 575, 579, 599,605,611,615,624-639 599, 605, 611, 615, 624-639 Twoness, 27, 46-48, 99, 105, 293, 357, 399, 402, 431, 599, 617 357,399,402,431,599,617 Uncertainty, 17, 52, 177, 352-355, 416, 437, 445-447, 459, 641 Unifurcation, 91-94, 98, 108, 110, 205, 205,207, 207, 333, 334, 336

SERIES ON KNOTS AND EVERYTHING Editor-in-charge: Louis H. Kauffman (Univ. of Illinois, Chicago) The Series on Knots and Everything: is a book series polarized around the theory of knots. Volume 1 in the series is Louis H Kauffman's Knots and Physics. One purpose of this series is to continue the exploration of many of the themes indicated in Volume 1. These themes reach out beyond knot theory into physics, mathematics, logic, linguistics, philosophy, biology and practical experience. All of these outreaches have relations with knot theory when knot theory is regarded as a pivot or meeting place for apparently separate ideas. Knots act as such a pivotal place. We do not fully understand why this is so. The series represents stages in the exploration of this nexus. Details of the titles in this series to date give a picture of the enterprise. Published: Vol. 1:

Knots and Physics (3rd Edition) by L. H. Kauffman

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