Worldviews,
Science and Us Philosophy and Complexity
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editors
Carlos Gershenson Brussels Free University, Belgium
Diederik Aerts Brussels Free University, Belgium
Bruce Edmotads Manchester Metropolitan University Business School,
UK
University o f Liverpool, Ul< 11- 14 September 2005
Worldviews,I 4 d
Science and Us 5
Philosophy and Complexity
World Scientific NEW JERSEY * LONDON
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CONTENTS
Introduction Carlos Gershenson, Diederik Aerts and Bruce Edmonds
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Restricted Complexi$y, General Complexity Edgar Morin
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Complexity Science as an Aspect of the Complexity of Science Don C. Mikulecky
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On the Importance of a Certain Slowness Paul Cilliers
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Simplicity is Not Truth-Indicative Bruce Edmonds
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Can the Whole be More than the Computation of the Parts? A Reflection on Emergence Camilo Olaya
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Why Diachronically Emergent Properties Must Also Be Salient Cyrille Imbert
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On the Relativity of Recognising the Products of Emergence and the Nature of the Hierarchy of Physical Matter Kurt A . Richardson
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Truth in Complex Adaptive Systems Models should be Based on Proof by Constructive Verification David Shipworth
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Complexity as an Epistemic Revolution: Considerations on the New Science in the Context of Western Intellectual History Damian Popolo
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Metaphors and Method: Epistemological Considerations on Complexity Science Rodrigo Zeidan and Maria Fonseca
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Some Problems for an Ontology of Complexity Michael McGuire
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How to Love the Bomb - Trying to Solve the Prisoner’s Dilemma with Evolutionary Game Theory Vasco Castela
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Physical Complexity and Cognitive Evolution Peter Jedlicka
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Informational Dynamic Systems: Autonomy, Information, Function Walter Riofrio
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Grasping the Complexity of Living Systems Through Integrative Levels and Hierarchies J. M. Siqueiros and Jon Umerez
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Simulation as Formal and Generative Social Science: The Very Idea Nuno David, Jaime S i m i o Sachman and Helder Coelho
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A Compromise Between Reductionism and Non-Reductionism Eray Ozkural
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The Complexity of Information-Processing Tasks in Vision John Symons
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On the Possible Computational Power of the Human Mind Hector Zenil and Francisco Hernandez- Quiroz
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How Does Complex Mathemical Theory Arise? Phylogenetic and Cultural Origins of Algebra? Helen De Cruz
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INTRODUCTION
CARLOS GERSHENSON~,DIEDERIK AERTS~,AND BRUCE EDMONDS~ Centrum Leo Apostel, Vrije Universiteit Brussel Centre for Policy Modelling, Manchester Metropolitan University
Scientific, technological, and cultural changes have always had an impact upon philosophy. They can force a change in the way we perceive the world, reveal new kinds of phenomena to be understood and provide new ways of understanding phenomena. Complexity science, immersed in a culture of information, is having a diverse but significant impact upon philosophy’. It has highlighted classes of phenomena composed of multiply interacting parts where there may be no simple adequate analytic model, so that new ways of modelling and understanding these phenomena become necessary. In turn these new methods, based upon complex simulation, have brought new phenomena into the domain of science by making possible their formal representation. The result has been a rapid co-development of new domains and new methods that suggests one of the “paradigm” shifts described by Kuhn2. Previous ideas do not necessarily sit comfortably with the new paradigm, resulting in new ideas or new interpretations of old ideas, that is to say the “knock-on” effect is a larger evolution of our worldviews. In this book, researchers from different backgrounds join efforts to update thinking upon philosophical questions with developments in the scientific study of complex systems. The contributions are quite diverse, in the sense that they focus on a wide range of topics. However, they all share the common goal of increasing our understandings and improving our descriptions of our complex world. Of course, the background to this is that there are many that hold worldviews that are essentially untouched by complexity science. To take an example there is the view that our world only appears complex but would, if we could only understand it in the right way, be revealed as essentially simple. Whether the world is simple or complex the fact is that, as humans, there are severe limits to the complexity which we can comprehend. Thus,
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regardless of how complex the world isa, there is an inescapable tension between the relative simplicity of human cognition and the apparent (or real) complexity of the phenomena they are trying to understand. The different philosophies and approaches can, to a large extent, be seen as responses to this tension. Thus some seek to show that this tension is not feasibly soluble, which may have consequences for how we think about or manage the world we inhabit. Some seek to explain productive ways forward-how one might explain and understand the complexity we observe. Others take a step back to examine what consequences the tension itself has upon the scientific method. This volume is the fourth in a series entitled ‘Worldviews, Science and Us’ published by World Scientific. The series collects interdisciplinary articles with the global aim of stimulating new insights about the world and the place of human in this world, and also about the role science plays in the construction of new aspects of worldviews. Many chapters in this volume are derived from presentations given at the Philosophy and Complexity session of the Complexity, Science and Society conference, held in Liverpool, UK, between September llthand 14th 2005. We appreciate the work of the program committee for that session, which was able to select relevant works from all the submissions received. The program committee members were: William Bechtel, Mark Bedau, Jacques Dubucs, Bruce Edmonds, Carlos Gershenson, Francis Heylighen, Alicia Juarrero, Michael Lissack, Chris Lucas, Edgar Morin, Robert Pennock, Kurt Richardson, John Symons, Pedro Sotolongo, Jean Paul Van Bendegem, Franz Wuketits, and Roger Young. We would also like to thank Robert Geyer, Jan Bogg, and Abbie Badcock for their organizational support at the conference. Clem6nt Vidal helped in polishing the translation of Edgar Morinls chapter. Finally the speakers and participants of the session and the quality of their discussions motivated us to compile this volume. After the conference, the participants were invited to prepare a manuscript and more people were invited to contribute to the volume. An internal review process followed, where contributors reviewed other submissions. From these, the actual chapters were selected to be included in the volume. In what follows, summaries of the chapters are given. They are diverse enough to make it difficult to classify in different topic areas, so the order is simply dictated by similarity. aThis is obviously not a question that can itself be settled in a scientific way.
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From a philosophical perspective, Edgar Morin reviews the historical development of complexity, noting that the current accepted notion of complexity is restricted. Morin aims for a generalized complexity, which implies an integrative change in our way of thinking and knowing, in education and science. Don Mikulecky discusses similar issues from a scientific perspective, putting an accent on scientific modeling. Paul Cilliers notes the importance of a certain slowness in modern life, since current practices seem to promote a cult of speed, where faster is better. However, this is far from being the case, as proper adaptation requires certain slowness to maintain the integrity of a system. In a similar spirit, Bruce Edmonds refutes Occam’s razor, arguing that there is no reason to suppose that a simpler theory is more likely to be true. Emergence is discussed by several authors. Camilo Olaya reflects on the use of rule-based modeling and process thought to understand complex systems. Cyrille Imbert develops the notion of salience as a requirement for diachronically emergent properties. Kurt Richardson explores the ontological status of emergent products. David Shipworth proposes the use of proof by constructive verification to determine truth in complex adaptive systems, since a realist truth model of emergent properties is not feasible, thus favoring epistemology over ontology. Damian Popolo discusses the impact of complexity in science as an epistemic revolution, while Rodrigo Zeidan and Maria Fonseca present epistemological considerations on complexity science. Michael McGuire discusses ontological problems of complexity. Vasco Castela uses evolutionary game theory to show the importance of the role of emotions in the evolution of cooperation and social modeling. Peter Jedlicka studies the evolutionary increase of physical complexity and its relationship with cognition. Walter Riofrio proposes ‘Informational Dynamic Systems’ to study the pre-biotic world, explaining naturalistically the physical emergence of functions and information. Jeszis Sigueiros and Jon Umerez present a conceptual overview of different perspectives that were developed during the 20th century to understand biological complexity. Nuno David, Jaime S i m i o Sichman and Helder Coelho propose the use of intentional knowledge to successfully simulate social systems, as opposed to formal and empirical perspectives. Eray Ozkural uses algorithmic information theory to propose a ‘mild’ non-reductionism, with implications for philosophy of mind. John Symons questions the use of the information-processingmodel of the mind, focussing
4 on vision. Hkctor Zenil and Francisco Herna’ndez Quiroz discuss the possibility of using artificial neural network models to characterize the computational power of the human mind. Helen De Cruz argues for an active externalism as a requirement for the emergence of algebra, studying its emergence in different cultural settings.
References 1. Heylighen, F., P. Cilliers, and C. Gershenson (forthcoming 2007). “Complexity and Philosophy”. In Bogg, J. and R. Geyer (eds.) Complexity, Science and Society. Radcliffe Publishing, Oxford. 2. Kuhn, Thomas S. The Structure of Scientific Revolutions. University of Chicago Press, 2nd Ed.
RESTRICTED COMPLEXITY, GENERAL COMPLEXITY*
EDGAR MORIN CNRS Emeritus Director Centre d’Etudes Transdisciplinaires. Sociologie, Anthropologie, Histoire Ecole des Hautes Etudes en Sciences Sociales
Why has the problematic of complexity appeared so late? And why would it be justified? 1. The three principles of the rejection of complexity by
‘classical science’ Classical science rejected complexity in virtue of three fundamental explanatory principles: The principle of universal determinism, illustrated by Laplace’s Daemon, capable, thanks to his intelligence and extremely developed senses, of not only knowing all past events, but also of predicting all events in the future. The principle of reduction, that consists in knowing any composite from only the knowledge of its basic constituting elements. The principle of disjunction, that consists in isolating and separating cognitive difficulties from one another, leading to the separation between disciplines, which have become hermetic from each other. These principles led to extremely brilliant, important, and positive developments of scientific knowledge up to the point where the limits of intelligibility which they constituted became more important than their elucidations. In this scientific conception, the notion of “complexity” is absolutely rejected. On the one hand, it usually means confusion and uncertainty; *Presented at the Colloquium “Intelligence de la complexit6 : Qpist6mologieet pragmatique”, Cerisy-La-Salle, France, June 26th, 2005”. Translated from French by Carlos Gershenson
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the expression “it is complex” in fact expresses the difficulty of giving a definition or explanation. On the other hand, since the truth criterion of classical science is expressed by simple laws and concepts, complexity relates only to appearances that are superficial or illusory. Apparently, phenomena arise in a confused and dubious manner, but the mission of science is to search, behind those appearances, the hidden order that is the authentic reality of the universe. Certainly, western science is not alone in the search of the “true” reality behind appearances; for Hinduism, the world of appearances, the m&y& is illusory; and for Buddhism the samsara, the world of phenomena, is not the ultimate reality. But the true reality, in the Hindu or Buddhist worlds, is inexpressible and in extreme cases unknowable. Whereas, in classical science, behind appearances, there is the impeccable and implacable order of nature. Finally, complexity is invisible in the disciplinary division of the real. In fact, the first meaning of the word comes from the Latin complexus, which means what is woven together. The peculiarity, not of the discipline in itself, but of the discipline as it is conceived, non-communicating with the other disciplines, closed to itself, naturally disintegrates complexity. For all these reasons, it is understood why complexity was invisible or illusory, and why the term was rejected deliberately.
2. Complexity: A first breach: irreversibility However, a first breach is made within the scientific universe during the nineteenth century; complexity would appear from it de facto before starting to be recognized de jure. Complexity would make its appearance de facto with the second law of thermodynamics, which indicates that energy degrades into caloric form: this principle lies within the scope of the irreversibility of time, while until then physical laws were in principle reversible and that even in the conception of life, the fixism of species did not need time. The important point here is not only the irruption of irreversibility, thus time, but it is also the apparition of a disorder since heat is conceived as the agitation of molecules; the disordered movement of each molecule is unpredictable, except at a statistical scale where distribution laws can be determined effectively. The law of the irreversible growth of entropy has given place to multiple speculations, and beyond the study of closed systems, a first reflection about
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the universe, where the second law leads toward dispersion, uniformity, and thus towards death. This conception of the death of the universe, long ago rejected, has appeared recently in cosmology, with the discovery of black energy. This will lead to the dispersion of galaxies and would seem to announce us that the universe tends to a generalized dispersion. As the poet Eliot said: “the universe will die in a whisper” ... Thus, the arrival of disorder, dispersion, disintegration, constituted a fatal attack to the perfect, ordered, and determinist vision. And many efforts will be needed-we are not there precisely because it is against the reigning paradigm-to understand that the principle of dispersion, which appears since the birth of the universe with this incredible deflagration improperly named big bang, is combined with a contrary principle of bonding and organization which is manifested in the creation of nuclei, atoms, galaxies, stars, molecules, and life.
3. Interaction Order/Disorder/Organization
How is it that both phenomena are related? This is what I tried to show in the first volume of La Mkthode (The Method). We will need to associate the antagonist principles of order and disorder, and associate them making another principle emerge that is the one of organization. Here is in fact a complex vision, which one has refused to consider during a very long time, for one cannot conceive that disorder can be compatible with order, and that organization can be related to disorder at all, being antagonist to it. At the same time than that of the universe, the implacable order of life is altered. Lamarck introduces the idea of evolution, Darwin introduces variation and competition as motors of evolution. Post-darwinism, if it has, in certain cases, attenuated the radical character of the conflict, has brought this other antinomy of order: chance, I would say even a vice of chance. Within the neodarwinian conception, to avoid calling “creation” or “invention” the new forms of living organization such as wings, eyesone is very afraid of the word ‘Linventionlland of the word ‘kreation”---one has put chance at the prow. One can understand the rest of the fear of creation because science rejects creationism, i.e. the idea that God is a creator of living forms. But the reject of creationism finished in masking the creativity that manifests itself in the history of life and in the history of humanity. And, from the philosophical point of view, it is rather recently
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that Bergson, and then in another way, Castoriadis, put at the centre of their conception the idea of creation. In addition, in the beginning of the twentieth century, microphysics introduced a fundamental uncertainty in the universe of particles that ceases to obey the conceptions of space and time characteristic of our universe called macro-physic. How thus these two universes, that are the same, but at a different scale, are compatible? One begins today to conceive that one can pass, from the micro-physical universe to ours, since between them a certain number of quantum elements are connected, in virtue of a process called decoherence. But there remains this formidable logical and conceptual hiatus between the two physics. Finally, at a very large scale-mega-physical-Einstein’s theory discovers that space and time are related to one another, with the result that our lived and perceived reality becomes only meso-physical, situated between micro-physic reality and mega-physical reality
4. Chaos
All this made that the dogmas of classical science are reached, but de fucto: although increasingly mummified, they remain. Yet a certain number of strange terms would appear. For example, the term “catastrophe”, suggested by RenC Thom to try to make intelligible the discontinuous changes of form; then the fractalism of Mandelbrot; then the physical theories of chaos, which distinguishes itself from the rest, since today it is thought that the solar system, which seems to obey an absolutely impeccable and measurable order with the most extreme precision, considering its evolution in millions of years, is a chaotic system comprising a dynamic instability modifying for example Earth’s rotation around itself or around the Sun. A chaotic process may obey to deterministic initial states, but these cannot be know exhaustively, and the interactions developed within this process alter any prevision. Negligible variations have considerable consequences over large time scales. The word chaos, in these physics, has a very limited meaning: that of apparent disorder and unpredictability. Determinism is saved in principle, but it is inoperative since one cannot know exhaustively the initial states. We are in fact, since the original deflagration and forever, plunged in a chaotic universe.
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5. The emergence of the notion of complexity However, complexity remained always unknown in physics, in biology, in social sciences. Admittedly, after more than half a century, the word complexity irrupted, but in a domain that also remained impermeable to the human and social sciences, as well as to the natural sciences themselves. It is at the bosom of a sort of nebulous spiral of mathematicians and engineers where it emerged at about the same time, and became connected at once, in the forties and fifties, with Information Theory, Cybernetics, and General Systems Theory. Within this nebula, complexity will appear with Ashby to define the degree of variety in a given system. The word appears, but does not contaminate, since the new thinking remains pretty confined: the contributions of Von Neumann, of Von Foerster will remain completely ignored, and still remain in the disciplinary sciences closed on themselves. One can also say that Chaitin’s definition of randomness as algorithmic incompressibility becomes applicable to complexity. consequently, the terms chance, disorder, complexity tend to overlap one another and sometimes to be confused. There were breaches, but still not an opening. This would come from the Santa Fe Institute (1984) where the word will be essential to define dynamical systems with a very large number of interactions and feedbacks, inside of which processes very difficult to predict and control take pla,ce, as “complex systems”, where the classical conception was unable to be considered. Thus, the dogmas or paradigms of classical science began to be disputed. The notion of emergence appeared. In “Chance and Necessity”, Jacques Monod makes a great state of emergence, i.e. qualities and properties that appear once the organization of a living system is constituted, qualities that evidently do not exist when they are presented in isolation. This notion is taken, here and there, more and more, but as a simple constatation without being really questioned (whereas it is a conceptual bomb). It is like this that it was arrived to the complexity I call “restricted”: the word complexity is introduced in “complex systems theory”; in addition, here and there the idea of “sciences of complexity” was introduced, encompassing the fractalist conception and chaos theory. Restricted complexity spread rather recently, and after a decade in France, many barriers have been jumped. Why? Because more and more a theoretical vacuum was faced, because the ideas of chaos, fractals, disorder, and uncertainty appeared, and it was necessary at this moment that the
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word complexity would encompass them all. Only that this complexity is restricted to systems which can be considered complex because empirically they are presented in a multiplicity of interrelated processes, interdependent and retroactively associated. In fact, complexity is never questioned nor thought epistemologically. Here the epistemological cut between restricted and generalized complexities appears because I think that any system, whatever it might be, is complex by its own nature. Restricted complexity made it possible important advances in formalization, in the possibilities of modeling, which themselves favor interdisciplinary potentialities. But one still remains within the epistemology of classical science. When one searches for the “laws of complexity”, one still attaches complexity as a kind of wagon behind the truth locomotive, that which produces laws. A hybrid was formed between the principles of traditional science and the advances towards its hereafter. Actually, one avoids the fundamental problem of complexity which is epistemological, cognitive, paradigmatic. To some extent, one recognizes complexity, but by decomplexifying it. In this way, the breach is opened, then one tries to clog it: the paradigm of classical science remains, only fissured. 6. Generalized complexity
But then, what is “generalized” complexity? It requires, I repeat, an epistemological rethinking, that is to say, bearing on the organization of knowledge itself. And it is a paradigmatic problem in the sense that I have defined “paradigm”a. Since a paradigm of simplification controls classical science, by imposing a principle of reduction and a principle of disjunction to any knowledge, there should be a paradigm of complexity that would impose a principle of distinction and a principle of conjunction. In opposition to reduction, complexity requires that one tries to comprehend the relations between the whole and the parts. The knowledge of the parts is not enough, the knowledge of the whole as a whole is not enough, if one ignores its parts; one is thus brought to make a come and go in loop to gather the knowledge of the whole and its parts. Thus, the principle of reduction is substituted by a principle that conceives the relation of whole-part mutual implication. =Cf La Me‘thode
4 , Les ide‘es, p.211-238, Le Seuil, 1990
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The principle of disjunction, of separation (between objects, between disciplines, between notions, between subject and object of knowledge), should be substituted by a principle that maintains the distinction, but that tries to establish the relation. The principle of generalized determinism should be substituted by a principle that conceives a relation between order, disorder, and organization. Being of course that order does not mean only laws, but also stabilities, regularities, organizing cycles, and that disorder is not only dispersion, disintegration, it can also be blockage, collisions, irregularities. Let us now take again the word of Weaver, from a text of 1948, to which we often referred, who said: the XIXth century was the century of disorganized complexity and the X X t h century must be that of organized complexity. When he said “disorganized complexity”, he thought of the irruption of the second law of thermodynamics and its consequences. Organized complexity means to our eyes that systems are themselves complex because their organization supposes, comprises, or produces complexity. Consequently, a major problem is the relation, inseparable (shown in La Me‘thode 1) , between disorganized complexity and organized complexity. Let us speak now about the three notions that are present, but to my opinion not really thought of, in restricted complexity: the notions of system, emergence, and organization.
7. System: It should be conceived that “any system is complex” What is a system? It is a relation between parts that can be very different from one another and that constitute a whole at the same time organized, organizing, and organizer. Concerning this, the old formula is known that the whole is more than the sum of its parts, because the addition of qualities or properties of the parts is not enough to know those of the whole: new qualities or properties appear, due to the organization of these parts in a whole, they are emergent. But there is also a substractivity which I want to highlight, noticing that the whole is not only more than the sum of its parts, but it is also less that the sum of it parts. Why? Because a certain number of qualities and properties present in the parts can be inhibited by the organization of the whole. Thus, even when each of
12 our cells contains the totality of our genetic inheritance, only a small part of it is active, the rest being inhibited. In the human relation individualsociety, the possibilities of liberties (delinquent or criminal in the extreme) inherent to each individual, will be inhibited by the organization of the police, the laws, and the social order. Consequently, as Pascal said, we should conceive the circular relation: ‘one cannot know the parts if the whole is not known, but one cannot know the whole if the parts are not known’. Thus, the notion of organization becomes capital, since it is through organization of the parts in a whole that emergent qualities appear and inhibited qualities disappearb. 8. Emergence of the notion of emergence
What is important in emergence is the fact that it is indeductible from the qualities of the parts, and thus irreducible; it appears only parting from the organization of the whole. This complexity is present in any system, starting with H 2 0 , the water molecule which has a certain number of qualities or properties that the hydrogen or oxygen separated do not have, which have qualities that the water molecule does not have. There is a recent number of the Science et Awenir journal devoted to emergence; to relate emergence and organization, one wonders wether it is a hidden force in nature, an intrinsic virtue. From the discovery of the structure of the genetic inheritance in DNA, where it appeared that life was constituted from physicochemical ingredients present in the material world, therefore from the moment that it is clear that there is not a specifically living matter, a specifically living substance, that there is no d a n vital in Bergson’s sense, but only the physicochemical matter that with a certain degree of organizing complexity produces qualities of the living-f which self-reproduction, self-reparation, as well as a certain number of cognitive or informational aptitudes, as from this moment, the vitalism is rejected, the reductionism should be rejected, and it is the notion of emergence that takes a cardinal importance, since a certain type of organizing complexity produces qualities specific of selforganization. The spirit (mens, mente) is an emergence. It is the relation brainbI develop the idea that organization consists of complexity in La Me‘thode 1, La nature de la nature,p.94-151, Le Seuil, 1977. ‘Science and Future, a popular French journal (Translator’s Note)
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culture that produces as emergent psychic, mental qualities, with all that involves language, consciousness, etc. Reductionists are unable to conceive the reality of the spirit and want to explain everything starting from the neurons. The spiritualists, incapable of conceiving the emergence of the spirit starting from the relation brainculture, make from the brain at most a kind of television.
9. The complexity of organization The notion of emergence is a capital notion, but it redirects to the problem of organization, and it is organization which gives consistence to our universe. Why is there organization in the universe? We cannot answer this question, but we can examine the nature of organization. If we think already that there are problems of irreducibility, of indeductibility, of complex relations between parts and whole, and if we think moreover that a system is a unit composed of different parts, one is obliged to unite the notion of unity and that of plurality or at least diversity. Then we realize that it is necessary to arrive at a logical complexity, because we should link concepts which normally repel each other logically, like unity and diversity. And even chance and necessity, disorder and order, need to be combined to conceive the genesis of physical organizations, as on the plausible assumption where the carbon atom necessary to the creation of life was constituted in a star former to our sun, by the meeting exactly a t the same t i m e a b s o l u t e coincident-f three helium nuclei. Thus, in stars where there are billions of interactions and meetings, chance made these nuclei to meet, but when this chance occurs, it is necessary that a carbon atom will be constituted. You are obliged to connect all these disjoined notions in the understanding that was inculcated to us, unfortunately, since childhood, order, disorder, organization. We then manage to conceive what I have called the self-ecc-organization, i.e. the living organization.
10. The self-eco-organization The word self-organization had emerged and had been used as of the end of the 50’s by mathematicians, engineers, cyberneticians, neurologists. Three important conferences had been held on the topic of “selforganizing systems”, but a paradoxical thing, the word had not bored in biology, and was a marginal biologist, Henri Atlan, who retook this idea, in
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a great intellectual isolation within his corporation, in the 70’s. Finally the word emerged in the 8O’s-9O’s in Santa Fe as a new idea, whereas it existed already for nearly half a century. But it is still not imposed in biology. I call self-eco-organization to the living organization, according to the idea that self-organization depends on its environment to draw energy and information: indeed, as it constitutes an organization that works to maintain itself, it degrades energy by its work, therefore it must draw energy from its environment. Moreover, it must seek its food and defend against threats, thus it must comprise a minimum of cognitive capacities. One arrives to what I call logically the complex of autonomydependence. For a living being to be autonomous, it is necessary that it depends on its environment on matter and energy, and also in knowledge and information. The more autonomy will develop, the more multiple dependencies will develop. The more my computer will allow me to have an autonomous thought, the more it will depend on electricity, networks, sociological and material constraints. One arrives then to a new complexity to conceive living organization: the autonomy cannot be conceived without its ecology. Moreover, it is necessary for us to see a self-generating and self-producing process, that is to say, the idea of a recursive loop which obliges us to break our classical ideas of product producer, and of cause + effect. In a self-generating or self-producing or self-poetic or self-organizing process, the products are necessary for their own production. We are the products of a process of reproduction, but this process can continue only if we, individuals, couple to continue the process. Society is the product of interactions between human individuals, but society is constituted with its emergencies, its culture, its language, which retroacts to the individuals and thus produces them as individuals supplying them with language and culture. We are products and producers. Causes produce effects that are necessary for their own causation. Already the loop idea had been released by Norbert Wiener in the idea of feedback, negative as well as positive, finally mainly negative; then it was generalized without really reflecting on the epistemological consequences which it comprised. Even in the most banal example which is that of a thermal system supplied with a boiler which provides the heating of a building, we have this idea of inseparability of the cause and effect: thanks to the thermostat, when 20” is reached, the heating stops; when the temperature is too low, the heating is started. It is a circular system, where the effect itself intervenes in the cause which allows the thermal autonomy of --f
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the whole compared to a cold environment. That is to say that the feedback is a process which complexifies causality. But the consequences of this had not been drawn to the epistemological level. Thus feedback is already a complex concept, even in non-living systems. Negative feedback is what makes it possible to cancel the deviations that unceasingly tend to be formed like the fall in temperature compared to the standard. Positive feedback develops when a regulation system is not able anymore to cancel the deviations; those can then be amplified and go towards a runaway, kind of generalized disintegration, which is often the case in our physical world. But we could see, following an idea advanced more than fifty years ago by Magoroh Maruyama, that the positive feedback, i.e. increasing deviation, is an element that allows transformation in human history. All the great transformation processes started with deviations, such as the monotheist deviation in a polytheist world, the religious deviation of the message of Jesus within the Jewish world, then, deviation in the deviation, its transformation by Paul within the Roman empire; deviation, the message of Mohammed driven out of Mecca, taking refuge in Medina. The birth of capitalism is itself deviating in a feudal world. The birth of modern science is a deviating process from the XVIIth century. Socialism is a deviating idea in the XIXth century. In other words, all the processes start by deviations that, when they are not suffocated, exterminated, are then able to make chain transformations.
11. The relationship between local and global
In logical complexity, you have the relation between the local and the global. One believed to be able to assume the two truths of the global and of the local with axioms of the style: “think globally and act locally”. In reality, one is, I believe, constrained in our global age to think jointly locally and globally and to try to act at the same time locally and globally. Also, which is also complex, local truths can become global errors. For example, when our immune system rejects with the greatest energy the heart that one grafts to him, like a nasty foreigner, this local truth becomes a global error, because the organism dies. But one can also say that global truths can lead to local errors. The truth of the need to fight against terrorism can lead to interventions, which will favor even more the development of terrorism, just look at Irak.
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12. Heraclitus: “live of death, die of life”
In this union of notions logically complex, there is a relationship between life and death. I often quoted the illuminating phrase of Heraclitus, from the VIth century b.C.: “live of death, die of life”. It became recently intelligible, from the moment when we learned that our organism degrades its energy, not only to reconstitute its molecules, but that our cells themselves are degraded and that we produce new cells. We live from the death of our cells. And this process of permanent regeneration, almost of permanent rejuvenilization, is the process of life. What makes it possible to add to the very right formula of Bichat, saying: “life is the ensemble of the functions that fight against death”, this strange complement that presents us a logical complexity: “Integrating death to fight better against death”. What one again knows about this process is extremely interesting: it has been learned rather recently that cells that die are not only old cells; in fact apparently healthy cells receiving different messages from neighboring cells, “decide”, at a given moment, to commit suicide. They commit suicide and phagocytes devour their remains. Like this, the organism determines which cells must die before they have reached senescence. That is to say that the death of cells and their postmortem liquidation are included in the living organization. There is a kind of phenomenon of self-destruction, of apoptosis, since this term has been taken from the vegetal world, indicating the split of the stems operated by trees in autumn so that dead leafs fall. On the one hand, when there is an insufficiency of cellular deaths following different accidents and perturbations, there are a certain number of diseases that are deadly in the long run, like osteoporosis, various types of sclerosis, and certain cancers, where cells refuse to die, becoming immortal, forming tumors and go for a stroll in the form of metastases (It can seem that it is a revolt of cells against their individual death that lead to these forms of death of the organism). On the other hand, the excess of cellular deaths determine AIDS, Parkinson’s, and Alzheimer’s disease. You see at which point this relationship between life and death is complex: it is necessary for cells to die, but not too much! One lives between two catastrophes, the excess or insufficiency of mortality. One finds again the fundamentally epistemological problem of generalized complexity.
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13. On non-trivial machines Living beings are certainly machines, but unlike artificial machines that are trivial deterministic machines (where one knows the outputs when one knows the inputs), these are non-trivial machines (von Foerster) where one can predict innovative behaviors. We are machines, this truth was already in L'homme-machine of La Mettrie. We are physical machines, thermal machines, we function at the temperature of 37'. But we are complex machines. Von Neumann established the difference between living machines and artificial machines produced by technology: the components of the technical machines, having the good quality of being extremely reliable, go towards their degradation, towards their wear, from the very start of their operation. Whereas the living machine, made up mainly by components far from reliable, degrading proteins-and one understands very well that this lack of reliability of proteins makes it possible to reconstitute them non stop-is able to be regenerated and repaired; it also goes towards death, but after a process of development. The key of this difference lies in the capacity of self-repair and self-regeneration. The word regeneration is capital here. One can say that the characteristic of innovations that emerge in the evolution of life (which are determined by environmental changes, or by the irruption of multiple hazards), such as the appearance of the skeleton in vertebrates, wings in insects, birds, or bats, all these creations, are characteristic non-trivial machines. That is to say, it gives a new solution to insurmountable challenges without this solution. All the important figures of human history, on the intellectual, religious, messianic, or politic levels, were non-trivial machines. One can advance that all the History of Humankind, which begins ten thousand years ago-is a non-trivial history, i.e. a history made of unforeseen, of unexpected events, of destructions and creations. The history of life that precedes it is a nontrivial history, and the history of the universe, where the birth of life and then of humankind are included, is a non-trivial history. We are obliged to detrivialize knowledge and our worldview. 14. To complexify the notion of chaos We have seen how the notion of system brings us to complexities of organization which themselves lead us to logical complexities. Let us look now at the notion of chaos, as it appears within chaos theory, and which comprises disorder and impredictibility. The beat of the wings of a butterfly
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in Melbourne can cause by a succession of chain processes a hurricane in Jamaica, for example. Actually, I believe that the word chaos must be considered in its deep sense, its Greek sense. We know that in the Greek worldview, Chaos is at the origin of Cosmos. Chaos is not pure disorder, it carries within itself the indistinctness between the potentialities of order, of disorder, and of organization from which a cosmos will be born, which is an ordered universe. The Greeks saw a bit too much order in the cosmos, which is effectively ordered because the immediate spectacle, the impeccable order of the sky that we see each night with the stars, is always in the same place. And if the planets are mobile they also come to the same place with an impeccable order. However, we know today with the widened conceptions of cosmic time that all this order is at the same time temporary and partial in a universe of movement, collision, transformation. Chaos and Cosmos are associated-I have employed the word Chaosmos-there is also a circular relation between both terms. It is necessary to take the word chaos in a much deeper and more intense sense than that of physical chaos theory. 15. T h e need of contextualization Let us take again the “complexus” term in the sense of “what is woven together”. It is a very important word, which indicates that the breaking up of knowledge prevents from linking.and contextualizing. The knowledge mode characteristic of disciplinary science isolates objects, one from another, and isolates them compared to their environment. One can even say that the principle of scientific experimentation allows to take a physical body in Nature, to isolate it in an artificial and controlled laboratory environment, and then study this object in function of perturbations and variations that one makes it undergo. This indeed makes it possible to know a certain number of its qualities and properties. But one can also say that this principle of decontextualization was ill-fated, as soon as it was ported to the living. The observation since 1960 by Jane Goodall of a tribe of chimpanzees in their natural environment could show the supremacy of observation (in a natural environment) over experimentation (in a laboratory) for knowledged. A lot of patience was necessary dSee “ L e Paradigme Perdu”, pp. 51-54
19 so that Jane Goodall could perceive that chimpanzees had different personalities, with rather complex relations of friendship, of rivalry; a whole psychology, a sociology of chimpanzees, invisible to the studies in a laboratory or in a cage, appeared in their complexity. The idea of knowing the living in their environment became capital in animal ethology. Let us repeat it, the autonomy of the living needs to be known in its environment. From now on, becoming aware of the degradations that our technoeconomic development makes to the biosphere, we realize the vital link with this same biosphere that we believe to have reduced to the rank of manipulable object. If we degrade it, we degrade ourselves, and if we destroy it, we destroy ourselves. The need for contextualization is extremely important. I would even say that it is a principle of knowledge: Anybody who has made a translation in a foreign language will seek an unknown word in the dictionary; but with words being polysemous, it is not immediately known which is the good translation; the sense of the word will be sought in the sense of the sentence in the light of the global sense of the text. Though this play from text to word, and from text to context, and from context to word, a sense will crystalize. In other words, the insertion in the text and in the context is an evident cognitive necessity. Take for example the economy, the most advanced social science from a mathematical point of view, but which is isolated from human, social, historic, and sociologic contexts: its prediction power is extremely weak because the economy does not function in isolation: its forecasts need to be unceasingly revised, which indicates us the disability of a science that is very advanced but too closed. More generally, mutual contextualization is lacking in the whole of social sciences. I have often quoted the case of the Aswan dam because it is revealing and significant: it was built in Nasser’s Egypt because it would make it possible to regulate the course of a capricious river, the Nile, and to produce electric power for a country which had a great need for it. However, after some time, what happened? This dam retained a part of the silts that fertilized the Nile valley, which obliged the farming population to desert the fields and overpopulate large metropolises like Cairo; it retained a part of the fish that the residents ate; moreover today, the accumulation of silts weakens the dam and causes new technical problems. That does not mean that the Aswan dam should not have been built, but that all the decisions taken in a techno-economic context are likely to be disastrous by their consequences.
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It is like the deviation of rivers in Siberia that the Soviet government made and where the perverse consequences are more important than the positive ones. It is thus necessary to recognize the inseparability of the separable, at the historical and social levels, as it has been recognized at the microphysical level. According to quantum physics, confirmed by Aspect’s experiments, two microphysical entities are immediately connected one to the other although they are separated by space and time. Even more, one arrives to the idea that everything that is separated is at the same time inseparable. 16. The hologrammatic and dialogical principles
The hologrammic or hologrammatic principle should also be advanced, according to which not only a part is inside a whole, but also the whole is inside the part; just as the totality of the genetic inheritance is found in each cell of our organism, the society with its culture is inside the spirit of an individual. We return again to the logical core of complexity which we will see, is dialogical: separability-inseparability, whole-parts, effect-cause, productproducer, life-death, homo sapiens-homo demens, etc. It is here that the principle of the excluded middle reveals its limit. The excluded middle states “A cannot be A and not A”, whereas it can be one and the other. For example, Spinoza is Jewish and non-Jewish, he is neither Jewish, nor non-Jewish. It is here that the dialogic is not the response to these paradoxes, but the means of facing them, by considering the complementarity of antagonisms and the productive play, sometimes vital, of complementary antagonisms.
17. For the sciences, a certain number of consequences Regarding sciences, we can see a certain number of consequences. First of all, classical science is somehow complex, even when it produces simplifying knowledge. Why? Because science is a quadruped which walks on the following four legs: the leg of empiricism made of data, experimentation or observation; the leg of rationality, made of logically constituted theories; the leg of verification, always necessary; and the leg of imagination, because great theories are products of a powerful creative imagination. Thus science is complex, produced by a quadruped movement, which prevents it from solidifying.
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The objective knowledge which is its idea, resulted in the need of eliminating subjectivity, i.e. the emotional part inherent to each observer, to each scientist, but it also comprised the elimination of the subject, i.e. the being which conceives and knows. However, any knowledge, including objective, is at the same time a cerebral translation starting from data of the external world and a mental reconstruction, starting from certain organizing potentialities of the spirit. It is certain that the idea of a pure objectivity is utopian. Scientific objectivity is produced by beings who are subjects, within given historical conditions, starting from the rules of the scientific game. The great contribution of Kant was to show that the object of knowledge is co-constructed by our spirit. He indicated us that it is necessary to know knowledge to know its possibilities and limits. The knowledge of knowledge is a requirement of the complex thinking. As Husserl indicated in the ~ O ’ S , in particular in his conference on the crisis of European science, sciences developed extremely sophisticated means to know external objects, but no means to know themselves. There is no science of science, and even the science of science would be insufficient if it does not include epistemological problems. Science is a tumultuous building site, science is a process that could not be programmed in advance, because one can never program what one will find, since the characteristic of a discovery is its unexpectedness. This uncontrolled process has lead today to the development of potentialities of destruction and of manipulation, which must bring the introduction into science of a double conscience: a conscience of itself, and an ethical conscience. Also, I believe that it will be necessary to arrive more and more to a scientific knowledge integrating the knowledge of the human spirit to the knowledge of the object which this spirit seizes and recognizing the inseparability between object and subject.
18. Two scientific revolutions introduced complexity de facto
I already indicated how the concept of complexity emerged in a marginal fashion in a sphere of mathematicians/engineers. It should be indicated now that the X X t h century knew two scientific revolutions which de facto introduced complexity without, however, recognizing this notion that remains implicit. The first revolution, after the thermodynamics of the XIXth century, is that of the microphysics and cosmophysics that introduced indeterminism,
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risk-where determinism reigned-and elaborated suitable methods to deal with the uncertainties met. The second revolution is that which gathers disciplines and restores between them a common fabric. It begins in the second half of the XXth century. Thus in the ~ O ’ S , Earth sciences designed Earth as a complex physical system, which makes it possible today to articulate geology, seismology, vulcanology, meteorology, ecology, etc. At the same time, ecology develops as a scientific knowledge bringing together data and information coming from different physical and biological disciplines in the conception of ecosystems. It makes it possible to conceive how an ecosystem either degrades, develops, or maintains its homeostasis. From the ~ O ’ S , the ecological conception extends to the whole biosphere, necessarily introducing knowledge from the social sciences. Although ecology, at the biosphere level, cannot make rigorous predictions, it can give us vital hypothesis, concerning, for example, global warming, which manifests itself by the melting of glaciers in the Antarctic or the Arctic. Thus ecology, cosmology, and Earth sciences have become poly-disciplinary sciences, even transdisciplinary. Sooner or later, this will arrive in biology, from the moment when the idea of self-organization will be established; this will arrive in the social sciencese, although they are extremely resistant. Finally, the observer, chased by the objectivity postulate, was intrcduced into certain sciences, such as microphysics where the observer perturbs what it observes. In the case of cosmology, even if one does not adhere to what Brandon Carter called the anthropic principle, which holds account of the place of humans in the universe, one is obliged to conceive that this universe, among its perhaps negligible possibilities, had the possibility of human life, perhaps only on this planet Earth, but perhaps also elsewhere. Thus, the common fabric between the human, the living, and the Universe can be restored, which implies a complex conception capable at the same time to distinguish the human from the natural and to integrate it. 19. The insertion of science in History
In addition, there is the problem of the insertion of the Sciences in human
History. You know that there are two conceptions of history of sciences, the internalist conception and the externalist conception. The internalist mode ‘Cf my Humanite‘ de l’humanite‘, La Me‘thode 5, Le Seuil.
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sees the development of sciences in isolation, only in function of their internal logic and their own discoveries. The externalist mode sees them in function of historical and social developments which determine the scientific developments. I think that it is necessary to link both, and this is appropriate for other developments than those of sciences. Thus, some wanted to understand the perversion of the Soviet Union starting from internal factors, such as insufficiencies of the Marxist doctrine, limitations of that of Lenin. Others wanted to impute it to external elements such as the surrounding and hostility of the capitalist powers with regard to the Soviet Union or former elements such as the backwardness of tsarist Russia. Whereas the true cognitive game is to link these two aspects in a dialogical fashion. If one continues to place oneself from the viewpoint of modern Western history of science, one sees how from its marginal and quasi-deviating birth in the XVIIth century, it is developed in the XVIIIth, introduced in universities in the XIXth, then in states and companies in the XXth, and how it becomes central and driving within human history in the form of techno-science, and produces not only all the major elements for a renewed knowledge of the world and beneficial effects for humanity, but also formidable and uncontrolled powers which threaten it. I don’t know if I am right or wrong in retaking an expression of Vico, but it is necessary for us to arrive to the “Scienza Nuova”. Very precisely, Vico inscribed the historical perspective at the heart of the scienza nuova. It is necessary to amplify the idea of scienza nuova by introducing the interaction between the simple and the complex, by conceiving a science that does not suppress disciplines but connects them, and consequently makes them fertile, a science which can at the same time distinguish and connect and where the transdisciplinarity is inseparable from complexity. I repeat it, as much as the compartmentalization of disciplines disintegrates the natural fabric of complexity, as much a transdisciplinary vision is capable of restoring it.
20. The link between science and philosophy
The link between science and philosophy has been broken. Still in the XVIIth century, the great scientists were at the same time great philosophers. Certainly, they did not identify Science and Philosophy. When Pascal made his experiments in Puy de DGme, he did not think about the bet problem. But in the times of Pascal, Gassendi, Leibniz, there was not
24 this cut. This became a frightening ditch. The ditch of ignorance separates the scientific culture from the culture of the humanities. But the current has started to be reversed: the most advanced sciences arrive to fundamental philosophical problems: Why is there a universe out of nothing? How was this universe born from a vacuum which was not at the same time the vacuum? What is reality? Is the essence of the universe veiled or totally cognizable? The problem of life is posed from now on in a complexity that exceeds biology: the singular conditions of its origin, the conditions of emergences of its creative powers. Bergson was mistaken by thinking that there was an e'lan vital, but was right while speaking about creative evolution. He could even have spoken about evolutionary creativity. Today we can foresee the possibility of creating life. From the moment when it is believed that life is a process developed starting only from physicochemical matter under certain conditions, in underwater thermal vents or elsewhere, one can very well consider creating the physical, chemical, thermodynamic conditions which give birth to organisms gifted with qualities that one calls life. We can also foresee the possibility to modify the human being in its biological nature. Therefore, we have to meditate about life, as we never did it. And at the same time we must meditate about our relationship with the biosphere. Thus all the most advanced sciences arrive to fundamental philosophical problems that they thought to have eliminated. They do not only find them, they renew them. If one defines philosophy by the will and capacity of reflection, it is necessary that the reflectivity is also introduced into the sciences, which does not eliminate the relative autonomy of philosophy nor the relative autonomy of scientific procedures compared to philosophical procedures. Finally and especially, any knowledge, including the scientific one, must comprise in itself an epistemological reflection on its foundations, principles, and limits. Still today there is the illusion that complexity is a philosophical problem and not a scientific one. In a certain way, it is true, in a certain way, it is false. It is true when you place yourselves from the point of view of an isolated and separated object: the fact that you isolate and separate the object made the complexity to disappear: thus it is not a scientific problem from the point of view of a closed discipline and a decontextualized object. But, as soon as you start to connect these isolated objects, you are in front of the problem of complexity.
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21. Second epistemological rupture with restricted complexity It is here that a second epistemological rupture with restricted complexity appears. Restricted complexity is interested essentially in dynamical systems called complex. That is to say, it constitutes its own field, within the field of sciences. But generalized complexity not only concerns all fields, but also relates to our knowledge as human beings, individuals, persons, and citizens. Since we have been domesticated by our education which taught us much more to separate than to connect, our aptitude for connecting is underdeveloped and our aptitude for separating is overdeveloped; I repeat that knowing, is at the same time separating and connecting, it is to make analysis and synthesis. Both are inseparable, and our atrophy of the capacity to connect is increasingly serious in a globalized, complexified mode, where it is a matter of generalized interdependence of everything and everyone. The International Ethical, Political and Scientific Collegium has formulated a declaration of interdependence which it would wish to see promulgated by the United Nations. We must think the interdependence in all fields, including the complex relation between the parts and the whole. We need to be able to face uncertainties of life whereas nothing prepares us for it. We need to face complexity, including for action, whereas one opposes the cautionary principle to the risk principle, while Pericles had truly expressed the union of the two antagonistic principles when he said during a speech to the Athenians during the Peloponnesian war: “we Athenians, we are capable of combining prudence and audacity, whereas the others are either timorous or bold”. It is the combination which we need. Also, precaution needs today sometimes much invention. We need to deeply reform all our way of knowing and thinking. 22. The principle of ecology of action
The principle of ecology of action is, in my opinion, central: from the moment an action enters a given environment, it escapes from the will and intention of that which created it, it enters a set of interactions and multiple feedbacks and then it will find itself derived from its finalities, and sometimes to even go in the opposite sense. The ecology of action has a universal value, including for the development of sciences, whose destructive nuclear consequences were absolutely unexpected.
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Think that when Fermi elucidated the structure of the atom in the ~ O ’ S , it was a purely speculative discovery and he had by no means thought that this could allow the fabrication of an atomic bomb. However, a few years later, the same Fermi went to the United States to contribute to the fabrication of the atomic bomb that would be used in Hiroshima and Nagasaki. When Watson and Crick determined the structure of the genetic inheritance in DNA, they thought that it was a great conquest of knowledge without any practical consequences. And hardly ten years after their discovery, the problem of genetic manipulations was posed in the biology community. The ecology of action has a universal value. One can think of examples in our recent French history: a dissolution of the Parliament by President Chirac to have a governmental majority led to a socialist majority; a referendum made to win general support led to its rejection. Gorbachev tried a reform to save the Soviet Union but this one contributed to its disintegration. When one sees that a revolution was made in 1917 to suppress the exploitation of man by his fellow man, to create a new society, founded on the principles of community and liberty, and that this revolution, not only caused immense losses of blood, destruction, and repression by a police system, but, after seventy years, it led to its contrary, i.e. to a capitalism even more fierce and savage than that of the tsarist times, and with a return of religion! Everything that this revolution wanted to destroy resurrected. How not to think about the ecology of action!
23. Creating “Institutes of fundamental culture”
The reform of the spirit seems to me absolutely necessary. Once that I had understood that the reform of thought, deep work that I carried out in La Me‘thode, is a necessity, I accepted the offer of a Minister of Education when he called me for the reform of the content of secondary education. I tried to introduce my ideas of reform of thought into an educational project. I saw its total failure-finally it did not failed, it was not applied!-That pushed me to reflect even more. I wrote a book called La TCte bien fuite (The head well made), then on the initiative of UNESCO I made a book called Les Sept savoirs ne‘cessaires a l’e‘ducation du f u t u r (The seven knowledges necessary in the education of the future). Following a University which will be created on these principles in Mexico, I had the more restricted but maybe more necessary idea of creating “Institutes of fundamental culture”, which would be sheltered in a University or independent, addressing everybody, i.e. before University or during
27 University or after University, students, citizens, members of trade unions, entrepreneurs, everybody. Why the word “fundamental culture”? Because it is that what is missing. In fact, it is the most vital matter to be taught, the most important to face life, and which is ignored by education. (1) Knowledge as a source of error or illusion; nowhere the traps of knowledge are taught, which come owing to the fact that all knowledge is translation and reconstruction. (2) Rationality, as if it were an obvious thing, whereas we know that rationality knows its perversion, its infantile or senile diseases. (3) Scientificity. What is science, its frontiers, its limits, its possibilities, its rules. Moreover, there is an abundant literature, but which has never been consulted by the scientists who are recruited at CNRS for example. Most of the time, they do not know anything about the polemic between Niels Bohr and Einstein, the works of Popper, Lakatos, Kuhn, etc. (4) What is complexity. And also: A teaching on “what is the human identity and condition”, which is not found anywhere. A teaching on the global age, not only today’s globalization, but all its antecedents starting from the conquest of America, the colonization of the world, its current phase, and its future prospects. A teaching on human understanding. A teaching concerning the confrontation of uncertainties in all the fields: sciences, everyday life, history (we have lost the certainty of progress, and the future is completely uncertain and obscure). A teaching on the problems of our civilization. That is for me the fundamental teaching that can aid the reform of the spirit, of thought, of knowledge, of action, of life. 24. I conclude: generalized complexity integrates restricted complexity Unfortunately, restricted complexity rejects generalized complexity, which seems to the former as pure chattering, pure philosophy. It rejects it because restricted complexity did not make the epistemological and paradigmatic
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revolution which complexity obliges. That will be done without a doubt. But in the meantime, we see that the problematic of complexity have invaded all our horizons, and I repeat “problematic”, because it is an error to think that one will find in complexity a method that can be applied automatically to the world and anything. Complexity is a certain number of principles which help the autonomous spirit to know. Whereas a program destroys the autonomy of the one who seeks, the problematic of complexity stimulates an autonomous strategy, obliges in the field of action-once that one knows that the ecology of action can pervert the best intentions-to reconsider our decisions like bets and incites us to develop an adequate strategy to more or less control the action. In other words, in all the fields, I would say “help yourself and the complexity will help you”, which has nothing to do with the mechanical application of a program or a rule. It is a deep reform of our mental functioning, of our being. These ideas now marginal, deviating, begin to constitute a tendency still in minority, or rather tendencies since there are several paths to go towards complexity. These ideas, these deviations, can be developed and become cultural, political, and social forces. The probabilities of a global future are extremely alarming: our spaceship is pulled by four engines without any control: science, technology, economy, and the search for profit-all this under conditions of cham since the techno-civilizational unification of the planet, under the Western push, causes singular cultural resistances and cultural and religious re-closings. The planet is in crisis with all the possibilities, ones regressive and destructive, others stimulant and fertile, such as invention, creation, new solutions.
25. We should even apprehend the possibilities of
metamorphosis We should even apprehend the possibilities of metamorphosis because we have completely astonishing examples of it from the past. The change in certain places where there have been demographic concentrations in the Middle East, in the Indus basin, in China, in Mexico, in Peru, from prehistoric societies of hundreds of men, without cities, without state, without agriculture, without army, without social class, to enormous historical societies with cities, agriculture, army, civilization, religion, philosophy, works
of art ... that constituted a sociological metamorphosis. Perhaps we are going towards a meta-historical metamorphosis suitable for the birth of a society-world at a global scale. I would say that complexity does not put us only in the distress of the uncertain, it allows us to see besides the probable, the possibilities of the improbable, because of those which have been in the past and those that can be found again in the future. We are in an epoch of doubtful and uncertain combat. That makes one think of the Pacific war, after the Japanese had broken into the Pacific Islands and had begun to threaten California, there was a gigantic naval fight over 200 kilometers along the Midways between the Japanese and American fleets: battleships, aircraft carriers, submarines, planes. The global vision was impossible for both of them: there were sunken Japanese ships, sunken American ships, planes that did not find the enemy fleet; in short, total confusion, the battle divided in several fragments. At a given moment, the Japanese Admiral realizing his losses in battleships and planes, thought that they were defeated, thus called for retreat. But the Americans, who had lost as much, were not the first to think that they were defeated; after the Japanese retreat, they were victorious. Well, the outcome of what will happen, we cannot conceive it yet! We can always hope and act in the direction of this hope. The intelligence of complexity, isn’t it to explore the field of possibilities, without restricting it with what is formally probable? Doesn’t it invite us to reform, even to revolutionize?
COMPLEXITY SCIENCE AS AN ASPECT OF THE COMPLEXITY OF SCIENCE
DONALD C. MIKULECKY Senior Fellow, Virginia Commonwealth University’s Center for the Study of Biological Complexity, Richmond, VA
1. INTRODUCTION How can we treat science as an object of scientific inquiry? The central problem arises with that question. Science has tried to rid itself of circularity and in so doing has become a very limited method for examining the complex world it tries to have us understand. Self reference is at the center of so many of the interesting thing we want to understand including and especially life itself. The existence of this self referential character is the essence of what we have come to call “complexity”. The works of Robert Rosen [l, 2, 31 spell this out in great detail. This series of investigations began over a half century ago yet still remains virtually unrecognized by the vast majority of those who call themselves “scientists”. That fact alone can be a springboard to launch a study of science as an object, which is what this study is all about. I have reviewed the technical aspects of Rosen’s work elsewhere [4]and will consider the broader philosophical implications here. Using the ideas Rosen developed, we can begin with the following working definition of complexity:
Complexity is the property of a real world s y s t e m that is manifest in the inability of a n y one formalism being adequate to capture all its properties. I t requires that we find distinctly different ways of interacting with systems. Distinctly diflerent in the sense that when we make successful models, the formal systems needed t o describe each distinct aspect are NOT derivable from each other. Rosen created a dichotomy between complex system and simple systems, or mechanisms. The essence of that dichotomy is summarized in Table 1.
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31 Table 1. Complex systems vs. simple mechanisms. Complex Simple No largest model Largest model Whole more than sum of parts Whole is sum of parts Causal relations rich and intertwined Causal relations distinct Generic Non-generic Analytic Synthetic Analytic = Synthetic Non-fragment able Fragmentable Non-comput able Computable Real world Formal system
This set of properties that distinguish disjoint categories of objects is the subject of Rosen’s life work. Any brief summary will be lacking the content developed to establish them in detail, but can give a sense of what the categorization entails. The categories are disjoint because of a central characteristic of the way we go about practicing science. We create a surrogate world, the world of simple systems, to enable our minds to try to grasp the complexity of the world we wish to comprehend. Hence the real world is complex and must be reduced to something less than its many faceted reality in order to be studied. The surrogate simple world is a world of formal systems or models, that replace the many faceted complex reality with something our minds can work with. Our understanding depends on this process. The process has consequences that can not be escaped. The table of characteristics is a summary of those consequences, and they will be discussed briefly.
1.1. The largest Model The formal system science has traditionally used to model the complex world has a largest model. This model is the crux of scientific description and can be called the “Newtonian Paradigm” using terminology adopted by Rosen. The Newtonian Paradigm is a world constructed in terms of non-linear dynamics in its many forms. The most modern forms all resolve to the largest model formulated as non-linear dynamics. Included are chaos theory, cellular automata, and non-linear systems of partial differential equations or state space descriptions, among others. These formalisms lend themselves well to the use of modern computing methods and therefore computability becomes a hallmark of the largest model used to represent
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simple systems. Real systems go beyond computable properties and can only be approximated by computer simulation. This has been said in many ways, such as “The map is not the territory”, and will often be acknowledged in specific instances, only to be denied vigorously when proposed as a general truth. In the working definition of complexity, this is manifest as the need for distinct formalisms in order to completely represent complex reality. In fact, there is no finite number of such descriptions.
1.2. Why is the whole more than the s u m of its parts? A mantra in complexity research is the notion that any complex whole is more than the sum of its parts. The world of simple systems created by science does not escape this idea. We will give some examples of models that can demonstrate that the same material parts can be assembled in different ways to make very different functioning wholes. The key word being “functional” for it is in function that this property of complex reality is rooted. More interesting is the recognition that function is as much an ontological aspect of complex reality as are the atomic and molecular material building blocks. This must be so if the notion that the whole is more than the sum of its parts is to have any meaning. Reducing a complex whole to smaller units and eventually to atoms and molecules destroys function and destroys the very identity of the complex whole. This thing called “function” that characterizes complex wholes is as real as the material aspects of the system. Simple systems can be reduced to their parts and are called machines or mechanisms for this reason. This leads to an unfortunate ambiguity between different meanings of the word “machine”. An automobile is a man made machine and can seem to be identical with the formal description used to create it. However, the real world automobile is a complex entity only approximated by its formal description even though it can be built from that formal description. It will be important to keep the vernacular meaning of machine, the complex reality, separated from its formal description as a machine or simple mechanism. In the relational systems theory being developed as an approach to complex system description using the ideas introduced by Rosen, the material description is sacrificed in favor of a functional description. The complex whole is reduced to a combination of functional components that can not be mapped to material parts on a one to one basis. These functional components only have definition in the context of the complex whole and are destroyed when it is reduced to material parts. Hence the functional components are the
33 way that the things that are “more than the sum of the material parts” become entities having an ontology of their own. This idea is central to an understanding of complexity. 1.3. Causality and information: Science of method and science of content Science has often been characterized by its methodology. This has been the key feature that has kept science from being “contaminated“ by the logical problems that are inherent in things like circularity and self reference. The limits imposed by this methodology also keep science from dealing adequately with complex reality for this very reason. Within science a very limited definition of 1Linformation77 was developed by Shannon and Weaver to provide a tool in communications theory. The shortcomings of this very sterile definition show up again and again because it does not satisfy the intuitive notion if what the term “information” connotes. This fact is closely linked to the relationship between syntax and semantics. The concept of information they formulated deals only with syntax while what is really needed is a way of also dealing with semantic content. Rosen introduced another kind of information. The difference between the two versions of information is related to the complexity/simple mechanism/machine dichotomy. Science, by dealing with mechanisms, led to questions about iihow” things work. The other aspect to information deals with “why” things are as they are. The question “how does it work?” is a reductionist/mechanist question. The strict methodology of hard reductionist science does not allow “Why?,’ questions because the method is impotent to deal with them. Yet there is much information content in the answer to the question “Why?” It was Aristotle that taught us that. Aristotle gave four answers to the question “Why?” These causes or LLbecauses’’ are the material, efficient, formal, and final causes. They are often illustrated as the answers to the question “Why a house?” Material cause: Bricks, wood, metal, glass, and other materials that make up the house. Efficient cause: The builders that put those materials into the form of a house giving it a function beyond that of the unassembled materials. Formal cause: The plan or blueprint used to give the house its form as a house. The purpose or function of the house, to be a Final cause: dwelling place.
34 In machines these causes can always be separated. In real complex systems they are entwined and not capable of being separated as in a machine. The example to follow, the distinction between an organism and a machine, will establish this in a clear example.
1.4. W h i c h i s generic, physics or biology? The widely accepted myth that biology is special and that physics is generic is totally wrong. In fact, far more can be learned about the material world by a careful study of biology than can ever be learned from physics. Physics is the model of hard reductionist science. Physics envy has done real damage to fields that want to be considered “scientific” such as psychology and sociology among others. Biological and social systems are clearly complex only because they have resisted the attempt to find an acceptable largest model as has been done in physics.
1.5. Analytic us. synthetic models The distinction between analytic and synthetic models is a mathematical one. It is based on the use of direct products and direct sums as the way the models are constructed. The definition of these structures comes from category theory. Rosen developed his own form of category theory but it does not differ that much from other versions. Category theory is that branch of mathematics created to overcome some problems in set theory. It is actually a way of modeling mathematics itself. To summarize the essential difference between analytic and synthetic models is a matter of looking at the way set like entities can be combined. Product sets are based on a set theoretical operation called a Cartesian product. The Cartesian product of a pair of sets A = (al, a2, “3) and B = (bl, b2) is symbolized as A x B and consists of the collection of pairs (al, b l ) , (all b2), (a2, bl), (a2, b2), (a3, b l ) , (a3, b2). The direct sum of these entities is merely the combination of the members of A and B. In simple systems the direct product can always be reduced to the direct sum. They are equivalent. This is simply a mathematical way of describing the reducibility or fragmentability of reductionist models. In the case of complex systems, this is never true. There is more involved because complex systems are modeled in terms of their functional components and these functional components consist of direct products that are not capable of being reduced to parts without the destruction of the functional component.
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1.6. h g m e n t a b i l i t y It follows directly from what has been developed so far that the complex system with its context dependent functional components can not be fragmented into material parts. Simple mechanisms or machines can always be fragmented into material parts.
1.7. Computability This subject can fill a number of books. It is the subject of heated debates and for those who have placed their faith in computers and computable models, the stakes are very high. The sides of this debate can be exemplified on one hand by the hard core proponents of “artificial life” and on the other hand by Robert Rosen and many others who have come to see his understanding of the complex real world as a fundamental breakthrough in world models. The proponents of the reductionist/mechanistic view believe that the Church-Turing thesis is correct. 2. SCIENCE AS A COMPLEX SYSTEM
Science is a complex system. It has many facets and many different ways of being defined, described and analyzed. The most obvious use of the word is as a noun. What does the noun stand for? It may stand for an ideal that we sometimes call ”pure” science. Such ideals are approximated in reality and never really realized completely. Science as a noun also stands for a body of knowledge. Science is also a set of human institutions. Science can also mean those things that the people we recognize as scientists do. When we speak of science in that way we can also speak of an activity and we sometimes refer to doing science so there is a verb form involved. We often describe things as scientific as in a scientific study or a scientific expedition. Then we see that there are adverbs and adjectives as well. There is also the scientific method. There is a philosophy of science. This philosophy is very important because it is the only way we can complete the system. That is, if we were forced to study science using science we would be caught in an impredicative self referential loop. This may be a partial explanation of why scientists seem to avoid philosophy, hoping to escape the need for another approach.. Science as a human institution also has a very important set of political facets. The products of scientific activity are often a source of wealth and power. The doing of science is an expensive enterprise and it must have
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its patrons. Both complexity theory and the philosophy of science run into this political aspect of science in a number of ways. By describing the limits of the reductionist/mechanist paradigm there is a danger of casting doubt on the ability of science to produce what its patrons expect from it. Teaching such things to science students can place them in situations that are difficult. Students must choose projects to satisfy their mentors who in turn must satisfy their patrons. Reflecting these strong shaping forces back on the definition we so roughly outlined, it should be clear that differences between science as an ideal and science as what is practiced by scientists can be very great if the ideal is involved with showing limits rather than convincing patrons that their investment will pay off. As the research tools and equipment grow in expense and sophistication, the tendency to occupy one’s time using the equipment also grows. Thus the activity we call science becomes driven by questions that can be answered by the equipment rather than the desire to know in its “purest” form. The methodology of science is not codified in any clear way. Books have been written about the best way to accept candidates for scientific law and scientific theory. Books have also been written about the failure of other disciplines to satisfy the criteria of the scientific method. Periodically there are so called paradigm shifts claimed. Often these are not universally recognized as such, but what ever name one wants to assign, change does occur in the method and this can be significant in its magnitude. Proponents of complexity theory in its many forms often ask for it to be a candidate for such status. Is there a model for this kind of complexity in systems of human thought and the activities that feed in to such systems? Clearly there is. Robert Rosen chose Number Theory as his example. He reviewed the efforts of the formalists to purge the field of all circularities and self referential loops. To make a very long story very short, the attempt failed miserably. Each attempt to present a finished product was met by demonstrations that important things about numbers were left out. This was because they were insisting that the theory be self consistent and rightly so. It took Kurt Godel to prove that such systems can not be both self consistent and complete. By requiring self consistency they doomed their efforts to produce an incomplete system. The only way to deal with complex systems was to rely on something external to attempt the completion. But then the larger system is subject to the same problem and an infinite regression results. This issue has come up often in discussions among complexity theory proponents. One way some seem to satisfy themselves that they need not heed
37 the problem is by claiming that Number Theory is mathematics and not science and that Godel’s proof has not been shown to apply to physical systems. This seems to be a false solution to the dilemma, especially since all the models science uses are mathematical 3. COMPLEXITY AS AN ATTRIBUTE OF NATURE
The use of the term “complexity” has come to be commonplace both in the scientific literature as well as in the lay press. A complex idea in its own right, complexity presents a challenge to those who would define it or codify its contents. Why is ”What is complexity” a question not so easily answered? Universities and other research institutions have programs in ”complexity research” and journals carry this word in their title. What is complexity? What does it mean to be ”complex”? The dictionary does not help us here. There is more to the idea than what a dictionary definition suggests. We need to look within science, where words are carefully defined and have more precise meanings, since it is here where the answer does lie. The concept of complexity that is of so widespread interest was born within the confines of the scientific community, had to struggle for existence, and finally grew into a substantial force in scientific thinking. The answer lies in the nature of science. Science helps us to understand the world around us by creating a surrogate world that is understandable. The real world is where complexity has its home. The world science gives us has become simple and understandable. 3.1. Hard Science i s built o n Cartesian Reductionism
Hard science can be best-defined in terms of Cartesian Reductionism and the machine metaphor. Descartes gave us the machine metaphor and he did it in a very interesting way. In the case of living systems he saw the body as a biological machine and the mind as something apart from the body. This is called Cartesian Dualism and survives to this day as one approach to the so-called mindlbody problem. What the machine metaphor did was to set the tone for modern science. It is still with us. Descartes really did not know what a machine is, or if he did, he never told anyone. Ironically, not only do we not have a good definition of complexity, but we also lack one for a machine. The duality between these concepts is the key to the resolution of the problem. The importance of the machine metaphor is in the intuitive concept of machine that almost everyone shares. A machine is
38 built up from distinct parts and can be reduced to those parts without losing its machine-like character. We call this idea ”Cartesian Reductionism”. We have seen that complex (real) systems can not be successfully reduced to material parts without the loss of some significant attributes in the process. This led to the axiom that the whole is more than the mere sum of its parts. Adopting this axiom as a truth leads to a conclusion that is inescapable. If the whole is more than the sum of its parts there must be more to things than atoms and molecules. Reducing a complex whole in the real world always destroys something. What is lost is an elusive entity, but is also the central idea in the concept of complexity as applied to the real world. If there is more to things in the real world than atoms and molecules then this something that is there has an existence, an ontology. This is the reason why as a concept complexity is a difficult one. It can not be both ways. Either a real world whole is more than the sum of its parts or it can be reduced to atoms and molecules with nothing being lost and the world is made of machine-like things. Cartesian reductionism does not work for making models of complex systems; it only reduces them to simple mechanisms that may reflect some aspect, but merely as a shadow of the complex whole
3.2. The Newtonian paradigm is the modern manifestation of hard science Newton gave us, among other things, three laws of motion, which were intended to describe the motion of the planets. It turned out that methodology spawned by the application of these laws could be applied in a seemingly perfectly general way. This broader application has been the foundation of the modern scientific method and will be referred to here as the Newtonian Paradigm. In the center of this paradigm is dynamics. Dynamics is the way the laws of motion get applied. The local description of the motion is formulated as a differential equation called an equation of motion. The equation of motion is manipulated by using the calculus (integrated) and results in a trajectory, which is an algebraic equation for calculating a particle’s position as a function of time. Later, this was made somewhat more complicated by quantum mechanics, but the central philosophy has never changed. The paradigm has been generalized from particle motion to all systems if we recognize that quantum mechanics is part of that generalization. The world-view called reductionism has as a central theme that anything in
39 the material world can be reduced to particle motion, that is, the motions and interactions of atoms and molecules. When we look carefully at the subject matter of physics, we see that it is the application of the Newtonian Paradigm to the universe. This application then makes the world into simple mechanisms. That is to say that the subject matter of physics is the study of simple mechanisms. Note that in this context, "simple" means the opposite of complex, not the opposite of complicated. 3.3. Complexity is the result of the failure of the
Newtonian Paradigm to be generic
A careful look at the real world tells us that it is complex. Yet, the success of the Newtonian Paradigm cannot be ignored. Most of modern science and technology is the result of it. For that reason alone it is difficult to suggest that it has limits and to then make that suggestion stick. Not only does the paradigm have limits, but also those limits are what gave rise to a concept like complexity. 3.4. The way science i s done: The modeling relation
How is science done? It is a combination of using our senses to observe the world around us and then to use some mental activity to make sense out of that sensory information. The process is what we will call the modeling relation. If we call the world we are observing and/or trying to understand the Natural System and the events that make it change as we observe causality, then that represents our object of study. What we do in our minds is to encode the natural system into another system that is of our making or choosing which we can call a formal system. Once we have chosen a formal system, we can manipulate it in various ways with the objective of mimicking the causal change in the natural system. These manipulative changes in the formal system we will call implication. Finally, once we think we have an appropriate formal system and have found an implication that corresponds to the causal event in nature, we must decode from the formal system in order to check its success or failure in representing the causal event. Figure 1 represents the modeling relation we have just described. If all the parts of the diagram are in harmony, in other words if 1 = 2 3 4, we say that the diagram commutes and we have a model. A model of the world is the outcome of a successful application of the scientific method, but it can also arise in other, less formal ways. Whenever someone tries to make sense out of the world, they are trying to construct a successful
+
+
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CAUSAL EVENT
DECODING IMPLICATION
SYSTEM
ENCODING Figure 1.
modeling relation, or a model. 3.5. Complex systems and simple systems are disjoint
categories that are related by the modeling relation The world therefore divides naturally into those things that are simple and those things that are complex. The real world is made up of complex things. It is something we encounter constantly and try to make sense of. The way we do that is to encode it into formal systems. Therefore the world of simple mechanisms is a fictitious world created by science or, more specifically, by physics as the hard version of science as a formal system which hopes to model the real world. This is the world of the reductionist. It is modeled by the Newtonian Paradigm and simply needs sufficient experimentation to make it known to us. Those experiments involve reducing the system to its parts and then studying those parts in a context formulated according to dynamics. Therein lays the reason for the restrictions on the scientific method. The method involves a rigid empiricism that feeds data into the formal system. Here is the philosophical rub. The epistemology spills over into an ontology. The modeling relation is forgotten (but it is always there) and the formal system has become reality. Now the definition of complexity is complete. The world, from which we single out some smaller part, the natural system, is converted into a formal system that our mind can manipulate and we have a model. The world is complex. The formal system we chose to try to capture it can only be partially successful. For years we were satisfied with the Newtonian Paradigm as the formal system, forgot about there even being and encoding and decoding, and gradually began to change the ontology so that the Newtonian Paradigm actually replaced or became the real world (at least
41 as seen through the eyes of science). As we began to look more deeply into the world we came up with aspects that the Newtonian Paradigm failed to capture. Then we needed an explanation. Complexity was born! This easily can be formalized. It has very profound meaning.
4. THERMODYNAMIC REASONING AS A
TRANSITION TO COMPLEXITY SCIENCE Rosen had little to say about thermodynamics in his critique of reductionism in the form of the Newtonian paradigm. There is probably a good reason for this. Clifford Truesdell [5] once made a very good case for thermodynamics having a certain “strangeness” as a part of physics, or we could say as part of the reductionist Newtonian paradigm. This strangeness needs to be considered in more detail for it reveals the seeds of the ideas Rosen found to be true about the mechanistic approach to reality. Thermodynamics is probably more poorly understood by mechanistic scientists than any other branch of physics. The reasons for this are deep and revealing. One of the most serious consequences of the inability of those doing either mechanistic science or thermodynamics to see the problem clearly is the resultant gap in the Newtonian largest model. It is possible to see mechanistic reasoning and thermodynamic reason as different models of complex reality in the spirit of the ideas discussed here. Instead, from its beginnings thermodynamics was put under severe pressure to conform to the mechanist’s largest model and thereby suffered a lack of development as its own alternative to mechanistic physics. Thermodynamics came into being for very practical reasons. The boring of cannons, the brewing of beer and the steam engine are but a few of the reasons that the frictionless world of Newton’s paradigm needed to be patched up. Heat as a form of energy also had to be dealt with. Perpetual motion machines had to be dealt with in a rational manner to curtail the squandering of time and energy, sometimes by very bright scientists. As progress was made, there were also immediate problems presented to the those who had been content with the frictionless world where heat was merely another form of energy and nothing more troublesome than that. Since the material world was to be understood in mechanistic terms, a new kind of mechanics called “statistical” mechanics had to be developed to try to make a bridge between thermodynamic reasoning and mechanistic reasoning. Why is this so? The answer is one of the best demonstrations of the
42 42 power of Robert Rosen’s analysis even though he may not have ever seen it himself. There is a fundamental difference between mechanistic reasoning and thermodynamic reasoning and it can not be erased by the limited successes of the use of statistical mechanics to bring them together. Thermodynamics is about those properties of systems that are true independent of their mechanism. This is why there is a fundamental asymmetry in the relationship between mechanistic descriptions of systems and thermodynamic descriptions of systems. From the mechanistic information we can deduce all the thermodynamic properties of that system. However, given only thermodynamic information we can deduce nothing about mechanism. This is in spite of the fact that thermodynamics makes it possible for us to reject classes of models such as perpetual motion machines. (This does not stop such models from appearing in subtle forms in the modern literature.) This asymmetry is poorly understood because thermodynamics is not a tool mechanists see as valuable. Some of this attitude is justified by the structure of thermodynamics as it exists in texts and courses. In some ways the field is a prisoner of its own history. It is useful to examine that history with this problem in mind. 4.1. Classical or LLequilibrium”t h e r m o d y n a m i c s a n d i t s limits
Thermodynamics recognizes distinct systems categories based on the constraints imposed on the system in order to study it systematically. This thought process is very much like the defining of a “universeof discourse” in other fields. A system is defined in terms of the way we allow it to interact with the outside world. Often it is useful to see these interactions as having to occur across some real or imaginary boundary or “skin” surrounding the system. There are only three possible categories based on this mode of reasoning:
(1) The isolated system. Isolated systems are isolated from the rest of the world by a boundary that is impermeable to both energy and matter flow. Such systems define the notion of “equilibrium”, in the thermodynamic sense, as the state the system is in after a sufficient amount of time is allowed to pass. The equilibrium state is characterized by the disappearance of the “transient” flows of matter and energy within the system that brought it to this final state wherein nothing further can happen. That is true in the large. Very locally, fluctuations around this equilibrium point are
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happening as a manifestation of the thermodynamic property called “temperature”. The fluctuations are atomic and molecular motion and increase in magnitude as heat energy is added to the system and decrease in magnitude as it is removed. Isolating the system will result in a system at constant temperature consistent with its heat content. (2) Closed systems are systems with boundaries that will allow the transfer of heat energy through them but these boundaries are impermeable to matter flow. Thus closed systems contain a fixed amount of material but can be warmed or cooled by manipulating their heat content. Such systems are capable of being put in contact with reservoirs of heat energy at different temperature to induce a flow of heat through them and are therefore capable of being maintained in stationary states away from equilibrium. (3) Open systems. These systems can exchange matter and heat energy with their environment and need never reach an equilibrium. These systems can exist in stationary states, periodic states, as well as chaotic states. The laws and ideas of thermodynamics were developed with great care by doing thought experiments on equilibrium systems. Virtual “quasistationary processes were conceived by imagining so called “infinitesimal” changes to take the isolated system from one equilibrium state to another. Sadi Carnot developed a clever method of bringing the system through a cycle so that it always ended in its starting equilibrium state. One central characteristic of equilibrium is the existence of a thermodynamic variable called “entropy”, S, defined as the quotient of the heat energy in the system, Q, and absolute temperature of the system, T:
S = Q/T More useful was the notion of the entropy change associated with an isothermal quasi-stationary process:
dS = dQ/T
(2)
The entropy of a system, to oversimplify somewhat, is a measure of the “quality” of the energy of that same system. This follows from reasoning about heat engines being operated in cycles. In order for a heat engine (e.g. a steam turbine) to produce work that can be used it must have a source of
44 hot steam and that steam must flow through it to a reservoir that is cooler. The First law of thermodynamics is nothing new to physics since it is simply the idea that energy can not be created or destroyed. Hence a stem engine uses some of the heat energy, converts it t o mechanical work, another form of energy, and allows the rest of the heat energy to pass through it with the matter (in this case water and/or water vapor) that is conserved in the process. The Second law of thermodynamics forbids the complete transfer of heat energy to mechanical work as well as forbidding the operation of the engine between a source and sink at the same temperatures. This is why the entropy became a useful and necessary concept. The result of “cooling” the matter in the process of extracting mechanical work, increased the heat/ absolute temperature quotient or the entropy of the system. One way of stating the second law is that there is a requirement that any real process must result in the increase of entropy overall. It is possible to make devices that locally decrease entropy, but only if the global result is an increase. At equilibrium, there is no change in the amount of entropy. dS = 0
(3)
>0
(4)
In any real process,
dS
The fact that so much of what we know about thermodynamics came from reasoning involving equilibrium and isolated systems is ironic when we recall that it was practical matters, the doing of things, the carrying out of processes that motivated the entire development. Nevertheless, by resorting to what now seems to be a rather clumsy thought process involving the carrying out of processes by performing small incremental changes, much was learned. What is problematic is that the world of real processes is what is of interest and equilibrium are the natural endpoints of some of those processes in the situation where the system is totally isolated. 4.2. Dissipation, frzction, and irreversibility
Energy is conserved, but entropy must increase in the carrying out of any process. The first two laws of thermodynamics are imbedded in that sentence. The statement is true of all systems regardless of mechanism. The result of this is that physics has two realizations. The original physics of
45 Newton and his followers was the physics of systems that had dynamics yet were without the creation of entropy. The “ideal” pendulum, for example, can not exist and is the end of a limiting process where friction is diminished to zero. Friction is another manifestation of the second law of thermodynamics. It is the recognition that in any real process some of the energy must be converted to heat energy. This heat energy can not be converted back to the original form of energy by the same process. The process is “irreversible”. One good way to see this is in a famous experiment performed by Joule to measure the factor that must be used when energy in the form of mechanical work is changed to heat energy by any process. The number he obtained was called the mechanical equivalent of heat. The device he used has value as a source of insight far beyond its utility in obtaining that number. The device was a jar of water surrounded by an insulating jacket having the purpose of isolating the system thermally. Thus heat energy could not enter or leave the system through its walls. At the top of the jar was mounted a well insulated crank attached to a paddle wheel inside the jar. Turning the crank allowed mechanical work to be performed on the water in the jar. The system allows a simple mechanistic explanation for how the mechanical work is converted to heat energy. The water is put into motion in a directed manner by the paddle wheels, but looses that directed motion eventually, the motion rather becoming “random” motion characteristic of heat energy. Having a thermometer mounted so that the water temperature can be monitored allows the direct relation between the work done turning the crank and the appearance of heat in the jar, using the heat capacity of water to calculate the amount of added heat energy from the increase in measured temperature. The process is irreversible. There is no way to reverse this randomization of molecular motion to turn the paddle wheel and thereby gain back the mechanical work. The energy has been converted once and for all as long as it is confined to the thermally isolated jar. This is a very revealing example of the nature of friction. Sometimes it is difficult to see a mechanistic picture of how this frictional “dissipation” of energy occurs. Chemical reactions have their own version of friction and are as irreversible as any mechanical process. In electricity the resistance to the flow of electrons results in electrical energy being converted to heat. Knowing this, physics has created two categories for the systems it studies, conservative and non-conservative systems. Newtonian dynamics was developed using conservative, frictionless systems (fictional) and then ex-
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tended to the more difficult non-conservative systems that, as real world processes, involved friction necessarily. These non-conservative systems were irreversible and needed to be open if they were to do anything other than wind down to an equilibrium state and stop.
4.3. Preserving the paradigm involved considering fraction, irreversibility and dissipation It wasn’t until the work of Onsager [6, 71 and others in the 1930’s that a systematic physics of non-equilibrium, irreversible systems was developed. This new physics was thermodynamic rather than mechanistic, but the field of statistical mechanics was later extended to the non-equilibrium domain making the problem of backing up the thermodynamic knowledge with mechanical interpretations in terms of atomic and molecular motion very much more difficult. The increase in difficulty has severely limited the scope of these endeavors. Onsager and the others developed a thermodynamic approach and escaped most of that difficulty. They did so in a way that had its own inbuilt limitations, but that would not be seen for about forty more years when Network Thermodynamics was developed by Oster, Perelson, and Katchalsky and independently by Peusner [8]. The approach Onsager and the others introduced is am “phenomenological” approach. This is very different from the mechanistic physics that was used to describe nonequilibrium dynamic systems up to that time. Onsager’s work was part of what won him a Nobel Prize. Later, Prigogine won a Nobel prize for building on the work of Onsager. One can speculate that Katchalsky may have been there in Prigogine’s place had he not been gunned down by terrorists in 1972. That event changed the history of science and the history of the world. It was Kedem and Katchalsky who introduced non-equilibrium thermodynamics to biology and changed the way we dealt with all the dynamic processes occurring in living systems. Then, along with Oster and Perelson, he explored the new approach that married non-equilibrium thermodynamics to the huge body of theory generated for dynamic electric networks. The impact of all this and the work of others that built on it is largely not understood by many even after complexity theory has grown in its impact on science. The reasons are many and not easily identified without being critical of the way science is practiced. The urge to preserve the mechanistic paradigm and to see thermodynamics as only an appendage has been too strong and in that way too destructive. When quantum theory was born it
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also was shaped by the same urges. The difference is that quantum theory is so much more adaptable to the mechanistic reductionist approach. Its mathematics and the interpretation of the mathematics could be given the very same form as what it was clearly showing to be a failure of Newtonian mechanics. Thermodynamics, on the other hand, uses a different form of mathematics. To most scientists satisfaction quantum mechanics simply helped further the knowledge generated by the Newtonian paradigm and did it little harm. It allowed the reductionist philosophy to appear to have established itself at all levels in the material description of reality. It became possible to see a more or less universal bottoms up approach to science. Yet there are findings from network thermodynamics that raise some very interesting, and possibly troubling questions about this. The lack of interest in these questions parallels a similar lack of interest in questions raised about science by Robert Rosen as he explored the complexity of the world science seemed to have mastered. It is very important that these questions and the findings that have been generated by the use of thermodynamic reasoning that is not constrained by the mechanistic mind set do not get totally ignored and forgotten Yet that may be exactly what is happening as reductionism forges ahead. Some insights into these events of scientific history and the philosophical oversight or lack of same can be had thanks to the contributions of Lakoff [9] who has applied cognitive linguistics to similar situations in politics. His ideas can be married to a concept of memes as “packages” of ideas that get passed along in a manner much analogous to genes.
4.4. Framing the question in science:” Don’t think about
the whole system” As we make models of the world we necessarily use what we have already put together in our minds. The idea that complete objectivity is possible arises when the nature of the modeling relation is misunderstood. A model has many components. It consists of a number of subjective choices. The choice of the formal system we use to encode sensory information in order to think about how the real world is actually operating is a subjective choice. The illusion of objectivity arises from the fact that the question has been framed in a particular way. The idea that there is only one encoding possible in order for the model to be “scientific” forces a choice. As soon as we acknowledge that complex reality can and indeed must be encoded into distinctly different formal systems, the illusion of objectivity is de-
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stroyed. Lakoff uses the sentence “Don’t think of an elephant” to illustrate the impossibility of escaping certain thoughts once such a framing event has occurred. Modern science is framed by reductionist thought and this framing is so effective that the illusion of objectivity can do very well. A large part of Robert Rosen’s work is devoted to helping us see the predicament we are in. It is very interesting how different people react to these ideas. If the concept of complexity being used here is not accepted by a person, there is almost no chance that the person will understand why objectivity is not ever possible. The irony is that that position is a subjective choice. If this is understood, it becomes a simple matter to understand why thermodynamic reasoning is only accepted when it has a mechanistic counterpart. The largest model must be able to encompass everything scientific. The idea that distinctly different formal systems must exist as valid models is unacceptable. Thus the “useful” ideas from thermodynamics are made to be derivable from mechanistic reasoning, namely statistical mechanics, and any other conclusion drawn independent of that mechanical base are suspect.
4.5. Reductionism needs a particular kind of mathematics
t o accomplish its goals The formal systems reductionist science use are mathematical. Yet among the rich formalisms in the total mathematical repertoire, only analytical mathematics is able to fill the needs of the reductionist paradigm. Calculus and differential equations are the essence of the Newtonian approach and were indeed created for that use. Thermodynamics and Rosen’s approach to complexity utilize another kind of mathematics. It is topology that enters as the formalism that provides the needed structure for encoding relationships in the real world. The analytical mathematicians also were forced to utilize topology in the breakthroughs that occurred when the realization that so much of interest had to be encoded using non-linear differential equations as the equations of motion. Topology and differential geometry then were found useful even to reductionists. Out of this the nature of chaotic systems was born and chaos theory had a central role during a brief period of the evolution of complexity theory. It is still not clear to everyone that chaotic dynamics are part of the Newtonian paradigm and do not constitute a distinct formalism different from its largest model. The topological mathematics used to model complex systems and the topological mathematics that must be used to arrive at certain unique new conclusions about
49 the real world using thermodynamic reasoning are very closely related. Rosen, as a student of Rashevsky recognized that topological mathematics was necessary to create the relational biology they both had envisioned as the approach to living systems that was not locked to the severe limits of the reductionist paradigm. The elusive qualities of living things that distinguished them from non-living mechanistic things could only be dealt with by encodings into topological mathematical formalisms. Hence Rosen developed the metabolism-repair M, R system as the formalism he would manipulate to come up with a clear distinction between the classes of things we call “organisms” and the class of things we call “machines”. In doing this he forced his audience to make a hard choice. Either they would accept a formalism that “kept the organization” but left out the “physics” or they were locked into the reductionist’s world of physics which necessarily lost crucial aspects of the complex whole as it was reduced to mere material parts. Thermodynamics in its most powerful form mimics this situation. There are many examples, but only a few need be mentioned to make this point.
4.6. Topological reasoning in thermodynamics leads to
powerful results One of the most interesting examples of the comparison between reductionist methods and relational or topological methods is in the proof of the second law of thermodynamics which was accomplished by Caratheodry after a discussion about the proofs existing up to then with Max Planck [8]. The existing proofs were done using the cyclic quasi-stationary processes developed by Carnot. Plank found these a very unsatisfying way to prove something having the global consequences of the second law. Caratheodry was able to construct a topological proof that rested on one piece of empirical input to confirm it. The second law had its global validity established by Joule’s experiment for it was only necessary to give one instance of irreversibility in the real world to make the model valid. The discovery of a metric structure for thermodynamics had been forsaken until Network Thermodynamics in the hands of Puesner revealed that the network thermodynamic model of a system was canonical. This discovery rests on the topological embedding of the system posited by Onsager, Prigogine and the others in a higher dimensional space[8].
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5. Will science extend to the modeling of complex reality or will it be restricted to the limited domain of the largest model formalism it clings to? This is a question that should not have to be asked. It is the self-imposed limits that scientists have used to frame the answer to the question “What is science?” that make it necessary. The framing of the question in this manner is strengthened by the enormous progress being made in technology. The hunger for more and more practical results makes it very difficult to persuade scientists to spend time and resources pursuing an approach that is just beginning to be recognized by significant minority among them. Should bright students be encouraged to work in this new area? Is it wise to devote any significant portion of the scarce resources given to science to the development of these radically new ideas? It seems to be easier for many scientists to choose an alternative definition for the word “complexity” and to make sure that this definition never allows those using it to step outside the reductionist paradigm. There are a few who will not be restricted in that way. Two examples of recent progress in complexity science are very different in their area of application yet they hold in common their dedication to the new challenge to find distinct formal systems that can not be reduced to the Newtonian paradigm. In their book Into the cool [lo] using earlier work by Schneider and Kay [ll]develop a thesis about the synergy between life on this planet and the conditions that sustain that life based on a broader interpretation of the second law of thermodynamics than used before. They see the second law as demanding that systems respond to imposed gradients by some form of self-organization in order to decrease the gradient. The alternative is to have enormous driving forces stressing the system. Hence the biosphere is believed to be the result of the tendency for the sun’s energy to create stressing gradients. They present evidence for the role that life forms, weather patterns, etc. play in keeping the system stable. Clearly, a concept like this one is not going to be something we prove or disprove. At a time when so much controversy centers around the impact of human activity on planetary conditions, their endeavors do provide a model worth examining further before dismissing it out of hand merely because it forces us to abandon the restricted universe of discourse reductionist science has forced upon us. The second area where some bold new ideas are being offered ins in
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the domain of what we often call the “mind-body” problem. The work of Bach-y-Rita as interpreted by Kercel [12, 131 and others goes tom the heart of many modern controversies. Their interpretation of real experiments involving the sensory behavior of humans is shaking quite a few foundations. At the center of all their models is the central role played by closed loops of causality. These loops are the self-referential heart of complex reality and the human mind seems replete with them. This work and he work of Louie [14], a student of Rosen, showing that Rosen’s {M,R} systems necessarily have non-computable aspects suggests that “artificial intelligence” and “artificial life” are indeed merely machine intelligence and simulations of systems that have some limited life-like qualities. These technological marvels are distinctly different from human intelligence and living systems in many import ways. These new investigations as well as the areas of thermodynamics that have been largely disregarded because of their distinctly non-mechanistic character strongly suggest that science will find a way to include other formalisms and break free from the restrictions it has imposed in itself.
References 1. Rosen, R. Anticipatory Systems, New York, Pergamoii ,1985 2. Rosen, R. LifeIitself, New York, Columbia, 1991 3. Rosen, R. Essays on LifeIitself, New York, Columbia, 2000 4. Mikulecky, D. C. The circle that never ends: Can Complexity be made simple? In Complexity in Chemistry, Biology, and Ecology, D. Bonchev and D. H. Rouvray, eds. New York, Springer, 2005. 5. Truesdell, C. Rational Thermodynamics, New York, McGraw-Hill, 1969 6. Onsager, L. Reciprocal Relations in Irreversible Processes I, Phys. Rev., 1931a, 37, 405-426. 7. Onsager, L. Reciprocal Relations in Irreversible Processes 11, Phys. Rev., 1931b, 38, 2265-2279. 8. Mikulecky, D. C. Applications of Network Thermodynamics to Problems in Biomedical Engineering, New York, New York University Press, 1993. 9. Lakoff, G, Don’t Think of an Elephant! Know Your Values and Frame the Debate White River Junction, Vermont, Chelsea Green Publishing, 2004 10. Schneider, E. D. and Sagan, D. Into the Cool, Chicago, University of Chicago, 2005 11. Schneider, E. D. and J. J. Kay, Life as a manifestation of the second law of thermodynamics, in Modeling Complex Biological Systems, hl. Witten and D. C. Mikulecky, eds, Special Issue of Mathematical and Computer modeling, 1994, 19, 25-48. 12. Kercel, S. W. Journal of Integrative Neuroscience, 2005, 4, 403-406. 13. Kercel, S. W., Reber, A. S. and Manges, W. W. Some Radical Implications
52 of Bach-y-Rita's Discoveries, Journal of Integrative Neuroscience, 2005, 4, 551-566. 14. Louie, A. H. Any Material Realization of the (M,R)-Systems Must Have Noncomputable Models, Journal of Integrative Neuroscience, 2005, 4, 423436.
ON THE IMPORTANCE OF A CERTAIN SLOWNESS Stability, memory and hysteresis in complex systems*
PAUL CILLIERS University of Stellenbosch fpc@sun. ac.za
In philosophy the winner of the race is the one who can run most slowly. Or: the one who gets there last. Wittgenstein (Culture and Value) 1. Introduction
As a result of a whole range of what one could call “pathologies” in contemporary culture, the idea of “slowing down” has of late been mooted in a number of contextsa. A few can be named briefly. The “Slow Food” movement, which started in Italy but has a worldwide following, extols the virtues of decent food made from decent ingredients without compromise. The resistance shown to “junk food” is not only based on aesthetic considerations, but also on ethical (and nutritional) ones. The movement promoting “Slow Cities”, also of Italian origin, fosters an understanding of cities which is more humane. Such cities should encourage walking rather than driving, have small shops with local products rather than shopping malls and, in general, provide opportunities for the community to interact, not to live in isolation. “Slow schooling” is a movement which questions educational processes in a world geared for instant results. It emphasises the contextual nature of knowledge and reminds us that education is a process not a function. On a more personal level, “slow sex” involves attitudes which try to prevent that the values of the marketplace also rule in our intimate relationships. We need to recognize that the journey is *This paper first appeared in Emergence: C o m p l e i t y and Organization. Permission to use the material is gratefully acknowledged. Honor6 (2004) for a discussion of the emergence of several movements which challenge the “cult of speed”.
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more important than the destination, and that takes time. An immediate or perpetual orgasm is really no orgasm at all. There are a number of very important issues at stake in these examples. In what follows, however, the focus will not be on these social movements as such, but on some of the underlying principles which make the debate on slowness an important one. Through an analysis of the temporal nature of complex systems, it will be shown that the cult of speed, and especially the understanding that speed is related to efficiency, is a destructive one. A slower approach is necessary, not only for survival of certain important values or because of romantic ideals, but also because it allows us to cope with the demands of a complex world in a better way. The argument will be made initially by briefly analysing current distortions in our understanding of time. These distortions result, on the one hand, from the rational and instrumental theories we have about a modern world, and, on the other, from the effects of certain technologies, especially communication and computer technologies. In order to show why these are “distortions”, or at least, to show why these distortions are problematic, the temporal nature of complex systems will be discussed. The relationship between memory and anticipation will be central to this discussion, but attention will also be paid to the importance of delay and iteration. These characteristics of complex systems have important implications for our understanding of the formation of identity, both individual identity as well as the identity of groups. In closing, a number of general cultural issues involving the fast and the slow will be looked at. It is important to realise that the argument for slowness is not a conservative one; at least not in the political sense of the word. It is not merely backwards-looking nor a glorification of what has been. Although it emphasises the historical nature of knowledge and memory, the argument for slowness is forward-looking; it is about an engagement with the future as much as with the past. Slowness is in itself a temporal notion, and in many ways the opposite of the notion “static”. In point of fact, it is actually an unreflective fastness which always returns you to the same place. It should also be stated up front that there is no argument against an appropriate fastness. A stew should simmer slowly, but a good steak should be grilled intensely and briefly. The argument is against unreflective speed, speed at all cost, or more precisely, against speed as a virtue in itself; against the alignment of “speed” with notions like efficiency, success, quality and importance. The point is that a system which has carefully accumulated the relevant memories and experiences over time will be in a better position
55 to react quickly than one which is perpetually jumping from one state to the other. Perhaps “slow” and “fast” are not exactly the correct terms to use. Terms like “reflective” and “unreflective”, or “mediated” and “unmediated” may be more accurate. Nevertheless, the debate taking place uses “slow” and “fast”, and the terms do have a certain rhetorical significance. If we stay with their use, it is done in a metonymical way. The whole point of this paper is to give them a richer meaning.
2. Living in the Present
In Tame: The Modern and Postmodern Experience Helga Nowotny (1994) argues for a certain shift in our experience of time. In short, in my paraphrase, and incorporating insights from Bauman (e.g. Bauman 1992), the argument is the following: One of the main aims of the instrumental rationality flowing from the Enlightenment was to create conditions in which we are not controlled by contingency. To achieve these conditions, it is necessary to understand, and preferably control, the future. This demands co-ordinated and goal-oriented action in the present. Modernism becomes a project which demands our total commitment against the forces of irrationality and chaos. The modernist project has two important effects on our understanding of time. In the first place, our actions need to be ceordinated. This can only happen if time is universalised in such a way that we all live in the ‘same’ time. This was achieved mainly through technology, i.e. the construction of accurate clocks, and by regulating time globally. Instead of each person or local community living in their own time, it was necessary to synchronise time in such a way that activities in say New York and Paris could be correlated. The effects of this, however, go much further than merely synchronising time in different parts of the globe. It also means that private time and public time are synchronised. We have to live our lives according to a generalised and controlled understanding of time. A subjective, or should one say phenomenological, experience of time has to be sacrificed in order to generate a universal temporal framework in which we can operate efficiently. The second effect of instrumental rationality on our understanding of time is a result of the desire to control the future; for the future to be made knowable. This would only be possible if the future, in some essential way, resembles the present. We cannot anticipate what we do not know, and
56 therefore we should do everything in our power to create a future which does not disrupt the steady progress we are making towards a better world. This modernist strategy is perhaps exemplified best in Hegel’s dialectic of history which is supposed to converge towards an ultimate solution. The actual result of this ideology is to extend the present into the future, causing us to live in a perpetual “present”. This collapse of the diachronic into the synchronic allows instantaneous interaction between everybody; it creates a world which is fast and efficient. The sacrifice made in order to achieve this, however, is nothing short of sacrificing the very notion of temporality. Nowotny (1994: 16) calls it “the illusion of simultaneity”. The way in which contemporary society lives in an eternal present, or what Eriksen (2001) calls the ‘‘tyranny of the moment”, is made possible, and augmented, by the surge in technology, especially computer and telecommunication technology. We are instantaneously in contact with everybody everywhere. Not only has the distinction between home and the workplace collapsed, but also the distinction between work time and private or leisure time. It is expected that we are available, always and everywhere. This state of affairs may have been less detrimental if it did not also demand instant response. The very reason for mobile phones and e-mail lies in the fact that immediate response is possible. It is in this “immediate” that the main problem lies. There is less and less time for reflection. Reflection involves delay, and in a cult of speed, delay is unacceptable. This move away from reflection to immediate response has profound implications for our understanding of what it is to be human (see Parkins 2004: 376-379), t o which we shall return. The “illusion of simultaneity”, the idea that if we live quickly and efficiently in the present we are somehow closer to reality, is nevertheless exactly that: an illusion. We cannot escape our temporal nature, and our persistence in trying t o do so can only lead t o pathology. The necessity of delay and reflection needs to be re-evaluated. This can be done from a number of perspectives. A Freudian analysis would show that instant gratification is actually a destruction of pleasure. More sublime pleasure can be found only if desire is delayed, anticipated as a memory of something still t o come, yet something which should also in principle be able to surprise us. Derrida calls the illusion of living in the present, of thinking that we have access to an objective understanding of reality if we live “in” it, the “metaphysics of presence” (Derrida 1976: 49). He introduces the notion of dzffkrance specifically to undermine the metaphysics of presence (62). DzffLrance is a notion which intertwines difference (as a spatial notion, one
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could say) and delay (to defer, a temporal notion) as the engines of meaning (Derrida 1982). The present consists only as a combination of memory (of what has been) and anticipation (of what is to come). In his novel Slowness Milan Kundera (1996) uses the metaphor of somebody riding on a motorcycle as being constantly in the present. Speed and the demands of the machine reduces his horizon to something immediate. Someone walking, however, is moving at a pace which allows for a much wider horizon. The stroll unfolds in time in a way which opens up reflection about where we are coming from and where we are going to, as we walk. This theme of both the past and the future being present in a meaningful experience of the present could be pursued in much more detail from both a Freudian and Derridean perspective - and several others too - but the argument for a meaningful temporality, i.e. something slower, will be made here from the perspective of the dynamics of complex systems. 3. Complex Systems, Temporality and Memory
An important aspect of complex systems, one which certainly complicates our understanding and modelling of such systems, is their temporal nature. Complex systems unfold in time, they have a history which co-determines present behaviour and they anticipate the future. Moreover, as we know at least since the work of Prigogine, the behaviour of complex systems are not symmetrical in time. They have a past and a future which are not interchangeable. This being “situated in time” does not always receive adequate attention in our analysis of complexity. The central notion at stake when we talk of time and complexity is that of “memory”. Memory is the persistence of certain states of the system, of carrying something from the past over into the future. It is not merely the remembering of something in the past as if belonging to that past, it is the past being active in the present. We should therefore not think of memory in abstract terms, but of memory as something embodied in the system. In many respects the system is its memory. If one accepts a n understanding of complexity which emphasises the relational nature of the system, it is useful to think of systems as networks where the connections between the nodes are more important than the nodes themselves. The nature of these connections is a result of which states of the network are “retained”, thus the structure of the system is a result of the sedimented history of the system.b bThis argument can also be made using the example of the brain, and links with many
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It is important to remember that memory is not merely a cumulative process. The structure in the network of relationships can only develop if certain states of the network are not maintained. Memory is a result of a process of selection. The states which are significant are repeated more often and therefore form more permanent links in the network. Less significant states will fade away over time. Memory is only possible if the system can also forget‘. What is important to note at this stage is that memory is not an instantaneous thing, it takes time to develop, it is slow. If one characterises memory as the past being carried over into the future, it follows that the future can only be anticipated in terms of the memory of the system. Anticipation is not, or at least, should not be, simply an extrapolation of the present. It is a complex, non-linear process which tries to find some trajectory, some way of “vaulting” from that which has already been experienced to that which has to be coped with. The quality of the anticipation is a function of the quality of the memory. A more varied, richer, deeper and better integrated memory will open up more sophisticated anticipatory capabilities. The obvious question now would be to ask how such a rich memory is formed. This is a complex issue, but for the sake of the argument at stake here, one can say the following: memory is information from the environment which has been filtered, it is that which has been interpreted - by the memory already sedimented in the system - as significant. The identity of the system is, in some sense, its collection of dynamic memories. The implication is that the system cannot reflect, or act upon, everything which is going on in the environment at a given moment. If that were the case, the system would always be merely a reflection of its environment and would have no identity of its own. In order for it to be a system at all, a system which has its own identity, which can react to the environment and not merely mirror it, a certain hysteresis is required. The system must be slower than its environment. The notion of hysteresis is an important oned. It links to the notions of delay and dzffirance discussed above. An event in the environment of the system does not have inherent and immediate significance for the system. Freudian arguments in an interesting way. See Cilliers (1998:4547,92,108)for further discussion. CThisprocess is known as the “use principle” or Hebb’s rule. For more detail see Cilliers
(1998: 17-18,93-94) dHysteresis is the “lagging of effect when cause varies” (Oxford Concise)
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Its significance is established in time as it is reenacted in the system and carried over into the future. In a way, the significance of an event has always already been established (in terms of the memory of the system), but never completely or finally since the significance is always also to be determined by what is still to come. The system has to hang on to some aspects with a certain tenacity; not let go of them too quickly. There is risk involved in this, of course. The system has to invest resources in this process. It cannot maintain everything; it has to select. If too many of the wrong things are carried over it will impair the system’s performance. However, if not enough is carried over, it will also fail. To put it in slightly different terms: the system has to find a way to discriminate between information and noise. If it follows every trend in its environment, it will also be following noise. If it reacts too slowly it will only follow the low-frequency trends, which may also be just noise. The system must be stable enough not to be buffeted around by every fluctuation, and it must be flexible enough to be able to adapt when necessary. Where this optimal point lies is not a question which can be answered from an objective viewpoint. The balance between stability and change is a contingent thing which plays itself out in time. What one can say, though, is that merely to be fast will destroy the system. The argument for a certain slowness should start to take shape now. A viable system has to be able to resist some of the dynamics in its environment. There should be a temporal space in which the past is allowed to play itself out in interaction with present. There must be time for reflection and interpretation. The faster the system becomes, the shallower its resources will be. Ultimately quick behaviour will be no more interesting than Brownian motion. It must be stressed again that the argument for a certain slowness is not a conservative argument. A certain amount of conservation is a prerequisite for a system to maintain itself, of course. The important point, to which we shall return, is that a “slow” strategy is not a backwards-looking one. If a somewhat slower tempo allows a system to develop a richer and more reflective memory, it will allow the system to deal with surprises in its environment in a better way. The argument of slowness is actually an argument for appropriate speed. There is no objective or immediate rule for what that speed is. If anything, it is a matter of experience, and experience (as Aristotle urged) has to be gained, it cannot be “given” in an immediate way. It is experience which determines which piece of meat should be fried quickly and which should simmer slowly in the stew. She who fries
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everything quickly will only have something nice to eat now and then, and then purely by chance.
4. Integrity, Identity and Reflection In his novel The Discovery of Slowness, Sten Nadolny (2003) g'ives us a fictionalised account of the life of John Franklin. Franklin, a l S t h century explorer primarily obsessed with finding the Northwest passage, was slow. His advance (in the Royal Navy) is also slow, mainly because being slow is confused with being stupid. Since he is not stupid he is gradually awarded command, and those working with and under him discover the advantages of being slow. Franklin is persistent, dependable and trustworthy. Even in war, thorough reflection pays dividends not always immediately apparent. His political career, as governor of Van Diemen's Land (now Tasmania), ends badly only because he is disgraced by those out for quick and selfish results. His principles are not negotiable. Franklin is a worthwhile human being because he has integrity. There is a substance to his personality which may seem opaque at first, but eventually shows itself as solidity. The nature of his integrity is directly coupled to his slowness. He assimilates, integrates and reflects before he acts. This is sometimes a ponderous process, and he pays a price for it. Under normal circumstances it is easy not to notice someone like this, or to pass him by, but when there is a crisis, it is him they turn to. He can be trusted, he will come up with something. This is most significant. It is exactly when one would think that being fast is what is required that slowness proves its worth. The link between slowness and integrity is also an issue in J.M. Coetzee's (2005) novel Slow Man. Here we have a character who resists change, despite the cruel demands being made on him. He clings to a set of values important to him, and this gives his personality substance. However, he is too stubborn, and eventually he cannot adapt to new circumstances. One has tremendous sympathy for him, but he turns out to be too slow, and pays the price for it. Even so, it is clear that when there is a choice between the loneliness of the slow and the superficial companionship of the quick, the author sides with the slow. Integrity is more important than a certain kind of success. Despite Coetzee's darker view, there is no reason why slowness should be solitary and sad. Quite the contrary is true. In his novel Slowness, Milan Kundera (1996) shows with great conviction how a certain slowness
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is a pre-requisite for being fully human. What is at stake in this novel is not moral integrity, or a kind of Calvinist dependability, but the sensuality of human interaction, the beauty of a relationship which unfolds in time, the ecstasy of a love which has a history and a future. Being human implies having a body, something with its own rhythms and demands. If we reduce all of this to something merely instrumental, to transactions written in legal terms (not in lyrical prose), if we demand results now, then we will stop being human. Language cannot be reduced to a code; it plays itself out in a certain context. What is more, even if we immerse ourselves in the context we have to wait beyond the last sounds. When all is said, the meaning has not finally arrived yet. It is the anticipation of what it could yet mean which draws us forward. Einmal ist Leinmal. Many may feel that the novel is an outdated art form, something to be replaced with the fast and immediate communication of the digital code. In his book The Moment of Complexity Mark Taylor (2003) seems to lean in this direction. For him, something of a paradigm shift has occurred in the last few decades. We live in a new world with new forms of communication and new forms of learning and human interaction - something he seems quite willing to sell. He resonates with a fast world, something new and exciting. His emphasis on the new goes hand in hand with a nearly interchangeable use of the notions “noise” and “complex”. This problematic conflation is the result of an understanding of complexity primarily informed by chaos theory and of information as entropy. Such an understanding, inspired by the theories of Shannon and Chaitin, will attribute the highest information content to a purely random sequencee. Although these notions are important in the context of computation, they are less useful when talking about complex systems in general. Living systems, including the social systems Taylor explores, are neither random nor chaotic. Despite the fact that they are constituted through non-linear interaction and that they are capable of novel and surprising behaviour, they are well-structured and robust. They persist through time and maintain themselves. When we encounter behaviour that we do not understand, or cannot decode, it often looks like noise, but once it is understood we can see the patterns. These patterns are not merely or only an order imposed by the observer, but also characteristics of the system itself. Complexity may look like noise, but all noise “See Hayles (1999) for a discussion of these issues. Primary sources are Shannon (1949) and Chaitin (1987).
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is not something complex waiting to be decoded. Sometimes noise is just noisef, Taylor’s argument is seductive, but, to my mind, wrong if not harmful. In his fervour to embrace the posthuman he looks at the history of being human with a certain disdain. It seems as if he thinks that complexity is a recent discovery and forgets that being human has always been complex. He embraces the present and wants to deal with it quickly and efficiently. We can be educated instantaneously by electronic means and thus we should make a radical break with old methods. In his excitement he forgets that complex systems, even those in our postmodern world, are constituted historically, that they develop and change and that one of their primary functions is to distinguish between information and noise. This cannot be done at the press of a button. The ideas of the posthuman and the cyborg are of undeniable importanceg, but in our enthusiasm to embrace new modes of being we should be careful not to effect a transformation into something inhumanh. Machines are fast, but they are machines. The present argument is not for an a prior2 rejection of the possibility of machines with human capabilities, or one that denies the intimate relationship humans have always had with technology. Our cultural existence presupposes the use of tools. The difference between using a quill and word-processor may have huge implications on a practical level, but they also share some essential features’. The notion “posthuman” is thus an ambiguous one. If it signifies a tight coupling between the body and technology, we have always been posthuman. If it signifies the obsolescence of the body, perhaps in the sense that a “person” could be downloaded instantaneously as software and run on a machine, it becomes a problematic notion at odds with the idea that human identity is also the result of a certain temporal embodiment. The general argument presented here maintains that any complex system, organic or not, would have to incorporate a certain slowness. The need for slowness, and a warning against the embracing of the
‘A similar, and more detailed argument is made in Cilliers (2005). Wee Badmington 2000 for a collection of philosophical essays on the posthuman. hSee Hayles (1999) for a detailed discussion of cybernetics, the development of the posthuman and the importance of embodiment. See Braidotti (2005) for an affirmative discussion of the posthuman which is neither a euphoric, uncritical acceptance of advanced technology, nor a nostalgic lament for the decline of classical humanism. ‘There would definitely be a lot less drivel to wade through if it was not possible to write so quickly.
63 fast, can perhaps be motivated best from the perspective of philosophy. Philosophy, in its most general form, is essentially the art of reflection. Wendy Parkins (2004) analyses contemporary culture as one moving away from reflection, and argues that what we need is an “ethics of time”. She does not elaborate much on what such a n ethics should look like, but it is something which needs careful attention, not only from a moral perspective, but also from the purely pragmatic perspective of how to live and survive in a fast world. Such an “ethics” will be complex in itself. It will have t o unfold in time and be conscious of its own temporal nature. For now, instead of rushing around like the red queen in a world where change is virtuous merely because it is change, we can start by taking some time out to reflect. At this point the argument for slowness becomes a political one: we should put up some resistance to a culture in which being fast is a virtue in itself. With a little more regularity we should say “no”.
References 1. Badmington, Neil (ed.). 2000. Posthumanism. London: Palgrave. 2. Bauman, Zygmunt. 1992. Intimations of Postmodernity. London: Routledge. 3. Braidotti, Rosi. “Cyberfeminsim with a difference.” http://www.let.uu.nl/womensstudies/rosi/cyberfem.htm (Accessed 8 August 2005) 4. Chaitin, G.L.J. 1987. Algorithmic Information Theory. Cambridge: Cam-
bridge University press. 5. Cilliers, Paul. 1998. Complexity and Postmodernism. Understanding Complex Systems. London: Routledge. 6. Cilliers, Paul. 2005. Complexity, Deconstruction and Relativism. Theory Culture €4 Society, Vol. 22 (5), pp 255-267. 7. Coetzee, JM. 2005. Slow Man. London: Seeker and Warburg. 8. Derrida, Jacques. 1976. Of Grammatology. Baltimore: John Hopkins University Press. 9. Derrida, Jacques. 1982. ”Diffkrance” in Derrida, Jacques. Margins of Philosophy. Chicago: The Harvester Press, pp. 1-27. 10. Eriksen, Thomas Hylland. 2001. Tyranny of the Moment: Fast and Slow Tame in the Information Age. London: Pluto Press. 11. Hayles, N Katherine. 1999. How W e Became Posthuman: Virtual Bodies in Cybernetics, Literature, and Informatics. Chicago: The University of Chicago Press.
12. Honork, Carl. 2004. I n Praise of Slowness: How a Worldwide Movement is Challenging the Cult of Speed. London: Orion. 13. Kundera, Milan. 1996. Slowness. London: Faber and Faber. 14. Nadolny, Sten. 2003. The Discovery of Slowness. Edinburgh: Canongate. 15. Nowotny, Helga. 1994. Time: The Modern and the Postmodern Experience.
Oxford: Polity Press.
64 16. Parkins, Wendy. 2004. “Out of Time: Fast subjects and slow living”. In Time and Society, Vol. 13 No 2, pp. 363-382. 17. Shannon, C.E. 1949. Communication in the presence of noise. Proc. IRE., Vol. 37, pp. 1cb21. 18. Taylor, Mark C. 2003. The Moment of Complexity: Emerging Network Culture. Chicago: The University of Chicago Press.
SIMPLICITY IS N O T TRUTH-INDICATIVE
BRUCE EDMONDS
Centre for Policy Modelling Manchester Metropolitan University http://bruce. edmonds.name
1. Introduction The notion of simplicity as an important property of theories is traditionally ascribed to William of Occam (1180), who extensively used the principle in argument to rebut over-elaborate metaphysical constructions. It has been invoked as part of the explanation why the Copernican account of planetary motion succeeded over the Ptolemaic one whilst the evidence was still equivocal. Newton made it one of his rules of reasoning: “we are t o admit n o more causes of natural things than such as are both true and suficient to explain their appearances f o r Nature is pleased with simplicity and aflects not the pomp of superfluous causes.” [Ref. 1, page 31. Einstein chose the simplest possible system of tensor equations to formalise his theory of General Relativity.2 Phrases like “for the sake of simplicity” are used to justify many modelling decisions (e.g. Ref. 3, page 1). More fundamentally, some go further, claiming (or more often, just assuming) that a simpler theory is somehow more likely to be true (or closer to the truth) than a more complex theory. For some surveys on the philosophy of simplicity see Refs. 4 and 5. In this paper I will argue (along side others, including those in Refs. 6 and 7) that, in general, there is no reason to suppose that the simpler theory is more likely to be true. In other words simplicity does not tell us anything about underlying ‘model bias’.a In this I am saying more than just that simplicity is not necessarily truth-indicative. For although I admit there may be special circumstances where simplicity is truth-indicative, I do not ~~~~
~
~
aModel bias is that effect that the form of a model has upon its efficacy, for example using a series of sinusoid functions to model some data rather than a polynomial of some order.
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66 see that there is any evidence that simplicity and truth are fundamentally related. By analogy, there may be special circumstances where the colour of an object is an indication of its mass (e.g. when someone has gone round calibrating weights and painting them accordingly) but, in general, colour is not at all an indication of mass. To say only that “colour is not necessarily an indication of mass” would be highly misleading, for unless somehow contrived, colour and mass are completely unrelated. I claim that there is no more connection between simplicity and truth than between colour and mass - they are unrelated properties that are only correlated where this is contrived to be so (i.e. by prior assumption or arrangement). Thus, in particular, when t w o theories have equal explanatory power there is no particular reason to prefer the simpler other than convenienceb - it may be that the more complex turns out to more useful in the future, for example by being more amenable to generalisation or explaining new data. Our preference for simpler theories (apart from their obvious practical advantages such as ease of manipulation) can be explained by the facts that, firstly, humans are known to elaborate unsuccessful theories rather than attempt a thorough revision and, secondly, that a fixed set of data can only justify adjusting a certain number of parameters to a given degree of precision. No extra tendency towards simplicity in the natural world is necessary to explain our preference for simpler theories. Thus Occam’s razor eliminates itself (when interpreted in this form). I will start by arguing that a tendency towards elaboration along with the pragmatic advantages are sufficient to explain our preference for simper theories. Then I will briefly look at a couple of a priori arguments that supposedly justify a bias towards simplicity. I follow this by reviewing some evidence as to whether simpler theories are likely to be true taken from the field of Machine Learning, since this is a case that helps distinguish between induction in general and induction by humans. This is followed by a section discussing some special cases where we do have some reason to expect there to be a bias towards simplicity. I briefly consider some of the concepts that have been called “simplicity” in the literature. I conclude with a plea for the abandonment of the use of simplicity as a justification for modelling decisions.
than the peculiar case where one has a limited set of data to fit as discussed in the section on special cases below.
67 2. Elaboration
If one has a theory whose predictions are insufficiently accurate to be acceptable, then it is necessary to change the theory. For human beings it is much easier to elaborate the theory, or otherwise tinker with it, than to undertake a more radical shift (for example, by scrapping the theory and starting again). This elaboration may take many forms, including: adding extra variables or parameters; adding special cases; putting in terms to represent random noise; complicating the model with extra equations or rules; adding meta-rules or models; or using more complicated functions. In Machine Learning terms this might be characterised as a preference for depth-first search over breadth-first search. Classic examples of the elaboration of unsatisfactory theories include increasing the layers of epi-cycles to explain the observations of the orbits of planets in terms of an increasing number of circles and increasing the number of variables and equations in the national economic models in the UK. In the former case the elaboration did increase the accuracy on the existing data because the system of epi-cycles can fitted arbitrarily well to this data, but this is better done with ellipses. Given enough data the system of epi-cycles can be used to successfully predict the orbits to any desired degree of accuracyc, but ellipses will do it with less data and considerably less calculation because the form of ellipses is more suited to describing the true orbits.d Once the a priori bias towards circles is abandoned the system of epi-cycles becomes pointless. In the later case of the macro-economic models the elaboration did not result in the improved prediction of future trends', and in particular these models have failed to predict all the turning points in the UK economy.e Why humans prefer elaboration to more radical theory change is not entirely clear. It may be that it is easier to understand and predict the effect of minor changes to the formulation of a theory in terms its content, so that, if one wants to make a change where one is more certain of improvement, 'One needs t o be a little careful here, unlike ellipses, the system of epi-cycles does not provide of itself any information about the future course of orbits, but given a postulated orbit shape (including ellipses) epi-cycles can be used t o express such orbits and hence used in accurate prediction of the future courses of the planets as well as ellipses. dBeyond a certain point they will do better than an ellipse because they will be able t o include the Eisteinian corrections, however this can still be done easier with corrections t o an ellipse. =Although one was apparently predicted, but this was due t o intervention by the modeller on the basis of his expert knowledge (that destocking that can occur after an oil shock) for details about this see Ref. 8.
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minor changes are a more reliable way of obtaining this. In this case a more certain but marginal improvement may well be preferred to highly uncertain significant improvement. Alternatively, it may be that using a certain model structure biases our view because we get used t o framing our descriptions and observations in this way, using variations of the model as our ‘language’ of representation - akin to Kuhns ‘theoretical spectacle^'.^ In other words, once we have started to think about some phenomena in terms of a particular model, it becomes difficult to think about it in other ways. Finally, it may be due to simple laziness - a wish to ‘fit’ the current data quickly rather than going for longer-term fundamental success ( e g prediction on unseen data). Regardless of the reasons for this tendency towards elaboration, we are well aware of this tendency in our fellows and make use of this knowledge. In particular, we know to distrust a theory (or a story) that shows signs of elaboration - for such elaboration is evidence that the theory might have needed such elaboration in the past - for example because it had a poor record with respect to the evidence. Of course, elaboration is not proof of such a poor record. It may be that the theory was originally formulated in an elaborate form before being tested, but this would be an unusual way for a human to proceed. Thus when presented with alternative theories developed by our fellows, one simpler than the other, we may well guess that the complex one has been elaborated and this would be some (albeit fallible) evidence that it has needed such elaboration. Here it is knowledge of the (human) process that produced the theories that informs us implicitly about their past record against the evidence and past record against evidence is the only guide we have to the future performance of theories. This knowledge, along with an understandable preference for theories that are easily constructible, comprehensible, testable, and communicable provide strong reasons for choosing the simplest adequate theory presented to us. An extra tendency for simplicity to be, of its own, truth-indicative is not needed to explain this preference. In addition to this preference for choosing simpler theories, we also have a bias towards simpler theories in their construction, in that we tend to start our search with something fairly simple and work ‘outwards’ from this point. This process stops when we ‘reach’ an acceptable theory (for our purposes) - in the language of economics we are ‘satisficers’ rather than ‘optimisers’f. fAn ‘optimiser’is someone who searches for the best solution, whilst a ‘satisficer’accepts
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This means that it is almost certain that we will be satisfied with a theory that is simpler than the best theory (if one such exists, alternatively a better theory). This tendency to, on average and in the long term, work from the simpler to the less simple is partly a consequence of the fact that there is a lower bound on the simplicity of our constructions. This lower bound might be represented by single constants in algebra; the empty set in set theory; or a basic non-compound proposition. An alternative approach might be to start from a reasonably complex theory an look at modifications to this (in both simpler and more complex directions). For example in ethology one might start from a description of how an animal appeared to behave and then eliminated irrelevant aspects progressively. In this case, unless one had definite extra evidence to the contrary the sensible bias is towards the original, more complex, account. It is important to constrain our theorising in order that it be effective, but one does not have to use simplicity as this constraint. In" we argue for the use of evidence to determine the starting point for model adaptation rather than simplicity. 3. A Priori Arguments
There have been a number of a priori arguments aimed at justifying a bias towards simplicity - I discuss two of these below. It is impossible to disprove all such arguments in a single chapter so I will confine myself to these two and then make some more general arguments why any such attempt is likely to be mistaken. Kemeny" makes an argument for preferring simpler theories on the presumption that there is a sequence of hypotheses sets of increasing complexity and that a completely correct hypotheses exists - so that once one has reached the set of hypotheses that contains the correct one it is not necessary to search for more complex hypotheses. Thus once the evidence shows one has an acceptable theory one should not look for more complex theories. However this does not show that this is likely to be a better or more efficient search method than starting with complex hypotheses and working from there. The conclusion is merely a reflection of the assumptions he has made. It also does not deal with the case where there is not a single completely 'Lcorrect7'theory but a series of theories of increasing complexity that more precisely fit the data as they get more complex. a solution that meets a given standard.
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Li and Vitbnyi12 show that it is possible to code hypotheses so that the shorter codes correspond to lower measures of complexity so that this coding can be interpreted as prior probabilities (in the Bayesian sense). Thus they suggest that this is a sensible a priori basis for Bayesian prior estimates of hypothesis probability. However, in this case, there is no necessary relation between the complexity of the hypotheses and the length of the codes that is evident before this relation to probabilities is established. Just because such numbers can be interpreted as prior probabilities is not sufficient reason for supposing that it is sensible to do so. As an indication that all arguments that simplicity is a priori likely to be truth-indicative are wrong, consider the following thought experiment. In this experiment there are two lkg masses, A and B, of the same weakly radioactive material, in which atoms currently decay at an average rate of 1 atom per minute. By each mass there is a Geiger counter which detects when an atom in the mass decays and sends a particle towards the counter. The task is to predict which counter will register a particle first after each hour on the clock begins. Now any model which predicts A and B half the time will, in the long run, do equally well. In this case it is abundantly clear that simpler theories are not more likely to be correct - correctness is determined by the proportion of A and B that the theory predicts and nothing else. Now, quite reasonably, one might object that a sensible model concerning radioactive decay is not a directly predictive one but one which specifies the unpredictability of the phenomena and concentrates on ‘second-order’ properties such as the probability distribution. However, this is beside the point - it is a truism to say that those phenomena where our simple theorising succeeds have some simple behaviour and those where such theories do not hold require more complex ones. If the thesis that simplicity is truthindicative is restricted to only those aspects of the natural world where it works, it has some legitimacy but this is merely begging the question - it can not then be invoked to justify the selection of theory about phenomena where it is not known before hand that the right theory is simple. For example, we rightly do not attempt to predict the exact position of each grain of sand with our mathematical models of sand piles but instead concentrate on those aspects of that are amenable to our modelling techniques, such as relation between the frequency and size of a~a1anches.l~ In general we are highly selective about what we attempt to model -we usually concentrate upon that tip of the natural world iceberg which is not too complex for our abilities. In fact there is evidence that we find more complex patterns more
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difficult to per~eive’~, so that we tend to notice the simpler patterns and attribute the more complex ones to meaningless background or randomness. Theoretical results in Machine Learningl5>l6show that, in general, no learning or search algorithm (i.e. method of induction) is better than another. In particular that if a bias towards simplicity is sometimes effective, there must be other domains in which it is counter-productive. To gain any improvement in inductive ability one must apply knowledge about the particular domain one is concerned with. However, these results are extremely abstract and dominated by search spaces that are seemingly random and discontinuous almost everywhere. These theorems do not rule out the possibility that Nature is biased towards producing data that is more amenable simple than these extreme cases. Thus we look to some evidence as to this.
4. Some Evidence from Machine Learning We have two explanations for our preference for simpler theories once the pragmatic advantages are factored out (all evidence being equal): firstly, our knowledge that theories tend to be elaborated when unsuccessful and, secondly, that there is an inherent bias towards simplicity in the natural world. If we were to hold to Occam’s razor (in the form that simplicity is truth-indicative) then we would choose the first because this is sufficient to explain the phenomena - the postulated bias in the natural world is an ‘unnecessary entity’. Since I don’t hold with this form of Occam’s razor I need to look for some evidence to distinguish between the two explanations. Since the tendency towards elaboration is a characteristic of a lot of human theory construction, the critical evidence needs to come from non-human theory construction - situations where theory construction is not based upon a process of elaboration to see if simplicity is truth-indicative there. If a bias towards simplicity was useful apart from our human prelediction for it, this would support its general use. Recently there have been such studies in the field of Machine Learning - where a computer program (rather than a human) attempts the induction. This gives one a test bed, for one can design the induction algorithm to use a simplicity bias or otherwise and compare the results. In one of these studied7 a comprehensive evaluation of all possible theories in a given formal language (to a given depth) were analysed against some real-world data series as follows: firstly as to their effectiveness at fitting some initial portion of the data (the in-sample part of the series), secondly as to their success predicting the continuation of this data (the
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out-of-sample part), and finally, as to the theory’s complexity (measured in this case by the size or depth of the formal expression representing the theory). The theories that were best at fitting the in-sample data were selected. Within this set of ‘best’ theories it was examined whether the simpler theories predicted the out-of-sample data better than the more complex theories. In some cases the simpler hypotheses were not the best predictors of the out-of-sample data. This is evidence that on real world data series and formal models simplicity is not necessarily truth-indicative. In a following study on artificial data generated by an ideal fixed ‘answer’18, it was found that a simplicity bias was useful, but only when the ‘answer’ was also simple. If the answer was complex a bias towards complexity aided the search. This result can be interpreted as exploiting available information about the solution in the search for it - the same lesson that one can draw from the “NO Free Lunch” theorem16. Webblg exhibited an algorithm which systematically extended decision trees (making them more complex) so that they gave the same error rate on the in-sample data, and, on average, gave smaller error rates on the out-ofsample data for several real-life time series. This method was based upon a principle of similarity, which was used to restrict the set of considered hypotheses. A useful survey of results in Machine Learning is Ref. 20 which could be considered a parallel paper to this one, concentrating on the usefulness of a simplicity bias in Machine Learning and only touching upon the wider, philosophical, issue. Thus there is some evidence that, when considering non-human induction, a simplicity bias is not generally helpful or truth-indicative. Rather it seems that it is often used as an ill-defined stand-in for domain knowledge - perhaps this is a reflection of our own ~ 0 g n i t i o n . lThe ~ evidence does not say that a biased towards simplicity is never useful but is sufficient to exclude it being routinely assumed.
5. Special Cases
Although, there is no reason to suppose simplicity is in general truthindicative, there are special circumstances where it might be. These are circumstances where we already have some knowledge that would lead us to expect that the solution might be simple. That is the evidence points to a particular theory (or class of theories) and those happen to be simple. I briefly consider these below. The first is when the phenomena are the result of deliberate human
73 construction. Deliberate human constructions are typically amenable to an almost complete analysis assuming a 'design stance', that is considering the construction from the point of view of it being designed.21 That is, that they are frequently modular, and the result of relatively simple principles iterated many times. If someone asks you to guess the next number is the sequence: 2 ,4,8, 16 you will correctly guess 32, because the nth power of two is the most familiar pattern that describes these five numbers, and you an rely on the fact that the human will have chosen such a pattern and that those patterns tend to be simple (if possibly obscure). It would not be sensible to guess the number 31, despite the fact that there is a rule that would make this the correct answer.g However here we already have some knowledge about what kinds of rule/pattern people are likely to choose and that these are more likely to be simple. The simplicity of these kinds of phenomena is only a hallmark of deliberate, conscious human construction. Products of our unconscious brain or social constructs such as language may be extremely complex for these were not the product of an intentional design process. Thus artists may construct extremely complex artefacts because they do not consciously design every detail of their work but work intuitively a lot of the time with parts and media that are already rich in complexity and meaning. Apart from human construction there are other circumstances where one has good reason to expect simplicity, namely the initial stages of processes that start with the simplest building blocks and work from there. That is the underlying process is known to be one of elaboration. Examples of these might include the construction of progressively higher elements in the early universe, the reactions of bacteria to external stimuli, or, possibly, the first stages in the evolution of life. Evolution started from relatively simple organisms and evolved from there. Obviously when life started the introduction of variety by mutation would be unlikely to result in simplification, since the organisms were about as simple as they could get while still being able to reproduce in their environment. Thus the effective lower bound on complexity of viable organisms means that there is a passive drift towards greater complexity (as opposed to an active drive towards complexity22). However this bias is only significant at the start of the process because the space of possible organisms is so great that once an organism has evolved to be somewhat complex it is almost as likely to evolve to be simpler as ~~~
gFor example, the number of areas that n straight lines, each crossing the perimeter of a circle twice and such that no three lines intersect in a single point, cut that circle into.
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more complex - the lower bound and the ‘inhabited’ part of the possibility space do not impinge upon the possibilities that much so as to significantly bias its evolution towards complexity. Another situation is where one already knows that there is some correct model of some minimum complexity. In this case one heuristic for finding a correct model is to work outwards, searching for increasingly complex models until one comes upon it. There are, of course, other heuristics - the primary reason for starting small are practical; it is far easier and quicker to search through simpler models. In more common situations it might be the case that increasingly complex models may approximate the correct model increasingly, but never completely, well or that no model (however complex) does better than a certain extent. In the first case one is forced into some trade-off between accuracy and convenience. In the second case maybe no model is acceptable, and it is the whole family of models that needs to be changed. Clearly if one has some information about the complexity of the sought after model before the search starts, using that information can make search more efficient, but then this is merely a case of exploiting some knowledge about the solution - it is not an reason for a general bias towards simplicity in other cases. In such circumstances as those above there is some reason to err towards simplicity. However in these circumstance the principle is reducible to a straight forward application of our knowledge about the phenomena that leads us in that direction - principles of simplicity do not give us any ‘extra’ guidance. In these circumstances instead of invoking simplicity as a justification the reason for the expectation can be made explicit. Simplicity as a justification is redundant here. Likewise if one had some evidence that the desired model or theory was complex before the search starts, a bias away from simplicity would be helpful.
6. Versions of “Simplicity”
In order to justify the selection of theories on the basis of simplicity, philosophers have produced many accounts of what simplicity as. These have included almost every possible non-evidential advantage a theory might have, including: number of parameter^^^; extensional p l ~ r a l i t ;y ~ ~ ~ ~ ~ fal~ifiability~~; likelihood26,6; stability27 logical expressive power28; and content2g. These approaches give an uncomfortable feeling of putting the cart before the horse - for instead of deciding what simplicity could meaningfully be and then seeing if (and when) it is useful to be biased towards
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simpler models when trying to explain or predict some observations, they seem to have started with the presumption that a bias towards simplicity is right and then try to find an account of simplicity that is compatible with this idea. In some cases this has almost come full circle. Sober3’ characterises simplicity as informativeness - so that instead of asking whether simplicity is informative he seeks to show that simplicity (as informativeness w.r.t. a specified question) is, in fact, simple! As a result of the prior philosophical need for a definition of “simplicity” to represent a useful bias in model/theory selection, these definitions do not tend to be properties that are the opposite of accounts of complexity. This, in itself, is evidence for the failure of the project to justify a bias away from complexity - it is not the case that a reasonable definition of complexityh is the starting point and then this shown to be counter truth-indicative, but that properties that have nothing to do with a lack of complexity are labelled as “simplicity” in an apparently desperate attempt to justify this assumed bias. If, as I have argued, simplicity is not truth-indicative, this whole enterprise can be abandoned and the misleading label of ‘simplicity’removed from these other properties. This epithet transferral, far from producing insight has produced a fog of differing ‘simplicities’and ‘complexities’which do much to hinder our understanding of the modelling process. Theories can posses a lot of different advantages that are not directly linked to its success at explaining or predicting the evidence, restoring the correct labels for these advantages will help (rather than hinder) the elucidation of their different and interacting roles.
7. An Example - Curve fitting by parameterisation
A particular case of hypothesis selection that has been discussed in the literature is curve fitting. This is the case of deciding which of a variety of hypotheses (in different functional curve ‘forms’) one will select given a set of data (typically given as data points). Typically these ‘forms’ include parameters that are adjusted to fit the data, so that each form corresponds to a family of curves, and the member of that family determined by the choice of values for the parameters. Curve fitting can be a misleading example as it can be difficult to rid oneself of ones intuitions about what sort of curves are useful to posit. One hFor this reason a definition of complexity is not relevant here. For those who are interested in what might be a reasonable definition of complexity see Ref. 31.
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can have strong visual intuitions about the suitability of certain choices which strongly relate to a set of heuristics that are effective in the domains one happens to have experienced. These intuitions might not be helpful in general. In particular, one might happen to know that there is likely to be some random noise in the data, so that choosing a curve that goes through every data point is not likely to result in a line that reflects the case when more data is added. In this case one might choose a smoother curve that might approximate to a local average of the data. A traditional method of smoothing is choosing a polynomial of a lower order or with fewer parameters. This is not, of course, the only choice for smoothing; one might instead use, for example, local regression32 where the fitted curve is a smoothed combination of lines to fit segments of the data. Thus an assumption that a curve with a simpler functional form might be more appropriate for a certain set of data can depend on: firstly, that one has knowledge about the nature of the noise in the data and, secondly, that one chooses the simplicity of the functional form as ones method of smoothing. If, on the other hand, one knew that there was likely to be a sinusoid addition to the underlying data one might seek for such regularities and separate this out. Here a preference for simplicity is merely an expression of a search bias which encodes one’s prior knowledge of the domain. argues that simplicity is justified on the A recent series of grounds that its use can result in greater predictive accuracy on unseen data. This is based on results obtained in Ref. 35. Simplicity in this case is defined as (effectively) the Vapnik-Chervonenkis (VC) dimension36 of the set of curves which in very particular circumstances is equivalent to the number of adjustable parameters in the equation form. The advantages of ‘simplicity’ in this account amount to the prescription not to try and fit more parameters that you have data for, since the larger the set of hypotheses one is selecting from the more likely one is to select a bad hypothesis that ‘fits’ the data purely by chance. The extent of this overfitting can be estimated in particular cases. The argument is that in these cases one can know to choose a form with fewer parameters if one does not have enough data to justify estimating any more, even if such more complex forms may appear to fit the data better. However, this does not effect the general argument - if you have two models whose predictive accuracy, once adjusted f o r its expected overfitting o n limited data, is equal then there would be no reason to choose the family which might be considered simpler to have a simpler form. In circumstances with a fixed amount of data the estimation
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of the extent of overfitting might or might not tip the scales to lead one to select the simpler model. This account gives no support for the thesis that the simplicity of a model gives any indication as to its underlying model bias. Thus, in circumstances where one can always collect more data (so that effectively there is an indefinite amount of data), these arguments provide no reason to select a simpler model, but rather suggest one should collect more data to distinguish which model is better in general. In this case, the decision of when to stop seeking for a model which gives increased predictive accuracy is a practical one: one has to balance the cost of collecting the additional data and using it to search for the most appropriate model against the goodness of the parameterised model. Also the connection between the VC dimension and any recognisable characteristic of simplicity in the family of curves is contingent and tenuous. In the special case where the only way of restricting the VC dimension (or in finite cases, the number of hypotheses) is through the number of adjustable parameters, then it is the case that an equational form with more adjustable parameters will require more data for accurate parameterisation. However there are other ways of restricting the set of hypotheses to reduce the VC dimension; as discussed abovelg successfully used a similarity criterion to do this. Thus one can avoid overfitting by restricting the VC dimension of the set of hypotheses without using any criteria of simplicity or parsimony of adjustable parameters. In a related study3’ examined the connection between the complexity of expressions and (indirectly) their ambiguity and concluded that any measure that restricted the space of models would be equally effective. Of course, one can decide to define simplicity as the VC dimension, but this is begging the question again and one would need to justify this transferred epithet. To summarise this section, there is a limit to the accuracy with which one can adjust a given number of unknown parameters given a certain, jixed amount data - one is only justified in specifying a curve to the extent that one has information on which to base this. Information in terms of a tightly parameterised curve has to come from somewhere. However, in the broader picture where different families of curves are being investigated (for example, by competing teams of scientists continually searching out more data) these considerations give no support to the contention that the simpler family has an advantage in terms of predicting unknown data better.
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8. Concluding Plea It should be clear from the above that, if I am right, model selection ‘for the sake of simplicity’ is either: simply laziness; is really due to practical reasons such as cost or the limitations of the modeller; or is really a relabelling of more sound reasons due to special circumstances or limited data. Thus appeals to it should be recognised as either spurious, dissembling or confusing and hence be abandoned. Indeed rather than assuming that there will always be a simple adequate theory (if only we were clever enough and worked hard enough to find it) we should keep an open mind. On the face of it, it would seem reasonable to expect that complex phenomena will require complex theories for many purposes, and that simple theories will only be adequate for a restricted range of phenomena. However we should always allow for the possibility that occasionally some apparently simple phenomena will require complex theories and apparently complex phenomena allow for simple theories. The point is one can not tell in advance and so it is unwise to make assumptions about this. However, there is a form of Occam’s Razor which represents sound advice as well as perhaps being closer to its Occam’s original formulation (usually rendered as “entities should not be multiplied beyond necessity”), namely: that the elaboration of theory in order to fit a known set of data should be resisted, i.e. that the lack of success of a theory should lead to a more thorough and deeper analysis than we are usually inclined to perform. It is notable that this is a hallmark of genius and perhaps the reason for the success of genius - be strict about theory selection and don’t stop looking until it really works.
Acknowledgements
I would like to thank all those with whom I have discussed or commented upon these ideas (most of whom were not inclined to change their opinions on this matter), including: the participants of the 20(th)Wittgenstein Symposium in 1999; and those at the workshop on the Evolution of Complexity at the VUB in 1997. Also to several anonymous referees who have motivated me to make my position clearer (if more stark). References 1. Newton, I. Philosophia naturalas Princapia Mathematica, (1686).
79 2. Einstein, A., Relativity: the special and the general theory - a popular exposition, London: Methuen, (1920). 3. Gertsbakh, E. and Gertsbakh, I., Measurement Theory for Engineers, Springer, (2003). 4. Hesse, M., Simplicity, in P. Edwards (ed.), The Encyclopaedia of Philosophy, vol. 7., New York: Macmillan, 445-448, (1967). 5. Zellner, A., Keuzenkamp, H. and McAleer, M. (eds.), Simplicity, Inference and Modelling. Cambridge: Cambridge University Press, (2001). 6. Quine, W. V. 0. Simple Theories of a Complex World. In The Ways of Paradox. New York: Random House, 242-246, (1960). 7. Bunge, M., The Myth of Simplicity. Englewood Cliffs, Prentice-Hall, (1963). 8. Moss, S., Artis, M. and Ormerod, P., A Smart Macroeconomic Forecasting System, The Journal of Forecasting 13,299-312, (1994). 9. Kuhn, T. S. The Structure of Scientific Revolutions. Chicago, University of Chicago Press, (1962). 10. Edmonds, B. and Moss, S., From KISS t o KIDS - an anti-simplistic modelling approach. In P. Davidsson et al. (eds.): Multi Agent Based Simulation 2004. Springer, Lecture Notes in Artificial Intelligence, 3415, 130-144, (2005). 11. Kemeny, J. G. Two Measures of Complexity. The Journal of Philosophy, 52, 722-733, (1953). 12. Li, M. and VitBnyi, P. M. B. Philosophical Issues in Kolmogorov Complexity, in Automata, Languages and Programming, 19th International Colloquium, Lecture Notes in Computer Science, 623,1-15, Springer, (1992). 13. Bak, P. How Nature Works: The Science of Self Organized Criticality. Oxford, Oxford University Press, (1997). 14. Charter, N. The Search for Simplicity: A Fundamental Cognitive Principle? The Quarterly Journal of Ezperimental Psychology, 52A,273-302, (1999). 15. Schaffer, C., conservation law for generalization performance. In Proceedings of the llth International conference on Machine Learning, 259-265. New Brunswick, NJ: Morgan Kaufmann, (1994). 16. Wolpert, D. The lack of a priori distinctions between learning algorithms. Neural Computation, 8, 1341-1390, (1996). 17. Murphy, P.M.; Pazzani, M.J. Exploring the Decision Forest: an empirical investigation of Occam’s razor in decision tree induction, Journal of Artificial Intelligence Research, 1, 257-275, (1994). 18. Murphy, P. M. An empirical analysis of the benefit of decision tree size biases as a function of concept distribution. Technical report 95-29, Department of Information and Computer Science, Irvine, (1995). 19. Webb, G . I. Further Evidence against the Utility of Occam’s Razor. Journal of Artaficial Intelligence Research, 4, 397-417, (1996). 20. Domingos, P. Beyond Occam’s Razor: Process-Oriented Evaluation. Machine Learning: ECML 2000, llth European Conference on Machine Learning, Barcelona, Catalonia, Spain, May 31 - June 2, 2000, Proceedings, Lecture Notes in Artificial Intelligence, 1810, (2000). 21. Dennett, D. C., The Intentional Stance. Cambridge, MA: A Bradford Book,
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MIT Press, (1987). 22. McShea, D. Meatzoan Complexity and Evolution: is there a trend? Ewolution, 50, 477-492, (1996) 23. Draper, N. R.; Smith, H. Applied Regression Analysis. New York: John Wiley, (1981). 24. Goodman, N. The Structure of Appearance. Indiapolis: Bobbs-Merrill, (1966). 25. Popper, K. R. Logic of Scientific Discovery. London: Hutchinson, (1968). 26. Rosenkrantz, R. D. Inference, Method and Decision. Boston: Reidel, (1976). 27. Turney, P. The Curve Fitting Problem: A Solution. British Journal for the Philosophy of Science, 41, 509-530, (1990). 28. Osherson, D.N. and Weinstein, S. On Advancing Simple Hypothesis. Philosophy of Science, 57, 266-277, (1990). 29. Good, I. J. Corroboration, Explanation, Evolving Probability and a Sharpened Razor. British Journal f o r the Philosophy of Science, 19, 123-43, (1969). 30. Sober, E. Simplicity. Oxford: Clarendon Press, (1975). 31. Edmonds, B., Syntactic Measures of Complexity. Doctoral Thesis, University of Manchester, Manchester, UK, (1999). (http://bruce.edmonds.name/thesis/) 32. Cleveland W. S., Devlin S. J., Grosse E. Regression By Local Fitting - Methods, Properties, And Computational Algorithms. Journal Of Econometrics, 37, 87-114, (1988). 33. Forster, M. and Sober, E. How to Tell when Simpler, More Unified, or Less Ad Hoc Theories will Provide More Accurate Predictions. British Journal fo. the Philosophy of Science, 45, 1-35, (1994). 34. Forster, M. Model Selection in Science: The Problem of Language Invariance. British Journal for the Philosophy of Science, 50, 83-102, (1999). 35. Akaike, H. Information Theory and an Extension of the Maximum Likelihood Principle, in Petrov, B. N. and Csaki, F. (eds.) 2nd International Symposium on Information Theory, 267-281. Budapest: Akademai Kiado, (1973). 36. Vapnik V. N. and Chervonenkis A. Y. , Necessary And Sufficient Conditions For The Uniform-Convergence Of Means To Their Expectations, Theory Of Probability Applications, 26, 532-553, (1981). 37. Pearl, J. On the Connection Between the Complexity and Credibility of Inferred Models, International Journal of General Systems, 4, 255-264, (1978).
CAN THE WHOLE BE MORE THAN THE COMPUTATION OF THE PARTS? A REFLECTION ON EMERGENCE
CAMILO OLAYA Institute of Management University of St. Gallen (HSG) Dufourstrasse 4Oa, CH-9000,St. Gallen, Switzerland E-mail:
[email protected] The term ‘emergence’ is frequently found in Complexity Science; however, it gives the impression that earlier debates on this topic are not taken fully into account. By considering this situation, the article underlines the need of a consistent discussion when addressing emergence if this term is going t o have an added and meaningful value for learning about complex systems. The promising suitability of process thought and the significance of detailed rulebased modeling are derived from this reflection as further paths t o explore.
1. Introduction
Lately everything seems to emerge. Qualities, properties, matter, life, mind, ideas, inventions, computed macro-states, and many other things, now ‘emerge’. In particular, in what is loosely known as Complexity Science (CS),” the term ‘emergence’ is widely invoked as a pivotal notion, although it is used in diverse senses. And it is not the purpose here to offer a new definition; the article presents important distinctions that usually are absent in CS, regardless of been heavily discussed in other areas, in particular in philosophy. The central point is that emergence, taken as a metaphysical inquiry, seems to be overlooked when developing explanations by means of computer simulation. However, as John Holland reminds us in his book ‘Emergence’,’ CS is committed to make models of the world. “In order to frame the subject, somehow, CS refers here t o approaches related t o nonlinear dynamics, agent-based modeling, chaos theory, artificial life, social simulation, complex adaptive systems, system dynamics, and alike, that claim t o address ‘complexity’ using typically computer simulation. Yet this does not exclude indirect connections to related areas that also address emergence like molecular and evolutionary biology, quantum theory, matter theory, and the philosophy of mind.
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a2
W h a t type of explanation regarding emergence can CS really deliver? The paper introduces a reflection on this question. As a result, an ontological shift to process philosophy arises as a natural option so as to address novelty and change, the motivating concerns behind the term ‘emergence’. The suitability of bottom-up computer modeling is particularly underlined, arising from this shift. 2. The Emergent Question
Emergence still remains as one of the hardest notions to demarcate beyond the sentence ‘the whole is more than the sum of the parts’. Usually the word ‘more’ refers to unpredictable novelty. It has produced an intense debate since we have to face the appealing paradox: How can something that arises from a set of parts be more than the sum of those parts? Fundamentally this question is a metaphysical inquiry, or at least it used to be so; the original thesis proposed the generation of new units, new kinds, new entities, new qualities. This task has been historically cumbersome, to say the least. Jones2 recently remarks: Emergence is largely used as an explanation: such and such an object - ranging from atoms through multicellular organisms to consciousness - is an emergent property of some ensemble of parts. But this leaves an inadequate level of understanding The term emergence has a somewhat equivocal press. For some it is an explanation for the appearance of wholes or coherent objects in any system of things or understandings; while for others it is either meaningless or, conversely, an invocation of something mystical (p. 418). The heated dispute may have been started in 1920 with Samuel Alexander for whom emergence necessarily admits no explanation; he claimed that it has to be accepted as a ”brute empirical fact” (as cited by Pap).3 The reply of Stephen Pepper in 1926 posts the warning sharply: either it is the sum of the parts or it is not4 (no paradox here). Looking again at the quote above of Jones, it seems there has not been too much advance since then. What follows is a brief account of some important distinctions through this philosophical debate;b these distinctions (highlighted in italics) are relevant today, on a first basis because many of them seem to be trivialized or overlooked. bFor comprehensive overviews see e.g. [5], [6].
a3 Going back to 1926, Pepper, ignoring the advice of Alexander, addresses the subject. First, he identifies emergence as a kind of change; second, this change, he summarizes, is derived from three propositions: (i) there are different levels of existence in terms of degrees of integration; (ii) there are marks that make these levels distinguishable from one another over and above the degrees of integration; (iii) these marks can not be deduced from marks at other higher or lower levels. He focuses on laws as the means to describe what emerges, though he remarks that "accurately speaking, we must first observe, laws can not emerge. Emergence is supposed to be a cosmic affair and laws are descriptions" (p. 242).4 Pepper challenges the implicit puzzle of the last two premises: On the one hand, (ii) affirms that there is cumulative change; however, he argues that if we work with laws then what take place are shifts at levels of description, where variables can always be distinguished and placed at proper levels. On the other hand, (iii) affirms that change is not predictable; Pepper asserts that either change is predictable (as in "part of the system") or it is epiphenomena1 since "if they represent irreconcilable inconsistencies in the physical system, they are . ~ alternot laws at all, but statements of chance occurrences" ( ~ . 2 4 4 )The native to laws is to a r m that what emerge are qualities (sensory qualities - metaphysical simples); Pepper dismisses this, rejecting such approach as a theory of epiphenomenalism (no added value) and therefore unsatisfactory for metaphysics. Therefore, for him emergence is meaninglessc Soon after in 1929, Watts Cunningham' underlines that novelty should not imply unintelligibility, i.e. if we have dynamic systems whose very nature change with time, there are emergents which, though non-predictable, can be intelligible; he affirms this assertion for both substancial emergence (a constituent or entity appears de novo) and structural emergence (a novel arrangement of old material). In 1939 Ablowitz conceives the emergence of unpredictable and intelligible qualities as due to a new togetherness of the partsg (hence structural emergence). However Malisoff, in the same year, emphasizes the level of description defined by the observer (thus, we can have alternative descriptions depending on the degree of organization that the observer attributes to the system); this eliminates the mystery on the question, he argues, since it is subject to the mode of observation, i.e .relative to particular specifications or postulates." Stace replies that emergence produces novelty, but what is interesting, he underlines, is absoC A full discussion and criticism of the argument of Pepper is developed by Meehl and
~el~ars.'
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lute novelty (anything which had never appeared before) and not relative novelty (relative to a particular situation).l' Gotshalk, in 1942, emphasizes that novel emergents are irreducible and that they bring into prominence individuality and quality; for him emergents are underivative ingredients of the real and not merely causal reductions;12 it is implicitly a criticism to Pepper (emergence now is meaningful) and Malisoff (for whom the question is only epistemological). Also in 1942 Campbell Garnett emphasizes that the failure of the theory of emergence to establish a vera causa (as it is was suggested by Alexander) implies the incompatibility with scientific methods; as a result, he adheres to the organismic interpretation: a single nature within which two irreducibly distinct types of process are functionally integrated in one organic whole;13 hence, he rejects ontological emergence since complete independence is proclaimed between layers. In the same journal, Henle criticizes the prominent role of the observer for addressing predictability (as in "quality A is predictable by person B on evidence C with degree of assurance D"); for him novelty exists in the universe though this does not entail emergence since two conditions have to be met: it must be logically novel relative to all previously exemplified characteristics, and it must not be merely a spatio-temporal characteristic.'* Bahm in 1947 supports organicism: things are organic unities, i.e. they are both one and many, identity and difference, permanence and change, stability and novelty, substance and function; for him, emergence is just a natural consequence of recognizing those levels or dimensions15 (and therefore there is no paradox). Pap in 1952 attacks the notion of absolute unpredictability ("pure metaphysical obscurantism"); he proposes the possibility of having laws that can correlate an a priori unpredictable quality Q with certain causal condition^.^ Berenda, in similar lines, supports the ability for understanding (structured in reason) as different from the ability for learning (developed in time), for him prediction is just a matter of time, therefore he rejects logical unpredictability.16 Somehow summarizing these earlier debates, Kekes in 1966 characterizes emergence with novelty (when a token of a type appears which never existed before) and unpredictability (this occurrence of novelty is unpredictable as based on the theories of lower levels of existence); his type of novelty is in the lines of Berenda, a priori unpredictability, prior to the occurrence of the event but explicable afterwards. Kekes postulates both novelty and unpredictability as necessary and sufficient conditions of emergence. Moreover, for him qualities and laws as well can emerge, and the emergence of any of
85 them would imply the emergence of an entity in general;d finally, he rejects the triviality of having a type of emergence where, in spite of an adequate lower level theory, logical (metaphysical) unpredictability persists.” More recently, Klee proposes an unified treatment of emergence favoring properties over laws as the emergent units within a micro-deterministic view of nature, i.e. parts determine wholes; however, the preference for properties is for practical reasons given the more complicated path, he argues, implied by a discussion around a theory of lawlikeness.18 In 1997 Bedau proposes weak emergence which is based on the necessary condition of deriving dynamically macrostates via computer simulation; here what emerges is a macrostate of a systemlg (though he seems to equate properties with behaviour). Recent significant questions on ontological emergence (and non-reductive physicalism) can be found in the work of Kim; e.g. he criticizes the notion of downward causation and he suggests the conditions of novel causal powers and non-functionalizability for having ontological emergen~e.~ In a needed call for order, Silberstein and McGeever2’ urge to distinguish between ontological and epistemological emergence; they underline that it is common to draw fallacious conclusions on the existence of ontological emergence (a feature of the world) based on epistemological emergence (fundamentally a description, an explanation, an artefact).e Cunningham in 2001 makes a similar clarification suggesting three types of emergence: ontological emergence (based on a duality, close to the proposals of Campbell Garnett of 1942 and Bahm of 1947) and two types of epistemological emergence: multiple realizable properties (determined fully by the organization of the parts) and highly configurational and holistic properties which is roughly similar to the notion of weak emergence of macrostates of Bedau since it is the power of computation that determines the possibility
dHe assumes order in nature which can be described by laws (determinism), then he argues: ”At any rate, emergent laws describe regularities holding in nature which must have been novel at some time. These regularities describe the behaviour of entities which may or may not have emergent qualities; yet the regularities described by emergent laws could not be described by laws formulated to describe the behaviour of entities on a lower level of integration” (p. 366). ‘Van Gulick’l makes a classification using this distinction, finding four types of epistemological emergence and six types of ontological emergence; e.g. Georgiou” favors the epistemological approach because for him emergent properties provide the identity of a system since they allow an observer to say ‘this is a system of such-and-such and not otherwise’ for they act as unifying reference points for the group of interrelated parts which constitute the system” (p. 242).
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of addressing system-level marks (these are properties for Cunningham); then, he places complex dynamic systems studies in general as an example of epistemological emergence.23 And the story goes on. After examining the discussion, a first impression is that, in CS, either emergence is implicitly taken as a basic principle not to be discussed (as the proposal of Alexander and thus rather unintelligible) or it is understood only as an epistemological issue (sometimes with hasty ontological claims). Or even worse, sometimes it reminds a basic premise treated also as a result .~ are various complications. First or conclusion - Petitio P r i n ~ i p i i There of all, regardless of the development of the previous discussions and the diverse proposals available, ambiguity seems more the rule than the exception; e.g. sometimes emergence seems to denote metaphysical assumptions, and sometimes it seems to point at a level of description or explanation; and many times what we find is a sophisticated (and sophistical) muddle; beyond a discussion around words like ‘ontology’ or ‘epistemology’, it is manifest the confusing inconsistent use of the term, e.g. in the lines of the warning made by Silberstein and McGeever, presented ab0ve.g This should not be a problem as long as assumptions are held consistently taking into account the relevance of that distinction (not very frequent in any case). A second complication is that the emergents take a wide range of forms; in the literature we witness the emergence of properties, behaviours, en-
Roughly speaking: ” Why is it emergent? Because it is complex”. ”Why is it complex? Well, because it is emergent.” Apart from the risk of explaining ‘emergence’ in terms of the perhaps more obscure term ‘complexity’, a short example may picture the panorama: On the one hand, ”Complexity is a marvelous and essential property of our universe. The existence of complexity provokes the emergence of behaviors full of richness but hard t o investigate”(p. 33).24 On the other hand, ”If ‘complexity’ is currently the buzzword of choice for our newly minted millennium, as many theorists proclaim, ‘emergence’ seems t o be the explanation of the hour for how complexity has evolved. Complexity, it is said, is an emergent phenomenon” (p. 18).25The problem for a research program like CS is not only the seemingly unavoidable ambiguity of the terms as such (though a modern Tower of Babel is not a desirable situation), the question aims at reflecting on assumptions, meaningfulness, consistency, and relevance. gThis illustrative example, cited in [20] may suffice: ”Chaos brings a new challenge t o the reductionist view that a system can be understood by breaking it down and studying each piece. This view has been prevalent in science in part because there are so many systems for which the behaviour of the whole is indeed the sum of its parts. Chaos demonstrates, however, that a system can have complicated behaviour that emerges as a consequence of simple, non-linear interaction of only a few components. The interaction of components on one scale can lead to complex global behaviour on a larger scale that in general cannot be deduced from knowledge of the individual components” (p. 186).
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tities, laws, structures, events, qualities, patterns, among others, treated in a seemingly careless way; even sometimes these terms are used on an exchange basis. As a further consideration, in order to hold a consistent position (specially if we are going to assume, accept, or address metaphysical emergence), we can consider to challenge also our ontological ground and not only our conceptualization of ‘emergence’, a term that as time goes by becomes too sophisticated, more disperse, and less useful. The presented historical account emphasizes some difficulties behind the real motivation of the endeavour: to address novelty and change. Could an ontological shift be a more suitable way for tackling the emergent question?
3. Explanations of Uniformity Emergence used to be a cosmic affair (as in ”emergence is a feature of the world”); in fact, a number of discussions within CS seem to point at absolute emergence, but what seems to prevail - at the end - is a particular level of description that habitually takes the form of causal accounts and/or universal laws; such view involves a sort of uniformity that makes harder to address novelty and change. This is presented next. Explanations based on causal accounts hold that there is something special about causal interactions that increases our understanding of the world; causality is the crucial relationship which makes information explanatorily relevant.26 An account of ontological emergence is naturally a formidable challenge for such approach, e.g. it has been widely addressed in terms of multiple complex causal networks or sophisticated law-like expressions.h Silberstein and McGeever summarize the popular position:20 Complexity studies is inclusive of chaos theory, connectionism and artificial life, in that it seeks a grand unified theory of the fundamental and universal laws that govern behavior of all complex and non-linear systems. It would be fair to say that many complexity theorists are after a unified theory of ‘emergence’ (see Kauffman and Wolfram for examples). Complexity theorists (often) reject part-whole reductionism, but they hold that there are fundamental laws of the universe which pertain not only to all of the physical, chemical and biological systems, in the universe, but also to all systems (such as the economy and other social systems) that reach certain degree of ‘complexity’. These ‘meta-laws’ or ‘power-laws’ hRather recent examples are [27], [28], [29].
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govern the emergence or evolution of a system’s behavior in the world (p. 190). Such quests seem inappropriate for coping with emergence; for instance, universal laws are opposed to individuality, ignoring the remark of Gotshalk of 1942: ”The most obvious philosophical importance of the principle of emergence, as I see it, is that it brings into intellectual prominence factors in the universe that actually have been present and in their way important all the time, namely, individuality and quality. In modern scientific causal analysis, both of these factors have tended to be lost from view”12 (p. 397, emphases added). Seemingly they are still lost from view since it can be said that many discussions on emergence have taken an uniform nature for granted (or explicitly as e.g. Kekes17, presented above), as it is introduced next. We try to make sense of a higher level ‘property’ (let’s say) called ‘emergence’ that is not only in function of the parts although it is derived from them. This should challenge some basic frameworks.’ Why? Within a causal view, we seem to follow Aristotle where there is a necessity in causal relations coming from the fact that they derive from the essential characteristics of material things.31 A very brief note on Aristotelian properties: ”essential properties of a thing are those on which its identity depends. They are the properties of a thing which it could never have lacked, and which it could not lose without ceasing to exist or to be what it is. Accidental properties of a thing are properties which that thing could either have had or lacked”(p. 374).32 Such a frame imposes strong constraints for having a notion of emergence within a world of properties ascribed to static substances which in turn seem to be assumed as self-identically enduring stuff - see e.g. [33],[34]; hence substancial emergence (as in Watts Cunningham,’ presented earlier) based on essential qualities, becomes difficult to address. This world depicted above is usually expressed with laws: ”The statement that an object follows a law involves the presumption that there is some informant agency that makes an object to behave in a certain way
‘For instance, Humphreys suggests the examination of the common ontological minimalism, a doctrine based on a small set of premises: (i) to hold a small set of fundamental constituents of the world; (ii) the primacy of intrinsic (non-relational) properties; (iii) all non-fundamental individuals and properties are composed from those fundamental entities. These premises are rooted in two doctrines: a pre-eminence of the logical reconstruction of concepts, and a Humean account of causality.30
89 and not to behave in any other way...If there is only one informant agency, for all objects of a kind in all time, we call it a law”(p. 9).35 We can appreciate why individuality and novelty are hard to meet, nature is assumed uniform;j more specifically this use of laws neglects endogenous change, e.g.: ”the events the law describes also do not change endogenously unless an exogenous force is introduced into the system. The model is universally deterministic. Given complete information about the initial and subsidiary conditions, the law allows us to retrodict events precisely on to the past and to predict them to precisely on to the future”(p. Claims of emergence, framed in such assumptions and focused on universal and abstract modeling, are - seemingly unnoticed - reductionist accounts (regardless of regularly affirming the opposite) whenever order is taken as reducible to a single mode of relatedness, but apparently believing, at the same time, in something ‘more than the sum of the parts’; this is indeed a mystic path. Already for Pepper was clear that we can not have both. If there is a function (non-linear usually; it comes to mind the condition of non-functionalizability of Kim), if there is a law (restricted in any form), or if there are causal statements, then to deal with absolute novelty beyond ‘the parts’ is not uncomplicated - see e.g. [37], [38]. The old warning of Gotshalk made in 1932 helps to rephrase the point and the relevance:3g Uniformity, if anything significant, is a relation between a genuine diversity. But the causal theory, as set forth, actually applies to no genuine diversity. We raise no question of the theory’s abstract truth; the theory, as stated, is abstractly true enough; the same cause, under similar conditions, no doubt should produce the same effect, again and again It merely states (in sum) that A is always A, and fails, so far as experience goes, to state a relationship between real diversity. In short, it amounts to a true but trifling proposition (pp. 142-143). In such scenario, prediction is very narrow: on the basis of empirical data”we may have a well-confirmed ‘emergence law’ to the effect that whenever a system instantiates basal condition M it instantiates an emergent, E” (p. 8);5 to label it ‘prediction’ is almost a compliment; and this type JThis is perfectly illustrated in the quote of the physicist Wigner: ”It is ...essential that, given the essential initial conditions, the result will be the same no matter where and when we realize these ...If it were not so ...it might have been impossible for us to discover laws of nature” - as cited by Schlesinger (p. 529).36
90 of inductive predictions is not the interesting matter around the emergent question and unpredictability. What we would like to understand is why A is not always A , and not why A is always A. In short, immutable substances related to a sort of causal forces or lawlike statements for complex systems is a contradiction in terms; it is the search for predictive theories of ‘novelty’. 4. Addressing Novelty
Complexity Science is supposed to address change, at least if the habitual allusion to ‘emergence’ is going to be conceived as a kind of change. There are already accounts of emergence understood as processes of interacting, immutable (unchanging) entities (or as transitions between different entities) where results can be repeated as long as the circumstances are similar. But a static concept of entities is at the center of the puzzle, that is, the neglect of transition within entities. Time is left out. Why? Leclerc expresses it ~ n m i s t a k a b l y : ~ ~ A stuff endures by virtue of its inertness; its endurance is conceived to be the retention of its self-identity... [which]is irrelevant to any temporal passage; the stuff is what it is quite irrespective of any transition ...it means that stuff cannot endure... it is eternal ... For if all substance be eternal, what then is duration? What is time? An ontology of eternity can in the end only explain duration as an appearance and thus as illusory (pp. 227-228, 229). How to include time? One natural option is to include duration in the very character of substances, i.e.”it must be the nature of substance to be in passage, in transition”(p. 230).33 A natural option, then, is to conceive them as processes of activities, e.g. a complex system might be conceived as a process of evolving agents; these agents are thus activities; moreover, they are agents because they act, which in turn can be conceived as the use of rules in interaction processes. The significant term is ‘process’ which takes the center of the stage. The basic shift is from static to changing entities. Our current foundations do not ease such a view given that we are embedded in Western metaphysics which since Aristotle favors things and static s ~ b s t a n c e sYet, . ~ ~ process can become a fundamental notion with which events and experience might be (re)-interpreted;*l Leclerc remarks the shift: ”For Aristotle substance is ‘informed’matter; for Whitehead substance or actual entity is ‘informed’activity” (p. 242).33 Therefore
91 emergents would not be merely things/properties/etc. that surface at some point of time within a particular ‘process’. Emergence would be fundamentally a process in the lines of thought outlined by thinkers like Bergson or Whitehead (and surely back to Heraclitus of Ephesus). An agent i s a process of activities as well. And the process of multiple inter-acting agents, i.e. rule users, that unfolds through time is what we distinguish as emergence. No interactions, no emergence. No process, no emergence. After all emergence is a kind of change. For instance, the earlier dilemma seems less complicated now. Emergence arises from unique interactions unfolding through time, in this sense is constituted by and generated from interacting dynamic agents. And this process only arises as long as we have time and interactions, in this sense is autonomous at the system level (by principle a process is not separable as such, it is a whole). hrthermore, regarding hierarchies, the spatial multilayered scale is confronted with a more important temporal scale where ”higher levels reproduce themselves over longer durations than lower levthis statement suggests a different way to explore the concept e l s ” ( ~9);42 . of ‘different layers’ of existence. In short, the system-level process of interactions unfolding through time as a unit cell-complex is what we would call emergence; the system i s that process whose behaviour we assess as emergent from local interactions. Emergence then is just the process at the system level, nothing more. To name the system is to name ‘what emerges’ so to speak. No need of something ‘ e ~ t r a ’ . ~ The main goal at this point is to consider this exploration for CS. To develop the connection between emergence and process thought is not the purpose of this article.’ But for now suggestive ideas would be: To act i s to exist. Being is becoming. To understand the becoming of a dynamic
k T ~ proposals o of dynamic interactions that would constitute non-magical explanans for ‘emergent’ phenomena are presented in [43]and [44]. ‘A broad view on process thought is introduced in [40]. The philosophy of organism, as proposed by Whitehead, particularly in his major work of 1929 ‘Process and can be a starting point for approaching process thought more formally. Yet, beyond this point, a process philosophy may have diverse interpretations and this article is not necessarily committed with particular assumptions; we can expand it in different ways, e.g. presentationalist/idealist paths closer t o the ideas of Whitehead or re-presentationalist/realist paths closer to the Evolutionary Epistemology of Campbell and Popper or the Evolutionary Realism of Dopfer. Also limitations and specific criticisms can be found, e.g. shortcomings related to the nature of composite entities in this in particular Douglas examines framework have been debated, e.g. [33],[45],[46],[47]; and rejects the possibility of characterizing emergence within process thought.48
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process is to explain it as such. Substances are processes of activities. Agency is constant transition and it is by nature social. Actual occasions are unique entities. There are no essential causes, entities exist in change and are social by nature. Durations, activities, and phases take place identifying an operating unit. Novel togetherness is a principle, not a derivative. But there is no morphological analysis by components of static ‘stuff’ although processes indeed can be characterized. The shift would underline that emergence, altogether with contingency, novelty, and creativity, become fundamental categories of metaphysical ~nderstanding.~’ This does not necessarily resolve the issue; but the debate would be seemingly more intelligibly. Intuitively a kind of change could be better addressed within an ontology of change; after all process philosophy presents an ontology committed to novelty.
5. And Individuality Another central point from the discussion on emergence is individuality. How to approach it? This question is related to the methods and types of explanation that CS aims to provide. The reflection above brings elements to bear in mind. The general concern is still model building which in fact is a major feature of CS: the use of computer simulation models. This particular characteristic is also a current challenge in the realm of explanation, as Berger notices: ”It is reasonable to say that modelling explanations dramatically increase our understanding of the world. But the modelling explanations found in contemporary scientific research show that the interesting claims of causal accounts are untenable...An adequate account of scientific explanation must accommodate modelling explanations, because they are simply too central to ignore”(pp. 329, 330).26 Keeping in mind the previous discussion, simulation models can be characterized as systems of interacting agents using evolving rules. Addressing the evolution of dynamic sets of rules (structure, origination, adoption frequencies, selection criteria, individual and collective retention, etc.) we can explain the becoming of emergents which are constituted by interacting evolving agents. This is particularly relevant for modeling social systems; for instance, the ‘parts’ can be related to agents using rules, e.g. cognitive, behavioural, and blueprint rules, see [49]. Each agent is unique and is changing constantly; they may belong to a generic class but each agent does not necessarily apply in the same way his particular set of rules, and a given agent does not act necessarily in the same way today than yester-
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day, even in similar circumstances; moreover, the set of rules of each agent evolves as well. And in a further level, the agents also evolve as such, that is, the generic class of agents evolves too; perhaps over a longer time scope. In one word, there is variety: ”many individuals of a kind, where each constitutes an actualization of a distinct idea. There are, on the one hand, many individuals that are many matter-energy actualizations, and, on the other hand, many ideas that can be actualized”(p. 14).35Furthermore, this variety changes through time - variation (e.g. mutations in biology). Explicitly, the implication is to question abstract modeling (e.g. ”Kauffman’s style”). A foundation on processes of activities underlines the primacy of acting individuals (agents), variety and variation. The inclination here is for a detailed, qualitative, rule-based, ’expert system’ approach where details do matter.m 6. Looking Ahead
Bearing in mind the emergent question, the last point to comment is that an approach based exclusively on computation has to specify clearly how it is going to meet ontological emergence when such claims are asserted. It is not straightforward to declare non-reductionism using computer simulation. Being closed software systems, it is not evident how something arising from a computation can be (or even just represent) more than essentially that computation (which is a formal deduction, or at least a positive calculation anyway) beyond suggestive metaphors or the association of reductionism with linearity. If we are going to address emergence then the type of epistemological bridge between computer simulation and metaphysical emergent entities has to be built - and carefully - if we are really going to meet it. Can it be done? After all ontological emergence used to be the original question. Already W i m ~ a t noticed: t~~ ”Most scientists regard a system property as emergent relative to properties of its parts if it depends upon their mode of organization - a view consistent with reduction”(p. 269).” He refers to areas such as non-linear dynamics, connectionist modelling, “‘Indeed, Chris Langton, leading researcher on artificial life, has already stated that ”the quest for global rather than local control mechanisms (rules) is the source of the failure of the entire program of modeling complex behaviors up to the present, especially, much of the work on artificial intelligence”(p. 24).50 - see also [51]. “It is also a matter of what is understood by ‘reduction’; Wimsatt clarifies: ”Most scientists see reductionism as a species of explanatory mechanistic materialism which may not even involve laws or theories, as those terms are traditionally understood by philosophers”(p. 292).
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chaos, and artificial life. In principle, epistemological - or ‘weak’ - emergence (close to equating ‘emergent’with ‘computed’) does not exclude with what might be labelled ontological reduction i.e. all higher level entities and processes are nothing more than certain combinations of lower base level entities and processes,52which habitually is what seems to be rejected in the discourse of CS. But there is nothing wrong with recognizing reducti0nism.O What is wrong is whenever scientists claim to have non-reducible accounts of (ontological) emergence on grounds that do not necessarily allow such attempts. Reduction concerns explanation; and it seems that when the term ’emergence’ is used in CS, many times can be successfully understood only as a type of reductive explanation. However, maybe there are real emergent (novel and unpredictable) entities, and maybe they can be suitable of being consciously targeted (or rejected) by CS. An ontological shift to process could be fully explored; even more, perhaps then, the question on emergence might be dissolved. A further step takes place in the roles and functions ascribed to simulation models; detailed modeling does not mean to dismiss the system-level focus of explanations. Quite the contrary. For example, we can follow a path closer to the semantic view where a theory is the whole class of its models (all possible interpretations), such a family of models would be a highly abstract conception, ”carrying no information other than the structure of its parent formal system”(p. 301).58The ‘synoptic vision’, closer to the metaphorical view of explanation, has been also suggested5’. Or we can develop for instance the proposal of Hayek“ with his ‘explanation of the principle’ where we focus on types of patterns to expect; instead of ‘prediction’ we can refer to ‘orientation’ and we can prefer the term ‘cultivation’ over ‘control’. To sum up, process thought arises as a natural option for addressing unpredictable novelty, the traditional concern behind the term ‘emergence’. It does not mean the usual notion of process in uniform nature where is a channel to represent the interaction of unchanging parts in order to label
OIn his stimulating paper, Bedaulg exposes the promising possibilities of working with weak emergence, though he also rejects the meaningfulness of addressing absolute emergence - ”logically possible but uncomfortable like magic; and irrelevant”. In related lines, B e ~ h t e lhas ~ ~to ‘defend’ and to make a case for the compatibility of complex systems and reduction; he is right and a defence should not be necessary; unfortunately it seems it is needed; moreover, the role of mechanism, as a kind of explanation, has been recently developed in this context - see [54], [55], [56];in particular for complex systems see [57].
95 the change of macro-states at the system level as ‘dynamic’; that is, it is not merely the variation between two or more consecutive states; this is misleading since processes of activities are left out, that is, agency (as acting) is left out. W h a t is underlined here is a foundational shift, with a first indication t h a t favors detailed modeling. This may shed a light on understanding novelty; and it may provide an intelligible discourse on emergence. After all, since 1926, the challenge of Pepper still deserves a satisfactory answer within CS. But all of these concerns are related to the questions of change and novelty coherent with a creative and diverse (complex) world; right there is where the discussion should take place.
Acknowledgments T h e author thanks three anonymous reviewers for their helpful criticism and suggestions. Further thanks go t o Peter Douglas, Kristjan Ambroz and Markus Schwaninger, for their valuable comments on earlier drafts of this paper. T h e usual disclaimer applies.
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98 353 (1984). 53. W. Bechtel, The Compatibility of Complex Systems and Reduction: A Case Analysis of Memory Research. Minds and Machines, 11, 483-502 (2001). 54. P. Machamer, L. Darden and C. F. Craver, Thinking About Mechanisms. Philosophy of Science, 67 (l),1-25 (2000). 55. S. S. Glennan, Rethinking Mechanistic Explanation. Philosophy of Science, 69, 342-353 (2002). 56. J. G . Tabery, Synthesizing Activities and Interactions in the Concept of a Mechanism. Philosophy of Science, 71, 1-15 (2004). 57. W. Bechtel and R. C. Richardson, Discovering Complexity: Decomposition and Localization as Strategies in Scientific Research. Princeton, N. J., Princeton University Press (1993). 58. M. Hesse, Models and Analogies. In: W. Newton-Smith (Ed.), A Companion to the Philosophy of Science, Malden/Oxford, Blackwell Publishers, 299-307 (2000). 59. A. L. Plamondon, Whitehead’s Organic Philosophy of Science. Albany, State University of New York Press (1979). 60. F. A. Hayek, Degrees of Explanation. The British Journal of the Philosophy of Science, 6 (23), 20S225 (1955).
WHY DIACHRONICALLY EMERGENT PROPERTIES
MUST ALSO BE SALIENT
CYFULLE IMBERT IHPST / Universit Paris 1 Panthon - Sorbonne In this paper, I criticize Bedau’s definition of ‘diachronically emergent properties’ (DEPs), which says that a property is a DEP if it can only be predicted by a simulation (simulation requirement) and is nominally emergent. I argue at length that this definition is not complete because it fails t o eliminate trivial cases. I discuss the features that an additional criterion should meet in order t o complete the definition and I develop a notion, salience, which together with the simulation requirement can be used t o characterize DEPs. In the second part of the paper, I sketch this notion. Basically, a property is salient when one can find an indicator, namely a descriptive function (DF), that is such that its fitting description shifts from one elementary mathematical object (EMO) to another when the property appears. Finally, I discuss restrictions that must be brought t o what can count as DFs and EMOs if the definition of salience is t o work and be non trivial. I conclude that salience (or a refined version of it) can complete the definition of DEPs.
In the literature about emergent properties, attention has recently been paid to properties that emerge diachronically in complex systems, for example when a tornado ends up appearing in a usually quiet area. The central idea behind diachronic emergence is that these emergent properties can be explained or derived, at least in principle, from the system microdynamics (so they have nothing mysterious), but only in a complex way, e.g. for the apparition of the tornado by numerically solving NavierStokes equations. In the past decade, different definitions have been proposed to characterize more precisely diachronically emergent properties (DEPs). Stephan’ emphasizes that DEPs are highly unpredictable, as demonstrated in the case of deterministic chaos. Bedau2 claims that a property is diachronically emergent (he uses the term ‘weakly emergent’) if it can be derived from the system’s microdynamics and external conditions but only by simulation. I label this latter condition the ‘simulation requirement’ (SR). In this paper, I focus on Bedau’s definition, which I am definitely sup-
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portive of, and I try to refine it further by making it more stringent. I agree that the definition is sufficiently broad to be fruitfully applied to a large variety of systems that exhibit properties that seem to be DEPs. Yet, I argue that the SR is not enough to define DEPs and that the definition, as stated by Bedau, encompasses too many properties. I try in a second step to build a notion, namely salience, that is appropriate to complete the definition and capture only the right set of properties.
1. Preliminaries In order to present the problem, I shall restrict for simplicity to an example belonging to discrete mathematics, namely the case of a one dimensional CA system composed of cells, each colored black or white.a A rule determines the color of each cell at each step. Below is rule 110. It says for example that when a CA and its neighbours are black, the CA turns white at the next step.
Figure 1. Rule 110
The evolution of such a CA system, composed of automata following rule 110, depends on its initial condition. Figures 2 and 3 represent this evolution when the initial condition is a single black cell. Each line represents the system state at a given step and the evolution is downwards. One can see on these figures that in this case, the evolution is neither highly regular nor completely random. We can witness the emergence of patterns such as occasional big triangles or as the vertical column of triangles in the right. For the discussion that follows, it is appropriate that I give pet names to the properties that the discussion is going to revolve upon. ‘Blackcell’refers to the property ‘having CA 10 in a black state’ and it is true at time 20. ‘Bigtriangle’ refers to the property ‘having a big triangle appearing around CA number 20 on the lattice’ and it is true around time 80. ‘Microstate50’ aFor a clear presentation of cellular automata, see for example [3].
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Figure 2. Rule 110, starting from a single black cell, 250 steps. Figure taken from A New Kind of Science, chap. 2, reproduced with permission of Stephen Wolfram, LLC.
refers to the property ‘being in the configuration that the system is in at step 50’ and it is true at time 50. ‘Verticalcolumn’ refers to the property ‘having a vertical column of triangles appearing around CA 60’ and it is true around time 350. These are property names but for linguistic commodity, I shall also use these names to refer to the instantiation of these properties at the mentioned times and also as if they designated emerging things. I also need to introduce scraps of terminology. I shall use ‘microproperty’ to refer to a property of a basic constituent. In our examples, the two basic microproperties of a CA are ‘being black’ or ‘being white’ and you can specify them by including time, e.g. ‘being black at time 3’. Following the uses in statistical physics, I shall call ‘microstates’ conjunctive properties that consist of the ordered enumeration of all the microproperties of the parts of the system S. I shall also call ‘macroproperties’ proper-
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Figure 3. Rule 110,500 steps. Figure from A New Kind of Science, chap. 2, reproduced with permission of Stephen Wolfram, LLC.
ties that can only be possessed by the whole system but not by its part. Such properties are sometimes referred to in the literature as ‘nominally emergent’.4 Structural properties, involving microproperties and a relation between them are a subspecies of nominally emergent proper tie^.^ Examples of macroproperties are Blaekcell, Microstate50 or, for a cup of water, fluidity or transparency, because molecules of water cannot be said to be fluid or transparent. I will not venture here in giving a more detailed general definition of macroproperties because I shall not need that much to define DEPs. Bedau himself acknowledges that “full understanding of nominal emergence would require a general theory of when macro entities have a new kind of property that their constituents cannot have”.4 That should not worry us too much because in our CA system example, we can very easily, if we need to, depart on a purely logical ground what counts as a macroproperty from what does not.
103 2. Statement of the problem (Pb)
I can now phrase precisely why I am not satisfied with Bedau’s definition of DEPs. The consequence of equating the fact of being a DEP with the fact of satisfying the simulation requirement (SR) is that
(1) Blackcell, Microstate 50 and any coined conjunctive property that you feel like building up by the conjunction of microproperties, e.g. ‘having CA 24 black at time 3 and CA 47 white at time 567’- I call these “deceptive properties’; (2) respectable properties such as Verticalcolumn, Bigtriangle, or any emerging pattern - I call these “target properties”; must be treated on a par and considered as DEPs because we need to run a computer simulation to predict them all.
I think this is an unpalatable consequence of the definition, which shows that the SR is not enough to define DEPs. 2.1. Two ways to face (Pb)
I shall now examine two ways to answer my claim that the SR is not sufficient to define DEPs and I shall show why I think these answers are unsatisfactory.
2.1.1. Is nominal emergence enough to solve (Pb)?
I have assumed in my phrasing of the problem that the SR is what matters in the definition of DEPs. Bedau may perhaps argue that I have not faithfully reported his view, because he says: “Assume that P is a nominally emergent property possessed by some locally reducible system S. Then P is weakly emergent if and only if P is derivable from all of S’s micro facts but only by simulation”. So according to Bedau the SR applies only to nominally emergent properties. Thus I can be reproached for having forgotten the condition about P being nominally emergent or else for having misused the notion: Blackcell (‘having CA 20 black’) seems to be a property of the whole system and so to be nominally emergent ... but isn’t it because I used a logical trick to forge Blackcell, instead of simply talking of a less intricate microproperty which applies to CA 20 at time 10, namely ‘being black’? Well, maybe. I leave to the reader’s metaphysical intuitions whether the property ‘having a big wart on her nose’ (which is true of the witch that gives the apple to Snow White) is not a very respectable property too and
104 is really the same as ‘being in a warty state’ (which, for a coarse-grained description of the witch, is true of the descriptive cell corresponding to the witch’s nose). In any case, the conclusion should at least be that if we want to be able to determine which properties are DEPs we really need much more theorizing about nominal emergence to select the right properties. But I strongly doubt that a good theory about nominal emergence will do. A reason is that, from a descriptive point of view, properties such as Bigtriangle or the appearance of a tornado in a fluid, which are paradigms for diachronical emergence, describe local features indeed,b and that these features do not necessarily involve the whole system for being predicated but can be predicated of just a few CAs, even if they are generated by the whole system evolution (just like Blackcell). So from the nominal emergence perspective, the difference between Blackcell and Bigtriangle is very slight, whereas my guess is that Blackcell is not a DEP in our example, whereas the appearance of a tornado is. Another problem is that properties which are pure conjunction of microproperties and involve the whole system, such as Microstate50, will still be nominally emergent, however unremarkable they may be. It is still possible to hope that a strengthening of nominal emergence may make it possible to get rid of them too. Yet it seems to me that with this strategy, we are progressively lead towards a different kind of emergence leaning on a strong distinction between whole and parts. The solution I propose in the second part of this paper, with the use of the notion of salience, does not make use at all of nominal emergence.
2.1.2. Is there more to diachronical emergence than mere computational irreducibility? A second way to face (Pb) is to hold tight like this: “Yes indeed, the SR is what only matters to define DEPs and there is no reason to make further distinctions between properties, because as far as weak emergence is concerned, these properties are really on a par. If you want to predict the apparition of Blackcell or Microstate50, you have to run a simulation and let all these properties diachronically emerge. These properties are so to speak “as diachronically emergent as” Bigtriangle or Verticalcolumn because the same computational effort (modulo time linearity to account for different appearance times) is required to predict them all. This computational effort bSee also note g.
105 corresponds precisely to the running of the dynamics of the whole system and this is where the notion of whole system has a part to play.” I do not think that Bedau would hold tight like this. In [2], the examples are about the emergence of periodic or stable configurations in the Game of Life and about adaptation of mutation rates in a model of evolving life. That is not exactly what one would call trivial or insignificant properties of a system, as Blackcell or Microstate50 can be assessed to be. So if the definition purports to include in its scope such insignificant properties, this should be made clear and the examples are misleading because they point at a specific class of very remarkable DEPs. Besides, if there is nothing more to diachronic emergence than the SR, then it is maybe better not to talk of emergence at all and to speak merely of properties of computationally irreducible systems6 , or of properties that are for a system computationally irreducible: if one views the evolution of a system as a computation, then a system is computationally irreducible if given its initial state, there exists no shorter computation that enables to predict a later state of the system. In other words, there exists no shortcut to predict the properties of the system. Yet, I am quite reluctant to content with an equivalence between diachronic emergence and computational irreducibility. Giving a clear definition of computational irreducibility and finding that there are systems that are computationally irreducible, as in the case of low-dimensional chaos7, is one thing. Then, it could be a brute fact about nature that the properties that cannot be predicted except by a simulation are not really worthy of interest. Take for example a classical gas. Perhaps it is true that there is no way to predict exactly its future microstates (that is to say, to predict the position and velocity for each of the particles), except by a simulation. But who really cares? We can still use statistical physics to (try to) calculate more remarkable properties. So computational irreducibility would not be such a big issue, if it was just met in the case of such anonymous properties. But this is not the case. And a good incentive to talk about diachronically emergent properties is the two-piece fact (S) that, as abundantly illustrated by [6] and as can be seen in figure 3 with Bigtriangle or Verticalcolumn: (Sl) there seems to be computationally irreducible systems and (S2) these systems generate among other things some properties (e.g. periodicity when Verticalcolumn appears) that can be as respectable, remarkable, new, worthy of interest or what you like as the properties we
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106 ordinarily predict using analytical methods. My conclusion is that there is really something wanting in a definition of diachronic emergence that only relies on the SR. Various requirements can be found in the literature’, for emergent properties, in particular novelty and irreducibility.c The SR requirement seems to fulfill the irreducibility requirement. So my claim is that, in the case of diachronic emergence, something like the novelty requirement must also be honored one way or another. 2.2. How to complete the simulation requirement?
It did not go unnoticed that I left (S2) quite vague and used so far unsatisfactory adjectives (‘interesting’, ‘remarkable’, etc.). The purpose was to keep my different claims distinct so that one can agree with my diagnosis (the SR is not enough) and possibly disagree with the way I try to solve the problem (what is missing). What I want to do now is to give a criterion that enables to depart the computationally irreducible properties that seem to have nothing special (deceptive properties) from the ones that seem to have something more (Verticalcolumn, Bigtriangle). But before presenting my solution, I think it is appropriate to list the constraints that weigh on this criterion. 2.2.1. T h e criterion m u s t n o t rely o n intrinsic features of the property but m u s t be contextual (Cl)
As I stated above, properties that are produced by a computationally irreducible system can be the same as the ones we predict in other analytically solvable cases, e.g. periodicity of a configuration. Therefore one should not be after a criterion that would be based on a logical analysis of each property, or on a complexity measure or any other feature characterizing intrinsically the properties. To put it differently, what is striking is not to witness a complex, or ordered or random behavior in a CA system but, for example, to witness the apparition of a complex or random behavior emerging out of an initial simple output or, like in the example of CA 110, of structures emerging out of an almost uniform initial condition.d In other ‘This is in no way is in a definition of or a necessary condition for emergent properties. In particularly, I do not assume that there is a single concept of emergence or that any concept of emergence must meet these requirements. dSee [6, pp.149-1521 for examples.
107 words, what matters is which new features the system dynamics is able to generate out of a context that did not possess these features, and that is why I say the criterion we look for is contextual.
2.2.2. The criterion must be local, that is to say must rely on preceding microstates only (C2) Most of the listed properties (deceptive and target properties) are new in a very weak sense: they are properties that were not possessed before (the
system was never in a state identical to Microstate50 before). Verticalcolumn and Bigtriangle seem to be new in a stronger sense because the system seems to locally undergo a change. In the same time, nothing precludes that similar instances of target properties may have appeared before or may appear again later: tornadoes do re-emerge in the same areas. I conclude that the desired criterion, if it is to characterize novelty, must be local in the sense that it is possible to determine if a property is novel only by looking at the microstates of the system just before the property appears. Local novelty is also an attractive feature because it is a weak requirement in contrast with other kinds of novelty such as absolute novelty (if the supposedly new features were never possessed before). And I am after a weak criterion because I believe that the SR is what matters first in diachronical emergence and I want only to refine it by disqualifying a very specific set of deceptive properties. The requirement of local novelty is also there to do credit to the idea that the apparition of an emergent property corresponds to an observable change in the system state. Emergent properties may involve no new causal power, as this is precisely the case with diachronic emergence, where all causal effects can be traced back to the system’s microdynamics. But one can still require that the emergence of these properties correspond to the apparition of novel features characterizing the system.
2.2.3. The criterion must be contextually absolute (C3) Once a context - that is to say the previous microstates - is given, the novelty of a property must be assessed on the basis of objective properties. For example, there seems to be an objective sense in which one can say that a tornado is a new structure that locally appears, because one can find objective indicators to signal this appearance, such as a sudden local increase of average vorticity. In particular, although I call ‘salience’ the property that emergent properties must possess, I do not want salience to
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be relative to an observer and her cognitive apparatus.
3. Salience In the last section of this paper, I try to develop a concept, salience, that fulfills the previously listed requirements and I claim that DEPs must also be salient. Salience is an independent notion and I believe that it can prove to have a wider application than the question of emergence.e The definition of salience also raises its own set of problems, but since it is not my goal to fully develop this notion here, I shall be quite sketchy, leave aside most of these problems and be content to show how salience could be used to complete the definition of DEPs. The idea I am going to develop is that a property is salient if one can find a descriptive indicator which can be calculated for any state of the system and that undergoes a change when a salient property appears. To make things clearer, I start with two clear-cut examples. In the case of phase transitions, order parameters (when one manages to find one) yield such indicators. For example, in the case of the transition from ice to water, the quantity pice - psystem,where p indicates the density, is zero till the transition and then grows. Another more elaborate example from dynamical system field, which I borrow from Rueger', is the case of the damped non linear oscillator, which is described by van der Pol's equation: x - a(1- x2)x x = 0, where x = d x / d t and a is a damping parameter. For a dynamical system, it is appropriate to study properties of the phase space, which plays for us the role of a descriptive indicator. With a = 0, the oscillator is undamped and the phase space can be portrayed by concentric ellipses, each ellipse representing a trajectory (see figure 4). If the damping is gradually turned on, trajectories are no longer periodic and the phase space is made of spirales converging to a limit circle (see figure 5). So the turning off of the damping makes new salient properties appear (e.g. periodicity) and this can be indicated by the topological change of the phase space, which is described by topologically inequivalent objects (two objects are topologically inequivalent if one cannot smoothly deform one object to transform it into the other). This specific and very well chosen example enables Rueger to provide a very clear criterion of novelty, using the notion of topological inequivalence.
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eFor example for the question of what it is to identify a non trivial property in a data basis obtained by a number crunching simulation or by experiments.
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Figure 4.
Figure 5.
Undamped oscillator, taken from Synthese, 124, 2004
Damped oscillator, taken from Synthese, 124, 2004
Yet it seems to me that he actually shows how novelty can be defined in a very particular case (dynamical system studies) and not in general. I am not sure my criterion of salience will be as clear and elegant, but it aims at being more general.
3.1. Preliminary definitions
I assume that at each time, the system can be suitably represented for the properties that are studied by data originating in n measurements and I call ‘state of the system’ this n-tuple of measurements. Examples of states are a triplet (P,V,T) for a gas at equilibrium, data describing a velocity field
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for a fluid, what I called ‘microstates’ for the above CA system or subparts of them (for example the subpart corresponding to CA number 15 to 25, that is to say where Bigtriangle does appear). I call ‘trajectory’ the sequence of states that one gets by varying a parameter describing the system. This parameter can be time, like in the case of the above CA system, but it need not always be. For example, temperature can be chosen for an ice to water phase transition. What is only required to get a well-defined trajectory along a parameter is that one single state can be ascribed to each new value of the parameter along the trajectory. Suppose for example you study properties of cooling of glasses. Since, for a similar initial condition, the end state of the glass and its properties depend on the cooling rate (see figure 6)’actual trajectories depend on the cooling rate. Therefore temperature cannot be taken as the varying parameter defining trajectories. Specifying exactly the trajectory does matter because salience is a contextual notion (Cl) and because the part of the trajectory before a property appear provides the context against which the property stands out. I call ‘descriptive function’ a single-valued mathematical function that
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Figure 6. Glass cooling modelled by a two well system (the fraction of the systems in the higher well is plotted). Figure taken from Dynamics of Complez systems,by Bar-Yam, reproduced with permission of Addison-Wesley.
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takes as an argument the n-tuple describing the system.f This is in a no way a definition of a new object. This definition only provides a label that is stamped on already existing functions. Here are examples of descriptive function:
0
0
0
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for a spin lattice, the total magnetization or typical size of clusters of similarly oriented spins; an estimation, using an auto-correlation function, of the correlation between measurements at spatial or temporal distance r or t ; the probability value of an event, for example of having two similar colors following each other on the above CA system; a complexity measure such as Kolmogorov complexity of a state; etc.
Descriptive functions are aimed at giving a common indicator all along the trajectory, so that it be possible to make comparisons and thus determine if the system exhibits a new behavior. In the case of Verticalcolumn, we can for example study the spatial correlations around CA number 60 in the 100 steps before Verticalcolumn is instantiated. On this interval, which plays the role of a context, the system undergoes fluctuations and correlations are low. When Verticalcolumn appears, fluctuations stop and the correlations suddenly get high. To be more precise descriptive functions should themselves be described by other more elementary mathematical object (EMO) which enable to fit them locally. In the case of the oscillator, the phase space was described by different geometrical figures (circles and spirales). The novelty is then signaled by the shift in the description of the descriptive function from one E M 0 to another one. In the case of single-valued functions, EMOs are elementary functions such as z2 and power laws, l o g ( z ) ,e z p ( z ) ,trigonometric functions, etc. 3.2. Towards a definition of salience
I can try now to propose a first definition of salience.
A property P of a system S, which appears at t or on interval I is fThis is actually a restriction that I make for simplicity because one may need more complicate objects than singlevalued function to describe suitably the systems. In Rueger’s example of the oscillator, the system was described for each value of the damping parameter by trajectories within a phase space,
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salient for trajectory T of S iff there exists different EMOs A and B and a descriptive function DF of the states of S’s trajectory such that: 0
0
DF is described by A on an interval C of T (the context) before t or I; the description of DF shifts from A to B at t or on I with the apparition of property P.
This definition, because of the existence condition, does not provide an algorithm to determine if a property is salient. So the burden of the proof is for those who want to claim that a given property is salient, because they need to find an appropriate indicator, which can be far from obvious, even for phase transitions. Further, this definition, stated like this, can easily be found wanting. For example, it would be necessary to have a way to determine what the minimal size of the context needs to be in each case. In the following paragraphs, I shall study a few obvious corrections that should be brought to the definition in order to make it work better and also indicate in which directions some work needs to be done if a definition of this kind is to be given a chance to be well-grounded in the end.
3.3. How to avoid ad hoc descriptive functions? Remember salience aims at eliminating undesirable properties such as Microstate50 or Blackcell. An immediate objection is that it is very easy to find descriptive functions that will exhibit a change in behavior when Microstate50 or Blackcell appear. ‘Blackcell’ refers to the property of having CA 10 in a black state at time 20. If I take the color of CA 10 as a 1-tuple state, and if ‘black’ is encoded by 1 and ‘white’ by 0, and if CA(t,x) denotes the state of CA number x at time t , then the function t Hb(t - 20).6(1- C A ( t ,lo)), where 6 denotes Dirac function, does exhibit a a sudden change in behavior when Blackcell appears. A similar trick can give the same result for Microstate50. That is why it is necessary to require that descriptive functions do not include functions of the parameter defining the trajectory (such as t H6(t - 20)) that have an ad hoc salient feature, which is made to appear at t or I (see definition above). Further, similar variables of the n-tuple should be treated similarly or contribute formally in a similar form to the descriptive function in order to avoid ad hoc treatments. The consequence is that most descriptive functions, like in the above examples, will be sums or integral functions. A cautionary remark needs to be made here. Such restrictions are not
113 aimed at getting rid of properties like Blackcell or Microstate50 in any circumstances. Suppose that CA 10 -happens to be white from step 0 to 19 and then turns black at step 20. Then it is legitimate to say that Blackcell is salient and for that we no longer need an ad hoc function as above. Function CA (t,10), which is tolerated by the definition, will nicely do the job because it will have a zero value till step 19 and then will abruptly take value 1 at step 20.g Similarly, if it happens that Microstate50 is random and appears after a succession of non-random states, then this provides a good ground to call it ‘salient’. 3.4. Requirements about describing EMOs
Notice first that I do not define in the abstract what can count as EMOs. What EMOs are will depend in each case of what kind of mathematical object the descriptive function is. For example, EMOs will be different if you want to study the evolution of a phase space or of an order parameter. A fully assumed consequence of my definition is that a curve can have different salient parts even if you can fit it with one single curve. Take for example a curve that you can fit with function x Hx2 0 . 1 ~ With ~ . my definition, it can be said to have different salient parts. Around x = 0, the curve is correctly described by x2. For large x, it is best described by 0.1x3. A more worrisome problem is this. Take a curve F that always has 0 value. Then you can very easily find two polynomials A and B such that 1) A has value 0 till x = l and then has a more complicated behavior 2) B has value 0 after x = 1 and a complicated behavior before.h A and B are 2 EMOs and the description of F shifts from one to the other. So it seems that it is possible to find salience really everywhere. To guard against that, it is necessary to require that there is no E M 0 that fits F on both intervals where A and B are supposed to fit it and that is in the same time simpler than A and B. Here, the function x H 0 is simpler than A and B. The outcome of this is that, in order to fully develop the notion of salience, I need to be able to estimate the simplicity of mathematical objects. In the previous example, one must be able to explain why x 2 0.1x3
+
+
gNote that in this case, nominal emergence would disqualify Blackcell. hIn short, I need to set restrictions on which EMOs can be used to fit the curves. It probably did not go unnoticed to the reader that the discussion of salience turns out to be reminiscent of discussions about induction, curve-fitting and projectibility, and here in particular of Goodman’s paradox about grue emeralds (see [9,chap. 3-41 and [lo, chap. 51. A complete definition of salience should show how to avoid the goodmanian pitfalls or how to get out of them.
114 is less simple than x2 or 0.1z3. Since the last two expressions are composed of one element and the former of these two elements, the answer may seem obvious. But this seems all too relative to the mathematical framework that is taken as basic. Taking as basic the functions z H g(z) = z2 0.1z3 one gets z2= 0.5(g(z) h ( z ) )and z2seems and z H h ( z )= z2- 0.1z3, now less simple than g(z). As a reviewer points out, this makes salience relative to a privileged descriptive mathematical framework. A way out of the deadlock would perhaps be to argue that there are good objective grounds, in each case of data mining and salient properties detection, to privilege a descriptive mathematical framework and basic EMOs on the basis of which projectable quantities characterizing the system the descriptive function and more generally the mathematical description represent. I do not go any further in the discussion of the concept of salience, since as just shown, this would require a close scrutiny of much debated questions, like simplicity and curve fitting. One more thing still. In this paper, the concept of salience was only aimed at giving a way to single out the properties that are considered as remarkable in the study of a system, e.g. in physics. But determining what patterns or properties are salient for a subject is also a question that is crucial in cognitive sciences.' I make no claim in this paper about the link between the two notions, which may be somewhat related, even if not identical. This latter point can be illustrated as follows. Indeed, a salient property (as defined above) in a data basis can be imperceptible for a subject. That is why data mining requires resort to statistical tests made by computers. In the same time, perceptual abilities for pattern recognition also prove very useful to detect interesting p r o p erties, for example in hydrodynamic simulations, and the existence of the supposedly detected properties can be checked afterwards with statistical indicators. Finally, a system (e.g. a Hopfield network3) could be trained to detect in any circumstances a given pattern of CAs whereas this pattern need not always be salient (in my sense), since the notion is contextual. Besides, the pattern detection system may treat differently inputs of the same kind ( i e corresponding to similar variables of the n-tuple in the mathematical description) and thereby use for detection a function that would not qualify as a descriptive function.
+
'See Ill] for example.
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4. Conclusion We can now check that the concept of salience meets the requirements listed above, or that a well-grounded and refined version of it could be hoped to. It is local, because it depends only on the preceding part of the trajectory. It is contextual because any property can happen t o be salient if it is generated by a context against which some of its features stand out. It is objective (at least provided a descriptive mathematical framework is given) because it relies on the construction of mathematical indicators and not on our epistemic interests, perceptual abilities or practical goals: for example, the position at a given time of a planet, on which one wants t o send a shuttle, is very unlikely t o be salient. Salience, as I built it, is a very weak and purely descriptive notion, which aims a t grasping the idea that the apparition of a non-trivial property is simultaneous with a significant change in some of the values of the observable quantities characterizing the system. Once again, I think that using a concept as weak as possible t o complete the definition of DEPs is appropriate because I believe that the SR is the crucial element in it. But my conclusion is that DEPs satisfy the SR and are salient.
Acknowledgements Special thanks to Anouk Barberousse, Jacques Dubucs and Paul Humphreys for discussing different versions of this paper and also to an anonymous reviewer for very helpful and very apposite critical comments, which helped a lot t o improve the paper. All remaining shortcomings are of course mine.
References 1. A. Stephan, “Phenomenal Emergence”, Networks, vol. 3-4, 91-102 (2004). 2. M. Bedau, “Weak emergence”, Philosophical Perspectives: Mind, Causation and World, 11, Oxford Blackwell Publisher (1997). 3. G. Weisbuch, Dynamique des systbmes complexes, Une introduction a m rkseauz d’automates, InterEditions/Editions du CNRS (1989). 4. M. Bedau, “Downward causation and the autonomy of weak emergence”, Princzpia, vol. 6, 5-50 (2003). 5. T. O’Connor, Hong Yu Wong, “The Metaphysics of Emergence”, N o h , forthcoming.
6. S. Wolfram, A New Kind of Science, Wolfram Media, Inc. (2002). 7. J.P Crutchfield, J.D Farmer, N.H Packard, R.S Shaw, “Chaos”, Scientific American, vol. 255, 46-57 (1986).
116 8. A. Rueger, “Physical Emergence, Diachronic and Synchronic”, Synthese, vol. 124, 297-322 (2000). 9. N. Goodman, Fact, Fiction and Forecast, Harvard University Press (1983). 10. N. Goodman, Language of Arts, Hackett Publishing Company, Inc. (1976). 11. D. Marr, Vision, A computational investigation into the human representation and processing of visual information, New York: Freeman (1982).
ON THE RELATIVITY OF RECOGNISING THE PRODUCTS OF EMERGENCE AND THE NATURE OF THE HIERARCHY OF PHYSICAL MATTER
KURT A. RICHARDSON
1. Introduction On the matter of privileging a so-called ‘scientific method’ over all other methods in the discovery of ‘truth ’ the philosopher Paul Feyerabend said:
It is thus possible to create a tradition that is held together by strict rules, and that is also successful to some extent. But is it it desirable to support such a tradition to the exclusion of everything else? Should we transfer to it the sole rights for dealing in knowledge, so that any result that has been obtained by other methods is at once ruled out of court?’ Like Feyerabend my answer to the question is “ a firm and resounding
NO.” In this chapter I would like to explore my reasons for this answer by exploring the ontological status of emergent products. I am particularly interested in demonstrating the relativity of recognising the products of complexity, i.e., that emergent-product recognition is problematic and not ‘solved’ by the application of one particular method over all others. I would also like to explore the consequences of this in regard to the hierarchy of physical matter and the hierarchy of human explanations. 2. A Theory of Everything My starting point for such an exploration is the assumption that the Universe, at some level, can be well-described as a cellular automaton (CA). Of course by selecting this starting point I am making the assertion that not only does some form of cellular automata represent a plausible theory of everything, but that a theory of everything does indeed exist. This would seem to be a radically reductionist starting point, but I am claiming a lot less than may at first appear. Rather than defend this starting point in
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118 the main part of the chapter, I have added a short appendix that discusses the reasonableness of the CA assumption. One thing is clear, a theory of everything doesn’t even come close to offering explanations for everything so we needn’t get too concerned about the ‘end of science’ or human thinking just because such a theory might exist and might be discoverable. Whether one accepts my starting point or not it should be recognised that this is a philosophical exercise; to explore the ontological and epistemological implications of assuming that the Universe is well-described as a CA at some level. It doesn’t necessarily follow that the Universe actually is and only is a CA. The details of the CA, however, do not change the philosophical conclusions. Richardson15 has explored these issues at length and argued that, whether or not a CA model is a plausible theory of everything, a philosophy of complexity based on this assumption does seem to have the capacity to contain all philosophies, arguing that each of them is a limited case of a general, yet empty, philosophy (akin to the Buddhist ‘emptiness ’. This seems to be a fantastically audacious claim, particularly given the heated debate nowadays over global (intellectual) imperialism. However, one should realise that the resulting general philosophy is quite empty - which I suppose is what we would expect if looking for a philosophy that was valid in all contexts - and explicitly avoids pushing to the fore one perspective over any other. Quoting Feyerabend’ again, “there is only one principle that can be defended under all circumstances and in all stages of human development. It is the principle: anything goes.” In a sense, all philosophies are a special case of nothing!
3. S o , What is Emergence? In the founding issue of the journal Emergence, Goldsteinlo offers the following description of ‘emergence ’: Emergence ... refers to the arising of novel and coherent structures, patterns, and properties during the process of self-organisation in complex systems. Emergent phenomena are conceptualised as occurring on the macro level, in contrast to the micro-level components and processes out of which they arise. For the rest of this paper I would like to consider how patterns and properties emerge in simple CA, and how the macro is distinguished from the micro. I will argue that the recognition of emergent products, which is often how the macro is distinguished from the micro, is method dependent
119 (and therefore relativistic to a degree). The recognition of emergent products requires an abstraction away from what is, and as with all abstractions, information is lost in the process. Of course, without the abstraction process we would have all information available which is no better than having no information at all. "Only a tiny fraction of [the richness of reality] affects our minds. This is a blessing, not a drawback. A superconscious organism would not be superwise, it would be p a r a l y ~ e d ". ~I do not intend to offer a full review of the term 'emergence' here. The interested reader might find Goldsteinlo or Corning3i4 useful as additional sources on the evolution of the term itself.
3.1. Complex cellular automata and patterns Figure l b shows part of the space-time diagram for the simple CA &36 ( n = 20, k = 3). Even though the initial conditions selected for the particular instance of CA were selected randomly, a pattern emerges that is neither totally ordered (an example of which is given in Figure la) nor quasi-chaotic, or quasi-random (Figure lc). CA &36 is an example of a (behaviourally) complex CA as defined by Wuen~che'~.There isn't a lot else we can say about the pattern (although there are a wealth of statistical analyses we might perform to quantify certain aspects of the pattern) that emerges except that maybe it is rather aesthetically pleasing and that its appearance from such a simple set of rules, as well as a random initial configuration, is quite a surprise. So even though it is often said that these patterns emerge from the application of the CA rule, it is not particularly clear as to what is emerging - what are the emergent products here? Is it appropriate to suggest that the space-time pattern is emergent, given that it is a perfect image of the ' micro '-level? What would the macro level be in this example? It is not immediately clear at all. There is no autonomy in this example, as all cells are connected to all others - the pattern is simply the result of applying the CA rule time step after time step. One thing we can say is that the pattern was not wholly predictable from the CA rules, and so in that sense the pattern is novel given our lack of knowledge of it before the system was run forward. But did it really emerge? Or, are our analytical tools just too feeble to characterise the patterns beforehand, in which case the fact that the patterns are regarded as emergent simply reflects our lack of knowledge about this simple system - our theories are simply not powerful enough. Following Bedeau', Goldstein" refers to this aspect of emergence as ostensiveness, i.e., the
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Figure 1. Examples of (a) ordered, (b) complex, and (c) chaotic automatons
products of emergence are only recognised by showing themselvesa. This is also linked to the idea of radical novelty'' , meaning that the occurrence of these patterns was not predictable beforehandb. These patterns are of interest in that they illustrate some aspect of the concept emeTgencec, but they do not tell us much at all about the dynamics of the space-time plot. If we look very closely however we begin to notice that there are patterns within the patterns. The triangles have different sizes and their evolution (shape and movement) 'down' the space-time plot seems to indicate some kind of interaction between local areas of the overall pattern. We might also notice that certain areas of the space-time plot are tiled with a common sub-pattern - a pattern basis. Nansen and Crutchfieldll demonstrated how an emergent dynamics can be uncovered by applying a filter to the space-time plot. Figure 2 shows the result of a ' pattern-basis filter' applied to a particular instance of the Space-time plot of CA rule &36. Once the filter is applied an underlying dynamics is displayed for all to see. What can we say about this alternative representation of the micro-detailed space-time plot? Firstly, we can develop an alternative macro-physics for this apparent 'Even though for the products t o show themselves, an observer must recognise them as products. bThough having run this particular CA on many occasions, the qualitative nature of the pattern was of no surprise to me at all - otherwise I would've found it very dificult indeed to preselect an appropriate case. It would be a very straightforward exercise indeed for me to produce a library of CA patterns from all possible initial conditions though I would be limited by such resources as time and, the related resource, processing power. The point is that I would have to run all the cases fully, there is no shortcut no algorithm - I could implement to speed the task up, i.e., CAs are intrxtable. CIt is still a little dissatisfying to regard these patterns as emergent as they are simply an alternative expression of the CA rule itself, cut-off at an arbitrary time step.
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Figure 2.
CA &36 after pattern basis filtering
dynamical behaviour that is entirely different (from a language perspective at least) from the micro-physics of the CA. If we see these two ‘physics’ side by side (Figure 3) it is plainly clear how different they are. The micrcphysics description uses a microlanguage16 (which is sometimes referred to as the ‘language of design’) comprised only of 0s and Is, whereas the macrolanguage is comprised of an entirely different alphabet: a , p, y+, y-. There is no simple mapping between these two languages/physics, i.e., there is no way (currently) to move between the two languages without some kind of information loss - the translation is lossy (as it is in the translation of human languages). As S t a n d i ~ h ’remarks, ~ “An emergent phenomenon is simply one that is described by atomic concepts available in the macrolanguage, but cannot be so described in the microlanguage”(p. 4). This imperfect relationship comes about because, although the macrophysics is a good theory, it is not a complete description of the micro-physics, it captures some of the details but not all. A qualitative change in language is equivalent to a change in ontology, but what is the ontological status of the emergent products? At the micro-level, only cells (that can only be in states ‘0’ or ‘ 1’) absolutely exist. But can we say with equal confidence that a-particles, for example, exist? Given the filtered version of the space-time diagram showing the apparent evolution of a set of quasi-particles, as well as their compelling macro-physics, it is very tempting indeed to answer in the af-
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a+y.--r y-+a+2y+ y+ + a 2y + a + 'y 111 110 101 100 011 010 001 000 0 0 1 1 0 1 1 0
(a) Figure 3.
R + VI - b y +' + ;
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Y++Y"P . . 7' + a + y- + y + a + y' y' + p + y- + 0 (b)
(a) The micro-physics of level 0 and (b) the macro-physics of level 1
firmative. However, we need to bear in mind how the original patterns were created and how we uncovered the quasi-particle dynamics. The patterns were generated by recursively applying a micro-rule to each cell in the system. Each cell is treated exactly the same as the others - none receive any special or unique treatment. The application of the rule does not change as the system configuration evolves. And, most importantly, each cell in the configuration depends on the states of all the other cells - a particular sequence of 0s and 1s representing the evolution of a particular cell, only occurs that way because all the other cells evolve in their particular way. Although the rule is only applied locally, the dynamics that emerge are a result of global interactions. So a-particles only emerge because P-particles emerge (as well as the other particles) - the emergence of a-particles does not occur independently of the emergence of ,&particles. As a result it would be a mistake to assume that some absolute level of ontological autonomy should be associated with these particles, though of course the macro-physical description provides evidence that making such an assumption is for many intents and purposes useful. However, as with all assumptions, just because making the assumption leads to useful explanations, it does not follow that the assumption is correct. Even the motion of these particles is only apparent, not real; it is simply the result of reapplying the CA rule for each cell at each time step. Whilst discussing Conway's Game-of-Life (a form of two-dimensional CA), philosopher Daniel Dennett6 asks: [Slhould we really say that there is real motion in the Life world, or only apparent motion? The flashing pixels on the computer screen are a paradigm case, after all, of what a psychologist would call apparent motion. Are there really gliders [or, quasi-particles] that move, or are there just patterns of cell state that move? And if we
123 opt for the latter, should be say at least that these moving patterns are real? Choosing ‘0’ and ‘1’ to represent the two cell states perhaps further suggests the illusion of motion and ontological independence. The choice of ‘0 ’ and ‘ 1’ is a little misleading as it can easily be interpreted as being ‘on’ and ‘off’ or ‘something’ and‘nothing’. Whether a cell is in state ‘0 ’ or ‘ 1’, the cell itself still exists even if a‘black square’ is absent. We could easily use ‘ x ’ and ‘ N ’ to represent the two states and the result would be the same. In uncovering the macro-dynamics we had to, however reasonable it may have seemed, choose a pattern-basis to be ‘removed’ or filtered-out. By clearing-out the space-time diagram we allowed ‘defects ’ in the space-time diagram to become more clearly apparent. We also chose to set to ‘0’ those areas of the space-time diagram that were tiled evenly with the pattern-basis, and ‘ 1’ those regions which represented distortions in the pattern-basis; we assumed an even ‘background ’ and then removed it to make visible what was in the ‘foreground’d. Again, it is tempting to interpret the ‘0’-covered (white areas) as ‘nothing’ and the ‘1’-covered (black) areas as ‘something’. This would be incorrect however, as all the cells that comprise the CA network are still there, we have simply chosen a representation that helps us to ‘see’ the particles and ignore the rest. However, it must be noted that though ‘0’ and ‘1’ do not map to ‘nothing’ and ‘something’ at the CA-substrate level, this is exactly the mapping made at the abstracted macro-level. So in any absolute sense, the emergent products do not exist as such. They do however exist in the alternative (although deeply - complexly related) macro-level description of the CA. The change in perspective is equivalent to an ontological shift, where the existence of the emergent products is a ‘feature’ of the new perspective though not of the absolute CA perspective; what existed at the micro-level does not exist at the macrolevel and vice versa. This new perspective is an incomplete description, yet the fact that the new description is substantially complete would suggest the substantial realism of the particles on which the new description is based. For this reason we say that though the particles do not absolutely exist, they do indeed exhibit substantial realism and as such, for many intents and purposes, can be treated as if they were real (for this reason they ~~~
dAt the CA-substrate level the background is not ontologically different from the foreground - any difference is achieved through filtering.
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are often referred to as ‘ quasi-particles’ rather than just ‘particles ’). Quoting Feyerabend again, Abstractions remove the particulars that distinguish an object from another, together with some general properties ... Experiments further remove or try to remove the links that tie every process to its surroundings - they create an artificial and somewhat impoverished environment and explore its pec~liarities.~ The process of abstraction is synonymous with the filtering process described above. Feyerabend goes on to say (p. 5): In both cases, things are being taken away or ‘blocked off’ from the totality that surrounds us. Interestingly enough, the remains
are called ‘real‘, which means they are regarded as more important than the totality itself. (italics added) So, what is considered real is what still remains after the filtering process is complete. What has been removed is often called background ‘noise’, when really what we have accomplished is the removal of ‘details’ not ‘noise’, for the sake of obtaining a representation that we can do ‘science’ with. 4. The Hierarchy of Reality: Nested versus Convoluted
This view of existence changes the popular image regarding the hierarchy of physical matter considerably. The popular image of the hierarchy of matter (illustrated in Figure 4ae) is that starting with atoms (for argument sake - of course more fundamental (or, more real) entities are known to the physical sciences) molecules are formed which are little more than agglomerations of atoms. Here, atoms are regarded as the ‘micro’ and molecules are regarded as the ‘macro’, and the filter applied is some mysterious process known as the ‘scientific method ’ (although any competent and experienced scientist would rightly question the existence of such a universal met hod). From molecules, molecular complexes are formed, from =In considering Figure 4b it is very tempting indeed to assume that the extra dots (in comparison to Figure 4a) are no more than noise. However, it is important to note (but not necessarily easily grasped) that the existence of the seemingly more real pattern (represented in Figure 4a) depends upon the existence of what is easily labelled ‘noise’ and vice verse. Each ‘noisy’ dot is potentially significant in the future evolution of the system as a whole as it is a part of the system, not just the result of some impure measurement.
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which cells are formed, from which multi-cellular organisms are formed, and so on right up to galactic clusters and beyond. In such a neat nested hierarchy every ‘entity’ has a place which distinguishes it from other entities as well as determining which ‘science ’ should be employed to understand it. Furthermore, every ‘thing’ at one particular ‘level’ in the hierarchy is made-up off those ‘things’ said to exist at the ‘level’ below. This would seem to suggest that molecular physics/chemistry, say, should in principle be derivable from atomic physics. However, even though such a trick is supposedly possible (assuming such a neat hierarchical organisation), in reality scientists are very far indeed from pulling off such a stunt. Nowadays the reason offered for this is simply the intractability of emergence which is well known to nonlinear researchers. Rather than derive biology from chemistry, scientists are forced to assume that the ‘entities’ of interest (which are the result of a particular filtering, or coarse-graining) to their particular domain do exist as such. Once such a step is taken, a science can be developed independently of the science that deals with the supposedly ‘simpler ’ ‘ lower-level ’ ‘entities ’. Making such an assumption (which is often made implicitly rather than explicitly) has worked out rather well, and an enormous amount of practical understanding has been accumulated that allows us to manipulate these ‘entities ’ in semi-predictable ways, even if they don’t happen to truly exist! Technology is the obvious example of such success.
4.1. Non-composite secondary structures
As well as the background ‘ pattern basis’ and the fundamental particles listed in Figure 3, CA &36 “supports a large number of secondary structures, some having the domain and particles as building blocks, some not describable at the domain/particle 1evel”ll . Though it has been acknowledged above that a complete ‘physics‘ of one level cannot be derived from the ‘physics’ of the layer below, it is often assumed that the lower-level contains all that is necessary to allow the higher level to emerge. This assumption needs to be explored further, but just because we don’t have access to a perfect mapping from the lower level to the next level up, it doesn’t mean that some day such a bootstrapping method will not be uncovered. In the CA model the fundamental ‘lowest’ level - level 0, say - does indeed contain ‘everything’ there is to know about the CA universe; the space-time diagram is indeed a complete description. However, the move to
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Figure 4. (a) Abstracted ‘reality’ versus (b) reality?
the particle level description - level 1 - is an imperfect ontological shift. As such, the set of quasi-particles describing the particle-level description is not s a c i e n t to describe all the structures that are observed at the lower level (as a result of ’background’ filtering), i.e., one cannot reverse the filtering process and perfectly reconstruct the micro-level. Hansen and Crutchfield’s discovery that secondary structures also exist, indicate that another level of ‘existence’ - level 2 - can be uncovered. if all of these secondary structures were made up of the particles already described ( a ,p, etc.) then we could argue that a ‘composite ’ particle level (2) exists ‘above‘ the quasi-particle level (1). In the natural sciences this would suggest that chemistry is indeed derivable from physics, or that all of chemistry emerges from all of phgszcs. However, the existence of “secondary structures’‘ that are not “describable at the domain/particle level” suggests that there are entities existing at the higher composite level (2) that can’t possibly be explained in terms of the particle level (1) description, even intractability was not an issue, i.e., there exist higher-level entities that are not combinations of a , p, or y quasi-particles. Another way of saying this is that matter is not conserved between these ascending levels. Assuming these observations have merit in the ‘real‘ world, this would suggest for example that chemistry cannot
127 possibly be derived from physics in its entirety. This perhaps is no great surprise; physics is an idealisation and so a chemistry derived directly from such a physics could only represent an idealistic subset of all chemistry even if we could somehow overcome the computational irreducibility of predicting the macro from the micro. This observation indicates a different meaning to the aphorism “the whole is greater than the sum of the parts.“ Traditionally this has only really meant that, because of networked causality, the properties of the whole can not be directly derived from an analysis of the interacting parts; basically, even though our ontology is (assumed to be) correct, our analytical tools aren’t quite up to the challenge of reconstructing the whole from its parts. Novelty in this particular interpretation simply comes from the fact that our ‘ science ’ is unable to predict the macroscopic behaviour from microscopic. The existence of ‘ non-composite secondary structures ’ suggests that, even if we could bootstrap from the micro to the macro, the ‘parts’ do not offer a complete basis from which to derive the ‘whole’f; the ‘whole’ is not greater than the sum of its ‘parts’ because the ‘whole’ is not even constructed from those ‘ parts’ (except in idealised computer models). In this context we would expect to observe chemical phenomena that could never be explained in terms of physics (however complete physics might get - in this view of the Universe physics can never be complete), and that might even contradict predictions made at the level of physics. There are entities that ‘exist’ within a chemical description of ‘reality’ that could never be explained in terms of atoms, say. The fact that each science has facilitated such enormous strides in our ability to rationally affect our environment suggests that, though they may be based on incomplete ontologies, they are in fact very good partial reflections of ‘reality’. The hierarchy of sciences is sustainable and justifiable, but is not an accurate representation of what is. However, the assumption that the physical matter the sciences attempt to explain organises into a nested hierarchy would seem to be questionable. Regarding our hierarchy of ‘explanations ’ as convoluted rather than nested would be more appropriate in light of the CA model.
‘Unless of course we were bootstrapping from level 0 to level 1, as entities existing at level 0 are by definition deemed to absolutely exist.
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realism ? Given that as we move away from the absolute CA reality information is lost, it would be tempting to suggest that the ‘entities’ that ‘exist’ at subsequently higher levels of description, though substantially real, are increasingly less real. If our descriptions at one level were always tied to descriptions at lower levels then this argument would be supportable. But given that particular scientific communities will often operate with little regard to the ontological and epistemological standards of another scientific community, it is quite possible that a macro-explanation contains entities that are more real than those comprising, what seems to be, a microexplanation. If this wasn’t the case and we did indeed tie ourselves to purely quantum physical explanations, say, it is quite possible that, as a result of the multiple abstractions that would be necessary to get from quantum to social reality, we would learn next to nothing about that particular ‘reality‘ (as we would have a partial description of a partial description of a partial description. . . ). The fact that we are comfortable with ignoring quantum descriptions and approaching ‘social reality’ in terms that seem more familiar to us (after all our human perceptions have been honed to give us rather good tools for dealing with this particular level of reality) enables us to make rather more progress in regard to the development of practical understanding for manipulating social reality. In short, a hierarchy of vertical ontologies can be inferred that, though they may actually be inconsistent (or even, incommensurable) with each other, they can still be incredibly useful in providing practical understanding. The hierarchy of physical reality is not a nested hierarchy like the hierarchy of the sciences has been traditionally regarded. 5. Multiple Filters and Horizontal Ontologies Given the fact that the process of filtering-out pattern bases to reveal ‘macroscopic ’ dynamics works so well in the example above, it would be tempting to assume that even though higher-level descriptions are incomplete, there is in fact a ‘ best ’ way to obtain these descriptions. So although the discussion thus far supports the assertion that the recognition of emergent products is tied to our choice of methodology, it also supports (or at least it does not deny) the possibility that one particular methodology is better than all others. I would like to briefly challenge this possibility
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next. This section of the chapter represents a move away from the more scientifically-basedphilosophy presented thus far to a more speculative philosophy. As we move up our constructed hierarchy of explanations, the reality that is ‘explained’ by our explanations seems to be more complex. By complex here I mean that we seem to have increasing difficulty in locating the boundaries, or the ‘quasi-particles’ that describe our systems of interest. This issue is perhaps exemplified at the ‘social level’, and more clearly illustrated by the methodological diversity of the social sciences. Whereas recognising the ‘atoms’ of the physical sciences is seemingly a rather straightforward affair (though still only approximately representative of what is), the recognition of the ‘atoms’ of social science seems rather more problematic. There are many more ways to ‘atomise‘ social reality in an effort to explain a particular phenomenon (of course our choice of ‘atomisation scheme’ determines the phenomena that then takes our interest, and to some extent, vice verse - although there are potentially many different (possibly contradictory) atomisations ’ that may lead to seemingly good explanations for the same phenomena). This is probably why social problems are often described as ‘messy’ problems” ; the articulation of the system of interest itself is problematic, let alone the development of explanations. The fact explanations of social phenomena often have low ‘fitting coefficients‘ whereas explanations of physical phenomenon often correlate very well indeed with perceived (measured) reality, may further suggest the legitimacy of multi-methodological approaches in the social science+. I don’t want to spend much time at all defending the view that multimethodological approaches for the social sciences are a must. For now I am content to point the reader towards the book Multimeth~dology~~ which argues rather well for a pluralist attitude in the social sciences. I think that the failed attempts in the past to develop a ‘Theory of Society’ satisfies me, for now at least, that pluralism is a feature of the social sciences rather than a failure of social scientists to construct such an all-embracing theoryh. gLow ‘ fitting coefficients ’ for explanations of social phenomena is clearly an indication that the explanations proposed are quite incomplete, suggesting the necessary consideration of alternative explanations. Whereas at the level of superstrings we might get very close t o the ‘truth’ with only one model, we might find that ‘truth’ at the social level, say, is at least the sum of all possible models, i.e., a monist notion of truth may work for ‘low-level’ explanations, where as a pluralist notion of truth is essential for explanations of ‘ higher-levels ’. hThe fact there is no complete theory of anything would suggest the importance of pluralism in all realms, but it is clear that some realms of human understanding have
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._ -mE
00 0 0 0 0 0 0 -
O O G O & -
a
Level 0 - CA ‘Reality’: no hierarchy
Figure 5. The convoluted hierarchy of existence. Each ellipse represents the set of ‘entities’ (a theory’s alphabet) that supposedly account for certain phenomena at a certain level ’
.
The different explanations of the same phenomena offered in the social sciences often rely on different ontological assumptions. Given our historical tendency to rank theories in terms of hierarchies of physical matter, we might ask ourselves as to how we might go about ranking social theories. In other words, are the entities used to construct explanation A more real that those entities used to construct explanation B? I very much doubt that a consistent answer exists for this particular question. The reason this issue is raised here is simply to support the suggestion that as we abstract away from the fundamental substrate of existence (level 0) towards the more familiar social level we experience a kind of ontological explosion (see Figure 5). This explosion occurs in explanation-space and represents the theoretical diversity inherent in our attempts to explain phenomenon in our terms rather than the Universe’s terms (whatever they might be). As the explosion grows in intensity we find that there are many more legitimate ways to approach our explanation building. Each approach relies on different ways to recognise the ‘atoms’ of what is and how they interact with each other, i.e., each approach recognises the products of emergence in a different way. Each approach is only capable of explaining certain aspects of the phenomenon of interest, encouraging the increased need for pluralist approaches. The notion of a ‘level’ becomes rather vague, as does the notion of a hierarchy; even a hierarchy of explanations is challenged. Taking this need for pluralism to its extreme leads us into the realms of relativistic philosophies, as opposed to the realist philosophies that tend to developed very well indeed without taking pluralism too seriously. For those fields to continue to develop though I would expect pluralism to become more common. So all my comments above regarding social sciences are true also for physics, just not equally so.
131 reign in the physical sciences. So how do we decide which are the ‘best‘ approaches that lead to the ‘best ’ theories? How do we avoid the choice of ‘filter’ from being completely arbitrary? In the physical sciences consistency with currently accepted theories is often used as an additional filter. Equally important is partial validation through experimentation, and limited empirical observation. Physical scientists are rather fortunate in that many of their systems of interest can be isolated to such a degree that the scientists can actually get away with the assumption that the systems are indeed isolated. This helps a great deal. In the social sciences there is a more ‘try it and see ’ attitude as the application of reductionist methodologies is highly problematic, because of the considerable difficulties in repr
