The International Journal of Systems & Cybernetics, Volume 32, Number 5 6, 2003

Kybernetes

ISSN 0368-492X

The International Journal of Systems & Cybernetics

Volume 32 Number 5/6 2003

Special double issue: Systems and cybernetics: new theories and applications – Part II Guest Editor Yi Lin

Access this journal online __________________________ 596 Editorial advisory board ___________________________ 597 Abstracts and keywords ___________________________ 598 Preface ___________________________________________ 606 Specific relonic patterns from non-specific or useless laboratory data Vadim I. Kvitash________________________________________________

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Raster space with relativity Yongli Li, Zhilin Li, Yong-qi Chen, Xiaoxia Li and Yi Lin ______________

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Normal sum decomposition of general systems Guoyang Liu ___________________________________________________

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Communities of learning: a case in local development Ernesto Lleras__________________________________________________

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A biocultural model of aging Mario E. Martinez ______________________________________________

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CONTENTS

CONTENTS continued

Adaptive dual control in one biomedical problem Konstantin N. Nechval, Nicholas A. Nechval and Edgars K. Vasermanis ___

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Effective state estimation of stochastic systems Nicholas A. Nechval, Konstantin N. Nechval and Edgars K. Vasermanis ___

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A learning model for the dual evolution of human social behaviors M. Nemiche and Rafael Pla-Lopez __________________________________

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Autocorrelation and frequency analysis differentiate cardiac and economic bios from 1/f noise M. Patel and H. Sabelli___________________________________________

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A holistic approach towards the validation and legitimisation of information systems O. Petkova and D. Petkov_________________________________________

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Development of an autonomous spacecraft for planetary exploration Gianmarco Radice_______________________________________________

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‘‘How much cybernetics can you handle?’’ James N. Rose __________________________________________________

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Axiomatic combinatorial world theory with emergent intelligence: simplifying understanding and professionalizing general education Donald O. Rudin ________________________________________________

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Mathematical development: a theory of natural creation H. Sabelli ______________________________________________________

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Aging and social systems H. Sabelli, M. Patel, L. Carlson-Sabelli, J. Konecki, J. Nagib and A. Sugerman___________________________________________________

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Life-long creation in the prevention of premature aging H. Sabelli and A. Sugerman_______________________________________

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Inside communication in nanostructured evolutionary automata — nanophysics and an information concept for viable technologies Salvatore Santoli ________________________________________________

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System dynamics modelling, simulation and optimization of integrated urban systems: a soft computing approach P.S. Satsangi, D.S. Mishra, S.K. Gaur, B.K. Singh and D.K. Jain_________

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Model following PID control system Stanislaw Skoczowski, Stefan Domek and Krzysztof Pietrusewicz _________

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Novelty, diversification and nonrandom complexity define creative processes A. Sugerman and H. Sabelli_______________________________________

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On the criterion of optimal product structure in the micro-economic system (enterprise) and adjustment of product structure Lixin Tao _____________________________________________________

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Smarter computer intrusion detection utilizing decision modeling Christopher C. Valentino _________________________________________

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Cybernetics and systems, from past to future Robert Valle´e ___________________________________________________

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Statistical validation of simulation models of observable systems Edgars K. Vasermanis, Konstantin N. Nechval and Nicholas A. Nechval ___

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SWARM based study on spatial-temporal emergence in flood Yiming Wei, Linpeng Zhang and Ying Fan __________________________

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Towards a cybernetics of value, presence, and anticipation John Wood ____________________________________________________

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Pansystems mathematics: an analysis of panweighted field-network Xiaolong Wu, Dinghe Guo, Jinghong Pan and Xuemou Wu _____________

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On stochastic optimal control for stock price volatility Ying Yi-rong, Lin Yi and Wu Chong-feng ___________________________

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Pansystems GuanKong technology and information quantization Yu Hong-Yi, Leon (Xiangjun) Feng and Yu Ran ______________________

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Randomization and eventual reordering: a number theoretic approach Barry Zeeberg __________________________________________________

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Data self-create in data storage system Zhou ke, Zhang Jiangling and Feng Dan_____________________________

CONTENTS

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EDITORIAL ADVISORY BOARD A. Bensoussan President of INRIA, France V. Chavchanidze Institute of Cybernetics, Tbilisi University, Georgia A.B. Engel IMECC-Unicamp, Universidad Estadual de Campinas, Brazil R.L. Flood Hull University, UK F. Geyer The Netherlands Universities Institute for Co-ordination of Research in Social Sciences, Amsterdam, The Netherlands A. Ghosal Honorary Fellow, World Organisation of Systems and Cybernetics, New Delhi, India R. Glanville CybernEthics Research, UK R.W. Grubbstro¨m Linko¨ping University, Sweden Chen Hanfu Institute of Systems Science, Academia Sinica, People’s Republic of China G.J. Klir State University of New York, USA Yi Lin International Institute for General Systems Studies Inc., USA

K.E. McKee IIT Research Institute, Chicago, IL, USA M. Ma˘nescu Academician Professor, Bucharest, Romania M. Mansour Swiss Federal Institute of Technology, Switzerland K.S. Narendra Yale University, New Haven, CT, USA C.V. Negoita City University of New York, USA W. Pearlman Technion Haifa, Israel A. Raouf Pro-Rector, Ghulam Ishaq Khan (GIK) Institute of Engineering Sciences & Technology, Topi, Pakistan Y. Sawaragi Kyoto University, Japan B. Scott Cranfield University, Royal Military College of Science, Swindon, UK D.J. Stewart Human Factors Research, UK I.A. Ushakov Moscow, Russia J. van der Zouwen Free University, Amsterdam, The Netherlands

Editorial advisory board

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Kybernetes Vol. 32 No. 5/6, 2003 Abstracts and keywords # MCB UP Limited 0368-492X

Specific relonic patterns from non-specific or useless laboratory data Vadim I. Kvitash Keywords Cybernetics, Biomedical Discusses how in 20 different hepato-biliary diseases, relonics for the first time, identifies previously unknown systemic relational networks of biochemical imbalances/ dysbalances which can be used as prototype patterns for early diagnosis, instant monitoring of treatment response, and individualized treatment adjustments.

Raster space with relativity Yongli Li, Zhilin Li, Yong-qi Chen, Xiaoxia Li and Yi Lin Keywords Cybernetics, Approximation concepts, Geographical information systems Practical needs in geographical information systems (GIS) have led to the investigation of formal, sound and computational methods for spatial analysis. Since models based on topology of R2 have a serious problem of incapability of being applied directly for practical computations, we have noticed that models developed on the raster space can overcome this problem. Because some models based on vector spaces have been effectively used in practical applications, we then introduce the idea of using the raster space as our platform to study spatial entities of vector spaces. In this paper, we use raster spaces to study not only morphological changes of spatial entities of vector spaces, but also equal relations and connectedness of spatial entities of vector spaces. Based on the discovery that all these concepts contain relativity, we then introduce several new concepts, such as observable equivalence, strong connectedness, and weak connectedness. Additionally, we present a possible method of employing raster spaces to study spatial relations of spatial entities of vector spaces. Since the traditional raster spaces could not be used directly, we first construct a new model, called pansystems model, for the concept of raster spaces, then develop a procedure to convert a representation of a spatial entity in vector spaces to that of the spatial entity in a raster

space. Such conversions approximation mappings.

are

called

Normal sum decomposition of general systems Guoyang Liu Keywords Cybernetics, General systems This paper introduces normal systems and the normal sum of general systems. A system S ¼ ðM ; RÞ is normal if and only if any two relations in R are not contained in the same Cartesian product Mn for any ordinary number n. Normal sum is a new kind of decomposition (composition) of general systems. Given a normal system S ¼ ðM ; RÞ; and two subsets A1 # M and A2 # M : One of the main results is that the normal sum of the A1-related subsystem and the A2-related subsystem of S equals the (A1 < A2)-related subsystem of S. This implies that every normal system is a normal sum of its subsystems which are non-trivial and non-discrete. Communities of learning: a case in local development Ernesto Lleras Keywords Cybernetics, Learning With the help of some notions developed by us, such as ‘ ‘community of learning’ ’, ‘ ‘powerover relations’ ’, ‘ ‘power-for relations’ ’, learning as observing relations and practices, and others, we describe an intervention in a community with a research-action methodology, aiming at creating learning spaces in different realms of everyday life like enterprise creation and operation, self-government and selfmanagement, and relationships with a traditional learning community as is the case of a high school. A biocultural model of aging Mario E. Martinez Keywords Cybernetics, Older people Addresses how the life sciences have concentrated on the pathology of aging while ignoring the biocultural aspects of health in the process of growing older.

Argues that growing older is a dynamic cognitive, biological and cultural coauthoring of health rather than a hopeless unfolding of progressive pathology. Proposes that this fragmented concept of aging precludes operationalizing and understanding the cultural markers that affect longevity. These cultural milestones, or biocultural portals include middle age markers, retirement markers, perceived wisdom, sexuality, status in the community, transcendental beliefs, sense of empowerment vs helplessness and any other biocultural phase in human development. Suggests that the biocultural portals define and trigger the phase transitions of life as well as influence how they are accommodated. For example, the markers for middle age established by a culture, strongly influence the cognitive and biological expectations for the second half of life. Adaptive dual control in one biomedical problem Konstantin N. Nechval, Nicholas A. Nechval and Edgars K. Vasermanis Keywords Cybernetics, Pharmaceuticals In this paper, the following biomedical problem is considered. People are subjected to a certain chemotherapeutic treatment. The optimal dosage is the maximal dose for which an individual patient will have toxicity level that does not cross the allowable limit. We discuss sequential procedures for searching the optimal dosage, which are based on the concept of dual control and the principle of optimality. According to the dual control theory, the control has two purposes that might be conflicting: one is to help learning about unknown parameters and/or the state of the system (estimation); the other is to achieve the control objective. Thus the resulting control sequence exhibits the closed-loop property, i.e. it anticipates how future learning will be accomplished and how it can be fully utilized. Thus, in addition to being adaptive, this control also plans its future learning according to the control objective. Results are obtained for a priori uniform distribution of the unknown dosage. Because answers can be obtained analytically without approximation, the optimum policy can be compared with the non-optimum

policy of optimizing stage by stage. An illustrative example is given. Effective state estimation of stochastic systems Nicholas A. Nechval, Konstantin N. Nechval and Edgars K. Vasermanis Keywords Cybernetics, Stochastic modelling In the present paper, for constructing the minimum risk estimators of state of stochastic systems, a new technique of invariant embedding of sample statistics in a loss function is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant estimator, which has smaller risk than any of the well-known estimators. There exists a class of control systems where observations are not available at every time due to either physical impossibility and/or the costs involved in taking a measurement. In this paper, the problem of how to select the total number of the observations optimally when a constant cost is incurred for each observation taken is discussed. To illustrate the proposed technique, an example is given and comparison between the maximum likelihood estimator (MLE), minimum variance unbiased estimator (MVUE), minimum mean square error estimator (MMSEE), median unbiased estimator (MUE), and the best invariant estimator (BIE) is discussed. A learning model for the dual evolution of human social behaviors M. Nemiche and Rafael Pla-Lopez Keywords Cybernetics, Modelling, Individual behaviour In this work we modelize, with an abstract mathematical model by computer simulation, the processes that have made to appear in the world a strong duality between orient and occident, by combining changes in conditions of initialization, natural system and the

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opposition gregarious/individualism of the social behaviors.Finally we present a statistical study of the influence of the repression adaptability, resignation and recycling on the ecological destruction and social evolution.This model can help us to analyze if the current capitalist globalization can be stopped, changed or regulated, and if it is possible to overcome it towards a Free Scientific Society. Autocorrelation and frequency analysis differentiate cardiac and economic bios from 1/f noise M. Patel and H. Sabelli Keywords Chaos, Economics, Cybernetics Mathematical bios and heartbeat series show an inverse relation between frequency and power; the time series of differences between successive terms of cardiac and mathematical chaos shows a direct relation between frequency and power. Other statistical analyses differentiate these biotic series from stochastically generated 1/f noise. The time series of complex biological and economic processes as well as mathematical bios show asymmetry, positive autocorrelation, and extended partial autocorrelation. Random, chaotic and stochastic models show symmetric statistical distributions, and no partial autocorrelation. The percentage of continuous proportions is high in cardiac, economic, and mathematical biotic series, and scarce in pink noise and chaos. These findings differentiate creative biotic processes from chaotic and stochastic series. We propose that the widespread 1/f power spectrum found in natural processes represents the integration of the fundamental relation between frequency and energy stated in Planck’s law. Natural creativity emerges from determined interactions rather than from the accumulation of accidental random changes. A holistic approach towards the validation and legitimisation of information systems O. Petkova and D. Petkov Keywords Cybernetics, Information systems The research aims to show that validation and legitimisation of an information systems

(IS) project need to be treated simultaneously to improve software project management. A starting assumption is that traditional aspects of model validity and legitimisation in operational research can be applicable to the field of IS. However, non-traditional types of IS are more suitable to be viewed from an interpretive viewpoint. Validation is explored both from hard systems and also from soft systems point of view. Some extensions on the notion of validation for soft systems are provided for that purpose. Issues regarding both validation and legitimisation in IS are illustrated on a case study regarding the management of an academic research management IS project. Issues related both validation and legitimisation in IS are illustrated on a case study regarding the management of an academic research IS project. The latter had eventually to be abandoned. The case study shows how the non-adherence to the principles of validation and legitimisation lead to that situation. Development of an autonomous spacecraft for planetary exploration Gianmarco Radice Keywords Cybernetics, Autonomy The purpose of this paper is to present a new approach in the concept and implementation of autonomous micro-spacecraft. The one true ‘ ‘artificial agent’ ’ approach to autonomy requires the micro-spacecraft to interact in a direct manner with the environment through the use of sensors and actuators. As such, little computational effort is required to implement such an approach, which is clearly of great benefit for limited microsatellites. Rather than using complex world models, which have to be updated, the agent is allowed to exploit the dynamics of its environment for cues as to appropriate actions to achieve mission goals. The particular artificial agent implementation used here has been borrowed from studies of biological systems, where it has been used successfully to provide models of motivation and opportunistic behaviour. The so-called ‘ ‘cue-deficit’ ’ action selection algorithm considers the micro-spacecraft to be a nonlinear dynamical system with a number of observable states. Using optimal control theory rules are derived which determine

which of a finite repertoire of behaviours the satellite should select and perform. The principal benefits of this approach is that the micro-spacecraft is endowed with selfsufficiency, defined here to be the ability to achieve mission goals, while never placing itself in an irrecoverable position. ‘ ‘How much cybernetics can you handle?’ ’ James N. Rose Keywords Cybernetics, Human-computer interaction Humanity is innately a composition of primitive cybernetic translations/ transmissions to begin with, from atoms through organizations of civilization. The last 75 years has seen us recognize and then extend those relations into sentience and sociological practicalities. It is the author’s intention with this paper to shed some new light and introduce new concepts into the field and understandings.

Axiomatic combinatorial world theory with emergent intelligence: simplifying understanding and professionalizing general education Donald O. Rudin Keywords Cybernetics, Evolution A theory of knowledge shows that all four systems of nature are recursive combinatorial-hamiltonian self-programmed flow-wave systems that can be deduced from the usual Conservation Law promoted to the Axiom of Science.

Mathematical development: a theory of natural creation H. Sabelli Keywords Systems theory, Chaos, Cybernetics The physical universe is the embodiment of necessary mathematical forms by everpresent flux. Interaction of these forms generates diversity, novelty, complexity, and higher levels of organization. Lattice order, group opposition, and topological transformation are generators necessary and

sufficient to construct mathematics (Bourbaki, 1946). Homologous cognitive structures generate human mental development (Piaget, 1949). Process theory proposes that these mathematical generators also create nature. Lattice order is embodied as action, group opposition as two-valued information, and topological transformation as spatial organization. Aging and social systems H. Sabelli, M. Patel, L. Carlson-Sabelli, J. Konecki, J. Nagib and A. Sugerman Keywords Social systems, Age discrimination In our society, medical care and economic progress have improved the duration and quality of life, but aging is accelerated by social norms and their psychological introjection. Healthy aging involves the continuing pursuit of creative activity. Changes in self-view and behavior will require and promote a change in social roles, and the emancipatory mobilization of senior adults of both sexes and all classes. Life-long creation in the prevention of premature aging H. Sabelli and A. Sugerman Keywords Cybernetics, Health Aging is a continuous process of growth and decay, both of which start at birth and continue throughout life. Activity develops muscles and neurons; inactivity atrophies them. Here we propose lifelong creative activity as a method to deal with aging. Decreased creative and learning capacity is a self-fulfilling prophecy. Changing personal perceptions and expectations can promote health care and productive behavior. Inside communication in nanostructured evolutionary automata — nanophysics and an information concept for viable technologies Salvatore Santoli Keywords Cybernetics, General systems On the background of previous research work concerning a nanoscale approach to a theory

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of biomimetic evolutionary systems and biomimetic information processing it is shown that strictly formal-logic based, ‘ ‘hard-wired’ ’ electronic hardware misses the very physical nature of bioevolvability. A new, physics-base concept of information, and a new concept of hierarchical, open and dissipative ‘ ‘evolware’ ’, much like biosystems ‘ ‘wetware’ ’, are required for developing an actually biomimetic ‘ ‘evolutionary automata’ ’ technology, but a basic inter- and intra-level communication problem is shown to affect the whole automaton’s nanostructure. The problem consists in the difficulty of setting forth causal links bridging the whole hierarchy, from the nanoscale up to the macroscopic structure-functions.

Systems dynamics modelling, simulation and optimization of integrated urban systems: a soft computing approach P.S. Satsangi, D.S. Mishra, S.K. Gaur, B.K. Singh and D.K. Jain Keywords Cybernetics, Modelling, Simulation, Optimization A systems dynamics (SD) simulation model has been developed to analyse dynamics of system behaviour in terms of various performance indicators representing city problems, on one hand, and city development, on the other, with three types of policy interventions: changes in the level of sectoral activities, structural changes in different sectors; and changes in the tolerable city problems index. An artificial neurals network (ANN) model has been successfully trained and used as a quick response model for fast feature extraction of the dynamics of the integrated urban energyeconomy-environment system such that the outputs are within reasonable acceptable error for values of inputs covered by the input space of training patterns. For the sake of further convenience and effectiveness in policy decision making, optimised simulation trajectories are generated by applying genetic algorithms (GAs) search and optimisation methods for alternative policy scenarios of

input variables. An application is shown in the context of the city of Jaipur.

Model following PID control system Stanisław Skoczowski, Stefan Domek and Krzysztof Pietrusewicz Keywords Cybernetics, Control systems The paper deals with robustness to plant parameter perturbations and sensitivity to disturbances of two-loop control structures containing a model of the controlled plant and two PID controllers. Special attention is paid to high robustness of considered structure to perturbations of the controlled plant in relation to its nominal model and to good reduction of disturbances. On the basis of presented simulation results one can compare properties of the proposed structure with properties of the Smith predictor and classic control system structure with single feedback loop. The proposed model following control structures may find wide application to robust control of parameter-varying plants.

Novelty, diversification and nonrandom complexity define creative processes A. Sugerman and H. Sabelli Keywords Cybernetics, Creativity We describe a theory of creative activity through the development and use of mathematical tools in the analysis of time series. The time series analyzed include empirical series and biotic and chaotic series generated by recurrent functions. Embeddings are used to measure the dimensionality of a series, and analyses of isometries of Euclidean norms at various embeddings reveal the relatively simple processes that generate and combine with complex structures. These tools identify and measure diversity, novelty, and complexity in complex natural processes and in mathematical bios. The presence of these properties shows that creative processes result from deterministic interactions among relatively simple components, not only from random accident.

On the criterion of optimal product structure in the micro-economic system (enterprise) and adjustment of product structure Lixin Tao Keywords Cybernetics, Product structure In order to make a thorough inquiry into the criterion of optimal product structure in the micro-economic system (enterprise), this paper has proposed and demonstrated the benefit-type linear programming model, and based on it, the concepts of enterprise’s product structure, feasible structure and optimal structure have been discussed and the criterion of optimal structure has been revealed. In this paper, the methods of simplex iteration and sensitivity analysis are both used to approach necessarily the adjustment of product structure under the circumstances of varied or invaried environment inside and outside the system, and as a final, it has come to a conclusion that the variation of resource price vector P would not affect the optimal product structure in enterprise, but the variation of resourceconstrained vector b will cause negative effects both on optimal product structure in enterprise and on determination of criterion for optimal structure. Smarter computer intrusion detection utilizing decision modeling Christopher C. Valentino Keywords Cybernetics, Decision making, Security Addresses specific problems within the area of performing computer system intrusion detection, and presents the reader with an effective decision model to addressing these problems. Current intrusion detection analysis methods are reluctant to properly evaluate the results of decisions made based on their analysis outcomes. These analysis outcomes influence the decision making process involved in response to an intrusion. Utilizing basic decision modeling methods we can develop a model that is both effective and easy to use. To form this model we must have the following within our environment; standard analysis procedure and the classification of information elements. These will feed into our

structured decision model and aid in our final decision outcome. Cybernetics and systems, from past to future Robert Valle´e Keywords Cybernetics, Systems The founders of cybernetics and systems are presented, among them N. Wiener, W.S. Mc Culloch and L. von Bertalanffy. Some precursors are cited from antiquity to 20th century. The basic concepts are exposed: feedback, quantity of information, requisite variety, homeostasis, local and global points of view, oprn systems, autopoiesis. The roles of the observer and of the actor are emphasized. Future is considered in three directions: development of epistemology and of praxiology, symbiosis of man and machine, role of requisite variety in the survival of mankind. Statistical validation of simulation models of observable systems Edgars K. Vasermanis, Konstantin N. Nechval and Nicholas A. Nechval Keywords Cybernetics, Systems, Simulation, Risk In this paper, for validating computer simulation models of real, observable systems, an uniformly most powerful invariant (UMPI) test is developed from the generalized maximum likelihood ratio (GMLR). This test can be considered as a result of a new approach to solving the Behrens-Fisher problem when covariance matrices of two multivariate normal populations (compared with respect to their means) are different and unknown. The test is based on invariant statistic whose distribution, under the null hypothesis, does not depend on the unknown (nuisance) parameters. The sample size and threshold of the UMPI test are determined from minimization of the weighted sum of the model builder’s risk and the model user’s risk. The proposed test could result in the saving of sample items, if the items of the sample are observed sequentially. In this paper we present the exact form of the proposed curtailed procedure and examine the expected sample size savings under the null

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hypothesis. The sample size savings can be bounded by a constant, which is independent of the sample size. Tables are given for the expected sample size savings and maximum sample size saving under the null hypothesis for a range of significance levels (a), dimensions (p) and sample sizes (n). The curtailed test considered in this paper represents improvement over the noncurtailed or standard fixed sample tests.

SWARM based study on spatial-temporal emergence in flood Yiming Wei, Linpeng Zhang and Ying Fan Keywords Cybernetics, Simulation, Disaster management In complex adaptive system (CAS), the complex behavior of system is emerged from the bottom, that agents’ adaptability bottom-up the complexity of the entire system. This idea can be simulated by the method of computer aid simulation. SWARM, which is developed by Santa Fe Institute, is such a tools kit based on the bottom-up modeling method that can be used in CAS simulation on computer. This paper presented a Swarm based simulation platform for the study on complexity in flood disaster. Its application is illustrated with a SWARM based model and program for simulating spatial and temporal emergence of flooding. This model offers virtually unlimited possibilities to simulate the emergence of flooding. Some rules have been elicited from the experimental results, which could provide useful information for the disaster reduction and management. Towards a cybernetics of value, presence, and anticipation John Wood Keywords Cybernetics, Values The paper asks whether we can popularise a cybernetics of human presence. It suggests that, despite its implicit critique of mechanistic thinking, cybernetics inherited its mindset from classical science, and therefore played a part in the evolution of technologically induced forms of alienation. Cybernetics also upholds a strongly western model of ‘ ‘self’ ’ that, given the technological

power implicit in established cybernetic principles, reinforces instrumentalist, solipsistic, and cynical modes of reasoning in the economically ‘ ‘advanced’ ’ nations. These effects, in turn, continue to precipitate ecological damage. In discussing more recent developments, the paper notes the possibilities for modes of cybernetics that could become operative at the site of our selfworld interface. At this level, it argues, our human ontology becomes more synonymous with our senses. This can also be shown by reminding ourselves of the crucial role of our ‘ ‘creative presence’ ’, in which a greater acknowledgement of anticipatory reasoning might inform an actative, flow-based grammar of cybernetics. It concludes that clocks need to be radically re-designed within terms that are in accord with (at least) secondorder cybernetics.

Pansystems mathematics: an analysis of panweighted field-network Xiaolong Wu, Dinghe Guo, Jinghong Pan and Xuemou Wu Keywords Cybernetics, Topology, Mathematics In this paper, we will introduce charm pansystems and provide mathematical models for panweighted field-network. Various mathematical models of pansystems will be discussed. Some traditional mathematical concepts such as topology space and rough sets theory will be analyzed within this framework.

On stochastic optimal control for stock price volatility Ying Yi-rong, Lin Yi and Wu Chong-feng Keywords Cybernetics, Risk, Stochastic modelling The dynamic measure of risk problem in a incomplete market is discussed when stock appreciation rates are uncertain. Meanwhile, a related stochastic game problem is studied. The value of a stochastic optimal control is regarded as a reasonable measure of the risk. The form of the optimal objective is obtained by employing the tools of BSDE theory.

Pansystems Guankong technology and information quantization Yu Hong-Yi, Leon (Xiangjun) Feng and Yu Ran Keywords Cybernetics, Systems theory A basic pansystems scientific view about the physical world is presented. The principle and methodology of pansystems GuanKong technology are introduced. Simple metrics for the quantization of information, risk and gain by comparison (GBC) are established and discussed, and the practical and simple membership function which realizes the transformation from qualitative to quantitative order are given, and an example showing the pansystems GuanKong in detail is also given. Randomization and eventual reordering: a number theoretic approach Barry Zeeberg Keywords Cybernetics, Computational methods Shuffling a deck of cards is normally used for randomization. An imperfect shuffle would not produce the desired randomization, since there would be residual correlation with the original order. On the other hand, from the classical card magic literature it is known that eight successive perfect riffle shuffles returns

the deck to the original order. The question addressed here is whether this observation is in fact unusual and surprising. Although a general closed-form analytical solution does not appear to be possible, a simple program could be written to determine deck sizes and numbers of shuffles for which eventual reordering occurs. This computational approach correctly predicts the original observation of eight shuffles for a deck of 52 cards; in fact if the trivial solutions of integral multiples of eight shuffles are discarded, eight shuffles appears to be the unique solution for a 52 card deck.

Data self-create in data storage system Zhou ke, Zhang Jiangling and Feng Dan Keywords Cybernetics, Data storage When the controller of a storage system becomes more and more powerful, it sometimes creates new data and stores this data in the system, just like parity information in RAID level 5 described by Chen and Lee (993). We call these phenomena data self-create. This paper provides a theory about data self-create which separates data self-create phenomena into 16 kinds. Three applications are introduced. From a pansystems (Wu XueMou, 1993) view, this paper also gives an explanation of data self-create.

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Preface Special double issue – systems and cybernetics: new theories and applications Guest Editor: Yi Lin Part I of this selection of papers from the 12th International Congress of the World Organisation of Systems and Cybernetics (WOSC), held jointly with the 4th Workshop of the International Institute of General Systems Studies (IIGSS) was published in Volume 31, Nos 9/10 2002. Part II of this specially selected collection of papers together with an index to the contents of Part I are contained in this Special Double Issue. We are grateful to Dr Yi Lin for accepting our invitation to be the Guest Editor of both the parts of this unique collection of contributions. The convenors of the congress symposia are also engaged in compiling special issues and features for publication in future issues. Brian H. Rudall Editor-in-Chief

Kybernetes Vol. 32 No. 5/6, 2003 p. 606 # MCB UP Limited 0368-492X

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Specific relonic patterns from non-specific or useless laboratory data

Specific relonic patterns from non-specific data 607

Vadim I. Kvitash Department of General Internal Medicine, School of Medicine, University of California at San Francisco and Personal Health Response, San Francisco, CA Keywords Cybernetics, Biomedical Abstract Discusses how in 20 different hepato-biliary diseases, relonics for the first time, identifies previously unknown systemic relational networks of biochemical imbalances/dysbalances which can be used as prototype patterns for early diagnosis, instant monitoring of treatment response, and individualized treatment adjustments.

Introduction and analysis In 20 different hepato-biliary diseases, relonics for the first time, identifies previously unknown systemic relational networks of biochemical imbalances/dysbalances which can be used as prototype patterns for early diagnosis, instant monitoring of treatment response, and individualized treatment adjustments. Hepatology is an area in which research is under great pressure to meet emergent clinical challenges (Maddrey, 2001), because routinely ordered tests of liver function are neither sensitive nor specific for liver diseases (Theal and Scott, 1996). Currently, the viral hepatitis epidemic has caused an influx of patients with asymptomatic liver diseases leading to clinically significant and even life-threatening complications. The purpose of this presentation is to show the effectiveness of new generation of Systems Sciences and Cybernetics domain-free tools – Relonics (Kvitash, 2002) and to demonstrate how it can be used for mining specific relational patterns from non-specific or useless data and its application in mining diagnostic information from non-specific biochemical variables routinely used in a clinical setting for assessment of liver diseases even if test results could be perceived as seemingly normal or diagnostically useless. The following pages present prototype Relonic patterns of Meta-Networks of Biochemical Imbalances in 20 common hepato-biliary and pancreatic diseases (Figures 1-20): cholestatic hepatitis, chronic hepatitis, chronic hepatitis C, anicteric hepatitis, hepatotoxic effect of alcohol, drug induced liver disease, liver metastases, chronic active hepatitis, obstructive hepato-biliary disease,

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acute viral hepatitis, hepato-renal syndrome, infectious mononucleosis with acute hepatitis, cirrhosis, acute hepatitis, obstructive jaundice, Dubin-Johnson syndrome, Gilbert’s disease, Wilson’s disease, acute pancreatitis and carcinoma of the pancreas. Each page displays a map which begins with a diagnosis, followed by already known non-specific biochemical changes usually associated with, but not specific, with that diagnosis. The next part of the map represents six windows with relational patterns of different types of Meta-Networks of Biochemical Imbalances: [Type 1 – Inversion, Type 2 – Simple Inversion, Type 3 – Integration, Type 4 – Inverted Integration, Type 5 – Disintegration, Type 6 – Inverted Disintegration (Kvitash, 1983, 1985, 2002)]. Each map concludes with a short analytic summary which is useful for early diagnosis, instant monitoring of treatment response, and individualized treatment adjustments. Note 1. Proceedings reprints can be obtained from Dr Kvitash. References Kvitash, V.I. (1983), “Balascopy as a tool for heuristic diagnosis”, AAMSI CONGRESS 83, Proceedings of the Congress on Medical Informatics, San Francisco, CA. pp. 121-5. Kvitash, V.I. (1985), “Balascopy: method for detecting and rapidly evaluating multiple imbalances within multi-parametric systems”, U.S. Patent No. 4,527,240. Kvitash, V.I. (2002), “Relonics: balascopy-based systems-specific technology”, Kybernetes, Vol. 31 No. 9/10, pp. 1471-80. Maddrey, W.C. (2001), “Update in hepatology”, Annals of Internal Medicine, Vol. 134, pp. 216-23. Theal, R.M. and Scott, K. (1996), “Evaluating asymptomatic patients with abnormal liver function tests results”, American Family Physician, Vol. 53, pp. 2111-19.

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Raster space with relativity

Raster space with relativity

Yongli Li Department of Computer Science and National Laboratory of Western China’s Environmental Systems, Lan Zhou University, Lan Zhou, Guansu, People’s Republic of China

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Zhilin Li and Yong-qi Chen Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People’s Republic of China

Xiaoxia Li Department of Computer Science and National Laboratory of Western China’s Environmental Systems, Lan Zhou University, Lan Zhou, Guansu, People’s Republic of China

Yi Lin Department of Mathematics, Slippery Rock University, Slippery Rock, PA, USA Keywords Cybernetics, Approximation concepts, Geographical information systems Abstract Practical needs in geographical information systems (GIS) have led to the investigation of formal, sound and computational methods for spatial analysis. Since models based on topology of R2 have a serious problem of incapability of being applied directly for practical computations, we have noticed that models developed on the raster space can overcome this problem. Because some models based on vector spaces have been effectively used in practical applications, we then introduce the idea of using the raster space as our platform to study spatial entities of vector spaces. In this paper, we use raster spaces to study not only morphological changes of spatial entities of vector spaces, but also equal relations and connectedness of spatial entities of vector spaces. Based on the discovery that all these concepts contain relativity, we then introduce several new concepts, such as observable equivalence, strong connectedness, and weak connectedness. Additionally, we present a possible method of employing raster spaces to study spatial relations of spatial entities of vector spaces. Since the traditional raster spaces could not be used directly, we first construct a new model, called pansystems model, for the concept of raster spaces, then develop a procedure to convert a representation of a spatial entity in vector spaces to that of the spatial entity in a raster space. Such conversions are called approximation mappings.

1. Introduction One main purpose of geographical information systems (GIS) is to analyze spatial data and provide supporting information for decision-making. So, the spatial analysis can be seen as the primary function and the soul of GIS. Currently there are two typical reference systems for spatial analysis. One is Yongli Li would like to thank the Hong Kong Polytechnic University for its research fellowship, which has made this work possible.

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the Euclidean space on R 2, the other raster spaces. As expected, each of the systems has its own strength and limitations. For example, when the topological spatial relations of all possible spatial objects by means of the point-set topology are described (Egenhofer and Sharma, 1993), for any two subsets A, B of the universe X, the boundary of A is denoted ›A and its interior A8. The relation of A and B can be expressed in terms of their boundaries and interiors such as ›A > ›B; ›A > B8; A8 > ›B; A8 > B8: More specifically, let P [ R 2 and D , R 2 be a point and a region (Figure 1), their spatial relations are described in Table I. Such a theoretical decision has an important weakness in terms of numerical computations unless the boundary of D is very regular. Also, most elemental propositions, say, P belongs to a line Q or an area D, is not decidable except when Q and D are presented by an elementary equation such as a circle, polygon, etc. This limitation of the Euclidean space as the reference system for spatial analysis is about the incomputability of models. It is concluded (Li et al., 1999) that “if a subset in R 2 represents a spatial entity, which can be studied in a vector space, then it can also be studied in a raster space. When an entity is studied in raster space, it is implied that there is a relationship between the vector space and the raster space. The observation of the entity has been transferred from the vector space to the raster space. In this transformation, some kind of invariability is retained. This invariance is the fundamental reason why topological properties and relations of spatial entities can also be studied in raster spaces. Indeed, it can be considered that each raster topology is the quotient space of a vector topology. Each topological relation of entities in a raster space has its correspondence in a vector space. Due to the fact that expressions of spatial entities in discrete spaces are more explicit than those in connected spaces, raster topologies provide an efficient means for the study of topologies in vector spaces”. Now, what is the meaning of computability? A computational procedure is a procedure consisting of an unambiguous description of a finite set of

Figure 1. A point P and a region D in R 2

Table I.

P inside of D P on the boundary of D P outside of D

›P > ›D

›P > D W

P W > ›D

P W > DW

B 1B B

1B B B

B B B

B B B

operations. The operations must be mechanically completable. Also, the order of operations must be well defined. Computer programs are examples of such effective procedures. Here, the finiteness of description and effectiveness of operations are the most important characteristics of computational procedures (Brainerd and Landweber, 1994). Compared to Euclidean spaces, models developed on raster spaces are suitable for computation purposes. For example, a spatial entity is usually represented by a finite subset in a raster space, while entities, such as lines and areas, are represented as infinite subsets in Euclidean spaces. Generally, it is easier to find a mechanical algorithm for an operation on finite subsets than that on infinite ones. Raster spaces not only have the advantage over Euclidean spaces in terms of computations, but also simulate the human being cognition better than Euclidean spaces. Since raster spaces possess advantages in computation over Euclidean spaces, we will use raster spaces as our platform to study spatial entities in vector spaces. That is to say, what interests us is the relationship between models of spatial analysis on vector spaces and those on raster spaces. To realize our idea, we will reconstruct the concept of raster spaces so that a link between vector spaces and raster spaces can be established. Then, we will construct mappings, called approximation mappings, which can convert the representation of a spatial entity in vector spaces to one in raster spaces. At the end, we will use raster spaces as a tool to study morphological changes, all kinds of equal relations, connectedness, and spatial relations of spatial entities existing in a vector space. We now conclude this section with some preparation. Let f and g be relations from A to B and B to C, respectively. Then, the composition of f and g is defined as f · g ¼ fða; cÞ : ’b [ B such that ða; bÞ [ f and ðb; cÞ [ g}: If f # A 2 ; f t ¼ f < f 2 < f 3 < f 4 < . . . is called the transitive closure of f, where f 2 ¼ f · f and f kþ1 ¼ f k · f ; for k $ 2: Let U be a set and d a semi-equivalence relation, which is defined as a reflexive and symmetric relation, on U. The semi-equivalent quotient set of U with respect to d is defined as a family of subsets of U, written U/d, as follows: ;B – A # U ; A [ U=d iff A 2 [ d and there does not exist B # U such that A , B and B 2 [ d: Each element in U/d is called a semi-equivalence class of U with respect to d. Let f # A £ B; D # A and C # B: Then, D · f ¼ fb [ B : ’d [ Dðd; bÞ [ f } is called the composition of D to f (or the image of D ), f · C ¼ fa [ A : ’c [ Cða; cÞ [ f } is called the composition of f to C (or the pre-image of C ), and D=f ¼ fb [ B : f · {b} # D} (Li et al., 1998) is called the division of D to f. Let us make the following convention: If C ¼ fc} and D ¼ fd} are singletons, then {d} · f equals d · f and f · {c} is the same as f · c: Then, we have the following: Theorem 1.1. If f # A £ B and D # A; then the following hold true: (1)

D · f ¼
(2)

If A · f ¼ B; then D=f ¼ fb : b [ D · f and f · b # D}:

(3)

For any D1, D2 # A; if D1 # D2 ; then D1 · f # D2 · f :

A

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2. The pansystems model of raster spaces From the point of view of pansystems (Wu, 1990), each raster space is a generalized system, where a generalized system consists of a hardware A and a software B, denoted S ¼ ðA; BÞ: The hardware A is a set, while the software B is a set of some relations on A. For the Euclidean space R 2, we use equally spaced horizontal and vertical lines to divide the plane into many grids. If each grid is viewed as an element, then all the grids of the plane form a set G, call grid set, which is seen as the hardware of the raster space. Now, a natural oneto-one correspondence between G and Z 2, the set of all ordered pairs of integers, exists so that G can be denoted {Gij : i; j [ Z } or simply Z 2, where Gij represents the grid in the divided plane located at (i, j ) consisting of the points in the interior and boundary of the grid in terms of the Euclidean topology on R 2 ( Janich, 1984). When the spacings of the horizontal and vertical lines, used to divide R 2 into G, are different, one obtains different raster spaces. Each fixed spacing is called the scale of the relevant raster space (Li, 1994). For practical purposes, it can be seen that all properties and spatial relationships of physical entities are relative in terms of through which raster space they are observed. So, in practice, one can always choose the most suitable raster space by adjusting the scales. The hardware of the raster space Z 2 is the semi-equivalence quotient set of R 2 with respect to d ¼ <ði; jÞ[Z 2 Gij : That is, G ¼ R 2 =d: When necessary, the raster space is also written as (G, edge, d ). One of the many important relationships between spatial entities is their adjacency relationship. Since there are many existing computational models about relation operations, we will employ relations and relation operations to define our adjacency relationship. Let (G, edge, d ) be a raster space. There exist two kinds of adjacency relations defined on G that are the 4-adjacency and 8-adjacency, denoted d 4 and d 8, respectively, where d 8 ¼ fðGij ; Gkl Þ : Gij, Gkl [ G and Gij > Gkl – B} and d 4 ¼ fðGij ; Gkl Þ : Gij, Gkl [ G; Gij > Gkl – B and jGij > Gkl j – 1}: Theorem 2.1. For any raster space (G, edge, d ), both 4-adjacency relation d4 and 8-adjacency relation d 8 are reflective, symmetric, but not transitive. A That is, d4 and d8 are semi-equivalence relations. And, d 4 # d 8: Connectedness is another important issue in the study of spatial entities. It will be shown that our approach can point out the relation from adjacency to connectedness by using some relation operations. So, our method does not contradicts the traditional approach. For any subset F # G; the hardware of our raster space, the 4-adjacency relation on F, denoted d 4jF; is the restriction of d4 on F. That is, d 4jF ¼ d 4 > F 2 : The 4-connected relation on F, denoted d 4* ðFÞ; is the transitive closure of d 4jF: That is, d 4* ðFÞ ¼ ðd 4jFÞt : Similarly, we can define the 8-adjacency relation on F as d 8jF ¼ d 8 > F 2 ; and the 8-connected relation on F as d 8* ðFÞ ¼ ðd 8jFÞt : Based on our definitions here, we can see the following result: Both d 4* ðFÞ and d 8* ðFÞ are equivalence relations on F.

Another important issue is the so-called connected components. A weakness of the traditional models is that they do not express the process going from a connectedness relation to connected components. Since based on our model, all connected components of a set form the quotient set of a connectedness relation on the set, it shows the advantage of our model. More specifically, 4-connected components of F are defined as the equivalent classes of F to d 4* ðFÞ; 8-connected components of F are defined as the equivalent classes of F to d 8* ðFÞ: If d 4* ðFÞ ¼ F 2 ; then the quotient set of F to d 4* ðFÞ is {F}: In this case, we say F is 4-connected. If d 8* ðFÞ ¼ F 2 ; we say F is 8-connected. Theorem 2.2. For any subset F of grid set G (F # G ), the following propositions hold true:

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(a) d 4jF and d 8jF are semi-equivalence relations on F rather than equivalence relations and d 4jF # d 8jF; (b) d 4* ðFÞ and d 8* ðFÞ are equivalent relations on F and d 4* ðFÞ # d 8* ðFÞ; (c) Any 8-connected component of F is the union of some 4-connected components of F; and (d) If F is 4-connected, then F is also 8-connected.

A

Example 4.1. Suppose that a raster space (G, edge, d ) is given and F # G; (Figure 2), where F ¼ f1; 2, 3, 4, 5, 6, 7, 8, 9, 10}, a 4-adjacency relation d4 on F is defined as {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (10,10), (2,3), (2,5), (3,2), (5,2), (3,4), (3,6), (4,3), (6,3), (5,6), (5,8), (6,5), (8,5), (7,8), (8,7), (9,10), (10,9)}, and a d8 can be expressed by Figure 3(a). So, d 8jF ¼ d 8jF < {ð1; 2Þ; (2,1), (3,5), (5,3), (4,6), (6,4), (5,7), (7,5), (6,8), ð8; 6Þ}; which is shown in Figure 3(b). d 4* ðFÞ ¼ ðd4jFÞt ; 4-connected relation on F, and d 8* ðFÞ ¼ ðd 8jFÞt ; 8-connected relation on F, are shown in Figure 4(a) and (b), respectively. Now, all the 4-connected and 8-connected components of F are given by F=d 4* ðFÞ ¼ f{1}; {9; 10}; {2; 3; 4; 5; 6; 7; 8}} and F=d 8* ðFÞ ¼ f{9; 10}; {1; 2; 3; 4; 5; 6; 7; 8}}; respectively. Let us now turn our attention to three approximation mappings from R 2 to Z 2. The goal for us to construct our pansystems model is to make it possible to study spatial entities in vector spaces. So, now, we see how representations of spatial entities in vector space can be converted to those in

Figure 2. The subset F in G

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Figure 3. The graphic expression of the 8-adjacency relation on F

Figure 4. 4- and 8-connected relations on F

raster spaces. Such conversions are called approximation mappings. Now, assume that X is an entity in the vector space R 2. Then, our raster space {Gij : i; j [ Z } also form a generalized system as follows: ðR 2 ; {Gij : i; j [ Z }Þ: This system can be a generalized subject which observes the entity X from both inside and outside of X. If the entity X is placed in the raster space, all the grids inside of X forms a set, called interior approximation of X. All the grids which are neither inside nor outside of X form a set, called the boundary approximation of X. The set of all the grids outside of X is called the exterior approximation of X. Now, we have defined three approximation mappings appin(d ). appex(d ) and appbnd(d ) from PðR 2 Þ to P(G ), the power sets of R 2 and G, such that for any X [ PðR 2 Þ; appin(d )(X ). appex(d )(X ) and appbnd(d )(X ) stand for the interior, exterior and boundary approximations of X, respectively. These three subsets of G are called an observation of the generalized subject ðR 2 ; {Gij : i; j [ Z }Þ of the object X. Proposition 2.1. For any raster space (G, edge, d ) and any subset X # R 2 ; (a) appbndðdÞX ¼ appexðdÞX 2 appinðdÞX; (b) appinðdÞX # appexðdÞX: A For convenience of theoretical computations, we now introduce some characteristics of the approximation mappings as just introduced earlier. Let Beto # R 2 £ G such that for any x [ R 2 ; x · Beto ¼ {Gij [ G : x [ Gij }:

Theorem 2.3. Any point-set of the plane can be converted to subsets of grid set of G through Beto such that for any X [ PðR 2 Þ; appinðdÞX ¼ X=Beto; appexðdÞX ¼ X · Beto; and appbndðdÞX ¼ appexðdÞX 2 appinðdÞX: A Proof. It suffices to show the following two equations: (a) X · Beto ¼ fGij [ G : Gij > X – B}; and (b) X=Beto ¼ fGij [ G : Gij # X}: If both (a) and (b) hold, from Proposition 2.1 it follows that the boundary approximation mapping has been characterized well. Now, let us prove (a) and (b). (a) It follows from Theorem 1.1 that X · Beto ¼ <x[X x · Beto: From the definition of Beto, it follows that for any G* in x · Beto; x [ G* holds. So, G* > X – B: So, x · Beto # {Gij [ G : Gij > X – B}: On the other hand, for any Gij [ G satisfying Gij > X – B; let x* [ Gij > X: From the definition of Beto, it follows that Gij [ x* · Beto: So, Gij [ X · Beto: So, X · Beto $ {Gij [ G : Gij > X – B}: That is, (a) holds true. (b) Since Beto is an onto mapping, Theorem 1.1 implies that X=Beto ¼ fGij [ X · Beto : Beto · Gij # X}: For any Gij * [ X=Beto; if there exists x* [ Gij * 2 X; then (x*, Gij * Þ [ Beto: From the definition of Beto · Gij * ; it follows that x* [ Beto · Gij * : So, x* [ Beto · Gij * 2 X; which contradicts with Beto · Gij * # X: So, Gij * # X: That is, Gij * [ {Gij [ G : Gij # X}: On the other hand, for any Gij * [ {Gij [ G : Gij # X}; since Gij * > X – B; Gij * [ X · Beto: Since Gij # X; from the definition of Beto, it follows that Beto · Gij * # X: So, {Gij [ G : Gij # X} # X=Beto: That is, (b) holds true. A 3. Properties of approximation mappings Proposition 3.1. For any raster space (G, edge, d ) and any X # R 2 ; (a)
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Figure 5. Morphological changes using approximation mappings

Figure 6 implies that if X is the union of some grids, then X is a fixed point of
if appexðdÞX ¼ appexðdÞY ; then we say that X is externally equal to Y relative to (G, edge, d );

(2)

if appinðdÞX ¼ appinðdÞY ; then we say that X is internally equal to Y relative to (G, edge, d ); and

(3)

if appinðdÞX ¼ appinðdÞY and appexðdÞX ¼ appexðdÞY ; then we say that X is equal to Y relative to (G, edge, d ).

Figure 7 implies that two distinct spatial entities X, Y of a vector space can be equal relative to some raster space. Now, let us consider the concept of observable equivalence as follows: For two entities X and Y of the vector space R 2, if X is equal to Y relative to some raster space (G, edge, d ), then we say X and Y are observable equivalent relative to the raster space. Here, Figure 7 provides a typical example of observable equivalence. For practical purposes,

we can also define other forms of observable equivalence. For example, if X is externally equal to Y relative to the raster space (G, edge, d ), then X is observable equivalent with Y relative to the raster space. Here, we should notice the property of relativity of the concept of observable equivalences. That is, it is relative to some raster space. It is very possible that two spatial entities are observably equivalent relative to raster space (G1, edge1, d1), but they are not observably equivalent relative to raster space (G2, edge2, d2). As for the connectedness of spatial entities in vector spaces, we have the following: Theorem 3.2. For any raster space (G, edge, d ), there exists a point-set X* ð# R 2 Þ such that X* is not connected relative to the Euclidean topology on R 2, but its exterior approximation appex(d )X is 4-connected. Consequently, there exists a point-set X* ð# R 2 Þ such that X* is not connected relative to the Euclidean topology on R 2, but its exterior approximation appex(d )X is 8-connected. A Theorem 3.3. For a point-set X ð# R 2 Þ is connected relative to the Euclidean topology on R 2, then its exterior approximation appex(d )X is 4-connected in any raster space. A Proof. Because X is connected relative to the Euclidean topology on R 2 and
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Figure 6. Areas in R 2 and G are identical

Figure 7. Distinct spatial entities may look the same in some oberver’s eyes

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topology on R 2, there must be a curve L* from a1 to a2 in appexðdÞD ¼ B; then P is outside of D. If appexðdÞP > appinðdÞD – B; then P is inside of D. If appexðdÞP > appbndðdÞD – B; then the horizontal or vertical distance from P to the boundary of D is not more than the scale of the raster space. In the last case, there are two methods for selecting the scale of the raster space. One is decrease the scale of the raster space. The other method is classify the grids in which appex(d )P lies. In the case, we only study P and the segment of the boundary of D in which appex(d )P lies. So, the problem of spatial relations

between a point and a region is converted to a problem between spatial entities of a raster space. 4. Summary In this paper, a pansystems model of raster spaces is presented, including the hardware, adjacency relationship, connectedness, and some discussion of relevant properties. Three approximation mappings that can convert any pointset of R 2 into three subsets of a chosen raster space are then put forward. Based on the pansystems model and approximation mappings, we use raster spaces to study spatial entities of R 2. What is discovered is that one can always choose an adequate raster space to make morphological changes to a spatial entity of R 2 and such changes could preserve the size relationship of spatial entities. When raster spaces are used as a subject to observe spatial objects of R 2, it is discovered that their equal relationships and connectedness satisfy an interesting condition of relativity, which is named as observable equivalence, strong and weak connectedness, respectively. Raster spaces can also be used to study spatial relations of spatial entities of R 2. Just as the philosophers have told us – any thing in the world that has two sides (Yin and Yang), vector spaces and raster spaces in our context here, as reference systems of spatial analysis, has its own limitations and advantages. From the viewpoint of computation, we present a new model for raster spaces and expect that the new model will bring forward conveniences in terms of computation. We have also tried to use raster spaces to study spatial entities in the vector space R 2. We expect that a new computational model for spatial analysis would come into being soon. References Brainerd, W.S. and Landweber, L.H. (1994), Theory of Computation, Wiley, New York, pp. 1-9. Egenhofer, M.J. and Sharma, J. (1993), “Topological relations between regions in 32 and 92”, in Abel, D. and Ooi, B.C. (Eds), Advances in Spatial Databases (SSD93), Lecture Notes in Computer Science, 692, Springer-Verlag, pp. 226-316. Janich, K. (1984), Topology, (translated by Silvio Levy), Springer-Verlag, New York. Li, Y., Liu, L., Shang, L. and Li, C. (1998), “The invariance and the nonlinearity in modal logics”, Journal of Gansu Sciences, Vol. 10 No. 3, pp. 7-11. Li, Z.L. (1994), “Reality in time-scale system and cartographic representation”, The Cartographic Journal, Vol. 31 No. 1, pp. 50-1. Li, Z.L., Li, Y.L. and Chen Y.Q. (1999), “Fundamental issues on topology in vector and raster spaces”, The International Archives of Photogrammetry and Remote Sensing, Dynamic and Multi-Dimensional GIS, 4-6 October, 1999, Beijing, China, Vol. XXXII, Part 4W12, pp. 67-71. Wu, X.M. (1990), The Pansystems View of the World, Press of Chinese People University, Beijing, pp. 1-316.

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Normal sum decomposition of general systems Guoyang Liu Department of Mathematics, The Catholic University of America, Washington, USA Keywords Cybernetics, General systems Abstract This paper introduces normal systems and the normal sum of general systems. A system S ¼ (M,R ) is normal if and only if any two relations in R are not contained in the same Cartesian product M n for any ordinary number n. Normal sum is a new kind of decomposition (composition) of general systems. Given a normal system S¼(M,R ), and two subsets A1#M and A2# M. One of the main results is that the normal sum of the A1-related subsystem and the A2-related subsystem of S equals the (A1
1. Introduction Several kinds of decompositions of a general system have been studied. Among the most interested ones are free sum decomposition (Lin, 1987, 1990) and direct sum decomposition (Ma and Lin, 1988). In this paper, we decompose a general system to a special sum of its subsystems regarding to a supporting set of the system. For the convenience of readers, we recall from (Lin, 1987) the definition of general system of multiple relations. The reader should consult (Mesarovic and Takahara, 1975, 1989) for the original definition of a general system of single relation. A general system is an ordered pair of sets, S ¼ ðM ; RÞ; such that M is the set of all objects of S, and R is a set of some relations defined on M. The sets M and R are called the object set and the relation set of the system S, respectively. In this definition, for any relation r [ R, there exists an ordinal number n ¼ nðrÞ such that r # M n : Assume that n ¼ nðYÞ ¼ 0: A system S ¼ ðM ; RÞ is trivial if M ¼ Y: S is discrete if R ¼ Y or R ¼ {Y} and M – Y: Given two systems S i ¼ ðM i ; Ri Þ; i ¼ 1; 2: S1 is a subsystem of S2 if M 1 # M 2 and for each relation r1 [ R1 there exists a relation r 2 [ R2 such that r1 # r2 jM 1 (Lin, 1999).

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2. Definition of normal systems and the normal sum of systems Definition 2.1. Let S ¼ ðM ; RÞ be a general system. If for every ordinal number n there exists at most one relation r in the relation set R such that n ¼ nðrÞ; the system S is called a normal system.

Given a system S ¼ ðM ; RÞ: If there are two or more relations in the relation Normal sum set contained in the same Cartesian product M n, i.e. with the same ordinal decomposition of number n. One may take the union of all these relations to normalize the general systems system. Definition 2.2. Let {S i ¼ ðM i ; Ri Þ : i [ I } be a set of normal systems, and IUan index U set. U We U define the normal sum of the systems Si, denoted by 641 S . . . S n ; if I ¼ {1; 2; . . .; n} is finite, to be the system S or S 1 2 i[I i ]

i[I S i

¼ ð
]

i[I R i Þ

U where i[I Ri ¼ { < r i : ri [ Ri and nðri Þ ¼ n for i [ I ; n is an ordinal number}. The following two theorems are directly from the definition. Theorem 2.3. The normal sum of a set of normal systems is a normal system. U Theorem 2.4. If S ¼ ðM ; RÞ is a normal system, and I is an index set, then i[I S ¼ S: 3. A decomposition of normal systems Definition 3.1. Let S ¼ ðM ; RÞ be a general system, and A a non-empty subset of M. For a relation r [ R; an A-related sub-relation of r, denoted by rA, is defined by r A ¼ {x : x [ r and xb [ A for some b , nðrÞ} The set of A-related sub-relations is denoted by RA ¼ {rA : r [ R}: Let M A ¼ A2 # rA1 > rA2 ;

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(iii) RA1 A2 # {rA1 > rA2 : r [ R}: Proof. (i) x [ rA1 A2 iff xb [ A1 > A2 for some b , nðrA Þ iff xb [ A1 and xb [ A2 : Therefore, x [ r A1 > rA2 : (iii) and (iv) follow immediately from (i) and (ii). We give an example to show that rA1 >A2 is not necessarily equal to r A1 > rA2 : Let M ¼ {a; b; c}; R ¼ {r; s}; where r ¼ {ða; bÞ; ðb; cÞ}; and s ¼ {ða; b; cÞ}: S ¼ ðM ; RÞ is a system. Let A1 ¼ {b} and A2 ¼ {a; c}: Then rA1 ¼ r and r A2 ¼ r: So that rA1 > rA2 ¼ r ¼ {ða; bÞ; ðb; cÞ}: However, A1 > A2 ¼ Y; and rA1 >A2 ¼ Y: If S is normal, we further have the following theorem. A Theorem 3.3. Let S ¼ ðM; RÞ U be a normal general system, A1 and A2 two subsets of M. Then RA1
It follows from Theorem 3.2 (i) that r{a;b} ¼ r {a} < r{b} for every r [ R: Normal sum Then Suppðr{a;b} Þ ¼ Suppðr {a} < r{b} Þ: Also decomposition of Suppðr{a} < r {b} Þ ¼ Suppðr{a} Þ < Suppðr{b} Þ:

general systems

Therefore,
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Communities of learning: a case in local development Ernesto Lleras Titular Professor, University of Los Andes, TESO (Systems Research Group), Bogota´, Colombia Keywords Cybernetics, Learning Abstract With the help of some notions developed by us, such as “community of learning”, “power-over relations”, “power-for relations”, learning as observing relations and practices, and others, we describe an intervention in a community with a research-action methodology, aiming at creating learning spaces in different realms of everyday life like enterprise creation and operation, self-government and self-management, and relationships with a traditional learning community as is the case of a high school.

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Some previous considerations Within the research program of the Systems Research Group one of our concerns have been related with how to intervene in local organizations, in order to develop better conditions for the development of emancipatory social settings. For “emancipatory conditions” we understand a collective which, instead of constraining individual creativity and self-expression, enables social conditions which make dialog possible. For dialog we understand communicative relations in which individuals express themselves from their particular “vital point” (interests, beliefs, groundings) but are open to the other’s particularity, and the “practical comprehension” of relationships as “world producing” (Buber, 1965; Freire, 1970). From these premises, an emancipatory space makes possible for individual potentialities to emerge and to contribute to collective agreements on what to do together and under which conditions. We have been working in extremely authoritarian settings. Labor conditions in Colombia have inherited practices that come from colonial times (Weiss, 1989), the old plantation pattern or the “hacienda” system. Within the “hacendary” tradition, the system of domination develops two extreme possibilities – pure coercion, or paternalism. In both cases, the psychology of the worker is one of subservience and lack of responsibility for himself, for others, or for his work. In terms of relations, responsibility is delegated to superiors, including responsibility for the person’s own life (Pe´rez, 2000). The basis of emancipation follows Heidegger’s (1951) definition of ontology as the particular manner in which a human being (being-there) interprets his own ways of being. Besides, his notion of “pre-ontological” being as that in

which we normally engage in practices allows us to understand human beings as undefinable by reason, as open to the future, as becoming. This going back and forth between pre-ontological and ontological practices with others determines the way we conceive our world. “Care” is another aspect of Heidegger’s thought that can help us in our endeavour. This is the way in which “we-are-with-others”, the particular feeling of concern for others. For instance, trust or lack of it, solidarity, respect for others and other social predispositions as well as awareness of others’ presence in our space of being. Because we belong to a social space pervaded by domination relationships, we identify as one of the main problems of our social structure, the relationship of domination that we denominate “power-over”. This type of relationship is very evident in formal organizations, which have vertical hierarchical structures. Power is given by the position of persons within the structure. But in everyday life “power-over” manifests as the need to dominate the other in every type of interaction, e.g. to “win” a conversation, to convince others of our point of view, to invoke higher authorities to sustain an argument, to give orders. In contrast to “power-over” we propose the notion of “power-for”, that is, relationships of co-operation. These aspects have been treated by scholars in the past, among others Freire (1972), Buber (1965) and a stream of neo-marxist social analysts. The development of “power-for” relations occurs in the process of transforming interaction from competitive to dialogical. We define that an organization becomes a community when relationships within it become dialogical. We postulate that the system structure is a strong influence in the behaviour of participants (Bourdieu, 1977; Echeverrı´a, 1996). Participants in an organization engage in practices that are interrelated. The patterns of interrelation are determined by practices that purport to respond to the interests of participants (Bourdieu, 1977). We postulate that the way to change the behaviour and structure of an organization is by way of the members’ decision to do so after they observe and reflect upon the patterns of relationship. That is, after they realize about the type of relationships they are having. We consider three dimensions of relationships to be crucial for the behaviour of the organization: power relations (that embed the other two), conversational relations, and service relations. Power relations can be observed in terms of domination or co-operation. Conversational relations can be observed in terms of “language games” and “speech acts” (Echeverrı´a, 1992; Searle, 1969; Witgenstein 1972) – that is, as “world co-creation”; ontological and “care” practices can act to transform language relationships from those determined by power-over to events of dialogue (Buber, 1965; Freire, 1970; Lleras, 1998a, b) or human encounter.

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Service relations can be observed in terms of language games which are instrumental for the organization although marked by the expression of the creativity or fulfilment of potentiality either of the individual or the group. It can be contrasted with Habermas’ relations of communication, interaction, and instrumentality, in terms of the purely rational focus that Habermas emphasizes. We stress the aspect of the development in the interpretation of power in an ever changing context (Freire, 1972). With all these considerations in mind we can approach the notion of a community of learning. As said earlier, the structure (relationships, ontological practices, care, mood) of a social organization determines the individual’s behaviour, but at the same time individual behaviour can have incidence on structural changes. From this perspective any organization is a space of learning, since the members have to learn how to behave, or said otherwise, their practices, in which they engage with their bodies, moods, and language (Bourdieu, 1977), have to accommodate to the structure in order for the individual to achieve his/her interests. But they also modify the structure by their practices. Practices are, hence, relational. Learning is a social transformation in which individuals affect the “structure” and are affected by it. This sort of learning occurs unconsciously. To develop a “conscious” learning, a kind of “second order learning”, participants have to develop an ontological reflection, they become observers of relations and moods (Lleras, 2001a, b), in particular their relations to others, and specifically their conversational or service relations, and the moods associated to them. This is a type of learning which is crucial, since it may lead members to change relationships in order to achieve their interests (individual and collective) of a better organization. A better organization is one that responds to individual and collective needs, as well as needs of institutional survival and care for clients or beneficiaries. This approach differs from “rational” systemic approaches such as those proposed by Checkland (1972), Ulrich (1983), Flood and Jackson (1991) and others. The difference consists in the opportunity for stakeholders or members of the social setting for developing their own practices for change, departing from a state of awareness and an ability to observe themselves engaged in social practices. We worked the learning community in a twofold manner: as a process in time, and as a structure in the space of practices. The process, described further on, began by working with neighbours of a poor community, in a process of construction of ways of earning their life, that ended up on a project for building enterprises that were to be treated as means for work, and as means for learning. Each enterprise was specialized in a certain aspect of building technology, like masonry, metal works, carpentry, etc. There was a curriculum for each enterprise, and we developed a plan of courses in different technical matters, as well as “basic” courses in reading and writing, management skills,

human development, and computer techniques. The enterprises were associated in a “multi-active co-operative”. Simultaneously, we worked with the technical high schools of the zone (a total of four). The work pretended to create linkages with the enterprises. The links were of different kinds. Students who wanted to participate in the enterprises could do a sort of assistantship there. The sophisticated technical tools owned by the schools could be used by the enterprises. The premises of the schools were used as rooms for the courses and other types of meetings. Teachers participated in whatever was of their interest, either teaching, working or facilitating processes. The third level of practices, was the political realm, also purported to be seen as a learning space. This is the space for participation of the different actors engaged in the project, which included other institutions from the community like government agencies, financial offices, and other associations (NGO’s in general). This space was used for the beginning of self-government practices. There was an excuse, which was the development of the mayor’s office development plan. The process is ongoing.

The project: a space of practices (based on Lleras and Arias, 2001) During the last 5 years the Colombian economy has suffered a state of depression. Unemployment has become a growing problem. Government policy for the creation of jobs has been focused on supporting the creation of enterprises. In the case of big organizations, there is a situation of unqualified work force, and hence the policy is at fault. In the case of small businesses, implementation and promotion have been imposed from above, and the poor have been far from modern entrepreneurial practices (Lleras, 1998). The low impact of those policies comes from precisely the type of approach which is “assistentialist” within the paternalistic tradition of the country. The mechanisms for incentives are depersonalized, and ignore the concrete situations in which the population is immersed. Consequently, government programs have not been sustainable. On the other hand, there are lots of community initiatives that are ignored or invisible for government agencies. Besides the inability to recognize the needs and perspectives of local development, these policies do not promote the development of autonomy and sustainability of small businesses, mainly because they are “government projects” rather than “community projects”. A group of institutions, under the concept of alliance, decided to approach the problem from another perspective. There were a number of postulates from the very beginning as supports of the whole approach. First, an integral notion of development (neither merely economic nor organizational). Second,

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we would depart from contextual reflections within local realities. Third, the communities themselves would do the reflection and generate the questions to guide the research and actions. The point of departure would be to create “spaces for reflection” about the actual conditions and the conditions considered as “development” by the actors themselves. This would create “disclosing spaces” (Heidegger, 1951) to reveal potentialities for learning, self-management, and encounter among potential actors. In other words, we wanted to create the conditions for “learning communities” to appear. These communities would then be able to propose their own manner of local development. The aim of this project was then to experiment the possibilities of selfmanagement at the personal and collective levels, opening up the opportunities for discovering their own potential as a community.

The scenery: “Tintal Central” We chose this locality of 160,000 inhabitants, which is one of the 20 localities of which the city of Bogota´ (6,500,000 inh.) is composed. This is one of the poorest sectors of the city, it began as a “pirate” neighborhood, developed by illegal land developers. In its inception there was no planning, and houses were very precarious shelters. Nowadays, houses are better built, and it has a trace of well delineated streets and parks. However, even though there are some public services, some are deficient, mainly sewage. The Tintal zone has the greatest food distribution center of the city (and of the country). There are some important city projects there in these days such as big road projects, decontamination of the river, a sewage system, new schools, and a big library. The population is about 160,000, with 36,000 households. The stratum (level of income) is in the borderline between extreme poverty and poverty. 33 per cent of the population does not have basic health coverage, there are 5,000 illiterates, 42 per cent of the population only went to primary school, while 51 per cent has done secondary school and some technical training. 72 per cent drop out of school for economic reasons (they need to work). According to DANE (National Statistics Office, 2000) 31 per cent of the population are construction workers, 20 per cent work in services and 11 per cent in the countryside outside the city. Another characteristic of the zone, is that it was chosen by the City Mayor’s office for the development of several infrastructure projects that will have an impact in the dynamics of the locality. We expected to make it possible for the community to engage actively in the planning and development of those projects.

Practices: what happened Between March 2000 and March 2001 we engaged in several activities that allowed the community to create several spaces of interaction that can lead to a learning community. We began by contacting key actors within the community. We began by civic leaders and social promoters. They are persons that seem to have an interest in the development of the sector. We also approached institutions which showed interest in the project, and could be future allies. Those were community schools, industry and commerce, construction sector institutions like shops and building developers (this was considered the predominant activity in the zone. Most people are construction workers). The call for participation made use of letters to school parents, and shopkeepers. There were also visits to households and local mass media like loudspeakers and radio. At the beginning we held a meeting at a high school. There were about 70 people present. They expected to get short term employment. We told them about the project, and proposed that they participate in it. Several persons walked out in disillusionment. Those who remained constituted the first nucleus of the learning community. The first encounters opened up the possibility to know each other, and to listen to the others realities, feelings and proposals. Encounters were evolving into dialogue, and into detecting the possibilities for constructing the learning community. Thematic debates made use of a sort of “rich pictures” (Checkland 1972; Freire, 1972). Around graphic representations they were diagnosing and designing scenarios of development. The first need to be detected by the actors themselves was one of being better qualified workers. From there evolved the curriculum designed to develop high quality enterprises in the construction business. There was a basic set of courses (human development, reading and writing, basic computing, administration, basic accounting, marketing), and an advanced and specialized set of courses (electricity, masonry, carpentry, metal works, building, plumbing). The second need detected by actors was to constitute a formal organization, with a legal basis, in order to have an associative way to deal with clients. This is the co-operative called “Constru-Tintal”. The diverse small enterprises, specialized in different aspects of the building business, associated around the co-operative. We made an alliance with the National Learning Service (SENA), a technical vocational school which covers all the country, for the specialized courses, and the basic courses were made by us. There were about 500 students in the different courses. However, only about 50 remained in the development of the enterprises. They also went to observe other experiments similar to this in the city of Medellin.

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In parallel to the development of this community of learning, some other groups of people began to conform their own organizations. Two of them asked to work directly with us. One, composed of youngsters, housewives, retired persons and other unemployed. The second, composed of teachers, students and parents from a school. These two groups contributed with other expectations and ideas about self-government and learning communities. The three communities began to compose the first scenarios of the community of learning: the enterprise as school, the school as a link, and the youngsters, older people, housewives, as groups for learning. Learning then had several aspects. To learn how to “make worlds” (enterprises, communities, alliances and the like), to learn basic skills, and to learn how to deal with everyday conflicts and “breaks”. (Lleras, 2001) In meetings between the enterprise members with professors, students, and parents belonging to the school, they defined a strategy for incorporating the school to the community. This strategy consists mainly in a space called community extension, which allows for direct contact between students, teachers, community leaders, etc. Students can have stages of work in enterprises, enterprises can get technical support from professors and appliances from the school. Groups of teachers and students also made enterprises within the school for promoting the interests of students and at the same time provide services for the community and earn some money. An example is an enterprise that designed and built a portable stage. With this, they present shows in different parts of the community of music, theater and the like, also made by students. They also plan to lease it for other types of uses. A last but very important aspect of the relationship with the school is the arena for political debate and community planning, as well as self-government proposals. This is the overarching scenario of the community of learning. The other group, housewives, youngsters, seniors, and others, made a group of 23 persons interested in a general services enterprise. They had training in basic computing, and the use of tools like Excel for accounting support for the other enterprises, as well as a messenger service, copy, fax and related aspects. Right now, they have five computers (donated by a government office) and are collaborating with other members of the community. They are also participating enthusiastically in the planning and self-government debates.

Tentative reflections The project is now about a year old, and we cannot make a clear analysis of what is going on. The notion of “community of learning” has been useful as a

guide of action and as a tool to understand the processes. We have experimented in the courses with the notion of practices as elements of the learning process, and with the notion of observation of relations in terms of the three aspects referred earlier, as well as with elements of self-government and self-management. There are some observable changes which are very significant in our eyes. The first and foremost is the development of a sense of confidence in the possibility for making world by themselves. We devised a tentative way of evaluating the results, by asking them to write letters to their friends about their experiences in the project. From those letters we can infer other aspects as the fact that they broke their isolation and made new friends, they began to explore the city out of their community, they gained more confidence in dealing with institutions and other external agents. A very palpable result is the existence of the co-operative, of the so called “units” (the enterprises), and the learning spaces they provide for making world, disclosing opportunities, and sell services. There are other spaces too, like those provided by the school and the self-government arenas. There are also lots of contradictions emerging from our own different histories, that is the case of power-over patterns of relation, individualism, intergenerational conflicts. But there are also “vicious” behaviours carried over from the past as are some “clientelistic” practices which were very helpful for the constitution of the co-operative ( Jime´nez, 2002). At this moment, we are entering a second stage of the project. We plan to work further in the evaluation of results, the consolidation of the spaces of practice opened, and the refinement of conversational possibilities, dialogue and abilities for observation and design.

References Bourdieu, P. (1977), Outline of a Theory of Practice, Cambridge University Press. Buber, M. (1965), The Knowledge of Man, Harper Torchbooks. DANE (Colombian Statistics Office) (2000), Reporte an˜o 2000, Imprenta Nacional. Echeverrı´a, R. (1992), Ontologı´a del Lenguaje, Dolmen Editores. Freire, P. (1970), Pedagogı´a del Oprimido, Siglo XXI Editores. Freire, P. (1972), Educacio´n Como Pra´ctica de la Libertad, Bogota´. Heidegger, M. (1951), Ser y Tiempo, Fondo de Cultura Econo´mica, Me´xico. Jime´nez, J. (2002), Elementos relevantes para la gestio´n del desarrollo local, Tesis de grado, CIDER, Universidad de Los Andes. Lleras, E. (1998a), “World construction as discovering language”, Proceedings of SCI’98 ISAS ’98, Orlando, USA, 12-16 July 1998. Lleras, E. (Ed.) (1998b), Memorias Taller de Participacio´n Ciudadana para la Construccio´n de Paı´s, Uniandes-CGR-RSC. Lleras, E. (2001a), “Observar relaciones”, TESOnotas, Universidad de Los Andes.

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Lleras, E. (2001b), “A social control proposal for system development at the general comptroller’s office of colombia”, Systems Practice, Vol. 14 No. 2. Lleras, E. and Arias, R. (2001), “Learning communities in local development”, Proceedings, OR43 Bath, UK. Pe´rez, I. (2000), Gerencvia de la MIPYME en Bogota´, EAN, Bogota´. Searle, J. (1969), Speech Acts, Cambridge University Press. Weiss, A. (1989), La tradicio´n empresarial colombiana, Editorial Universidad Nacional. Wittgenstein, L. (1972), Investigaciones filoso´ficas, Alianza Editorial.

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A biocultural model of aging

A biocultural model of aging

Mario E. Martinez Institute of Biocognitive Psychology, Nashville, TN, USA Keywords Cybernetics, Older people

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Abstract Addresses how the life sciences have concentrated on the pathology of aging while ignoring the biocultural aspects of health in the process of growing older. Argues that growing older is a dynamic cognitive, biological and cultural coauthoring of health rather than a hopeless unfolding of progressive pathology. Proposes that this fragmented concept of aging precludes operationalizing and understanding the cultural markers that affect longevity. These cultural milestones, or biocultural portals include middle age markers, retirement markers, perceived wisdom, sexuality, status in the community, transcendental beliefs, sense of empowerment vs helplessness and any other biocultural phase in human development. Suggests that the biocultural portals define and trigger the phase transitions of life as well as influence how they are accommodated. For example, the markers for middle age established by a culture, strongly influence the cognitive and biological expectations for the second half of life.

Biocognitive theory Research in psychoneuroimmunology (PNI) has demonstrated how the immune, endocrine and nervous pathways maintain a constant and bidirectional communication that interacts with cognition to affect health, illness and aging (Ader, 2000; Solomon, 2000). Although, we can strongly suggest from the research that thoughts affect biology and biology affects thought, PNI has failed to incorporate the influence that culture has on the mind-body communication. The evidence for the cultural components that interact with health, healing and aging remains isolated in the field of medical anthropology (Romanucci-Ross et al., 1997; Sargent and Johnson, 1996). In our theory of biocognition we outline a cognitive, biological and cultural model to suggest how aging is influenced by the established medical, ethical and transcendental beliefs that are assimilated from the cultural history. While science identifies disease and pathological aging, culture defines illness and influences the process of how we grow older. In other words, disease is the physical evidence of pathology identified by the life sciences of the culture, and illness is the anthropological interpretations the culture makes of the pathology. We propose that cognition, biology and historical culture simultaneously coauthor a bioinformational field that modulates health, illness and aging. Biocognitive theory integrates the research in PNI and medical anthropology within a model of contextual coemergence to provide an alternative to the upward and downward causalities of the life sciences. Bioinformation is The 12th International World Organization of Systems and Cybernetics Congress. March 24-26, 2002, Pittsburgh, Pennsylvania.

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defined as the cognitive, biological and cultural history that communicators contextually share in their communication. In other words, bioinformation is exchanged history between communicators in a coemerging field that seeks contextual relevance (Martinez, 1999). The contributions of historical culture and its meaning in bioinformational theory are differentiated from the concept of society. Cognition and biology are inseparable and they coemerge within a cultural history. Culture is defined as the internalized ethical, scientific and transcendental beliefs that a group shares, while society is the external rules of behavior that control a group. Hahn and Kleiman (1983) argue that expectations about the prognosis of an illness are not merely propositions about outcome; they are cognitions reflected in the biology of those who assert them and are thus associated with neurotransmitters and hormones that affect physiological functioning.

Biocultural context Langer (1989) investigated the effects of contextual change on aging. She took a group of male subjects aged 75-80 to a retreat and divided them into an experimental group that was to behave and speak as if they were living 30 years earlier and a control group that was instructed to only reminisce about 30 years earlier while maintaining their context in the present. In the area where the experimental group was housed; all the music, news, dress, speech and surroundings reflected the era they were instructed to recreate, whereas the control group lived in surroundings reflecting the present. Pre-post measures were taken of strength of handgrip, bideltoid breadth, triceps skinfold, vision with and without glasses, visual memory and other physical and cognitive markers of “aging”. Several measures were repeated throughout the stay and the experiment was concluded after 5 days. The pre-post measures showed improvement in all areas for the experimental group with no change in the control group. Remarkably, independent raters reported that subjects in the experimental group looked an average of 3 years younger from pre-post photographs after only 5 days of re-enactment, whereas no differences were noted for the control group. Payer (1996) illustrates in her comparative review of medical practice in the United States and Western European countries how the etiology of a migraine is vascular in the United States, hepatic in France and gastrointestinal in Britain. Additionally, while hypotension is a predictor of longevity in the United States, in Germany, hypotension is diagnosed as a pathological condition called Herzinsuffizienz (cardiac insufficiency). Payer also reports a study conducted with a normal population in Hamburg that evaluated cardiac functioning in which 40 per cent of the subjects were diagnosed with an abnormal ECG when German rules of diagnostics were applied, whereas only 5 per cent of the ECG’s were found abnormal using American criteria.

We argue that growing older is the cognitive and biological accumulation of time, whereas aging is the consequences of our behavior contextualized within a cultural history. In other words, the passing of time is necessary but not sufficient to account for the cognitive and biological changes that transpire in the aging process. A culture defines the biocultural portals as well as interprets the health and the quality of aging. The biocultural portals are defined by the scientific, aesthetic and transcendental beliefs that are assimilated by the culture. For example, while a 62 year old from an industrialized culture is engaged in behaviors conducive to achieving retirement, a Tarahumara Indian counterpart of the Chihuahua region of Mexico may be running up to 200 miles in a competitive racing sport called “kick ball” that can last several days (Pelletier, 1981). The Tarahumaras, known for their longevity, believe that growing older makes them stronger and consequently better runners. Retirement is not one of their biocultural portals. Interestingly, since the Tarahumaras look forward to their expected physical gains from growing older, “middle age crisis” is unknown and the usual degenerative pathology associated with aging is rare in their culture.

Biocultural portals and their attributions Biocultural attributions originate from assimilated cultural beliefs and personal history. At an operational level it is not difficult to see that the interpretations of daily events based on how one should behave according to one’s age can have considerable differential effects across time. For example, if a 22 year old feels a muscle spasm coming out of a small sports car, the biocultural attribution of the spasm may lead to consider doing stretching exercises in the mornings. A 65 year old in the same situation however, may decide that it is time to trade the sports car for a larger car ignoring the stretching exercises that could correct the problem. Once a biocultural portal is triggered, the expectations that define the corresponding developmental phase descend on the individual to promote the behaviors reflective of that phase. The “endorsements” of a biocultural phase have cognitive and biological consequences on health and the aging process. Statements such as “you’re too old for that” or “your medical condition is age-related” are mostly based on biocultural convention rather than hard science. Yet, the biocultural collusions that support these aging admonitions become self-fulfilling prophecies and consequently physical reality. For example, the effects of placebos and nocebos are well documented in the literature as examples of how cognition can affect biology positively or negatively, respectively, based on expectations (Brody, 2000; Hahn, 1995). The number four is associated with bad omens in China and Japan because the word for that number sounds like the word for death in the Mandarin, Cantonese and Japanese languages. Phillips and his colleagues (2001) compared death certificates from 1973 to 1998 of Chinese, Japanese

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and white Americans and found a statistical significance for higher cardiac mortality on the fourth day of every month in Oriental Americans. The study also tested the effects of the number 13 (unlucky number in white American culture) and found no lethality associated with that number. The researchers hypothesized that although the number 13 is considered “unlucky” by whites, the word for the number 13 lacks the linguistic association with death that the number four has in the Oriental languages cited. Since the life sciences identify pathology with a diagnostic model of upward causality, the biocultural variables that gradually contribute to the pathology are not considered in the etiology. In the life sciences, an operational assumption is made that the individual interacts with an environment void of cultural history. This mechanistic assumption views aging as a functional dance between genetics, behavior and physical environments across time. While contemporary medicine acknowledges that aversive interpretations of events trigger stress responses that can affect health, the consequent damage is relegated to a psychosomatic nosology that defines, which pathologies can be considered stress-related. Such selective diagnostic procedures perpetuate the Cartesian mind-body split that assumes disease can be divided between medical and psychological where only some diseases can be affected by stress and none are affected by cultural history. Conclusions Considering that the healers of a culture are not immune to cultural postulates, the life sciences share an epistemology assimilated from a cultural history that influences the concepts of aging as well as the diagnosis and prognosis of disease. If the assimilated cultural beliefs define aging as an inevitable deterioration of health, then the gerontology of that culture will study and treat the pathology of aging rather than the dynamics of health in the process of growing older. Cognition, biology and historical culture coemerge in a bioinformational field that constantly seeks contextual relevance. Cognition and biology occur simultaneously as a biocognition within a context of cultural history that can only be separated artificially and the separation can only yield heuristic data about the total experience. Rather than cognitive epiphenomena of biology, cultural beliefs are biocognitions that influence the health and aging process of the believer. Beliefs are assimilated from the cultural and personal history of the believer. The assimilated beliefs determine when the individual enters the biocultural portals and how the admonitions of these developmental portals affect health and the aging process. We argue that aging is the cognitive and biological effects of biocultural influences, whereas growing older is the cognitive and biological accumulation of time. The life sciences in general and gerontology in particular, must shift from focusing exclusively on the pathology of aging to studying the cultural influences that promote growing older in good health.

References Ader, R., Felten, D.L. and Cohen, N.(Eds) (1999), Psychoneuroimmunology, 2nd ed., Academy Press, New York. Brody, H. (2000), The Placebo Response: How You Can Release the Body’s Inner Pharmacy for Better Health, Cliff Street Books, New York. Hahn, R.A. (1995), Sickness and Health: An Anthropological Perspective, Yale University Press, New Haven. Langer, E.J. (1989), Mindfulness, Perseus Books, Reading, Massachusetts. Martinez, M.E. (1999), Belief Systems and Health: A Biocognitive Model, Lecture presented at the World Congress of the World Federation for Mental Health, Santiago, Chile, September, 1999. Payer, L. (1996), Medicine and Culture, H. Holt and Co., New York. Pelletier, K.R. (1981), Longevity: Fulfilling our Biological Potential, Dell Publishing Co., New York. Phillips, D.P. et al. (2001), “The Hounds of the Baskervilles effect: natural experiment on the influence of psychological stress on the timing of death”, British Journal of Medicine, Vol. 323, pp. 1443-6. Romanucci-Ross, L., Moerman, D. and Tancredi, L. (Eds) (1997), The Anthropology of Medicine: From Culture to Method, Bergin and Garvey, London. Sargent, C.F. and Johnson, T.M. (Eds) (1996), Handbook of Medical Anthropology Contemporary Theory and Method, Rev. ed., Greenwood Press, London. Solomon, G.F. (2000), From Psyche to Soma and Back: Tales of Biopsychosocial Medicine, Xlibris Corp.

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Adaptive dual control in one biomedical problem Konstantin N. Nechval, Nicholas A. Nechval and Edgars K. Vasermanis Applied Mathematics Department, University of Latvia, Riga, Latvia Keywords Cybernetics, Pharmaceuticals Abstract In this paper, the following biomedical problem is considered. People are subjected to a certain chemotherapeutic treatment. The optimal dosage is the maximal dose for which an individual patient will have toxicity level that does not cross the allowable limit. We discuss sequential procedures for searching the optimal dosage, which are based on the concept of dual control and the principle of optimality. According to the dual control theory, the control has two purposes that might be conflicting: one is to help learning about unknown parameters and/or the state of the system (estimation); the other is to achieve the control objective. Thus the resulting control sequence exhibits the closed-loop property, i.e. it anticipates how future learning will be accomplished and how it can be fully utilized. Thus, in addition to being adaptive, this control also plans its future learning according to the control objective. Results are obtained for a priori uniform distribution of the unknown dosage. Because answers can be obtained analytically without approximation, the optimum policy can be compared with the non-optimum policy of optimizing stage by stage. An illustrative example is given.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 658-665 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443752

1. Introduction The present study is concerned with the problem of finding an optimal dosage of certain drugs, which in addition to their therapeutic effects have secondary harmful effects. The effect on which we concentrate here is the toxicity of the drug, which can be measured on a continuous scale by blood tests. Physicians specify a threshold toxicity level. The objective is to determine the largest dosage for which a patient will have a toxicity level that does not exceed the specified threshold. Such a dosage is called the optimal dosage. The problem is to find this optimal dosage. The procedures of dual (and non-dual) control which are developed in the present paper are designed to prescribe dosages for individual patients in a sequential manner so that a specified risk function will be minimized. Here we consider an application of control theory to the above problem. One of the most important features of control theory is its great generality, enabling one to analyze diverse systems within one unified framework. A key idea which has emerged from this study is the necessity of viewing the process of finding an optimal dosage of certain drugs as, using the terminology of This work was supported in part by Grant No.02.0918 and Grant No.01.0031 from the Latvian Council of Sciences and the National Institute of Mathematics and Informatics of Latvia.

Feldbaum, (1965), Nechval (1982), (1984), (1988) and Nechval et al., (1998), a “dual control” process, the concept of actively acquiring information via the decisions made. Varying amounts of information are acquired depending upon the particular decision sequence chosen. That is, one must balance or trade off degradation in present performance of the search process for the gain in information about unknown parameters, in order that better decisions can be made in the future. In other words, the dual control has two purposes, which might be in conflict with each other. One is to help learn about any unknown parameters and/or state of the system (estimation) and the other is to control. In view of this, one can see that the open-loop feedback control is, from the estimation point of view, passive, since it does not take into account that learning is possible in the future. In contrast to this, the dual control is active, not only for the control purpose but also for the estimation purpose because the performance depends also on the “quality” of the estimates. Therefore, the dual control can be called actively adaptive since it regulates its adaptation (learning) in an optimal manner. To make the above introduction more precise, consider a risk function (performance criterion) ( ) N X RðU 0 Þ ¼ E rs ðus ; xs Þ ; ð1Þ s¼0

where U 0 ¼ {U 0 ¼ u0 ; . . .; uN } is a control sequence, E{.} denotes the expectation, rs(us, xs) is a loss function, xs might be the state of the system or the parameter. Further introduce: ( ) N X * ð2Þ RðU ; Pt Þ ¼ min E r s ðus ; xs Þ; Pt : t

ut ;...;uN

s¼t

This function can be interpreted as the optimal cost-to-go (N þ 1  t steps) given the information state Pt at time t. The information state can either be a vector containing all inputs and outputs respectively that are available at time t or more usually the conditional distribution of the state and the parameters. In the first case, the information state is growing with time while the dimension is fixed in the second case. The minimum of R(U0) with respect to u0,. . . uN is given through: min RðU 0 Þ ¼ RðU 0* ;P0 Þ

u0 ;...;uN

E ¼ min u 0

8 < r0 ðu0 ;x0 Þ  E : þmin u1

9 = E{r N ðuN ;xN Þ;PN };PN 21 ... r 1 ðu1 ;x1 Þ þ ··· þ min uN ;P0 : ; 

ð3Þ

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It is in essence these nested expectations and minimizations that create the large difficulties in the determination of the control sequence, u0 ;...;uN : Using the principle of optimality and dynamic programming it is possible to show that the optimal cost-to-go satisfies the functional equation: RðU t* ; Pt Þ ¼ min E{rt ðut ; xt Þ þ RðU *tþ1 ; Ptþ1 ðPt ; ut ÞÞ; Pt }: u

ð4Þ

t

In principle the optimal control problem now is solved, but the practical problems how to solve the functional equation are large. There are very few cases where it is possible to solve the functional equation (4). This is due to the fact that the conditional distribution of the estimated state and the estimated parameters is infinitely dimensional. Further, the control law generally is non-linear in the information state, which makes it necessary to determine the control signal from a control table. The number of variables in the control table increases with the square of the number of unknown variables (states and parameters). This will soon make the problem unsolvable even on large computers. Numerical solutions of the functional equation have, however, been made for some simple examples. These solutions have given valuable insight into the properties of the optimal solution even if it is not a method that can be used for any practical problems. There are many ways to approximate the functional equation (4). The approximations must, however, be done with some care in order to preserve the dual property of the optimal solution. In order to illustrate the idea of dual control, a simple example relevant to process of finding an optimal dosage is given below. The example has two outstanding virtues: the performance index is not the usual quadratic one, and analytic solutions without approximations are possible, thus affording the opportunity of comparison with reasonable but not optimum policies.

2. Problem statement Let m designate an optimal dosage for an individual patient. It is appropriate to measure the loss incurred by using an estimator u to estimate m by a piecewise loss function of the form 8
control theory, the control variable is u and the risk associated with u is the expected value of the loss function (5), i.e.

Adaptive dual control

Rðu; a; bÞ ¼ E{rðu; mÞ; a; b} Z b Z u ðm 2 uÞfðm; a; bÞ dm: ¼ q ðu 2 mÞfðm; a; bÞ dm þ

ð6Þ

u

a

The measurement of error in estimation by absolute error, ju 2 mj; rather than squared error, ðu 2 mÞ2 ; was selected since the risk associated with squared error often becomes disproportionate when large errors are likely. The corresponding root-mean-square can then be more difficult to interpret than the risk associated with absolute error. Absolute error is generally thought to be the “natural” way to measure error, but its use often leads to intractable mathematical expressions. Fortunately, such is not the case for the estimators of m which will be compared in this paper under the loss function (5). Let us assume that the state equation of a plant (i.e. the dosage search process to be controlled) is described by rðu0 ; . . .; unþ1 ; mÞ ¼ rðu0 ; . . .; un ; mÞ þ rðunþ1 ; mÞ; ð7Þ n ¼ 0; 1; 2; . . .; N 2 1; where rðu0 ; . . .; un ; mÞ ¼

n X

rðui ; mÞ

ð8Þ

i¼0

is the cumulative loss function at the nth stage of finding an optimal dosage m, un is the estimator of m (control) at the nth stage. Given the a priori probability density function for m, fðm; a; bÞ; the control law U 0 ¼ ðu0 ; . . .; uN Þ must be chosen based on all data which will be observed. ui $ m ! ðaiþ1 ¼ ai ;

biþ1 ¼ ui Þ;

ui , m ! ðaiþ1 ¼ ui ;

biþ1 ¼ bi Þ;

ð9Þ i ¼ 0; 1; . . .; N;

where a0 ¼ a and b0 ¼ b; such that the cumulative risk ( ) N X RðU 0 ; a; bÞ ¼ E{rðu0 ; . . .; uN ; mÞ; a; b} ¼ E rðui ; mÞ; a; b i¼0

is minimized. Thus, the problem is to find

ð10Þ

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U *0 ¼ ðu*0 ; . . .; u*N Þ ¼ arg min RðU 0 ; a; bÞ:

ð11Þ

U0

3. Dual control law In order to find the dual control law (11), we apply Bellman’s dynamic programming principle (Bellman and Kalaba, 1964) to obtain: for N ¼ 0; RðU *0 ; a; bÞ

Z ¼ min q u 0

u0

ðu0 2 mÞfðm; a; bÞ dm þ

Z

b

 ðm 2 u0 Þfðm; a; bÞ dm ;

u0

a

ð12Þ for N $ 1; RðU *0 ; a; bÞ ¼ min RðU 0 ; a; bÞ U0

Z ¼ min u 0

þ

u0

a

Z

½qðu0 2 mÞ þ RðU *1 ; a; u0 Þfðm; a; bÞ dm

b

½ðm 2 u0 Þ þ

u0

RðU *1 ; u0 ; bÞfðm; a; bÞ dm

 ;

ð13Þ

where U *1 ¼ ðu*1 ; . . .; u*N Þ: 4. Non-dual control law In this case, we deal with repeated application of the single-stage policy. Thus, for N $ 0; Z u^ †0 † † ^ RðU0 ; a; bÞ ¼ ½qðu^ †0 2 mÞ þ RðU^ 1 ; a; u^ †0 Þfðm; a; bÞ dm a

þ

Z

ð14Þ b u^ †0

½ðm 2 u^ †0 Þ þ

† RðU^ 1 ; u^ †0 ; bÞfðm; a; bÞ dm;

† where U^ 0 ¼ ðu^ †0 ; . . .; u^ †N Þ is the non-dual control law,

Z ^u†0 ¼ arg min q u 0

a

u0

ðu0 2 mÞfðm; a; bÞ dm þ

Z

b

 ðm 2 u0 Þfðm; a; bÞ dm :

u0

ð15Þ

5. Comparison of control laws In order to judge which control law might be preferred for a given situation, a comparison based on some criteria should be made. The following approach is commonly used. Consider two control laws, say, U †0 and U 80 having risk function RðU †0 ; uÞ and RðU 80 ; uÞ; respectively, where u is a parameter (in general, vector). Then the relative efficiency of U †0 relative to U 80 is given by: rel:eff:R {U †0 ; U 80 ; u} ¼ RðU 80 ; uÞ=RðU †0 ; uÞ:

ð16Þ

When rel:eff:R {U †0 ; U 80 ; uþ } , 1 for some u+, we say that U 80 is more efficient than U †0 at u+. If rel:eff:R {U †0 ; U 80 ; u} # 1 for all u with a strict inequality for some u+, then U †0 is inadmissible relative to U 80 :

6. Illustrative example The case is considered when the decision maker’s a priori knowledge about m is expressed by means of a probability density function fðm; a; bÞ ¼ 1=ðb 2 aÞ;

m [ ða; bÞ;

ð17Þ

i.e. a priori distribution for m is uniform. In this case we have the following. Dual Control Law: The cumulative risk is given by aN bN b 2 a ; aN þ bN 2

ð18Þ

aN ¼ a0 þ

aN 21 bN 21 ; aN 21 þ bN 21

ð19Þ

bN ¼ b0 þ

aN 21 bN 21 ; aN 21 þ bN 21

ð20Þ

RðU *0 ; a; bÞ ¼ where

a0 ¼ q; with

b0 ¼ 1;

ð21Þ

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u*0 ¼

aN a þ bN b : aN þ bN

ð22Þ

Non-Dual Control Law: The cumulative risk is given by 0 " #j 1 N 2 2 X † a0 þ b0 A b 2 a a0 b0 @ RðU^ 0 ; a; bÞ ¼ 1þ ; 2 a0 þ b0 2 j¼1 ða0 þ b0 Þ

ð23Þ

with u^ †0 ¼

a0 a þ b0 b : a0 þ b0

ð24Þ

† The relative efficiency of U^ 0 relative to U *0 is given by † † rel:eff:R {U^ 0 ; U *0 ; u} ¼ RðU *0 ; uÞ=RðU^ 0 ; uÞ

0

¼

aN bN a0 þ b0 @ 1þ a0 b0 aN þ bN

N X j¼1

"

a20

b20

þ ða0 þ b0 Þ2

#j 121 A ;

ð25Þ

where u ¼ ða; bÞ: If, say, q ¼ 10; N ¼ 5; then we have that † † rel:eff:R {U^ 0 ; U *0 ; a; b} ¼ RðU *0 ; a; bÞ=RðU^ 0 ; a; bÞ ¼ 0:52:

ð26Þ

7. Conclusions This paper describes an approach for obtaining a control algorithm that exhibits the dual characteristic of appropriately distributing the control energy for learning and control purposes. The main feature of this algorithm is the fact that it is actively adaptive, i.e. the control plans the future learning of the system parameters as required by the control objective. The adaptive control is obtained by using the stochastic dynamic programming equation in which the dual effect appears explicitly. The algorithm yields a closed-loop control that takes into account not only the past observations but also the future observation program and the associated statistics. A simple example is used to demonstrate the computational feasibility of the algorithm and its performance level when applied to a specific problem of optimization of dosage of certain drugs, and to provide some insight into the dual control theory.

References Bellman, R. and Kalaba, R. (1964), Dynamic Programming and Modern Control Theory, Academic Press, New York. Feldbaum, A.A. (1965), Optimal Control Systems, Academic Press, New York. Nechval, N.A. (1982), Modern Statistical Methods of Operations Research, RCAEI, Riga. Nechval, N.A. (1984), Theory and Methods of Adaptive Control of Stochastic Processes, RCAEI, Riga. Nechval, N.A. (1988), “A new efficient approach to constructing the minimum risk estimators of state of stochastic systems from the statistical data of small samples”, Preprint of the 8th IFAC Symposium on Identification and System Parameter Estimation, IFAC, Beijing, P.R. China, pp. 71-6. Nechval, N.A., Nechval, K.N. and Heimanis, B.M. (1998), “Variational approach to adaptive optimization of stochastic systems”, in Trappl, R. (Ed.), Cybernetics and Systems’98, Austrian Society for Cybernetic Studies, Vienna, Austria, Vol. 1, pp. 44-9.

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Effective state estimation of stochastic systems Nicholas A. Nechval, Konstantin N. Nechval and Edgars K. Vasermanis Applied Mathematics Department, University of Latvia, Riga, Latvia Keywords Cybernetics, Stochastic modelling Abstract In the present paper, for constructing the minimum risk estimators of state of stochastic systems, a new technique of invariant embedding of sample statistics in a loss function is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant estimator, which has smaller risk than any of the well-known estimators. There exists a class of control systems where observations are not available at every time due to either physical impossibility and/or the costs involved in taking a measurement. In this paper, the problem of how to select the total number of the observations optimally when a constant cost is incurred for each observation taken is discussed. To illustrate the proposed technique, an example is given and comparison between the maximum likelihood estimator (MLE), minimum variance unbiased estimator (MVUE), minimum mean square error estimator (MMSEE), median unbiased estimator (MUE), and the best invariant estimator (BIE) is discussed.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 666-678 q MCB UP Limited 0368-492X 10.1108/03684920210443761

1. Introduction The state estimation of discrete-time systems in the presence of random disturbances and measurement noise is an important field in modern control theory (Aoki, 1967; Bertsekas, 1976; Nechval, 1984; Sage and White, 1977). The problem of determining an optimal estimator of the state of stochastic system in the absence of complete information about the distributions of random disturbances and measurement noise is seen to be a standard problem of statistical estimation. Unfortunately, the classical theory of statistical estimation has little to offer in general type of situation of loss function. The bulk of the classical theory has been developed about the assumption of a quadratic, or at least symmetric and analytically simple loss structure. In some cases this assumption is made explicit, although in most it is implicit in the search for estimating procedures that have the “nice” statistical properties of unbiasedness and minimum variance. Such procedures are usually satisfactory if the estimators so generated are to be used solely for the purpose of reporting This work was supported in part by Grant No. 02.0918 and Grant No. 01.0031 from the Latvian Council of Sciences and the National Institute of Mathematics and Informatics of Latvia.

information to another party for an unknown purpose, when the loss structure Estimation state is not easily discernible, or when the number of observations is large enough to of stochastic support Normal approximations and asymptotic results. Unfortunately, we systems seldom are fortunate enough to be in asymptotic situations. Small sample sizes are generally the rule when estimation of system states and the small sample properties of estimators do not appear to have been thoroughly investigated. 667 Therefore, the earlier procedures of the state estimation have long been recognized as deficient, however, when the purpose of estimation is the making of a specific decision (or sequence of decisions) on the basis of a limited amount of information in a situation where the losses are clearly asymmetric – as they are here. There exists a class of control systems where observations are not available at every time due to either physical impossibility and/or the costs involved in taking a measurement. For such systems it is realistic to derive the optimal policy of state estimation with some constraints imposed on the observation scheme. It is assumed in this paper that there is a constant cost associated with each observation taken. The optimal estimation policy is obtained for a discrete-time deterministic plant observed through noise. It is shown that there is an optimal number of observations to be taken. The outline of the paper is as follows. A formulation of the problem is given in Section 2. Section 3 is devoted to characterization of estimators. A comparison of estimators is discussed in Section 4. A general analysis is presented in Section 5. An example is given in Section 6.

2. Problem statement To make the earlier introduction more precise, consider the discrete-time system which, in particular, is described by vector difference equations of the following form: xðk þ 1Þ ¼ Aðk þ 1; kÞxðkÞ þ BðkÞuðkÞ;

zðkÞ ¼ H ðkÞxðkÞ þ wðkÞ;

k ¼ 1; 2; 3; . . .;

ð1Þ

ð2Þ

where xðk þ 1Þ is an n vector representing the state of the system at the ðk þ 1Þth time instant with initial condition x(1); z(k ) is an m vector (the observed signal) which can be termed a measurement of the system at the kth instant; H(k ) is an m £ n matrix; Aðk þ 1; kÞ is a transition matrix of dimension n £ n; and B(k ) is an n £ p matrix, u(k ) is a p vector, the control vector of the system; w(k ) is a random vector of dimension m (the measurement noise). By repeated use of (1) we find

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k21 X

Aðk; i þ 1ÞBðiÞuðiÞ;

j # k;

ð3Þ

i¼j

where the discrete-time system transition matrix satisfies the matrix difference equation,

668

Aðk þ 1; jÞ ¼ Aðk þ 1; kÞAðk; jÞ; Aðk; kÞ ¼ I ; Aðk; jÞ ¼

k21 Y

;k; j;

Aði þ 1; iÞ:

ð4Þ

i¼j

From these properties, it immediately follows that A 21 ðk; jÞ ¼ Að j; kÞ; Aða; bÞAðb; gÞ ¼ Aða; gÞ;

;k; j; ;a; b; g:

ð5Þ

Thus, for j # k; xð jÞ ¼ Að j; kÞxðkÞ 2

k21 X

Að j; i þ 1ÞBðiÞuðiÞ:

ð6Þ

i¼j

The problem to be considered is the estimation of the state of the earlier discrete-time system. This problem may be stated as follows. Given the observed sequence, zð1Þ; . . . ; zðkÞ; it is required to obtain an estimator d of x(k1) based on all available observed data z k ¼ { zð1Þ; . . . ; zðkÞ} such that the expected losses (risk function) Rðu; dÞ ¼ E u {rðu; dÞ}

ð7Þ

is minimized, where rðu; dÞ is a specified loss function at decision point d ; dðz k Þ; u ¼ ðxðk1 Þ; vÞ; v is an unknown parametric vector of the probability distribution of w(k ), k # k1 : It is assumed that a constant cost c . 0 is associated with each observation taken. The criterion function for the case of k observations is taken to be rk ðu; dÞ ¼ rðu; dÞ þ ck:

ð8Þ

The optimization problem can be stated as min min Eu {r k ðu; dÞ} k

d

ð9Þ

where the inner minimization operation is with respect to d ; dðz k Þ; when the k observations have been taken, and where the outer minimization operation is with respect to k.

3. Characterization of estimators Estimation state For any statistical decision problem, an estimator (a decision rule) d1 is said to of stochastic be equivalent an estimator (a decision rule) d2 if Rðu; d1 Þ ¼ Rðu; d2 Þ for all systems u [ Q; where R(†) is a risk function and Q is a parameter space. An estimator d1 is said to be uniformly better than an estimator d2 if Rðu; d 1 Þ , Rðu; d2 Þ for all u [ Q: An estimator d1 is said to be as good as an estimator d2 if Rðu; d 1 Þ # 669 Rðu; d 2 Þ for all u [ Q: However, it is also possible that we may have “d1 and d2 are incomparable”, that is, Rðu; d 1 Þ , Rðu; d 2 Þ for at least one u [ Q; and Rðu; d 1 Þ . Rðu; d 2 Þ for at least one u [ Q: Therefore, this ordering gives a partial ordering of the set of estimators. An estimator d is said to be uniformly non-dominated if there is no estimator uniformly better than d. The conditions that an estimator must satisfy in order that it might be uniformly non-dominated are given by the following theorem. Theorem 1. (uniformly non-dominated estimator). Let ðjt ; t ¼ 1; 2; . . .Þ be a sequence of the prior distributions on the parameter space Q. Suppose that ðd t ; t ¼ 1; 2; . . .Þ and ðQðjt ; d t Þ; t ¼ 1; 2; . . .Þ are the sequences of Bayes estimators and prior risks, respectively. If there exists an estimator d* such that its risk function Rðu; d* Þ; u [ Q; satisfies the relationship lim ½Qðjt ; d* Þ 2 Qðjt ; d t Þ ¼ 0;

t !1

ð10Þ

where Qðjt ; dÞ ¼

Z

Rðu; dÞjt ðduÞ;

ð11Þ

Q

then d* is an uniformly non-dominated estimator. Proof. Suppose d* is uniformly dominated. Then there exists an estimator d ** such that Rðu; d * * Þ , Rðu; d* Þ for all u [ Q: Let A 1 ¼ inf ½Rðu; d* Þ 2 Rðu; d* * Þ . 0:

ð12Þ

Qðjt ; d* Þ 2 Qðjt ; d* * Þ $ 1:

ð13Þ

Qðjt ; d* * Þ 2 Qðjt ; dt Þ $ 0;

ð14Þ

lim ½Qðjt ; d* * Þ 2 Qðjt ; d t Þ $ 0:

ð15Þ

u2Q

Then

Simultaneously,

t ¼ 1; 2; . . .; and t !1

On the other hand,

K 32,5/6

Qðjt ; d* * Þ 2 Qðjt ; d t Þ ¼ ½Qðjt ; d* Þ 2 Qðjt ; d t Þ 2 ½Qðjt ; d* Þ 2 Qðjt ; d* * Þ

ð16Þ

# ½Qðjt ; d* Þ 2 Qðjt ; dt Þ 2 1

670

and lim ½Qðjt ; d* * Þ 2 Qðjt ; d t Þ , 0:

t !1

ð17Þ

This contradiction proves that d* is an uniformly non-dominated estimator.A 4. Comparison of estimators In order to judge which estimator might be preferred for a given situation, a comparison based on some “closeness to the true value” criteria should be made. The following approach is commonly used ( Nechval, 1982). Consider two estimators, say, d1 and d2 having risk function Rðu; d1 Þ and Rðu; d2 Þ; respectively. Then the relative efficiency of d1 relative to d2 is given by rel:eff:R {d1 ; d2 ; u} ¼ Rðu; d2 Þ=Rðu; d 1 Þ:

ð18Þ

When rel:eff:R {d1 ; d2 ; u0 } , 1 for some u0, we say that d2 is more efficient than d1 at u0. If rel:eff:R {d1 ; d 2 ; u} # 1 for all u with a strict inequality for some u0, then d1 is inadmissible relative to d2. 5. General analysis 5.1 Inner minimization First consider the inner minimization, i.e. k is held fixed for the time being. Then the term, ck, does not affect the result of this minimization. Consider a situation of state estimation described by one of a family of density functions, indexed by the vector parameter u ¼ ðm; sÞ; where m ; xðkÞ and s ; vð. 0Þ are respectively parameters of location and scale. For this family, invariant under the group of positive linear transformations: z ! az þ b with a . 0; we shall assume that there is obtainable from some informative experiment (a random sample of observations z k ¼ {zð0Þ; . . .; zðkÞ}Þ a sufficient statistic ðmk ; sk Þ for ðm; sÞ with density function pðmk ; sk ; m; sÞ of the form pðmk ; sk ; m; sÞ ¼ s 22 f k ½ðmk 2 mÞ=s; sk =s:

ð19Þ

We are thus assuming that for the family of density functions an induced invariance holds under the group G of transformations: mk ! amk þ b; sk ! ask ða . 0Þ: The family of density functions satisfying the earlier

conditions is, of course, the limited one of normal, negative exponential, Estimation state Weibull and gamma (with known index) density functions. of stochastic The loss incurred by making decision d when m ; xðk1 Þ is the true systems parameter is given by the piecewise-linear loss function 8 c ðd 2 mÞ > ðm # dÞ; < 1 s 671 rðu; dÞ ¼ ð20Þ > : c2 ðms2 dÞ ðm . dÞ: The decision problem specified by the informative experiment density function (equation 19) and the loss function (equation 20) is invariant under the group G of transformations. Thus, the problem is to find the best invariant estimator of m, d * ¼ arg min Rðu; dÞ; d2D

ð21Þ

where D is a set of invariant estimators of m, Rðu; dÞ ¼ E u {rðu; dÞ} is a risk function. 5.2 Best invariant estimator It can be shown by using the invariant embedding technique (Nechval, 1982, 1984) that an invariant loss function, rðu; d Þ; can be transformed as follows: rðu; dÞ ¼ r€ðv; hÞ;

ð22Þ

where ( r€ðv; hÞ ¼

c1 ðv1 þ hv2 Þ

ðv1 $ 2hv2 Þ;

2c2 ðv1 þ hv2 Þ

ðv1 , 2hv2 Þ;

ð23Þ

v ¼ ðv1 ; v2 Þ, v1 ¼ ðmk 2 mÞ=s, v2 ¼ sk =s, h ¼ ðd 2 mk Þ=sk : It follows from (equation 22) that the risk associated with d and u can be expressed as Rðu; dÞ ¼ E u {rðu; dÞ} ¼ E k {€rðv; hÞ} ¼ c1

Z

1

dv2

Z

0

2 c2

1

ðv1 þ hv2 Þf k ðv1 ; v2 Þdv1

2hv2

Z 0

1

dv2

Z

2hv2

21

ðv1 þ hv2 Þf k ðv1 ; v2 Þdv1

ð24Þ

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672

which is constant on orbits when an invariant estimator (decision rule) d is used, where f k ðv1 ; v2 Þ is defined by (equation 19). The fact that the risk (equation 24) is independent of u means that a decision rule d, which minimizes (equation 24), is uniformly best invariant. The following theorem gives the central result in this section. Theorem 2. (best invariant estimator of m ). Suppose that ðv1 ; v2 Þ is a random vector having density function Z 1

21 Z 1 v2 f k ðv1 ; v2 Þ v2 dv2 f k ðv1 ; v2 Þdv1 0

21

ðv1 real; v2 . 0Þ;

ð25Þ

where fk is defined by (equation 19), and let Gk be the distribution function of v1/v2. Then the uniformly best invariant linear-loss estimator of m is given by d* ¼ mk þ h* sk ;

ð26Þ

Gk ð2h* Þ ¼ c1 =ðc1 þ c2 Þ:

ð27Þ

where

Proof.

From (equation 24) Z 1 Z 1 ›E k {€rðv; hÞ} ¼ c1 v2 dv2 f k ðv1 ; v2 Þdv1 ›h 0 2hv2 Z 1 Z 2hv2 2 c2 v2 dv2 f k ðv1 ; v2 Þdv1 ¼

0

Z

1

Z

21 1

f k ðv1 ;v2 Þ dv1 ½c1 P k

v2 dv2 0

21

{ðv1 ; v2 Þ : v1 þ hv2 . 0} 2 c2 P k {ðv1 ; v2 Þ : v1 þ hv2 , 0} Z 1 1 v2 dv2 f k ðv1 ;v2 Þ dv1 ½c1 ð1 2 Gk ð2hÞÞ 2 c2 Gk ð2hÞ: ð28Þ ¼ Z

0

21

Then the minimum of E k {r¨ðv; hÞ} occurs for h* being determined by setting ›E k {r¨ðv; hÞ}=›h ¼ 0 and this reduces to c1 ½1 2 Gk ð2h*Þ 2 c2 Gk ð2h*Þ ¼ 0;

ð29Þ

which establishes (equation 27). A Corollary 2.1. (minimum risk of the best invariant estimator of m ). The minimum risk is given by

Estimation state of stochastic systems

Rðu; d * Þ ¼ E u {rðu; d * Þ} ¼ E k {€rðv; h* Þ} ¼ c1

Z

1

dv2

Z

0

Z

1 2h* v2

Z

1

2 c2

v1 f k ðv1 ; v2 Þdv1

673

2h* v2

v1 f k ðv1 ; v2 Þdv1

d v2 0

ð30Þ

21

with h* as given by (equation 27). Proof. These results are immediate from (equation 24) when use is made of ›E k {r¨ðv; hÞ}=›h ¼ 0: A 5.3 Outer minimization The results obtained earlier can be further extended to find the optimal number of observations. Now E u {rk ðu; d* Þ} ¼ E u {rðu; d* Þ þ ck} ¼ E k {€rðv; h* Þ þ ck} ¼ c1

Z

Z

1

dv2 0

2 c2

Z

1 2h* v2

1

dv2 0

Z

v1 f k ðv1 ; v2 Þdv1

ð31Þ

2h* v2

v1 f k ðv1 ; v2 Þdv1 þ ck 21

is to be minimized with respect to k. It can be shown that this function (which is the constant risk corresponding to taking a sample of fixed sample size k and then estimating x(k1) by the expression (26) with k for k*) has at most two minima (if there are two, they are for successive values of k; moreover, there is only one minimum for all but a denumerable set of values of c ). If there are two minima, at k* and k* þ 1; one may randomize in any way between the decisions to take k* or k* þ 1 observations.

6. Example Consider the one-dimensional discrete-time system, which is described by scalar difference equations of the form (1)-(2), and the case when the measurement noises w(k ), k ¼ 1; 2; . . . (equation 2 ) are independently and identically distributed random variables drawn from the exponential distribution with the density

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f ðw; sÞ ¼ ð1=sÞ expð2w=sÞ;

w 2 ð0; 1Þ;

ð32Þ

where the parameter s . 0 is unknown. It is required to find the best invariant estimator (BIE) of x(k1) on the basis of the data sample z k ¼ ðzð1Þ; . . .; zðkÞÞ; where k # k1 ; relative to the piecewise linear loss function 8 d $ m; < c1 ðd 2 mÞ=s; ð33Þ rðu; d Þ ¼ : c2 ðm 2 dÞ=s; otherwise; where u ¼ ðm; sÞ; m ; xðk1 Þ; c1 . 0; c2 ¼ 1: The likelihood function of z k is " # k X 1 ½zð jÞ 2 H ð jÞxð jÞ=s Lðz ; m; sÞ ¼ k exp 2 s j¼1 k

" # k X 1 að jÞ½ yð jÞ 2 m=s ; ¼ k exp 2 s j¼1

ð34Þ

where yð jÞ ¼

zð jÞ þ bð jÞ ; að jÞ kX 1 21

að jÞ ¼ H ð jÞAð j; k1 Þ bð jÞ ¼ H ð jÞ

ð35Þ

Að j; i þ 1ÞBðiÞuðiÞ;

ð36Þ

i¼j

It can be justified by using the factorization theorem that ðmk ; sk Þ is a sufficient statistic for u ¼ ðm; sÞ; where mk ¼ min yð jÞ; 1#j#k

sk ¼

k X

að jÞ½ yð jÞ 2 mk :

ð37Þ

j¼1

The probability density function of ðmk ; sk Þ is given by 2 hðmk ; sk ; m; sÞ ¼ nðkÞ s e

nðkÞ½mk 2m s

s 1 k22 2 sk k21 sk e Gðk 2 1Þs

mk . m; sk . 0 where

ð38Þ

nðkÞ ¼

k X

ð39Þ

að jÞ:

j¼1

Since the loss function (equation 33) is invariant under the group G of location and scale changes, it follows (equation 23) that ( rðu; dÞ ¼ r€ðv; hÞ ¼

c1 ðv1 þ hv2 Þ=s;

v1 $ 2hv2 ;

2ðv1 þ hv2 Þ=s;

otherwise;

ð40Þ

where v ¼ ðv1 ; v2 Þ; v1 ¼

mk 2 m ; s

v2 ¼

sk ; s

h¼

d 2 mk : sk

ð41Þ

Thus, using (equation 26) and (equation 27), we find that the BIE of m is given by

dBIE ¼ mk þ h* sk ;

ð42Þ

h* ¼ ½1 2 ðc1 þ 1Þ1=k =nðkÞ ¼ arg inf E k {€rðv; hÞ}; h

ð43Þ

where

E k {€rðv; hÞ} ¼ ½ðc1 þ 1Þð1 2 hnðkÞÞ2ðk21Þ 2 1=nðkÞ 2 hðk 2 1Þ:

ð44Þ

The risk of this estimator is Rðu; d BIE Þ ¼ E u {rðu; dBIE Þ} ¼ E k {€rðv; h* Þ} ð45Þ ¼ k½ðc1 þ 1Þ

1=k

2 1=nðkÞ:

Here the following theorem holds. Theorem 3. (characterization of the estimator dBIE). For the loss function (equation 33), the BIE of m, dBIE, given by (equation 42) is uniformly non-dominated. Proof. The proof follows immediately from Theorem 1 if we use the prior distribution on the parameter space Q,

Estimation state of stochastic systems 675

K 32,5/6

2m 1 e2tst jt ðduÞ ¼ st

1=t 1 1 1 e2st dmds; Gð1=tÞs 1=tþ1 t

ð46Þ

m2ð21; tÞ; s 2 ð0; 1Þ:

676

This ends the proof. A Consider, for comparison, the following estimators of m (state of the system): The maximum likelihood estimator (MLE): dMLE ¼ mk ;

ð47Þ

The minimum variance unbiased estimator (MVUE): d MVUE ¼ mk 2

sk ; ðk 2 1ÞnðkÞ

ð48Þ

The minimum mean square error estimator (MMSEE): d MMSEE ¼ mk 2

sk ; knðkÞ

ð49Þ

The median unbiased estimator (MUE): dMUE ¼ mk 2 ð21=ðk21Þ 2 1Þ

sk : nðkÞ

ð50Þ

Each of the above estimators is readily seen to be of a member of the class C ¼ {d : d ¼ mk þ hsk };

ð51Þ

where h is a real number. A risk of an estimator, which belongs to the class C, is given by (equation 44). If, say, k ¼ 3 and c1 ¼ 26; then we have that ð52Þ rel:eff:R {d MLE ; d BIE ; u} ¼ 0:231; rel:eff:R {dMVUE ; dBIE ; u} ¼ 0:5;

ð53Þ

rel:eff:R {d MMSEE ; d BIE ; u} ¼ 0:404;

ð54Þ

rel:eff:R {d MUE ; dBIE ; u} ¼ 0:45:

ð55Þ

In this case (equation 31) becomes E u {rk ðu; d* Þ} ¼ E u {rðu; dBIE Þ þ ck} ¼ E k {r€ðv; h* Þ þ ck} ð56Þ ¼ k½ðc1 þ 1Þ

1=k

2 1=nðkÞ þ ck ¼ J k :

Now (equation 56) is to be minimized with respect to k. It is easy to see that Estimation state 0 1 of stochastic ðk 2 1Þ½ðc1 þ 1Þ1=ðk21Þ 2 1=nðk 2 1Þ systems A þ c: J k 2 J k21 ¼ 2@ ð57Þ 1=k 2k½ðc1 þ 1Þ 2 1=nðkÞ

677

Define

wðkÞ ¼ ðk 2 1Þ½ðc1 þ 1Þ1=ðk21Þ 2 1=nðk 2 1Þ 2k½ðc1 þ 1Þ1=k 2 1=nðkÞ:

ð58Þ

Thus .

.

,

,

c wðkÞ , J k J k21 :

ð59Þ

By plotting w (k ) versus k the optimal number of observations k* can be determined. For each value of c, we can find an equilibrium point of k, i.e. c ¼ w ðk † Þ: The following two cases must be considered: (1) k † is not an integer. We have k ð1Þ , k † , k ð1Þ þ 1 ¼ k ð2Þ ; where k (1) and k (2) are neighboring integers. Since w (k ) is monotonically decreasing, we know that w ðk ð1Þ Þ . c and w ðk ð2Þ Þ , c: Thus, by using these properties, (equation 57) becomes J k ð1Þ 2 J k ð1Þ 21 ¼ 2w ðk ð1Þ Þ þ c , 0;

ð60Þ

J k ð2Þ 2 J k ð1Þ ¼ 2wðk ð2Þ Þ þ c . 0:

ð61Þ

J k ð2Þ . J k ð1Þ , J k ð1Þ 21 :

ð62Þ

Thus

Therefore, k (1) is the optimal number of observations. We conclude that the optimal number k* is equal to the largest integer below the equilibrium point. (2) k † is an integer. By the same sort of argument, we know that k † is as good as k † 2 1: Consequently, both k † and k † 2 1 are the optimal number of observations. Notice that in this case, Jk* can be computed directly and precisely from (equation 56).

K 32,5/6

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7. Conclusions In this paper we construct the minimum risk estimators of state of stochastic systems. The method used is that of the invariant embedding of sample statistics in a loss function in order to form pivotal quantities which make it possible to eliminate unknown parameters from the problem. This method is a special case of more general considerations applicable whenever the statistical problem is invariant under a group of transformations, which acts transitively on the parameter space. For a class of state estimation problems where observations on system state vectors are constrained, i.e. when it is not feasible to make observations at every moment it is possible to do so, the question of how many observations to take must be answered. This paper models such a class of problems by assigning a fixed cost to each observation taken. The total number of observations is determined as a function of the observation cost. Extension to the case where the observation cost is an explicit function of the number of observations taken is straightforward. A different way to model the observation constraints should be investigated. References Aoki, M. (1967), Optimization of Stochastic Systems – Topics in Discrete-Time Systems, Academic Press, New York. Bertsekas, D.P. (1976), Dynamic Programming and Stochastic Control, Academic Press, New York. Nechval, N.A. (1982), Modern Statistical Methods of Operations Research, RCAEI, Riga. Nechval, N.A. (1984), Theory and Methods of Adaptive Control of Stochastic Processes, RCAEI, Riga. Sage, A.P. and White, C.C. (1977), Optimum Systems Control, Prentice-Hall, New Jersey.

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A learning model for the dual evolution of human social behaviors

Evolution of human social behaviors 679

M. Nemiche and Rafael Pla-Lopez Department of Applied Mathematics, Universitat de Vale`ncia, Spain Keywords Cybernetics, Modelling, Individual behaviour Abstract In this work we modelize, with an abstract mathematical model by computer simulation, the processes that have made to appear in the world a strong duality between orient and occident, by combining changes in conditions of initialization, natural system and the opposition gregarious/individualism of the social behaviors. Finally we present a statistical study of the influence of the repression adaptability, resignation and recycling on the ecological destruction and social evolution. This model can help us to analyze if the current capitalist globalization can be stopped, changed or regulated, and if it is possible to overcome it towards a Free Scientific Society.

1. Introduction We work from a mathematical model of social evolution (Castellar-Buso´ and Pla-Lopez, 1997), to which we call model of Adaptive, Historical, Geographical and multidimensional Evolution with resignation, build from a General Theory of Learning (Pla-Lopez, 1988), formulated in terms of the General Theory of Systems. By means of this model Pla-Lopez and Castellar-Buso´ have studied: (1) the processes that produce repressive social behaviors in the real world, (2) the relationships that provoke these social behaviors among the population’s elements, (3) their influence on the environment, and (4) the necessary conditions to be able to overcome the repression with less repressive and more satisfactory social behaviors. This model showed a general social evolution through one only way: in each set of all possible state (dimension) there were an only ideal behavior, which tended univocally to predominate. Thus, there were a correspondence between the successive dimensions and the successive predominant behaviors. Perhaps the dimensions were overcome before its ideal behavior arrived to predominate, but it did not alter the linearity of the social evolution. Nevertheless, in the real history of the humanity a clear dualism between orient and occident appears. Godelier (1970) already showed that the occidental Winner of the Kybernetics Research Award (Sponsored by Emerald).

Kybernetes Vol. 32 No. 5/6, 2003 pp. 679-691 q MCB UP Limited 0368-492X DOI 10.1108-03684920210443770

K 32,5/6

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evolution from slavery to capitalism were singular and not general and the experience of the bureaucratic regimens of orient shows other singularity which cannot be embedded in the Engels (1884) scheme, but it have not either been such a ephemeral phenomenon to be explained as an anomaly by Revolt Effect (Pla-Lopez, 1996). Thus, we have to change our model in order to modelize this dual evolution by using the opposition gregarious/individualism approach and considering the influence of the geographical natural conditions in a new approach on the Natural System.

2. Description of the dualizing model According to the principles of “Theory of Learning”, each social behavior (U ) can change to new behaviors to be adapted to the apparition of new relationships with the other systems and with the common environment. We call Learning to this process that takes place first starting from the own experience of the system and that also can be produced from the knowledge of the experience of the other systems (Learning for diffusion or scientific communication). The model is built by means of a Probabilistic Learning, supposing the interaction between a population of NP social subsystems (societies), operated in a common ecological environment and taking a function of fulfillment of its goal PG ðU ; N Þ ¼ p ðU Þð1 2 s ðU; N ÞÞ where p (U ) indicates a technical possibility of satisfaction of U, and s (U,N ) an eventual social repression of U in the individual subsystem N. The better situation is when the technical possibility reaches its maximum value of 1, and there is not social repression from any N against U ðs ðU; N Þ ¼ 0Þ: in this case, the fulfillment of the goal is 1. The social repression can also be adaptable, so that the produced repression tended to approach to the suffered repression. On the other hand, to compare the fulfillment PG(U, N ) of the goal with its mean value PG(U, N ) expresses a personal “resignation” with this mean value: only fulfillments worse than this mean value provokes rejection. This “resignation” is especially flagrant in flighty situations if the mean value PG(U, N ) to compare is updated instantaneously. We can simulate a lower “resignation” through a delay in this updating. Finally, in order to simulate an ecological adaptation, we can introduce a global limit to the natural resources, which can be surpassed if too many resources are simultaneously dedicated to “satisfaction” and “repression”. In this case, the system will have to take away resources to recycle, at the expense of the consumption in “satisfaction” or “repression”. The possibility of an ecological recovery will depend on the celerity in this adaptation to the ecological necessities.

We consider a social evolution with discrete time. Each social subsystem N is defined for two variables: (1) A function of probability P(U, N ) on a vector U ; ðU m21 ; . . .; U 1 ; U 0 Þ of dimension m, with binary components: U i [ {0; 1} U ¼ Si 2i U i : The function P corresponds to the weight of the different social behaviors (state-value) in a social system. The values one or zero of each one of the components represent the presence or absence of some property of the social behavior (also called attribute) (2) The variable mðNÞ [ {1; . . .; m} expresses the native dimension of the system (actual variety of state), which limits the possible behaviors (state) for the restriction: PðU; N Þ ¼ 0 ;U $ 2mðNÞ when the system is initialized. It is necessary to define functions to modelize the level of technological advance, the repressive capacity and the satisfaction of the different social behaviors, also the processes of birth, death, and relay of the systems. We want the satisfaction that increases with the technological progress. The most simple dependence is fðU Þ ¼ Si Ui, and if we normalize it, we obtain an expression for the technical possibility of initial satisfaction. In a previous work (Nemiche and Pla-Lopez, 2000), in order to minimize the initial difference in technical possibility of satisfaction between social behaviors, we modelize it with

p 0 ðUÞ ¼ Si–0 U i =m þ ð0:8Þ12U 0 =m Also, in a previous work (Castellar-Buso´ and Pla-Lopez, 1997), a new entropic factor had been added to the technical possibility of initial satisfaction, to obtain the current technical possibility of satisfaction (p ). The core of the model is the Learning System, through positive and negative reinforcement: the probability (P) of each social behavior (U ), in each individual subsystem (N ) of a social population, is given by PðU ; N Þ ¼ FðU; N Þ=BðNÞ; such that BðN Þ ¼ SV F(U, N ) indicates the accumulated memory, and F(U, N ) is a memory accumulator function, which increases when the goal is fulfilled and decreases when the goal is not fulfilled from the social behavior U for the individual subsystem N. If no social behavior is available to an individual subsystem that produces goal fulfillment, then the accumulated memory (B ) can become 0 and the individual subsystem is destroyed. We use a continuous approximation by supposing that, through each interval of time Dt, each subsystem has the state-value U and the fulfillment of the goal a number of times proportional to its probability, and therefore DFðU; N Þ ¼ max{ 2 FðU ; NÞ; DtlðN Þ½PG ðU ; N Þ 2 PR ðN ÞPL ðU ; N Þ} where PG(U, N ) is the fulfillment probability of the goal from the social behavior U for N, PL(U, N ) is the Learning probability from U for the individual

Evolution of human social behaviors 681

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subsystem N, PR(N ) is a reference value of the satisfaction for the individual subsystem N, and l (N ) is a scale factor for the individual subsystem N. The fulfillment probability (PG) depends on its technical possibility (p ), which is weighted by a factor determined by the social organization (12 s ). This factor is generated by a Repression System: each social behavior, according to its repressive capacity (k ), its scope (F ) in each individual system and the impact (imp) of the social behavior, produces a decrease of this factor for the other social behaviors. Thus, each social behavior (U ) represses the other social behaviors, by decreasing its goal fulfillment. In a previous work Nemiche and Pla-Lopez (2000), modelized the suffered social repression with

s ðU; N Þ ¼ SV –U SM FðV ; M ÞstsðV ; M ÞimpðV ; M ; N Þ where sts(U, N ) is the repressive capacity of U in an individual subsystem N, then

F ðU ; N Þ ¼ P2 ðU ; N Þ=S indicates the scope of U in the individual subsystem N, with a number S of active subsystems, and imp(V, M, N ) is the impact of the behavior V at the circular distance between the systems M and N. A Relay System produces a random substitution of an individual subsystem for a “child subsystem” with initial equiprobability of every available social behavior. A “child subsystem” can also occupy the niche of some destroyed system. Thus, relay causes the loss of the information accumulated in the substituted individual system. Also, a Science System determines the probability of learning ( PL ) for each social behavior in each subsystem from the probability that the experience of the other subsystems. That is weighted by factors of emission (EM), reception ( RE) and impact (IMP) between individual subsystems, were added to its own experience. This system expresses the relations of intellectual communication between different individual subsystems. An Historical System simulates historical evolution through the random increase of the dimension (m ) of the state-variable in each subsystem, and therefore, of the number of its available social behaviors. The probability of evolution is increased (b ) by the existence of social behaviors, which would be theoretically not available but are forced by System Science from the experience of other subsystems. This system expresses technological progress and technological diffusion (we characterize a technologically higher society by a greater capacity of choice between different social behaviors). An Adaptive System determines the dynamic evolution of the repressive capacity of a social behavior in a subsystem toward its suffered repression (s ), from an initial value (k ) when it is a “child subsystem”. The initial repressive

capacity depends on the might (m) and ferocity (n ) of the social behavior, kðU Þ ¼ mðU Þn ðU Þ; see Table I. A Resignation System expresses the influence of subjective factors through a tendency to a statistical normalization of the reinforcement from satisfaction and dissatisfaction. We name this tendency “resignation”, and express it by a time of delay (Tr) according to a model of systems dynamics: with a low delay Tr, the satisfaction will tend to be compared with its mean value PGM(N ), and the individual subsystem tends to be resigned with global low values of satisfaction. An Impact System expresses the influence that has a social subsystem N on another M; we express it by a factor that we call IMP, determined by the function

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IMPðN ; M Þ ¼ SU PðU ; N Þ impðU ; M ; NÞ where imp(U, M, N ) is the impact of the behavior U at the circular distance between the systems M and N. In the previous works, the impact of a social behavior (imp(U, d )) decreased lineally with the distance, and it is maximum when distance is equal to 0 ðd ¼ 0Þ; that is to say, on the own system. This effect only affected to the repression (between different social behaviors). There are several factors that differentiate the Eastern from the Western social behavior (technical possibility of satisfaction, might, initial repressive capacity. . .), these differences will also affect their impact: Individualistic in the occidental, and more socially cohesive (gregarious) in the oriental zone. Now, we will change the impact function imp(U, d ), using the opposition gregariousness/individualism of the social behaviors: (1) if U 0 ¼ 0 (gregarious behaviors ), the imp of the social behavior U ; ðU m ; . . .; U 1 ; U 0 Þ is maximum when d ¼ 0; decreases with d and increases with natal, but (2) if U 0 ¼ 1 (individualist behaviors ), the impact is equal to zero when d ¼ 0; that is to say, the repression which is produced by such behaviors only acts on other social systems. Thus, the individualist behaviors do not only look for to satisfy its own interest, but rather they make it in such way that abuse to the interests of others.

m U p0 m n k

1 0 ; 0000 0.2 0 1 0

1 1 ; 0001 0.25 0.1429 1 0.1429

2 2 ; 0010 0.45 0.2857 1 0.2857

2 3 ; 0011 0.5 0.4286 1 0.4286

3 6 ; 0110 0.7 0.8571 1 0.8571

3 7 ; 0111 0.75 1 1 1

4 E ; 1110 0.95 2 0 0

4 F ; 1111 1 2.1429 0 0

Table I. Technical possibility (p 0(U )) and initial repressive capacity (k(U ))

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Figure 1. Some impact functions

In the case of NP ¼ 50 we will take impðU ; M ; N Þ ¼ expð20:5 c 2 Þ gre(U, N ) ind(U, M, N ) where greðU; N Þ ¼ ½natalðN Þð2:3019expð20:5U 2 =7:25Þ þ U =21Þð12U 0 Þ indðU ; M ; N Þ ¼ ½cðUexpð20:5U 2 =8:064Þ6:124 þ 0:15Þ=1:32U 0 where c ¼ d=dis; with dis ¼ ðU =2Þ12U 0 (2U/3)U0. We can see in Figure 1 some impact functions. Natural System expresses a diversity of initial conditions (natal) of the individual systems. In the previous model, the Natural System appears isolated without input variables. In this work, we will make that initial conditions to (natal ) depend on the ecological factor. For that reason, we have included a new factor, to which we call factor of the evolution (km ). Then we have changed the definition of the Natural System: a Natural System determines the dynamic evolution of the

initial conditions (natal ) of each individual subsystem N, in case of ecological degradation, from an initial value (natal 0) toward an ideal value (ntl ) with a delay (Tm ). The initial value of natal is natal 0 ðN Þ ¼ natal min þ 161dðN P=4; N Þ=NP; where natal min ¼ 5 and the value of ntl and natal through the time will be 8 < ntl t ðN Þ ¼ 2 þ ðnatal t ðN Þ=ð220 ec2 þ 25ÞÞ; ec , 1 ) : nataltþDt ðN Þ ¼ natal t ðN Þ þ ðntl t ðN Þ 2 natal t ðN ÞÞ=km; where km ¼ Tm=Dt; ec ¼ E=E 0 : E represents the ecology, and E0 the initial value of the ecology. Through processes of reutilization and recycling, E can increase without overcoming its initial value, and therefore natal(N ) can also increase without overcoming the value 2 þ natal 0 =5: Moreover, an Ecological System expresses the degradation of the environment as a consequence of the consumption in satisfaction and repression: the possibility of consumption decreases, so much in satisfaction like in repression, in order to recover the environment by means of the recycling. Finally, a Delay System expresses the decrease of the adaptation time Ta with might m and the increase of the resignation time Tr with ferocity n, by means of the parameters Ka and Kr respectively. Moreover, ecological time Te increases with ferocity and decreases with might by means of a parameter Ke. 3. A specification of the model We work with NP ¼ 50 individual subsystems, and a maximum dimension m ¼ 4: We speak about predominance of a behavior U if its probability is the majority ðP . 1=2Þ in a relative majority of subsystems. Moreover, we speak about strong predominance if additionally its probability of satisfaction (PG) is the maximum. 4. Results and interpretation With our model we have obtained an evolution with behaviors 1-3-7-F (“individualists”) in the “occidental” area and 0-2-6-F (“gregarious”) in the “oriental” area. This can be explained because in the “oriental” area natal has a superior initial value (next to 37.5), and so the bigger “gregarious” impact which is generated can compensate the bigger intrinsic satisfactoriness of the “individualistic” behaviors.

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U ; ð0; 0; 0; 1Þ ¼ 1 : occidental slavery (3) Dimension m ¼ 2 : technological increase U ; ð0; 0; 1; 0Þ ¼ 2 : oriental feudalism U ; ð0; 0; 1; 1Þ ¼ 3 : occidental feudalism (4) Dimension m ¼ 3 : industrial revolution U ; ð0; 1; 1; 0Þ ¼ 6 : state socialism U ; ð0; 1; 1; 1Þ ¼ 7 : capitalism (5) Dimension m ¼ 4 : technological revolution U ; ð1; 1; 1; 0Þ ¼ E; U ; ð1; 1; 1; 1Þ ¼ F : free scientific society Other values of U can represent anomalous social behaviors (fascism, Stalinism. . .) that appear from which we have named “revolt effect”. 5. A statistical study We have programmed our model in C language, and executed it on the CraySilicon Graphics Origin 2000 computer, with 64 processors (MIPS R1200 to 300 MHz), 16 GB by memory central and 390 GB in disk. The operating system is the IRIX 6.5.5, which is a variant of the Unix developed by Silicon Graphics (Servei Informa`tic de la Universitat de Vale`ncia ). We have executed our model 3125 times, with ðKa ; Kr ; Ke Þ [ {1; 5; . . .; 97} £ {1; 5; . . .; 97} £ {1; 3; . . .; 9}: In this paper we limit our study to the following five evolutions (see Figure 2): (1) Type 1: when appears (predominance) the “2” (oriental feudalism) in the “oriental” area and the “3” (occidental feudalism) in the “occidental” area. (2) Type 2: when the oriental and occidental feudalism is overcome with the strong predominance of “7” (capitalism) in the “occidental” area and “6” (state socialism) in the “oriental” area. (3) Type 3: when the ecological hecatomb takes place during the strong predominance of the “6” and the “7”. (4) Type 4: when a capitalist globalization appears with strong predominance of “7” without to overcome it neither to arrive at an ecological destruction. (5) Type 5: when the capitalist globalization or the duality is to overcome toward a free scientific society “F”.

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Figure 2. Some possible evolutions with duality

In order to study how the previous evolutions depend is to on ka and kr and ke, we use the REGINT (Caselles, 1998) program. The proportions p1 to p5 of the evolutions of types 1 to 5 respectively in function of ka are p1 ¼ 0:686891 2 0:420046=ka þ 0:017904 logðka Þ with a correlation coefficient of R ¼ 0:828205 p2 ¼ 20:056168 2 0:000041 ka 2 þ 0:000009 expð0:1 ka Þ þ 0:051254 ka 1=2 with a correlation coefficient of R ¼ 0:828643 p3 ¼ 0:015199 þ 0:000003 expð0:1 ka Þ þ 0:005177 expð20:1 ka Þ 2 0:015602 cosð0:0625 ka Þ with a correlation coefficient of R ¼ 0:693814 p4 ¼ 20:044751 2 0:000036 ka 2 þ 0:000007 expð0:1 ka Þ þ 0:043222 ka 1=2 with a correlation coefficient of R ¼ 0:831534 p5 ¼ 0:035582 2 0:000003 ka 2 2 0:091535=ka þ 0:06191 expð20:1 ka Þ with a correlation coefficient of R ¼ 0:83663 In sum, there is a strong correlation of the evolutions 1, 2, 4, and 5 with ka.

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To find the group of the parameters that facilitate or hind the apparition of the previous evolutions, we show the distributions of the probabilities graphically (see Figure 3). We observe that small values of ka facilitate the apparition of the evolution type 5. On the other hand, the proportions p1 to p5 of the evolutions of types respectively 1 to 5 in function of ke are p1 ¼ 4:875047 þ 0:01956k2e 2 1:956964 expð0:1ke Þ 2 2:271176 expð20:1ke Þ with a correlation coefficient of R ¼ 0:98772 p2 ¼ 5:287976 þ 0:028110k2e 2 2:587476 expð0:1ke Þ 2 2:555235 expð20:1ke Þ with a correlation coefficient of R ¼ 0:992130 p3 ¼ 20:523937 2 0:003813k2e 2 0:047725ke þ 0:530948 expð0:1ke Þ with a correlation coefficient of R ¼ 0:914072

Figure 3. Distribution of the probability of ka

p4 ¼ 3:189116 þ 0:015755k2e 2 1:513678 expð0:1ke Þ

2 1:544209 expð20:1ke Þ

Evolution of human social behaviors

with a correlation coefficient of R ¼ 0:75466 p5 ¼ 0:058542 2 0:000441k2e 2 0:052729=ke þ 0:017277 cosð0:75ke Þ with a correlation coefficient of R ¼ 0:972099: In summary, there is a strong correlation of the evolutions 1, 2, 3, and 5 with ke. Finally, the proportions p1 to p5 of the evolutions of types respectively 1 to 5 in function of kr are p1 ¼ 0:695407 þ 0:000006k2r 2 0:119897=kr þ 0:194476 expð20:1kr Þ with a correlation coefficient of R ¼ 0:381090 p2 ¼ 0:405072 2 0:259922=kr 2 0:089528 logðkr Þ þ 0:015044k1=2 r with a correlation coefficient of R ¼ 0:602309 p3 ¼ 0:006503 þ 0:147729 expð20:1kr Þ with a correlation coefficient of R ¼ 0:924124 p4 ¼ 20:090991 þ 0:000090k2r 2 0:019123kr 2 0:000007 expð0:1kr Þ þ 0:13504k1=2 r with a correlation coefficient of R ¼ 0:6125882 p5 ¼ 0:038877 þ 0:000015k2r 2 0:001066kr 2 0:000004 expð0:1kr Þ with a correlation coefficient of R ¼ 0:47813. In sum, there is a strong correlation of the evolution 3 with kr (see Figure 4). We observe that small values of kr facilitate the apparition of the evolution type 3.

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Figure 4. Distribution of the probability of kr

6. Conclusions We show an interesting result: after a dual evolution with capitalism in “occidental” zone and state socialism in oriental zone, a globalization of capitalism arrives, but later it is overcome with a free scientific society without ecological destruction. Then the current capitalist globalization is an ovecome process. No evolution (in the model) finishes with ecological hecatomb when the duality overcame with a capitalist globalization, it is consequence of the decrease of the consumption of the resources in repression and satisfaction. According to our model and a first statistical study, with low ka values (quick evolution of the repressive capacity toward the suffered repressive) the probability of the overcoming of the capitalist globalization with a free scientific society increases. This can explain adaptive pacifism (disarmament due to a lack of enemies). References Caselles, A. (1998), “REGINT: a tool for discovery by complex function fitting”, Cybernetics and Systems’98, Austrian Society for Cybernetic Studies, Vienna, pp. 787-92. Castellar-Buso´, V. and Pla-Lopez, R. (1997), “Un modelo de desarrollo sostenible opuesto a la hecatombe ecolo´gica”, 14th International Conference of WACRA-Europe on Sustainable Development, Madrid. Published in Revista Iberoamericana de Autogestio´n y Accio´n Comunal, 32, pp. 151-62, http://www.uv.es/~buso/wacra/wacra_cas.html Engels, F. (1884), Der Ursprung aus der Familie, der Privateigentum und der Staat. Zurich (translated to Spanish as El Origen de la Familia, la Propiedad Privada y el Estado. Fundamentos, Madrid, 1970).

Godelier, M. (1970), Sche´ms d’evolution des socie´te´s (translated to Spanish as Esquemas de evolucio´n de las sociedades, Miguel Castellote Editor, aprox. in 1970). Nemiche, M. and Pla-Lopez, R. (2000), “A model of dual evolution of the humanity”, 2nd International Conference on Sociocybernetics, Panticosa, 25-30 June, http://www.uv.es/ ~pla/models/panticosa/mdeh.htm Pla-Lopez, R. (1988), “Introduction to a learning general theory”, Cybernetics and Systems: An International Journal, Hemisphere Publishing Corporation, The Austrian Society for Cybernetic Studies, Vol. 19, pp. 411-29. Pla-Lopez, R. (1996), “Cua´nto puede perdurar una revuelta?”, 1a Reunio´n Espan˜ola de Ciencias de Sistemas, Vale`ncia. Published in Revista Internacional de Sistemas, Vol. 8 No. 1-3, pp. 59-73, http://www.uv.es/~pla/CUANTOPE.DOC Pla-Lopez, R. and Castellar-Buso´, V. (1999), “Models of dual social evolution”, 4e´me Systems Science European Congress, Sociedad Espan˜ola de Sistemas Generales, Vale`ncia, pp. 337-45, http://www.uv.es/~buso/modduale/modduale.html

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Autocorrelation and frequency analysis differentiate cardiac and economic bios from 1/f noise M. Patel Medical Surgical Department, Research Resources Center, Biostatistics Facility, College of Nursing, University of Illinois at Chicago

H. Sabelli Chicago Center for Creative Development, Chicago, IL, USA Keywords Chaos, Economics, Cybernetics Abstract Mathematical bios and heartbeat series show an inverse relation between frequency and power; the time series of differences between successive terms of cardiac and mathematical chaos shows a direct relation between frequency and power. Other statistical analyses differentiate these biotic series from stochastically generated 1/f noise. The time series of complex biological and economic processes as well as mathematical bios show asymmetry, positive autocorrelation, and extended partial autocorrelation. Random, chaotic and stochastic models show symmetric statistical distributions, and no partial autocorrelation. The percentage of continuous proportions is high in cardiac, economic, and mathematical biotic series, and scarce in pink noise and chaos. These findings differentiate creative biotic processes from chaotic and stochastic series. We propose that the widespread 1/f power spectrum found in natural processes represents the integration of the fundamental relation between frequency and energy stated in Planck’s law. Natural creativity emerges from determined interactions rather than from the accumulation of accidental random changes.

Introduction Biological and cosmological evolution demonstrate empirically that natural processes are creative. Physiological processes that continually generate new patterns provide an opportunity to investigate the empirical features of creative processes. In many natural processes (astronomical, physical, biological and psychological), the power spectrum often shows an inverse relation between frequency and energy (Gilden, 2001; Handel and Chung, 1993; Press, 1978; Schro¨eder, 1991). The inverse power law applies to multiple levels of organization indicating their isomorphism or self-similarity. It must reflect a Kybernetes Vol. 32 No. 5/6, 2003 pp. 692-702 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443789

Supported by Society for the Advancement of Clinical Philosophy. We are thankful to Drs Arthur Sugerman, Louis Kauffman, Jerry Konecki and Linnea Carlson-Sabelli for useful discussions of the data.

fundamental feature of natural processes. Here we propose that it reflects their creation by the interaction of deterministic action rather than by the sum of random changes. Change is universal. At all levels of organization there is undirected flux and directed action. Since mechanism cannot account for the generation of novelty, it is often assumed that innovations are independent events, the occurrence of which can only be explained probabilistically. However, time series with creative features (which we call bios) can also be generated deterministically by recursions of bipolar feedback. The process equation Atþ1 ¼ At þ g sinðAt Þ generates periods and chaos at low gain, and bios at higher gain (Kauffman and Sabelli, 1998). The deterministic generation of biotic patterns gives credence to the hypothesis that the generation of diverse, novel, and complex processes can be the necessary consequence of interactions among simple processes. Deterministic interactions need not be mechanical. Creativity can be stochastic or deterministic. Both undirected flux and directed action can create aperiodicity and complexity in natural processes. Spontaneous, apparently random, erratic fluctuations are observed at all levels of organization. Planck discovered that radiation can be emitted only in multiples of a quantum h that has the dimensions of action¼energy £ time. Within its limits, change is continual and unpredictable; the uncertainty principle excludes absolute rest. Above this limit, determined, directed action (not energy alone) appears to be the sole constituent of the universe. Einstein showed the equivalence of matter and energy, and information is always associated with energy or material tokens (Shannon and Weaver, 1949). The principle of least action implies that energy and time are inseparable. They are quantum conjugates (Heisenberg’s principle). Also, at macroscopic levels, energy is indissolubly associated with unidirectional time. Temporal action causes change. What generates novelty and complexity in specific processes? Is it random flux or directed action? The characteristic features of deterministic action are: (1) temporal asymmetry; (2) transitivity (continuity, causation); and (3) a direct relation between energy E and frequency f (Planck’s law E ¼ hf ). In contrast, random flux is: (1) symmetric; (2) acausal, composed of independent events; and (3) variable along the entire frequency spectrum with no prominent peaks, and with no relation between frequency and energy (white noise). These differences can be detected with statistical methods such as

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autocorrelation, skewness, and frequency analysis. In this manner, we have analyzed empirical and mathematical time series to investigate the role of deterministic action and probabilistic flux in creative processes.

Asymmetry Complexity requires and generates asymmetry. The degree of asymmetry of a time series is measured by its statistical distribution. The statistical distributions of heartbeat intervals, economic series, meteorological data, colored noise (e.g. random walk), and mathematical bios all are asymmetric. Asymmetry is also present in biotic series generated by the process equation and in random walks. In contrast, symmetry is the rule for the distribution of random, periodic, and chaotic series. The asymmetry of natural processes must then result from the unidirectionality of time embodied in deterministic action or in the integration of random changes. Pasteur, based on his discovery of biomolecular asymmetry, postulated the existence of a fundamental physical asymmetry that has since been found in physical, biological and psychological processes (Anderson, and Stein, 1987; Corballis and Beale, 1976; Haldane, 1960; Sabelli, 1989). Asymmetry is a fundamental feature of time and creation. Creative action involves temporal unidirectionality, as contrasted to the time reversibility of classic, relativistic and quantum mechanics. Transitivity Causality is transitive in the mathematical sense. Such transitivity can be detected by statistical correlation. Time series of empirical data, mathematical bios, and statistical noise (pink, brown) show high positive autocorrelation for at least 16 lags. In contrast, there is a negative autocorrelation between successive terms for periodic series and for chaotic series generated by the process equation; chaotic series generated by the logistic equation resemble random data in showing no autocorrelation. Interpreting these results, in periodicity and chaos, change embodies opposition, while in bios and in biological processes, change connects similars. Notably, correlation techniques show the presence of an underlying period 2 during the early phase of chaos generated with either the logistic or the process equations (Figure 1). We call this pattern “period 2 chaos”. While, in retrospect, this could have been inferred from observation of the time series, we have not seen it reported anywhere. This coexistence of a periodic and chaotic regime is noteworthy because attractors are often described as mutually exclusive. Overlapping attractors may explain the generation of novel and complex patterns from simple pre-existing natural forms, and thus provide a deterministic rather than probabilistic account of creative processes.

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Figure 1. Autocorrelation shows the coexistence of period 2 and chaos. Top: period 2 chaos generated by the process equation Atþ1 ¼ At þ g sinðAt Þ; g ¼ 3:65: Bottom: autocorrelation analysis of this time series. X-axis: number of lags. Y-axis: Pearson’s correlation coefficients

The partial autocorrelation coefficient measures the association between At and At+k when the effects of other time lags (1, 2, 3. . ., up to k21) are partialled out (Kendall, 1973). Time series recorded from some natural processes known to generate novel patterns, heartbeat interval series, respiration, climatic and paleoclimatic changes, and other natural processes all show extended partial autocorrelations, indicating deterministic rather than probabilistic origin (Figure 2). Positive and negative partial autocorrelations are also observed in biotic series generated by the process equation for several lags. In contrast 1/f noise and brown noise correlate for only one lag. This is to be expected: change is random in these series.

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Figure 2. Partial autocorrelation. Top: heartbeat intervals. Middle: bios generated by the process equation Atþ1 ¼ At þ g sinðAt Þ; g ¼ 4:61: Bottom: 1/f noise

These results support the view that creative processes can spring from the interaction of preexisting simple patterns, and not only as meaningful consequences of accidental events. Negative correlation between successive differences At 2 Atþ1 is observed for physiological processes and for mathematical bios, but not for economic data (Figure 3). In random walks generated by the addition of random changes, there is no correlation between successive changes. The same lack of correlation also obtains for deterministic bios generated with high gain.

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Consecutive proportion To consider other forms of continuity not represented by autocorrelation, we developed a method to compute continuous proportion (Figure 4). It measures the stability of ratios between consecutive terms of the time series At =Atþ1 ¼ Atþ1 =Atþ2 : The difference ðAt =Atþ1 Þ 2 ðAtþ1 =Atþ2 Þ is computed, and whenever it is smaller than a chosen tolerance (range/100), a continuous proportion is counted. Continuous proportions are abundant in creative processes (cardiac, economic, meteorological and mathematical biotic series),

Figure 3. Autocorrelation between successive terms and between differences of successive terms, in empirical and mathematical series

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Figure 4. Consecutive proportion (see text)

and scarce in random and chaotic data. Note also the low rate of consecutive proportions in pink noise in comparison to cardiac and biotic series. Power frequency relation The relation between energy and frequency (1/time) is essential to consider the role of action (energy £ time) in creative processes. In physics, energy is a function of frequency. At the quantum level, Planck’s constant establishes this relation. At higher levels of organization, many physical, biological and psychological processes are aperiodic. Simple determined processes are steady, periodic, or tend to equilibrium, while complexity implies aperiodicity. Fourier analysis decomposes a complex aperiodic trajectory into a set of sine and cosine waves. The power spectrum represents a histogram of the different frequencies of the sine and cosine waves into which the curve has been decomposed. The horizontal axis is the temporal frequency (frequency ¼ 1/time) and the vertical axis is the power, which can be regarded as equivalent to the energy of these components. Power spectra reveal significant properties of time series; e.g. the average power spectrum slope b of heartbeat interval (RRI) series is higher ðp , 0:05Þ during wakefulness than during sleep (Table I). In many aperiodic time series, the power of the periodic components into which the curve has been decomposed is inversely proportional to their frequency f. In the log-power/log-frequency plane, the spectra are straight lines, and can be described by a single parameter, the slope b, including b ¼ 21 (1/f or pink noise), b ¼ 22 (brown noise), and larger exponents 22, b ,2 4

(black noise). b ¼ 0 corresponds to randomness (white noise); note, however, that chaotic series also can have b ¼ 0 (Table I). Continuing the color analogy, we coin the expression green power spectrum to indicate that power is a positive function of the frequency with a slope of 1. These patterns are schematically represented in Figure 5. Processes with 1/f and 1/f 2 patterns can be generated by the addition of random changes. 1/f patterns can also be generated deterministically, as demonstrated by the occurrence of harmonics in any type of oscillatory mechanism, mechanical or electrical. Music, which is created, illustrates a third process that can generate 1/f pattern. Also biotic series generated deterministically by bipolar feedback show power spectra inversely proportional to frequency; b grows with the intensity of the gain, nearing 22 with intense feedback. A biotic pattern with homeostatic-like distribution and 1/f power spectrum is generated by Atþ1 ¼ At þ ðg sinðAt ÞÞ 2 ððAt =jAt jÞ ðAt ðmod 2pÞÞÞ; a recursion that combines bipolar feedback with a new type of equilibration. Recursions of bipolar feedback such as the process equation and its variant, the diversifying equation Atþ1 ¼ At þ sinðAt jt Þ (Sabelli, this volume) generate a cascade of bifurcations generating periodic series with a dominant frequency 0.49, corresponding to period 2, and decreasing amplitude at slower frequencies. The cascade generates chaotic series with a similar power spectrum. With larger gain or diversifier, a second major peak emerges in the periodogram ð j ¼ 3:75Þ; and at still higher value ð j ¼ 4:1- 4:3Þ; the spectrum shows a positive slope at the high frequencies. A flat spectrum occurs near the edge between chaos and bios ð j ¼ 4:6Þ: Following the chaotic phase starts the biotic series with 1=f b spectrum slope (Figure 4). This shift from f 0 to f b emerges exactly at the edge

Brown noise Dow Jones Bios, g ¼ 4:61 Corn Silver RRI awake (average, 10 subjects) Pink noise RRI asleep (average, 10 subjects) Logistic chaos g ¼ 3:99 Gaussian white noise Process chaos, g ¼ 4:3 Uniform random 0 to 1 EEG Speech (eh sound)

Series

Differences

Cumulative

2 2.11 2 1.91 2 1.76 2 1.71 2 1.67 2 1.04 2 1.00 2 0.67 2 0.28 0.00 0.06 0.10 0.63 1.05

20.10 0.24 0.37 0.28 0.29 0.92 1.01 1.31 1.60 1.50 0.32 0.78 2.58 0.25

2 1.90 2 2.00 2 2.00 2 2.02 2 2.00 2 2.00 2 3.01 2 2.01 2 2.01 2 2.00 2 2.00 2 2.00 2 1.34 2 0.40

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Table I. Power spectrum analysis. b exponent for the time series, the time series of differences, and the time series of cumulative values. N ¼ 2000; 32 harmonics

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Figure 5. Four canonical types of aperiodic patterns. Left: time series. From top to bottom: chaos Atþ1 ¼ 3:9 sinðAt Þ: RRI: R to R intervals in electrocardiogram. Bios generated with high gain Atþ1 ¼ At þ 10 sinðAt Þ: DRRI: difference between successive heartbeat intervals. Right: idealized representation of power spectrum: Y ¼ log power; X ¼ log frequency

between chaos and bios ( g ¼ 4:6035 for the process equation) and evidences the fundamental difference between these two patterns. Logistic chaos does not generate 1/f pattern. What process, stochastic, deterministic, or creative, generates the prevalent 1/f patterns found in nature? To investigate, we have found it useful to calculate the power spectra of the time series, its derivative (time series of differences), and its integral (time series of cumulative values). For most of the time series examined, the power spectrum exponent is larger (more positive) for the time series of the differences, and smaller (more negative) for its integral (Figure 6). Differencing random walks generates a random series. Differencing mathematical bios generates chaos, and likewise differencing heartbeat series generates a chaotic-like series. Differencing brown noise generates a time series with an exponent near 0 (as random data). The time series of differences has a positive value for b in the case of cardiac and economic series, bios, and pink noise. The human electroencephalogram (EEG), that has a near green spectrum, shows

a near 1/f spectrum after integration, and the integral of the integral of the EEG has slope 22. In a similar manner, speech shows a positive spectrum slope and its integral shows a 1/f spectrum (Figure 7). The average value for the b exponent for RRI series recorded during wakefulness is near 21, for RRI differences is near 1, and for the integral of RRIs is 2 2, corresponding to pink, green, and brown patterns (Table I). Similarly, time series of economic processes show an inverse relation between frequency and power, while the time series of differences show a direct relation. Notably, for series with a white noise spectrum (uniform and normal random, process chaos), the time series of differences between consecutive terms shows a positive exponent b. These observations suggest that different power spectrum patterns may represent the recording of different aspects of a single natural process, not necessarily different types of processes. Recognizing the fundamental relation between frequency and energy in physics, we speculate that time series with positive b are recordings of the actions that constitute the process. Actions are cumulative. Cumulative actions display a 1/f pattern. For instance, the time series of differences between heartbeats would represent individual changes of action that become integrated in the time series of heartbeats. We thus propose that

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Figure 6. Power spectrum slope of time series, the time series of differences between consecutive terms, and the integral (cumulative)

Figure 7. Effect of differentiating and integrating on the power spectrum of time series

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the widespread 1/f spectrum found in natural processes results from the integration of actions the functional relation between frequency and energy stated in Planck’s law. In summary, statistical analyses of time series of natural creative processes and of bios show asymmetry, transitivity (autocorrelation) and a determined relation between energy and frequency, three features of directed action. In contrast, random processes are symmetric, and composed of independent events (non transitive) that display no relation between frequency and power. These observations support the view that creativity emerges from deterministic interactions of low dimensional (simple) processes, not only from meaningful coincidences in high dimensional (random) processes. References Anderson, P.W. and Stein, D.L. (1987), “Broken symmetry, emergent properties, dissipative structures, life. Are they related?”, in Yates, F.E. (Ed.), Self-Organizing Systems, Plenum, New York, pp. 459-74. Corballis, M.C. and Beale, I. (1976), The Psychology of Left and Right, Erlbaum, Mahwah, New Jersey. Gilden, D.L. (2001), “Cognitive emissions of 1/f noise”, Psychological Reviews, Vol. 108, pp. 33-56. Handel, P.H. and Chung, A.L. (1993), Noise in Physical Systems and 1/f Fluctuations, American Institute of Physics, New York. Haldane, J.B.S. (1960), “Pasteur and cosmic asymmetry”, Nature, Vol. 185, p. 87. Kauffman, L. and Sabelli, H. (1998), “The process equation”, Cybernetics and Systems, Vol. 29 No. 4, pp. 345-62. Kendal, M. (1973), Time Series, Charles Griffin, London. Press, W.H. (1978), “Flicker noises in astronomy and elsewhere”, Comments in Astrophysics, Vol. 7, pp. 103-9. Sabelli, H. (1989), Union of Opposites: A Comprehensive Theory of Natural and Human Processes, Brunswick, Lawrenceville, Virginia. Schro¨eder, M. (1991), Fractals, Chaos, Power Laws, W. H. Freeman, New York. Shannon, C.E. and Weaver, W. (1949), The Mathematical Theory of Communication, University of Illinois, Urbana, Illinois.

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A holistic approach towards the validation and legitimisation of information systems

Validation and legitimisation of IS 703

O. Petkova Central Connecticut State University

D. Petkov Eastern Connecticut State University and University of Natal Keywords Cybernetics, Information systems Abstract The research aims to show that validation and legitimisation of an information systems (IS) project need to be treated simultaneously to improve software project management. A starting assumption is that traditional aspects of model validity and legitimisation in operational research can be applicable to the field of IS. However, non-traditional types of IS are more suitable to be viewed from an interpretive viewpoint. Validation is explored both from hard systems and also from soft systems point of view. Some extensions on the notion of validation for soft systems are provided for that purpose. Issues regarding both validation and legitimisation in IS are illustrated on a case study regarding the management of an academic research management IS project. Issues related both validation and legitimisation in IS are illustrated on a case study regarding the management of an academic research IS project. The latter had eventually to be abandoned. The case study shows how the non-adherence to the principles of validation and legitimisation lead to that situation.

Introduction The purpose of this paper is to present a holistic view of validation and legitimisation that may ensure that a system is successfully completed. The importance of this approach is that it can lead to an increase in the success rate of IS development through improvement of its management. Such a framework is an extension of the traditional understanding of software project evaluations as that is usually based on ideas related to the systems development life cycle. A starting point for this research is the fact that the process of operational research (OR) (Keys, 1997) as well as that of a general systemic intervention has quite a lot in common with the field of IS. This is particularly relevant for systems that deal with activities which are not strictly formalised across different organisations. Following the terminology of enterprise resource This work was partly supported by the research office of the University of Natal, South Africa, for which the authors are deeply grateful.

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planning (ERP) systems (Kumar and van Hillegersberg, 2000), there are no clear “best practices” defined for such activities as they themselves are often unique, organisation specific, too complex and difficult to define. The management of research at an university is such an activity as there is greater knowledge accumulated about the academic administration of other activities like student records, student fees or examination results. There is a link between legitimacy and validation of models in OR. However, very little work on this problem has been done in the area of IS. In both legitimacy and validation there is a comparison of the aspects of the model with a set of abstract entities comprising values, norms or symbolic reference systems, which are referred to as “code” by Landry et al. (1996). According to the same authors, “the big difference between model validation and model legitimisation is that the code to which the two processes refer is not the same, scientific in the first place and social in the second” (Landry et al., 1996). They proceed to ascertain that while the concern of the OR specialists is with the validation of the model, “for the other stakeholders of a model, it is model legitimisation that is of importance” (Landry et al., 1996). These two issues will be considered separately in the following subsections. It is the belief of the authors that legitimisation and some aspects of validation like conceptual validation can be very useful as additional techniques of IS project assessments enriching the current practice of project inspection. This paper proceeds as follows: Section 2 discusses the issue of validation of software projects, Section 3 reviews the existing understanding on how legitimacy can be enhanced in an IS project and the Section 4 presents some considerations on how adherence to the principles in the previous two sections could have prevented the pulling of the plug of a complex project about the computerisation of the research management function at an university.

Perspectives on the validation of an information system While the issue of validation is discussed generally in the Software Engineering literature (Pfleeger, 2000; Sommerville, 1995), it has not been considered amongst the major topics in the area of IS development to the best knowledge of the authors. Some attention was paid to it in the area of decision support systems (DSS) (Finlay and Wilson, 1997), which can be explained with the close relationship between DSS and Operational Research.

Some aspects of the validation of information systems from a hard systems point of view According to Finlay and Wilson (1996) there is agreement across disciplines that validity is a measure of the “goodness of a final product or outcome”. Validation is the process by which this validity is determined. A complete

review of validation methodologies is beyond the scope of this paper. The same authors present a concise review of the current state of affairs on this issue in many disciplines, including OR and DSS. Their conclusion is that the theoretical writings are not consistent or coherent, and contain over 50 different types of validity in the literature, which leads to confusion (Finlay and Wilson, 1996). A relatively simple and clear pattern for validation in OR is suggested by Landry et al. (1983). It is shown in Figure 1 at the end of the paper. Due to the nature of IS, a similar scheme for validation can be applied to them. The strength of this framework is in the fact that it can be easily adapted to various situations. The text below will provide comments on its elements. However, in some problems, like the validation of DSS, the framework may need extension as was shown by Finlay and Wilson (1996). With respect to conceptual validity, the consideration would be whether the system as a whole is appropriate (Finlay and Wilson, 1996). One can justify the conceptual validity of an IS on the basis of the triangulation framework suggested by Landry and Banville (1992) and Robey (1996). The goals of the organization usually are seen as determinants of the goals of the IS and of the theoretical foundations of the IS methodology to be applied. The latter pre-determines the appropriateness of the IS development techniques involved. Logical validity is about the checking of the analytical verification of the relationships within a model. This is quite a difficult issue in large IS projects.

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Figure 1. A framework for validation in Operational Research

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With respect to the IS methodologies that might be applied, one can note that they are based on foundations which have certain following but have often failed to convince the supporters of the opposing camps in the methodologies movement. This is a further complication of the check for logical validity. It can be suggested here that as a whole an IS development methodology should be considered as soft in nature because of the human element involved in the process, following Checkland (1995). Then there is a shift of emphasis from validation of the data (or the outcomes from the techniques that were used in the building of an IS) to validating the process of combining those techniques in a particular IS development project. Operational validity is related to whether the IS is of value to the client in tackling the problem situation for which the system was built (Finlay and Wilson, 1997). Here, according to the same authors, the check would be about whether the system was available to help with decision making and whether it was sufficiently understandable for the user to explain the system and its outputs. Partial evidence for the operational validity of an information system can be revealed through post implementation interviews. Experimental validity is further treated by Finlay and Wilson (1997) as being comprised of: .

predictive validity when the values of selected output variables will be stored and matched against values that actually occur in the future;

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replicative validity, when past information on selected output variables would be compared with a model’s predictions;

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verification, when checks are made on whether the calculations are performed as intended.

The literature on Software Engineering (Sommerville, 1995) deals predominantly with this type of validity.

On the validity of information systems treated as a soft systems model This paper is concerned mostly with more complex IS projects that involve multiple stakeholders and require the incorporation of multiple perspectives towards a particular problem associated with a particular IS. The latter features usually are associated with a shift towards soft approaches which have been increasingly in the focus of attention of IS researchers over the past decade (Mingers and Stowell, 1997; Nissen et al., 1991). The essence of an interpretivist framework for complex IS project development can be defined as “soft”, following Checkland (1995). Sometimes a soft framework may include even the “hard” traditional techniques in structured or object oriented analysis and design as they can be seen within it

as hermeneutic enablers. Checkland (1995) points, that there is a critical difference “between on the one hand an approach which assumes the world to be a complex of systems, some of which may be malfunctioning, and on the other, an approach which makes no assumptions about the nature of the world, beyond assuming it to be complex, but assumes that the process of enquiry can be organised as a system of learning”. The approach which assumes the world to be systemic is “hard”; the approach which assumes that the process of enquiry can be systemic is “soft” (Checkland, 1995). Further details on alternative, soft approaches to problem solving can be found in Rosenhead (1989). Checkland (1995) has discussed the issue of model validation in soft systems methodology (SSM). His findings can be generalized to other soft approaches and hence for the interpretivist IS methodological approach advocated for complex IS here. He views models in SSM as “epistemological devices” which can be judged for goodness according to whether they are relevant and whether they are competently built (Checkland, 1995). The first question is resolved according to him through the learning process of SSM as one cannot know for sure whether or not a given root definition and model is relevant; one learns his/her way to relevance by going round the cycle of the process of SSM. With respect to the second question, it is rephrased in SSM to whether a pairing of root definition and a model is defensible (Checkland, 1995). On the basis of the previous discussion, one can view that a soft IS development framework used as a learning process leading to a better understanding of the problem situation is more appropriate for complex IS. Jackson (2000) also concludes that an interpretivist soft approach almost always is preferred in the initial stages of complex problem solving which may involve techniques from different methodologies and paradigms (see also Mingers, 2000). Using a similar line of thought like Checkland (1995), it may be claimed that the relevance of an interpretivist approach to the development of complex information systems is proven by the fact that it supports learning in an iterative process. With respect to whether the proposed IS development framework is competently built [the second criterion suggested in Jackson (2000)], one can conclude that it can be defensible if the techniques involved serve complementary purposes and if they are aligned with the overall aim of the system. Thus the traditional understanding about logical validity, operational and experimental validity of an IS that is in its early stages of development are suggested here to be replaced by Checkland’s notion of relevance and competency. The latter, following Checkland (1995), can be only completely proven through practice.

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What is meant by legitimization of an information systems project The view of legitimacy, supported by Landry et al. (1996), assumes that the “code” against which an IS is judged for legitimacy, is socially constructed. Thus it is much less stable across time and across organizational actors. This feature makes it quite difficult to define criteria for achieving legitimacy of projects in OR or in the area of IS. Landry et al. (1996) define a set of seven claims and seven heuristics that can increase the likelihood of obtaining legitimate models, though never guaranteeing it. For the purposes of the evaluation of the potential legitimacy of an IS, the features of the heuristics suggested in Landry et al. (1996) will be adapted slightly so that they can relate to the field of IS in more relevant terms: Heuristic 1. The IS developers should be ready and willing to work in close cooperation with the strategic stakeholders in order to acquire a sound understanding of the organizational contract. In addition, the IS specialists should constantly try to discern the kernel of organizational values from its more contingent part. Heuristic 2. The IS developers should attempt to strike a balance between the level of system sophistication/complexity and the competence levels of the stakeholders. Heuristic 3. The IS developers should attempt to become familiar with the various logics and preferences prevailing in the organization. Heuristic 4. The IS developers should make sure that the possible uses of the IS are well documented. Heuristic 5. The IS developers should be prepared to modify or develop a new version of the system, or even completely a new system, if needed that allows to adequately explore unforeseen problem formulation and solution alternatives. Heuristic 6. The IS developers should make sure that the system developed provides a buffer or leaves room for the stakeholders to adjust or readjust themselves to the situation created by the use of the system. Heuristic 7. The IS developers should be aware of the preconceived ideas and concepts of the stakeholders regarding problem definition and likely solutions. The legitimacy of an IS, by analogy to the respective claim about OR projects by Landry et al. (1996), can be improved by adhering to these heuristics. At the same time, though there is no formal proof for that, it can be deducted that non-adherence to these heuristics may lead to poor legitimacy and the subsequent failure of a project. The case study discussed in the following section illustrates this idea further.

Application of the ideas of validation and legitimization of information systems on a case study The previous discussion of IS validation and legitimization provides a holistic and innovative way for the control of IS project development. A similar process of validation and legitimization can become part of the standard procedures in IS project development reviews. There is no evidence at present that it is considered by those working in that area (see Sauer et al., 2000). The use of the principles of validation and legitimization of IS development is demonstrated below on the example of a project that failed. The most widely used packaged IT product by tertiary educational institutions in South Africa is supplied by a local company, Integrated Tertiary Software (Pty) Ltd (ITS). It did not have a module on research management until recently. The company released at the beginning of 1998 their new research office management component. It was duly evaluated by the university office concerned with this area. However, its functionality was found to be inadequate for the purposes of the research office. As a consequence to that, the university decided to embark on the development of an in house system for management of the research function. The team comprised of lecturing staff working on the project on a part time basis. The project was initiated in the beginning of 1998. As a result of various problems caused by the users and the developers the project was not completed by March 2000 and then the client decided that it should be stopped. The losses in terms of money were minimal as the project was done on the understanding that the funding for it will be seen as a funding for an internal research project and hence did not reflect the salary costs covered already from other university sources. However, the loss of opportunity to improve the management of the research activity had a much greater implication for the university. The full range of reasons that lead to the failure of the project is too long and complicated and will not be discussed here for space reasons. The purpose here is to show that adherence to the principles listed above could have ensured a successful completion of the project within time and budget. The IS project of concern in this case study is a web accessible IS for the administration of the research activity at an university. It involves several functions: .

monitoring of research expertise within the university for the purposes of aligning research strategy with the overall goals of the institution;

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administration of the grants from the university research fund;

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record keeping of publications output by university staff for the purpose of claiming a state subsidy from the Department of Education;

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facilitation of the links of university staff with national and international granting agencies;

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facilitation of networking within the university community on research matters or between it and outside researchers.

The following paragraphs will present a post mortem analysis on how the application of some of the validation and legitimization principles discussed above could have unveiled earlier potential problems with this system for the purpose of avoiding its failure. The following account will be based on ethnographic observations of how this project evolved.

How the validation theory could be applied in this case The issue of computerization of the management of the research function at an university is a very complex activity with many stakeholders: the university research community, the research office administration, the university management, the national, private and international funding agencies and the national ministry of higher education as well as industry. Due to the complexity of the problem, an interpretivist approach towards IS requirements determination would have been more appropriate. However this was against the culture of some of the developers and that opportunity was not utilized. How can validation principles outlined in Section 2 earlier apply to an IS project at the early stages of its development? Operational validity cannot be measured at such early stages before the phase of industrial usage of the system. Experimental validity was practiced up to the level of unit and subsystem testing, as the project was never completed to a stage when the whole system could be tested. Logical validity of the data relationships was also not verified beyond the scope of individual subsystems or pairs of subsystems. The idea for logical process validation along the lines of thought expressed by Checkland (1995) as specified earlier was not explored as no soft systems techniques were used by the developers. Conceptual validation plays much greater role for the early detection of problems with IS development projects and hence it has the greatest potential for avoiding project failures at the early stages of a project. The reasons why this opportunity could not be used is in the fact that the broader vision of the developers that the system should take care of any research projects funded internally or externally. That was documented in the original conceptual data model for the system. It was, however, changed after 1 year by the client in a way reflecting only the administration of internal research project funding. At the same time, the university research office started preparations for the establishment of the new office for management of external research contracts whose data needs were already reflected in the original data model for the system. The reasons for this situation were related to the insufficient involvement of the top management of the university research function. In addition, over the two years the elected post of a Chairman of the University Inter-Faculty

Research Committee was occupied in quick succession by three different persons who had differing ideas on the details related to this project like what data should be involved in the assessment research project proposals. Thus the possible alignment of the goals of the project under concern here with the goals of the bodies administering various aspects of the research activity did not materialize. The developers insisted that the system should be designed as an open system, taking care of the links with outside bodies like the Department of Education. That idea could materialize due to the fact that the client was concerned mostly with the narrow computerization of its immediate tasks. The lack of willingness on the client side to consult with the developers lead to the purchase of a separate system on a different but related task. Its functions could, however, be easily incorporated within the project described here if the original conceptual data model of the designed system was accepted by the client. The problems with this project did not emerge as a result of technical incompetence of the developers though there were some difficulties related to the fact that at the beginning of the project the principles of web technologies used in this project were still relatively new and poorly documented in the literature. Hence extra effort had to be put into uncovering the necessary technical information on the development techniques. The major issues were the lack of effective top management support for reasons outlined above and the lack of adherence to the heuristics ensuring legitimacy as suggested in Landry et al. (1996). These will be discussed further in the following section.

On possible application of the legitimization heuristics to the case It is clear that there was insufficient cooperation with the strategic stakeholders in this project. In particular very little involvement was attempted by anyone not directly related to the administration of the university research project funding and the process of getting a subsidy for research publications from the national department of education. The already mentioned decision to purchase a separate packaged solution for the new office for management of contract research is the evidence for that. The organizational values were not completely grasped by the developers as they had the wrong assumption that the values of the clerical staff in the Research Office are reflecting the guiding values of the university with respect to the proper functioning of this system. In spite of the fact that the developers tried to expand beyond the narrow view on the problem and to cover the needs of the university research community as a whole, they were often reminded that the primary purpose of the system is to provide for the clerical needs of administering the research activities within the research office. Thus the desire of the developers to reflect

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the recommendation in the second heuristic of Landry et al. (1996) as stated earlier, lead to the extreme simplification of the original data model designed initially to provide the future flexibility of the system. As a result the subsequent version of the data model was only catering for the narrow needs of the section of the research office dealing with the administration of the internal research fund. While every effort was attempted by the developers to become familiar with the various logics and preferences prevailing in the organization (heuristic three above) it was not easy for them to understand why the application form for internal research funding had to be modified substantially by the client three times over a 2 year period. The last three heuristics suggested in Landry et al. (1996), were adhered to by the developers to the maximum possible degree. However, it could only be done under the organizational circumstances that prevailed, some of which were communicated earlier. However, the user requirements were often communicated in small portions to the developers and were often changed drastically. The major reason for that seems to be the fact that the project was never seen as a top level priority by the ordinary staff of the research office. Each time when they had something imminent related to their day to day operation any action related to this project from their side was delayed. Another issue was the slow approval process of the user requirements by the respective committee. The latter is an indication of the need to adapt organizational procedures to the dynamics required by the contemporary IT dominated environment and the dynamics of software development. The analysis of the case study shows that the proposed combined approach to validation and legitimization can serve the purpose of providing a learning environment leading to better understanding of the nature of the relationships between the factors affecting a software development project.

Conclusions The issue of computerization of the management of non-routine management tasks in organizations is of growing importance since most of the shelf packaged solutions do not cover such tasks. In addition, the existence of such non-computerized tasks in an organizational environment characterized by a high degree of use of other information sub-systems produces additional inconveniences for the organization as a result of the lack of integration of its data and broader organizational memory. The complexity of such non-routine tasks requires greater attention towards their validation and legitimization. This paper provided a discussion on the validation and legitimisation of IS in general. It is illustrated on the case of a project about the computerisation of

research management at an university. It aimed to show that traditional aspects of model validity and legitimisation in OR can be applicable to the field of IS. However, the validation considerations in this case sometimes need considerable modification since a more appropriate way of viewing complex IS projects is through an interpretivist viewpoint. In particular, the traditional notions about logical validity, operational and experimental validity of an IS that is in its early stages of development are suggested to be replaced by Checkland’s notion of relevance and competency. The latter, following Checkland (1995), can be proven through practice. Future research may focus on additional field research of the extension of the ideas on validation and legitimisation suggested here. Another direction of future work is linking legitimisation to research in IS success, which seems to ignore this important aspect of IS implementation (see Drury and Farhoomand, 1998). The presented post-mortem application of the combined view of validation and legitimisation with respect to a failed IS project serves to conclude that adherence to the principles of validation and legitimisation could have increased the chance for success of that particular project.

References Checkland, P. (1995), “Model validation in soft systems practice”, Systems Research, Vol. 12 No. 1, pp. 47-54. Drury, D.H. and Farhoomand, A.F. (1998), “A hierarchical structural model of information systems success”, INFOR, Vol. 36 No. 1/2, pp. 25-40. Finlay, P.N. and Wilson, J.M. (1997), “Validity of decision support systems: towards a validation methodology”, Systems Research and Behavioural Science, Vol. 14 No. 3, pp. 169-82. Jackson, M.C. (2000), Systems Approaches to Management, Kluwer/Plenum, Boston. Keys, P. (1997), “Approaches to understanding the process of OR: review, critique and extension”, Omega, Vol. 25 No. 1, pp. 1-13. Kumar, K. and van Hillegersberg, J. (2000), “ERP experiences and evolution”, Communications of ACM, Vol. 43 No. 4, pp. 23-6. Landry, M. and Banville, C. (1992), “A disciplined methodological pluralism for MIS research”, Accounting, Management and Information Technology, Vol. 2 No. 2, pp. 77-97. Landry, M., Banville, C. and Oral, M. (1996), “Model legitimisation in operational research”, European Journal of Operational Research, Vol. 92, pp. 443-57. Landry, M., Malouin, J-L. and Oral, M. (1983), “Model validation in operational research”, European Journal of Operational Research, Vol. 14, pp. 207-20. Mingers, J. (2001), “Combining IS research methods: towards a pluralist methodology”, Information Systems Research, Vol. 12 No. 3, pp. 240-60. Mingers, J. and Stowell, F. (1997), Information Systems: An Emerging Discipline, McGraw- Hill, London. Nissen, H-E., Klein, H.K. and Hirschhleim, R. (Eds) (1991), Information Systems Research: Contemporary Approaches and Emergent Traditions, Elsevier Science Publ., New York.

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Pfleeger, S.L. (2000), Software Engineering: Theory and Practice, 2nd ed., Prentice-Hall, New Jersey. Robey, D. (1996), “Research commentary: diversity in information systems research: threat, promise and responsibility”, Information Systems Research, Vol. 7 No. 4, pp. 400-8. Rosenhead, J. (Ed.) (1989), Rational Analysis for a Problematic World, Wiley, Chichester. Sauer, C., Jeffery, D.R., Land, L. and Yetton, P. (2000), “The effectiveness of software development technical reviews: a behaviorally motivated program of research”, IEEE Transactions on Software Engineering, Vol. 26 No. 1, pp. 1-15. Sommerville, I. (1995), Software Engineering, 5th ed., Addison-Wesley, New York.

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Development of an autonomous spacecraft for planetary exploration

Development of an autonomous spacecraft 715

Gianmarco Radice Department of Aerospace Engineering, University of Glasgow, Glasgow, Scotland Keywords Cybernetics, Autonomy Abstract The purpose of this paper is to present a new approach in the concept and implementation of autonomous micro-spacecraft. The one true “artificial agent” approach to autonomy requires the micro-spacecraft to interact in a direct manner with the environment through the use of sensors and actuators. As such, little computational effort is required to implement such an approach, which is clearly of great benefit for limited micro-satellites. Rather than using complex world models, which have to be updated, the agent is allowed to exploit the dynamics of its environment for cues as to appropriate actions to achieve mission goals. The particular artificial agent implementation used here has been borrowed from studies of biological systems, where it has been used successfully to provide models of motivation and opportunistic behaviour. The so-called “cue-deficit” action selection algorithm considers the micro-spacecraft to be a non-linear dynamical system with a number of observable states. Using optimal control theory rules are derived which determine which of a finite repertoire of behaviours the satellite should select and perform. The principal benefits of this approach is that the micro-spacecraft is endowed with self-sufficiency, defined here to be the ability to achieve mission goals, while never placing itself in an irrecoverable position.

Introduction The development of autonomy technologies is the key to three vastly important strategic technical challenges facing future spacecraft missions. The reduction of mission operation costs, the continuing return of quality science products through increasingly limited communications bandwidth and the launching of a new era of solar system exploration, beyond reconnaissance, characterised by sustained presence and in depth scientific studies. New deep space missions, coupled with the challenge to do things “faster, better, cheaper” have highlighted the need for increasingly more autonomous spacecraft and rovers. Spacecraft autonomy will bring significant advantages by improving resource management, increasing fault tolerance and simplifying payload operations. Also, when considering the communication delays in deep space missions, the requirement for autonomy becomes clear. Ground stations and controllers will not be able to communicate and control distant spacecraft in real-time to guarantee precision and safety. There is a need, therefore, to provide autonomous and semi-autonomous computational capabilities to enable further

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deep space missions. One approach to autonomy is concerned with the modelling and building of adaptive autonomous agents, which are systems that inhabit a dynamic, unpredictable environment in which they try to satisfy a set of goals. This behaviour oriented approach is appropriate for the class of problems that will face the new generation of micro-satellites currently under development for Earth monitoring and interplanetary missions. These missions will require a high degree of autonomy to meet stringent cost and performance goals. An autonomous micro-spacecraft has multiple integrated tasks such as navigation, battery charging, etc. Similarly neural network, fuzzy logic and expert systems, although successful in some terrestrial fields, such as camera focusing, automobile cruise controls and subway automation, are extremely difficult to validate to ensure the survival of the spacecraft and are software intensive. In contrast recent developments in artificial agents borrow heavily from ethology where the agents respond directly to environmental stimuli. The satellites are situated in their environment, typically orbiting a planet, and connected to its problem domain directly through sensors and actuators. It then has to monitor the environment and determine in isolation what the next problem or goal to be addressed is. In the approach presented in this paper such an artificial agent is proposed that provides a method for action selection that balances the demands of the satellite users – gathering or transmitting data – and the actions necessary to guarantee the survival of the spacecraft – charging the battery and thermal control. The spacecraft is modelled as a non-linear dynamic system with a state space consisting of key internal parameters such as battery charge, memory level and internal temperature. The state space will have a set of lethal limits that define the useful operating domain. A finite repertoire of behaviours is then used to generate a set of actions to control the internal dynamics of the spacecraft. A cost function, which provides the measure of the deviation of the spacecraft from its normal equilibrium state space operating point, is then generated. Applying Pontryagin’s maximum principle from optimal control theory we obtain a set of optimal action selection rules. The action selection algorithm must then maintain this equilibrium in the presence of perturbations due to the spacecraft’s own behaviour or from environmental change. For example switching on the heater during eclipse will maintain the internal temperature level, but at the same time drain the battery charge.

The resource problem Self-sufficient, autonomous agents, just like people or animals, have to decide how to allocate environmental and internal resources among a number of possible uses. It is evident that to maintain its viability and effectiveness the micro-satellite should perform a basic cycle of activities. The satellite will have to work, by storing data and downloading it to the ground station, while still

remaining functional, by recharging the battery and maintaining the internal temperature when necessary. The satellite therefore, has to control its behaviour so that it never allows any of its basic state variables to reach a lethal limit.

The state space The state space model, proposed by Sibly and McFarland (1974), for biological systems, allows us to characterise the satellite as a minimal set of internal variables that can completely describe its state. In such a description of a biological system we could possibly identify hunger, thirst, temperature, hormone level, as essential physiological state variables. For a satellite we could identify energy, internal temperature and memory level as being essential state variables (Gillies et al., 1999). These variables sit within a Euclidean vector space as its orthogonal axes. Within this space there will be regions that the satellite can physically never encounter, for instance negative memory level or above the maximum battery level, and regions that, should the satellite cross into, it would cease to function, such as below the lower or above the higher possible operating temperatures. The boundaries that separate the regions that are fatal to the satellite from those that are not are called lethal limits as shown in Figure 1. The task of the satellite within such a model is therefore to maintain the homeostasis (local equilibrium) of its own state variables under the perturbation of its own behaviour. The spacecraft also has to monitor the environment’s impact on its resources, for example, during eclipse the satellite must activate the heater to stay above the lower lethal temperature while also draining the battery.

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Figure 1. An example of a possible three-dimensional state space with local origin O. The current state is indicated by the vector P. The boundary volume V separates the possible state values from the lethal limits. T is a possible trajectory the satellite could take within the lethal region

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Pontryagin’s maximum principle Pontryagin approached the problem of optimal control by defining a state function H, now called the Pontryagin or Hamiltonian function. H depends on some objective function and on the equations that characterise how behaviour determines the rate of change of the state space variables. The maximum principle states that the problem of finding the path of least cost is the same as the more direct problem of maximizing H. If we consider a state vector x Pontryagin’s maximum principle states that to minimize some cost function C such that Z T C dt ð1Þ 0

a control function u must be chosen so as to maximize the Pontryagin state function H H ¼ l T fðx; u; tÞ 2 Cðx; u; tÞ

ð2Þ

with the constraint x_ ¼ fðx; u; tÞ where the function fðx; u; tÞ defines the rate of change of the state variables. The co-state vector l is a set of Lagrange multipliers introduced to satisfy the control equations and given by the equation

›H l_ ¼ ›x

ð3Þ

and a similar equation can be found for the rate of change of the state x_ ¼ 2

›H ›l

ð4Þ

This formulation will be used later, following the introduction of the cost function. Availability and accessibility Two parameters, the availability r and the accessibility k model the resources in the environment. The availability is associated with the density of the resource in the environment. The satellite is equipped with sensors that determine the availability ri of any resource ði ¼ 1 2 nÞ: For example, when the satellite detects, via a sun sensor, that it is in sunlight r sun ¼ 1 while we have rsun ¼ 0 if the satellite is in eclipse. The availability rtransmit ¼ 1; when the satellite detects through a global positioning system or up-link signal, that the ground station is present, otherwise rtransmit¼0. Similarly rrecord ¼ 1; if the satellite is flying over the target area and rrecord ¼ 0 if not. The accessibility is

associated with the ease with which the satellite can obtain the resource through its behaviour. The accessibility ki models the rate at which the satellite can perform a certain task ði ¼ 1 2 nÞ: For example, the rate ksun at which the satellite can charge the battery by pointing towards the sun is the maximum array power output. If the satellite detects that the solar array is damaged then ksun is lowered: for example if 50 per cent of the array fails at t ¼ tfailure ; then ksun ðtfailure Þ ¼ 0:5ksun ðtlaunch Þ: Similarly, we will have ktransmit, and krecord defined by hardware constraints before launch. Should the satellite suffer an antenna, transmitter or recorder failure these parameters would be lowered accordingly.

Cost function In this section, we select a quadratic cost function associated with the state space of a satellite possessing three essential state variables: battery charge, memory level and internal temperature. To obtain optimal behaviour Pontryagin’s maximization principle is used. The model formulated is the following b_ ¼ 2rsun us

_t ¼ 2rtransmit ut

_ ¼ 2rrecord ur m

ð5Þ

with 0#

us ut ur þ þ #1 ksun ktransmit krecord

ð6Þ

where ˙b represents the battery charge deficit, ˙t represents the data transmission ˙ the data recording deficit. A deficit is defined as the magnitude of deficit, and m the difference between some current state variable and its nominal equilibrium value. The variables rsun, rtransmit, and rrecord are the availabilities of the resource, ksun, ktransmit, and krecord are the rates at which the satellite can perform a task and us, ut, and ur are control variables. The cost function for the satellite is then hypothesized to be: _2 C ¼ b_ 2 þ _t 2 þ m

ð7Þ

The choice of a quadratic function over any other convex function has been made for mathematical simplicity. It has to be noted that the cost function has the desirable property that the cost of possessing any particular deficit increases more rapidly the further away from the homeostatic equilibrium point the satellite’s variable lies.

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Action selection algorithm To ensure its survival the satellite must never drain the battery below the lower lethal limit. To achieve battery control the satellite battery deficit ˙b is a measure of how much the batteries have discharged. Pointing the solar panels towards the Sun and charging the battery may reduce this deficit. The payload ˙ and will be associated with a work deficit composed of a recording deficit m transmitting to Earth ground station deficit t. McFarland and Spier (1997) have shown that a quadratic cost function and Pontryagin’s maximum principle can be used to find the optimal behaviour. They found that the behaviour to be performed is associated with the highest d·r·k product summarizing the problem of optimal control as: deficit £ availability £ accessibility. _ sun ·ksun  ) charge battery Max½b·r Max½_t·r trans ·ktrans  ) transmit to ground station

ð8Þ

_ rec ·krec  ) record data Max½m·r The satellite selects the optimal behaviour by computing the various deficits, taking environmental cues for resource availability and accessibility and finally computing the d·r·k product associated with each behaviour. The optimal behaviour at any time is therefore, the one that yields the highest of the above products. This algorithm also shows a degree of opportunism, because it considers environmental factors together with internal deficits. For example, if the battery deficit is low and the work deficit is high, the satellite may still opt to charge the batteries if sunlight is available and cues for doing work – visibility of ground station or target area – are low. Such opportunism is one of the major benefits of this algorithm and is difficult, if not impossible, to code into conventional artificial intelligence engines.

Case study The satellite will operate in different orbits and is considered to have three rotational degrees of freedom that can be controlled by reaction wheels. The electrical power system consists of a solar array, battery and several electrical loads. The payload is a camera that records at a steady rate when active and a radio transmitter to broadcast data to the ground station. The individual subsystems are coupled together: switching the transmitter on drains the battery and reduces the amount of stored data. The spacecraft is controlled by switching the camera, the transmitter and an internal heater on or off, and commanding the attitude control subsystem to track one of the three targets – Sun, Earth ground station and Earth target – by activating the reaction wheels. The spacecraft has an internal heater which may be switched

on or off independently of what other task the spacecraft may be performing; the heater is automatically activated when the temperature drops below a certain threshold value fixed at 240 K and is not commanded by an action selection algorithm. The heater however, drains the battery, and therefore, indirectly influences the action selection process. The spacecraft selects the optimum behaviour at any time by evaluating the deficits of the state variables – battery and memory level – assessing the availability and accessibility of the environmental resources – Earth ground station, Sun and Earth target – and finally computing the d·r·k product. The spacecraft will switch between different behaviours when the difference between two d·r·k products surpasses a fixed threshold. In Figure 2, we can see the complete model. The user selects the ground station and target co-ordinates within the appropriate blocks. Other parameters that can be defined by the user are the orbital parameters – apogee, perigee, inclination, ascending node and perigee argument – the inertia moments (I1, I2, I3) of the spacecraft and the free parameters a and k which influence the pointing control algorithm. Finally, the user can change the state variables lethal limits – internal temperature, memory space and battery power. To test the action selection algorithm the spacecraft is inserted into a low Earth polar orbit. The orbit is circular with a 500 km altitude, and an inclination of 868. There is one single ground station presently placed at 57.38 latitude. There are also six different target areas

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Figure 2. Complete simulink model

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Figure 3. Internal temperature

Figure 4. Battery level

situated at 808 latitude and evenly spaced in longitude between each other. The simulation runs for just over 90 orbital periods, which equates approximately to six mission days. In Figures 3 – 10 we can see the results of this. As can be noted from Figures 3 – 5 the temperature oscillates as the spacecraft goes in and out of the eclipse part of the orbit – the temperature increases while the spacecraft is in direct sunlight, and the temperature decreases while the spacecraft is in eclipse. When the internal temperature reaches the threshold value of 2408K the heater automatically switches on to maintain the temperature above the minimum

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Figure 5. Sun availability

Figure 6. Stored data

lethal level. The threshold value is selected by the user and is quite arbitrary although, this value is linked to different spacecraft components that have an optimal operational range. It can also be noted how the spacecraft charges the battery when in direct sunlight by pointing the side mounted with the solar array towards the Sun. It is interesting to note what happens during the eclipse phase of the orbit to the battery charge level. We can see different slopes as the battery charge level decreases. This is due at first because the transmitter or payload are active; when either is operational there is a demand on the battery for their activation. After that, there is a period during which the transmitter or

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Figure 7. Target availability

Figure 8. Transmitted data

payload are not active and the discharge in the battery level proceeds at a lower rate. When the heater is then turned on to maintain the internal temperature, the battery is discharged at an increased rate. Several interesting comments can be made by looking at Figures 6 and 7. First of all it should be noted that the spacecraft does not fly over the six different target areas during one orbit period. There are then two interesting differences that we can highlight while looking at the stored data and the target availability. When the availability of the resource is high the spacecraft records significant data. However, when the availability of the target area is low the spacecraft may opt not to image. This is because the spacecraft may have more

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Figure 9. Ground station availability

Figure 10. Spacecraft tasks

pressing needs, or because recording data during a low availability flyby is not an efficient activity from an energetic point of view. Similar considerations can be made by looking at Figures 8 and 9. Again the spacecraft does not see the ground station during each orbit, and it actually goes approximately five orbits without ever passing over it. We can see how, when the ground station has a good availability the spacecraft transmits significant data. On the other hand when the ground station availability is poor there is not much data transmitted back to Earth.

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In Figure 10, we see the spacecraft “at work” performing the different behaviours – charging the battery, recording data, transmitting data and drifting. During every orbit the spacecraft charges the battery when in direct sunlight. This is because the battery level has just been drained by the activation of the heater during the eclipse. The spacecraft will however, not record or transmit data during each orbit; this will depend on the strength of the environmental cues and state variables deficit as explained earlier. The spacecraft also has an additional behaviour which is not directly linked to the action selection algorithm: drift. The spacecraft will drift when it is not performing any other behaviour. The spacecraft is not performing other behaviours because the availability of the environmental resources is null or low; therefore, it is either impossible or energetically not viable to perform the task. Alternatively, if the availability is high the spacecraft may still opt not to perform the behaviour if the deficit of the associated state variable is low, meaning that there is little need for the spacecraft to acquire this resource.

Conclusions We have introduced a scheme for sequencing tasks on a spacecraft. The action selection algorithm is easily implemented by virtue of its computational simplicity. Moreover, the strategy is derived from optimal control theory. The model is however somewhat simplified, and an actual spacecraft may have several more operational tasks that may be autonomously controlled or be scheduled or commanded by ground control. This method however, may easily incorporate additional tasks which will either form part of the action selection process, or which can be scheduled at a particular time by setting the d·r·k product to equal unity at a fixed time. Adding extra tasks is straightforward; each new behaviour will be given a deficit, availability and accessibility. The resulting behaviour will always be the one with the highest d·r·k product. A significant advantage of such a method is that the spacecraft measures environmental parameters (such as the presence of sunlight or ground station) and internal parameters (such as battery charge and memory level). Complex models of the environment are not required to select the appropriate behaviour. Also it is not necessary to have complex models of the spacecraft components and subsystems. If we consider the battery charge as an example, the model used for it is not directly relevant to the performance of the action selection algorithm; the algorithm uses the measure of the battery charge rather than using a model of the battery charge. Therefore, we can expect that the modelling of more complex and numerous spacecraft subsystems will not change the qualitative behaviour of the algorithm. The study of such a method can be extended to a constellation of satellites, in which the individual spacecraft co-operate with each other. The co-operation may be as simple as

passing data to each other when the memory level is full and the ground station is not available, or as complex as having one master spacecraft commanding the other slave spacecraft in the constellation. The method, because of its computational simplicity, can also be easily applied to planetary rovers and future “satellites-on-a-chip”, where the algorithm and behaviours can be hardwired into the spacecraft. References Gillies, E.A., Johnston, A.G.Y. and McInnes, C.R. (1999), “Action selection algorithms for autonomous micro-spacecraft”, Journal of Guidance Navigation and Control, Vol. 22 No. 6, pp. 914-16. McFarland, D.J. and Spier, E. (1999), “Basic cycles, utility and opportunism in self-sufficient mobile robots”, Robotics and Autonomous Systems, Vol. 20, pp. 179-90. Sibly, R.M. and McFarland, D.J. (1974), “A state approach to motivation”, Motivational Control System Analysis, Academic Press.

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“How much cybernetics can you handle?” James N Rose Ceptual Institute, Minden, NV, USA Keywords Cybernetics, Human-computer interaction Abstract Humanity is innately a composition of primitive cybernetic translations/transmissions to begin with, from atoms through organizations of civilization. The last 75 years has seen us recognize and then extend those relations into sentience and sociological practicalities. It is the author’s intention with this paper to shed some new light and introduce new concepts into the field and understandings.

Introduction and discussion Humanity is innately a composition of primitive cybernetic translations/transmissions to begin with, from atoms through organizations of civilization. The last 75 years has seen us recognize and then extend those relations into sentience and sociological practicalities. It is the author’s intention with this paper to shed some new light and introduce new concepts into the field and understandings. Cybernetics is semiotics is complexity is meaning. Essentially, it is communication and correlation among different domains and dimensional bounds. By introducing the concepts of “fluences” and “correlettes” to improve on understandings of dimensionality and on the relations that bind and enable cybernetic percepts, it’s hoped that we will have a better fully paradigmed architecture on which we can significantly improve our comprehensions and engagements re “existence”. Specifically, re knowledge management concerns and global social polity-health, begun and sustained for the benefit of current and future populations. “I greet you, respected ancestors, dear companions, and cherished future.”

Kybernetes Vol. 32 No. 5/6, 2003 pp. 728-737 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443815

We were all present in the furnace of the Beginning, which is the Shinn-yu Event, using the Nippon ideogram concept of “motion” and the seminal event when all time and space “became”. We swirled and intermingled as potential, and then as realized forms, in sequences of titanic stars and then in histories of atoms and molecules and metabolisms, which assembled and reassembled in explorations of process. No matter our individual lineage, we are literally made of the ancestors of our existence, and we will contribute to the shapes and comprehensions of all progeny who succeed us. Sensations and thoughts.”. . . This recognition about the qualities and nature of our existence is the product of those qualities as educed through the actions of information

exchange and transformation. The experience is filtered by local existential beings within the manifold which provides all first order capacities and mechanisms. This arrangement is therefore called the Integrity Paradigm because it recognizes behavior and performance primacy which is based on requisite systemic consistency and coherence – not a happenstance of human definition but on functional necessity. It is addressed through the Ceptual Philosophy, relying on a memetic and semiotic awareness used by ancient Latin language developers and their forebears among others, who identified that ideas are fundamentally those event-relations which are at once exterior to us and also gathered in – made part of us. “Concept” literally means – “with that which is gathered in”. It is literal and figurative “incorporation”, “ingestion” of information relations or energy and made constituently part of us. Such activity is the seminal act of all existential being. For at the core is – “gathering in” – encountering and being substantively modified by “encounter”. This is the foundation of our existence. More so than any analysis that comes afterwards. It is firstly sourced from amenable interactive events, resulting in effective ingestion of experience and knowledge of that which shares the universe with us. You might call it the “binding capacity”, something we share in common with even the fundamental particles. We all “encounter” and are changed by all such encounters, as understood through the light of both Relativity and Quantum Mechanics and plain common sense. Whether as a whole or in part, variance distinguishes the phenomena of events and encounters. Therefore – by existential requirement – systems are “informed” both through ingestion and exgestion transactions, since the standard for what information “is” must include the Bateson concept of some smallest distinguishable variance (internally held or externally noted) – the “difference that makes a difference” – as well as the Shannon identification of a probability which orders versus dis-orders a given system. Both ceptual notions involve pertinence, meaning and impact for an integrity, where Bateson’s perception, though non-mathematical, acknowledges the symmetry of information exchanges, while Shannon’s version of information hints at it but mathematically conflates information with thermodynamic asymmetry and is therefore more limiting even if better scientifically designated. The semiotic, cybernetic and even practical challenge for us and the future then is to reconcile these diversities as “local alternatives” within a larger holism. Another route in to this challenge – if not its solution – derives from certain information got from observation functions per se and completed comparisons about them. We call these deductions, inductions, and subsequent generalizations “models”, and if pandemic enough – “laws of nature”. Made cautious by generations of experience where new information led to replacing models, and then by Godel’s “Incompleteness Theorems” that formalized the investigative modeling process, we assume that yes, there are

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rules of performance that seem to pervade the universe, but instead of jumping to absolute and final pronouncements, we have taken to overlaying a recognition that models are typically incomplete, open to revision and improvement, being additionally constrained by human thought invention and parochial limited perceptions. I think that way of thinking tends to hobble us as much as it helps limit noise or prevent errors or misleading conclusions. It prevents us from looking at given information and inventively reorganizing our appreciations of the resident content and interpretive content that is there but may not be obvious under prior schemata. My alternative cybernetic/general systems notion starts with the sensibility that models – any and all of them – present some viable arrangement of information at hand. That’s what makes them feasible and acceptable in the first place, before amendments or superceding paradigms. Even ones that seem inappropriate in the light of subsequent findings. So what we have in our models are essentially “different windows” that come out of a single and shared commonality. One which is necessarily capable of having all these diverse progeny. Which situation means that, models – both mathematical and non – indicate an existential presence which embodies “qualities” – call them relations and performance operations – that must be pandemicly real and residential “a priories”. Which are “theoretic” in as much as divining them requires semiotic intervention and association, but, they must also have an independent presence completely antecedent to all the tangible and relational phenomena which flowed out of them and which we identify them from. Which brings us to certain practical knowledge that requires a subtle but crucial shift in comprehension since the phenomena in question relates directly to the nature of manifested existence. It is the thesis of current physics and math that entities are “carriers” of forces. A particle or some instantiable entity – a wave or knot of dimensions – holds quantae of forces in some unexplained but rigorously associative way. I look at the same information set, those notions are derived from, but using the new perspective, identify a conceivable alternative. Relying on relativity notions about spacetime that “relative relations” exist which are true at any and all velocities, the unavoidable conclusion is that the fully connective feedback association of essential dimensionality with matter/energy in it and of it, points to “forces” being dual with dimensionality, where dimensionality itself is the source and instantiation of all subsequent “fundamental force(s)” even in the absence of energy or matter being present; which things are byproducts – the emerged progeny of characteristics and qualities that were already resident in existential and intangible but real Potentia. The relation that flows out of this primacy is that waves and particles are in fact cybernetic instantiations, and are therefore not “carriers” in the sense that

they are hardware and force is some separately “carried” software, but rather, than that energy/matter are localities of dimensions – configured in regionally compacted or coded/decoded ways – which exist therein within dimensional manifolds that are on one hand, their source and on another, their environment. We have in this paradigm then a universe which has both open and closed boundaries aspects and we are pressed to consider the mathematical and performance relations commensurate with both – not “either”. Cousins of this perception are Cantorian transfinities and Zadeh (fuzzy) Logic, where computational models also cope with the interactions, content and relations of systems which have order but are ostensibly unbounded and have plural though connected frames of reference. Besides this, I will mention quickly that I use the label Stochastic Logic to umbrella this manner of thinking, which includes quantum mechanics and its notions of superpositioning [UIU, 1992]. Though we deal with specific “sufficiently bounded” systems as if they were sealed isolate entities, re Heisenberg and re Einstein the essential property of existence is that nothing is existentially independent, be they “things” or fluencial, existential domains. And therefore, the essential activity of this totally integral integrated entity called universe is the activity of communication, where some might intone further that this also makes existential sentience a property of everything, from the simplest to the most involved and hyper coded. I agree, but am here committed to describing how that translates into a substantive dynamic architecture of fluencial timespace. The proffered arrangement existence points to emerged energetic/ materialistic qualities arising from what was once considered intangible or purely existential; and more recently, to what was only casually assumed to be humanly modeled information and therefore random if not happenstantial artifact which could be conceptually reformed or re-mastered in any convenient but not necessarily permanent way, as new discoveries come along to replace and improve prior stepping stones. But if the tenet of my arguments is true, then we have to begin to understand how conceptual space can – and through very specific mechanisms, forms and processes – become materiality, energy and the performance behaviors, all of this Potentia eventually displays in the universe and through all the tiers of existential arrangement. There just may be a ceptual terra firma from which existence manifests. Superstring theory, even Bohm-ian explicate and implicate domains, come from such assumed properties of pre-space, but have gone surprisingly undefined even by those leading edge thinkers. Essentially we need to revamp ideas about what “dimensions” are, being less “rigid architecture” or even “alternative parameters” as much as they are “elastic topology” and “alternative parameters”. This is important since topology work deals with such information pluralisms and normal malleable rearrangements of them as well.

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Toshihiko Ono of University of Tokyo and Hosei University, has also been exploring this, there via Reimann geometry, and has stated In my opinion, what is more doubtful is our vague understanding on the relationship between a field and particles. It is a challenging problem and must not be confused with that between a wave and a particle. [“Existence” dialogue list, yahoo.com]

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In 1992 I proposed the term “fluences” to replace “dimensions” for both practical and conceptual/semiotic reasons in order to deal with this transformation of thinking. While conceptually similar to “dimensions”, fluences are envisioned as elastic and are not rigorously independent from each other even though distinguishable. In a sense, they are attractor variables that meld and blend with one another in plural ways. The word “fluence” therefore conveys dynamic semiotic and linguistic relational attributes in addition to numerical ones. It does superpositioned multiple cybernetic duty and more. It conveys qualitative information concurrent with quantitative information which makes it more utile and meaningful – comprehendible in plural contexts – with a linguistic accessibility that the more static term “dimension” does not afford. Its vernacular language connection offers descriptive adjectival alternatives that mathematical specificity finds burdensome to express. So melding the two can only expand our cognitive and descriptive range and competence. There is dynamic and mathematically relational information conveyable in such terms as “confluence” “influence” “transfluencial effects” “fluencially inductive phenomena” and so forth, which, much more easily than terms like “bidirectional” “interdimensional” “dimensionally orthogonal” etc., gets across the activities that dimensional (sic) manifolds are enactors of, not just some scaffolding on which to hang energy and matter, as if they were separate “behavers” existing in a neutral template. Such is not the nature of existence we ascribe to with relativity and quantum mechanics and supersymmetry string theories. We already embrace a notion of the universe as having subliminal fundamentals which both produce and is the playground for all energy and matter. So to shift into a combinant language that bridges formal recognitions with easier ceptual expressions – ones quite natural and fundamentally intuitive – is quite the proper step to take. As a bonus, the general paradigm proposed here enables us to parse out several different kinds of “information” and introduces – or rather, extends – the conditions/events notion that the presence of a single datum or even a whole single fluencial continuum, will impart into systems, new vastnesses of information and relations that compound with those already present. In both enumerative ways and relational ways, individual factor/parameter/fluence introduction accomplishes (in compounded ways) exactly what factorial multiplication does. When “single” datums are factors, then intramural manybodied relations dominate. When “single” domains are the factor, then new

wholecloth relation fields are generated – they “emerge”. With the added condition for both that in the general paradigm they must be included in the “register-potential” for operational presence, even if such factor states are not present or used in active mathematical arrangements. Just as the number zero acts as an enumerative “value”, is also acts as a place-holder in the midst of a continuous domain, in which locus every other possible value can be substituted and thus instantiated. Whether as a base number line or in exponent location or superpower location, each locus represents a domain of fluences and each individual value placable there is a particular fluencial extent. So we have the ability now to deal with information Potentia as an unbounded wellspring of available information and novel relations. It is even utile in coding and fluencial compression events such as wave collapse/reconstitution, and can be seen as the phasespace in which particle/wave “duality” is really alternative fluencial arrangements of selfsame fluencial packets of energy/information. When the fluencial environment or conditions vary, so will the expressed form of the packet, which conforms to what is available. This means that dimensional , fluences are both some sort of physical reality and n-number of parameters in a possibility space – really quite closely aligned, and not disparate characterizations. We no longer have to separate one as a meaningful pertinence and the other as a mathematical artifact. They are one body showing different attributes. And, they are treated with full presence and capacities even if dormant in certain calculation postures (i.e. alternative fluencial forms). Essentially, this identifies the existential/transcendental relationships which bridge physics and metaphysics. Cybernetics becomes the performance methodology to accomplish the best of the best thinking hinted at by general systems intuitions. And the philosophy of it – which rendered the meaning and interpretive associations of the higher ordered motivational components of behaviors and systemic performances – could be the Integrity Paradigm. Because fluences are now appreciated to have in common the innateness of being “the difference that makes a difference” – “information which impacts information” – we can now evaluate the content of iota/minima and of continua and of all relations that span through them, as being zero order, first order, second order, third order, and so on cybernetic correlations where non-uniform scalarity is both an event pressure – aka “force” – and a source of new information events/fields. Plus, we are additionally led to dealing with and coordinating what might be termed “intrinsic invariant information” – that presents/emerges in various and variable ways, depending on the fluencial arrangements present (as I indicated with the wave/particle references). Which is semiotic information, and second and third order and more, cybernetic information. With the plausibility of our dropping down anywhere in the extended matrices of this topology and using any one of them or combinants of

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them as “frame of reference” thus adding another layer of cybernetic interpretation to the milieu. There is intrinsic information and extrinsic/presentational information. And many possible frames of reference and loci to relate to them from. Which means, that the alert competent mind has to be able to discern: .

the presence and pertinence of any possible number of local criteria and information;

.

the overarching presence and pertinence of global interrelationships;

.

the co-presences of other local criteria and information perspectives/ realities – and most importantly – must be able to juggle;

.

all these information group alternatives simultaneously and be able to transduce, reform and re-compose among presentational information sets and the global manifold.

These are local correlations that are co-extant with broad panoramic correlations, and can be thought of as “correlettes” (though if some one comes up with a more alliterative succinct word, I would be happy to shift. I like creating words to fit new memes and concepts, but I appreciate other people’s inventiveness and creative suggestions too. And even urge we do not restrict ourselves to Latin/Greek/European phonemes and cepts. There are many Oriental and African and Native American phomene/meme words and combinants that are equally if not more useful and appropriate to these explorations and others.) We do all of the earlier mentations under the banner of recognizing that in-fluencial involvements are forced to have and exhibit scalar variabilities in many different ways. It is convenient then to think of these non-uniform continua as gradients. Like stretched elastic number lines where the amount of elasion varies with the distance from some locus base point, the points spread differently and therefore can be said to have a smooth but varying “density”, and so, are intrinsic gradients in their mere fluencial existence. This aspect is the primordial manifold of Tro’pic (long ‘o’ sound) gradients. Forces and fields in this essential existential manifold are therefore antecedent to the so-called “fundamental” forces, and the “fundamental forces” can now be appreciated as products of those confluencial interactions. So what is our relation to this now massive, involved and hyper-infinite rendition of the form and behaviors of the universe? It is a challenge. We have to transcend linearly choosing individual mindsets or frames of reference, which linear act of thought forces us to preclude alternatives. And though it is necessary to opt for field-consistency when dealing with venues and subjects, it is just as if not more crucial to be able to cross correlate to anything and anywhere beyond tentative system boundaries. Because that is the true

measure of open, extensively integrated and natural systems – which is how the universe operates, according to holistic first principles. All these several aspects bring us to the state where we appreciate both pragmatic and perceptual ramifications. As we push the motivating and operating principles of the universe further into the realm prior to instantiations of energy and matter, it becomes necessary to ascribe effective action forces and impeti as coming from this so-perceived “intangible realm”. Religions explore it, Quantum Mechanics explores it, Bohm and Hiley explored it. And now, general systems theorists and cyberneticists take their best shot. Essential dimensional/fluencial process-architecture embodies activity motivations whenever there is any scalar variance anywhere and severally within manifolds. This corresponds with differential information arrangements and “densities” as it were, which are effective primordial sources of “gradients”. Much before their inter-involvements produce energy and matter, which progeny acts out their own scale behaviors that interacting gradients dictate as possible. This becomes compounded, in that this firmament architecture of fluencial space is the topology generally referred to as spacetime, and the generated material – energy and matter – have behaviors among themselves and with their formative: SpaceTime (plural fluencial phasespace). All events therefore are “subjective” in so far as they are exemplars of the only “things” that can ever be “objective” and invariant – the relations embedded and displayed in the process architecture: i.e. the “laws” of nature. Nothing else is “objective” – only the non-object intangibles called “relationships”. To dwell on these things is to stay in the field of theory and transcendent thought. But, to appreciate the extent and vastness of reality however means we bring all that into everyday living – materialistically, personally, psychologically, socially, economically – gaianly. And use cybernetic languaging in not just second order ways but multi-ordered ways. There are idealisms that come into play with these considerations, but in hard core reality there is competition among mindsets and systems values that will not just go away if they conflict with other operating systems. And it can be shown that these too come from the arrangements and interplay of seminal fluences. We can trace our behavioral lineage not just our material lineage right back to those essential gradiented fluences and how they interact and secure and improve their existential presences. Existential continuation becomes a committed to behavior that improves as a system or organization builds improved competence to deal with larger unknowns or specific existential confrontations. This requires extraordinary capacity – resident simply as dormant possibility. Which means that as we humans evolve into the next species that will supercede us (we are the source of those who will be superior to us) we transit there by testing new ceptual and conceptual and extraceptual capacities, bringing to bear the newly discovered

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capacity to juggle pertinently, locally and superpositionedly – vastnesses of information unheralded before – within subject fields and among them. And as sapien physiology changes we will have the mindset to use there, not because it arose spontaneously as if we were gadgets performing as constructed, but as sentient co-designers of our own becoming. Humanity is in the toddler stage of these transformations, creative leading edge toddling, but toddling none the less. We have to directly cope with vast pluri-potentials and make competent decisions that not only get missions or needs accomplished but also support and improve the prime-directive that stems from original timespace: to explore sentience and all the potentialspace that is or can exist. Comprehending what they are, dealing with our own component potentials – be they good or bad – improvable or inappropriate – requires having local agendas yes, but also having as part of us the overarching agenda to explore all of life’s potential and encourage other lifeforms to do the same. To value potential in general means to esteem that which may be nascent in other lives as well. Human or not. And as far as human with human interactions, raising the competency of local organizations and global organizations jointly through mutual education and exposure, through shared interests and views, while making sure that Ashby’s “requisite diversity” is seen to as material expression of all-important Integrity Paradigm “option spaces”. In this way we set the real foundation for the future so that in many thousands of years, and millions, we can be looked on as having been the forebearers of sentient transformation evolution – at the dawn of time. So just how much cybernetics can you handle? How much can you transmit to others? How many people can you transform? What venues can you take and apply your expanded perceptions to? How effective can you be in your personal life and in long term commitments to the gaian harmonious furthering of life in the solar system? How can you, how can we, change the mindset of the human environment as well as the mindset(s) of individuals who run independently through it?

Addenda information, graphs, references Addenda 1. Single event j Superpositioned “meanings” Imagine that you are a resident in the otherwise-empty chamber of Maxwell’s “dual chambers with Demon”. The valve suddenly opens and your space is now populated in a way it wasn’t before. Your local perspective is that information has increased (even if you postulated that there existed a global system which in that context is now less ordered). One could deduce two possible views of this.

(1) There is net conservation of “information” among non-intersecting local regions and the combinant global region.

(2) Conservation of information is not a direct factor since information bits can be independently defined and therefore there must be a new class of information handling which can cope with information transduction and translations among alternative (yet interacting) definitions. The conclusion is that, yes, there are situations in which information and energy/entropy have easy correlations – and – there are other co-present situations in which a new framework of thinking is necessary – where information shares distribution and presence characteristics with energy/entropy but where they are not rigidly linked, and pluralisms are present. Addenda 2. Producing information from “relations” rather than data (example research pgms)

(1) Jonathan Shade, Steven Gortler, Li-we He and Richard Szeliski (Microsoft). Layered Depth Images, Lumigraph. .

http://research.microsoft.com/MSRSIGGRAPH/1998/ldi.htm

.

http://research.microsoft.com/features/images.asp

(2) Leonard McMillan (MIT) [ref: http://graphics.lcs.mit.edu/~mcmillan/pubs.html] .

Every pixel has an independent reservoir data set.

.

Process involves a continuous averaging method using the chaos technique of last output as being next new-input.

.

Images are built furthest to nearest rather than side to side.

.

Effectively encodes parallax information (z-dimension) as a part of the processing rather than as an independent system parameter set.

(3) Software for Manipulating Belief Networks http://bayes.stat.washington.edu/almond/ belief.html

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The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/0368-492X.htm

Axiomatic combinatorial world theory with emergent intelligence: simplifying understanding and professionalizing general education Donald O. Rudin International Institute for Advanced Studies, Baden-Baden, Germany Present address: 1B1 President Point Dr., Annapolis, MD 21403, USA Keywords Cybernetics, Evolution Abstract A theory of knowledge shows that all four systems of nature are recursive combinatorial-hamiltonian self-programmed flow-wave systems that can be deduced from the usual Conservation Law promoted to the Axiom of Science.

Introduction The four systems of nature are: (1) nonadaptive physics/chemistry, (2) adaptive physics/chemistry or biology, (3) sentient physics or sociopsychology, and (4) representational physics or language.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 738-751 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443824

They can all be formulated as self-programming computers. Their extremal controlling laws (decision criteria, performance indices, PIs, or Generalized profits) taken from the hamiltonian are: extremization of (1) Action (physics) or Energy (chemistry), subject to environment or constraints. (2) Survival number, subject to constraints. (3) Fulfillment, happiness, or quality of life, subject to constraints, and (4) Information Gain, IG. Like any profit, each is the difference between an output and input. In system #1, this is the kinetic minus potential energy minimized. In system #2, it is number surviving minus the number dying maximized as a function of genome and environment. In system #3, it is emotional gain minus emotional cost maximized. In system #4, it is theorem gain minus axiom cost maximized. System #1 cannot learn. System #2 or biology can learn intergenerationally but it is not intelligent. Systems #3 and #4 are intelligent.

That is, they can personally learn in real time by forming electrochemical Boolean nets with excitatory/inhibitory connections and variable geometric connections. When sufficiently elaborated, these model-building nerve nets can perform all possible logical operations and relations. Hence, they can build models of the world, which anticipate future behavior. With this, the present state of System #3 at time, t, Xt, becomes a function of its future expected state so that: X t ¼ fðU tþ1 Þ. Then the operation of the brain at any instant of time covers all time in complex time, t*, or n-dimensional time, t n. It is now conscious and sentient, since it is generally motivated by servoing emotional states. Ultimately, a lawful world must be axiomatic. We promote the Conservation Law of science and its set of combinatorial world constants, c, to the Axiom of Science (and of the World). It characterizes the quantities and qualities of the primordial combinatee of motion and the primordial combinator of substance, probably a superfluid. A general combinatorial system has a combinatorial generating function, which, in given time, occupies all possible states permitted by c or its analogous string constants, T, of the Euler-Veneziano string equation the vibratory modes of which produce the elementary particles of a relativistic string. The hamiltonian function is the mature form of all physical equations. It constrains the combinatorial generator, forcing it to follow an extremal performance index or controlling law from initial to final state, subject to optimal control-state history of the functions of the control and state variables. The lawful world is a finite procedure or program consisting of the underlying combinatorial-hamiltonian program. This processes the world constants, c, into World Theory or a General Theory of Evolution (Rudin, 1996, 1999, 2000, 2001a, b, c).

Nature as four recursive self-programmed computers Computer System #1 or ordinary physics is a flow-wave structure computer driven by a combinatorial hamiltonian program. Physically, it consists of motion as primordial combinator driving a primordial substance or combinatee, probably a superfluid, into all possible vibratory modes of string motion permitted by the world constants, c. In effect, this computes the set of elementary particles, both matter (fermions) and field (bosons). The generating function is the string equation or related relativistic twister equation. More explicitly, the kinetic energy, K, is a state variable vector, X, while the potential energy, V, can be viewed as the control variable vector, U. The generating function is the 2nd order Lagrangian or first order Hamiltonian.

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Computer System #2 uses the nucleotide bases, DNA (RNA), as the control variable vector, U, combinator. It combines and permutes combinatee amino acids into specific proteins acting as state variable vector, X. The combinatorial generating function is just the series of bases in DNA/RNA. The computed results are the set of organisms. System #2a is the electrochemical, neural net. When it evolves to System #3, it forms all possible Boolean functions and their compounded nets. It ultimately computes a model of the world. It then becomes conscious and sentient (consciously motivated), operating in complex or multi-dimensional time, t*. It then discovers the generating functions of all four systems and develops their inter-system recursion mechanics. System #4 is language. It mimics particle physics. Linguistic particles are the noun, X, vs stable matter particles or fermions. Conjunctions, NOR(NOR), replace unstable field particles or bosons. Language also has a generating function. It is abstract and omits the physical constants, c ¼ T . It computes word/terms, sentence/equations, abstract stable structures, and abstract sciences.

Definitions: (1) Intelligence is the capacity to model the world (Rosen, 1985). (2) Ultimately, in a lawful world, computational intelligence, as well as the object world itself, must be axiomatic. This requires a set of combinatorial world constants, c, that characterize basic world attributes. A program or finite procedure, consisting of the underlying combinatorial-hamiltonian form of Boolean algebra and equivalent arithmetical operations, processes the world constants, c, into World Theory or General Theory of Evolution (Rudin, 1996, 1999, 2000, 2001a, b, c). (3) Following the failure of philosophers to develop the theory of knowledge, which they call epistemology, scientists and mathematicians have expended great effort recently to develop the corresponding scientific theory of cybernetics, systems theory or optimal control. It turns out that all systems, theories and story grammars are generalized forms of the well-known hamiltonian function holding for all mature theories of physics and chemistry. By combining the universal hamiltonian system structure with a universal system formation principle based on generalized combinatorics, one obtains a mathematical theory of knowledge. This is a universal program or software technology and the strategy of the scientific method. (4) By processing world constants, c, into World Theory, this axiomatic combinatorial-hamiltonian world program generates the chain of four systems comprising nature. (5) A corresponding chain of extremal controlling laws identifies each system and directs its evolutionary trajectory along the extremal part of the

hamiltonian function. Physically, the world is a combinatorial computer in which motion, the primordial combinator, generates symmetrical flow-wave structures in a primordial substance-combinatee, probably a super-fluid. Thus, the elementary particles arise plus the recursive hierarchy of the remaining three combinatorial-hamiltonian systems of nature. The physical combinatorics is given by the string-vortex equation of Euler-Veneziano. Language is a combinatorial system with linguistic particles analogous to physical elementary particles. The result is scientific philosophy. Although the genetic system can learn, it is not intelligent, because it has no personal or intra-generational learning ability. Genes can only learn intergenerationally. They carry out unintelligent chemical learning by varying the permutations of the four DNA/RNA bases from which the environment selects those best leading to survival of the fittest, after the fact. This is a game of 20-Questions. Intelligence involves intra-generational or personal learning. It requires the evolution of an electrochemical learning system using nerve signals in nerve nets to carry out real-time Boolean operations tied both to logic and to personal experience with a given environment. While both genetic and neural learning systems arise combinatorially and are hamiltonian-organized only the latter has an adaptive controller (DNA double helix) which makes intelligence possible through the brain cortex. The level of intelligence is proportional to the competence of the model building, hence, the ability to learn personally. In turn, these are proportional to the level of sentiency or conscious goal seeking. Consciousness arises in model building systems, because they operate in multidimensional time, t n, which can also be called complex time, t*. The state, X, of a sentient, model-building system operating in complex time, t*, is a function of the future state anticipated by the model in control time, U(t+1), at time t+1. The present is a function of the future and the future determines the present or X t* ¼ fðU tþ1 Þ. Since an intelligent system also has memory of the past, t 2 1, the state of the system at each complex instant of time, X t*, is a function of all time, up to model-building competence. This conscious, sentient multidimensional psychological time, t *, contrasts with 1D unconscious physical time, t ¼ t 1 . It has long been questioned whether a universal knowledge structure might underlie intelligence, possibly acting as a universal program, which could generate a theory of the world and greatly simplify understanding by laying out the world story-line in a unified way. Philosophers call this subject epistemology. AI workers refer to frames. Some general educators speak of cognitive structure. Linguists call this story grammar or case grammar and so on. After centuries of failure to develop the topic, many natural language, folk speakers now conclude that no such thing exists. However, scientists, backed by powerful mathematical methods and

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experimental results, have, in recent decades, taken up the search under such names as cybernetics, systems theory, mathematical optimal control, computational intelligence, and meta-theory. After a 30-year study, my reviewers and I think I have developed the theory of theory or metatheory. This is the combinatorial hamiltonian function. It provides a universal knowledge structure that acts as a world program. It is equivalent to the strategy, though not the tactics, of the scientific method. This makes it a scientific not a philosophical problem. Apparently, a lawful world is a combinatorial-hamiltonian program that processes a database of world constants, c, into a theory of the world or General Theory of Evolution. This is materially realized as a supersymmetrical combinatorial flow-wave computer driven by motion (a combinator) of a primordial substance (a combinatee), perhaps a superfluid (Rudin, 1996, 1999, 2000, 2001a, b, c). We know something when we: (1) understand how it is formed universally (combin.), (2) how it operates universally (as a hamiltonian), (3) how it relates (recursively) to other systems, (4) what the (harmonic) stability conditions are for each subsystem, and (5) the Godel completion conditions.

World theory by the numbers (1) We promote the well-established Conservation Law to the Axiom of Science in the object domain: E total ¼ E 1 þ E 2 þ . . . þ Mc 2 ¼ world constants; c: (2) We adopt coordinate systems theory as the dual axiom of science holding in the analytical codomain. (3) From the Conservation Axiom, we deduce a universal mathematical knowledge (system, theory, optimal control, cybernetic) structure called the Combinatorial Hamiltonian. The generalized combinatorial generating function is a Universal System Formation Principle. The generalized hamiltonian is a Universal System Organizing Principle. (4) The World Program with acronym ACHR (ah’-ker) program is Universal Software Technology. (5) It recursively processes a database of world constants, c, given by the Conservation Axiom, into a chain of four unified systems comprising nature: .

Nonadaptive physics,

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Adaptive physics (biology),

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Sentient physics (sociopsychology),

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Representational physics (language).

(6) A chain of four extremal controlling laws, the 1st of the three parts of the hamiltonian, identifies the systems and, following Euler, directs their extremal trajectories: Information Gain includes Happiness (Quality of life ) includes Survival includes Energy (Action). In the opposite direction, they form a reverse inclusion chain of constraints. (7) Motion, a primordial combinator, drives a primordial combinateesubstance, possibly a superfluid, into a set of Benard vortex lattice flowstructures stabilized by constructive harmonics. Feigenbaum reduplication occurs twice and is limited by chaotic breakdown. Macro-vortex rim eigenstates produce the set of 4+ fermions and induce a corresponding supersymmetric set of tuned wave systems (the 4+ bosonic force fields traveling over the micro-vortex lattice). Rim flexing may account for gravity, rim circulation for electric charge; rim spiraling for the weak force, rim breaking for the quark. These 4+ vortical flow structures induce the supersymmetric cumulative fields: Gravity alone, Gravity + EM, Gravity + EM + Weak force, Gravity + EM + Weak force + Strong force (gluon); Higgs field. This completes the set of elementary particles up to the 2nd Feigenbaum (1978) doubling (Miller 1994). Fermion-boson model from (Argyris et al., 1999; Bevan et al., 1997; Desabbata and Sivaram, 1995; Holmes et al., 1997; Vollhardt and Wolfle, 2000; Volovik, 1998; Winterberg, 1994). (8) These particles recursively and combinatorially form atoms, genes, organisms (topologically based), societies and language. All are hamiltonians with properties fixed by c. Each force dominates one aspect of evolution. Gravity controls cosmology or gravitational chemistry. Weak and strong forces control nuclear chemistry. EM controls living systems. Life, sentiency, and language are formed by the EM force, fed by the nuclear forces and housed by gravity. (9) Using combinatorial generating functions and obeying intersystem recursion mechanics organized by the hamiltonian, the ACHR world program processes c into a unified World Theory also called the General Theory of Evolution or Post-Newtonian Generalism. (10) The basis for the combinatorial-hamiltonian is already contained in the speciality science foundations of Newton and Leibniz. However, the hamiltonian must be generalized to include maximization of Survival, Happiness (quality of life), and Information Gain as well as minimizing the Action and Free Energy. The rest of the hamiltonian is discussed below. (11) The parts of the hamiltonian comprising each of the four systems is shown Table I, where the PIs are to be extremized subject to constraints.

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(12) Intersystem Recursive Mechanics given in terms of the hamiltonian: h01 ¼ See #7 combining motion and substance. h12 ¼ AATE genetranscription model (adenine amino triacetate ester). h23 ¼ Boolean circuitry with Pavlov-Hebb coincidence memory + Sutherland (1999), analog phase coherent adaptive filtering finding phrase-coherence or syllogistic streaming based on a holographic synaptic model. h34 ¼ k1; MLT;X, NOR, cl ¼ Leibniz or logical alphabet, which generates universal grammar and language. h41: X (noun) combinatees ø fermion combinatees; NOR combinators ø boson combinators. (13) Each of the four systems of nature is stabilized harmonically. Quantum phase coherence generates the elementary particles as Benard vortical flowwave (fermion-boson) structures (Prigogine, 1991). Molecular orbital methods treat molecular systems enclosed in the bimolecular lipid membrane forming the holistically selected biological cell. Electrochemical signaling, which is related to immune system neurotransmitters, can be either excitory or inhibitory. In appropriate circuit configurations, they can perform all Boolean operations, both irrelational (operators) and relational (relators or permutors). (14) The combinatorial logic of the four systems is: h1: Feynman, try all, select coherent quantum waves. h2: Darwin, try all base permutations, select half, because genetic evolution is a biological game of 20-Questions (Is it bigger than a breadbox, then die). h3-4: Using reasoning, try solving by algorithm, that is, select the solution. Finally, h4: Stop. The interior world model is complete (axiomatic). (15) One can view this Axiomatic World Theory as a generalization of Euclid’s axiomatization of geometry, L (1), to the axiomatization of all elements of the world, kqq;cc,cl, i.e. kquantity and quality of combinatee and combinator subject to constraintsl. However, it must be put in combinatorial form, as given by the Logical or Leibnizian Alphabet: k1,MLT;X,NOR,cl. (16) The final unified theory of physics is nearly achieved by superstringvortex theory. Often called the Theory of Everything, it is only a theory of nonadaptive physics and, so, should be called the Little TOE. The present world theory of all four systems of nature, put in standard combinatorial hamiltonian form, is an attempt at a truly universal theory of general physics – the BIG TOE. Ham. PI #

Table I. Hamiltonian components for the four systems

1. Action 2. Survival # 3. Happiness (Ceruleum 4. Info. Gain

State vector X

Control vector U

Adapt. control Ua

Kinetic E, K #Born (f1 genes) SlG(XG)emot.gain Hypothal-hindbrn Theorem bits

Potential E, U #Dying (f2 genes) SlG(UG)emot.cost Subcortic nuclei Axiom bits

None DNA/RNA Thinking Cortex) Analysis

(17) Godel completion criteria are evaluated. The interior, knowable world is complete and consistent, resting only on the Conservation or Lawfulness Axiom plus simple combinatorial-hamiltonian procedures. Hence, the world could be a fully lawful perpetual motion system of the second or frictionless kind (The Oscillatory Big-Bang theory). However, the world as a whole, finite but unbounded in space and time, has no context and, so, it could have a metaphysical exterior. Hence, the global world program is Godel incomplete and undecidable. (18) In place of the expert’s complicated Problem Solving Language (PSL), we combinatorially construct from 1st principles a far simpler Problem Formulating Language (PFL) everyone can understand. (19) This permits formation of a substantive Common Culture able to understand Axiomatic Education, AE, based in Axiomatic Science, AS, leading to Scientific Philosophy and the Scientific Enlightenment. We then know the logic of the world and of the world storyline, up to knowability limits. The three parts of the hamiltonian The first part of the hamiltonian (see 11) is the set of extremal controlling laws (decision criteria, performance indices, PI). These drive each system along its necessary trajectory. Each PI acts like a profit: (1) the energy profit (to be minimized or conserved), (2) the life or survival profit, (3) the happiness profit, and (4) the intellectual profit. Each is the scalar difference of the state vector (as summed scalars) minus the control vector (also as summed scalars), viewed as the vector difference of the summed returns, SX i, minus summed costs SUi. This is analogous in economics to the Bernoulli Utility function (Happiness) ¼ Sai log (X i 2 Ui) ¼ maximize, where X i refers to i return commodities, Ui to i investments having values ai and the log is the marginal utility. The second part of the hamiltonian gives the possibility set. It specifies all the things that could have happened, as allowed by the mechanics of the system given by the function, f. This is formulated as vector differential equations of state: dX=dt ¼ fðX; UÞ relating state, X, to control vectors, U, via f. These are transposed in the hamiltonian to put them in their zero form: dX=dt 2 fðX; UÞ ¼ 0; so they add nothing to the extremal equation of the first part of the hamiltonian. In physics, the nonadaptive state vector is qp (momentum and position), related by their various lagrange and hamiltonian differential equations. But, in the life sciences, we must maximize the PIs and develop a set of adaptive state vectors, we call the g state instinct vectors, standing for group, associational,

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material, mapping and sensory or aesthetic instincts ðg ¼ gammaÞ: For sentient humankind, these become the G/G* interest-emotion state bivectors, standing for political, social, economic, intellectual and aesthetic interests and emotions. The objective G vector (GAMMA) has units of votes, contacts, dollars, bits, and aesthetes. Their valuation by the individual is weighted by the emotion G* (GAMMA*) vector analogous to the usual lagrange factor, lG, in the hamiltonian (In economics, this is the market price determined by emotional demand). In sociology, an inclusive happiness principle operates with a corresponding set of G0 institutions: Political, Social, Economic, Intellectual, and aesthetic. Humankind is a hamiltonian. Institutions are hamiltonians. Language is a hamiltonian. The environments in which they operate are also hamiltonians. A hamiltonian derived from another hamiltonian and experience either in reality or gedanken is an explanation. Humor is the illogical hamiltonian. Buddha, Epicurus, Bentham, Hegel, Marx, Freud, Parsons, etc. were all seeking the hamiltonian. The nth (1– 4) hamiltonian, hn equals Z X   PIn ¼ gXtf þ ln ðX i 2 U i Þ þ dX=dt 2 fðX; UÞ dt ¼ extremize; subj: to constraints

ð1Þ

gX tf refers to the final state, tf, where there is no longer any control exerted, U. Since the time integral to the right gives the path to the final state, it vanishes in the final state. Conversely, gX tf vanishes during the transition to the final state. Like the Bernoulli equation of economics, the first term under the integral is a scalar sum of returns and costs weighted by the lagrange, l, while the second term is the zero value of the vector equation of state. Although, this adds no numerical value to the equation, its function, f, constrains the values that X i and Ui can take. This is a dynamical constraint. The third part of the hamiltonian specifies the static constraints, boundaries, context or the limiting values the state and control values can take. They are usually appended as a set of inequalities and act as the conservation law or, in economics, as the available investment. In physics, it supplies the properties of matter via the string tension, T, here, the world constants, c, of the Conservation Axiom of science. The hamiltonian is a universal system organizing principle and has long been recognized as the mature form of all physical theories. Appropriately generalized, as above, from Bellman (1961) and Pontryagin et al. (1964), it can treat the life sciences and their maxima. Note, for example, that the detective’s motive, method, and opportunity are the three parts of the hamiltonian in nonmathematical form. Novelists will see this as the long sought grammar of story equivalent to the universal structure of all systems and their theories. The combinatorial hamiltonian is also the strategy of the scientific method. Repeating: The hamiltonian is the dynamic structure of all systems, theories,

story grammar, complete logic and strategy of the scientific method. It is also modal logic; that is, it treats the logic of necessity (the 1st or extremal part of the hamiltonian) plus possibility (the 2nd or differential part) plus setting up their relationship.

Axiomatic combinatorial world theory

The world as a chain of four computers and their programs The nonadaptive physical/chemical system minimizes the action in physics and the free energy in chemistry. Like all systems, it is combinatorial and is constrained by the hamiltonian and world constants, c. It can be deduced from the Conservation Axiom of Science. Motion acts as the primordial world combinator. It drives the primordial combinatee or substance, a frictionless superfluid, into the set of stable flow structures, comprising the elementary matter particles or fermions. These have gravitational, electric, weak and strong charge properties. The properties collect cumulatively to form the set of fermions. Each matter property induces a characteristic translational wave motion or field boson – graviton, photon, weakon, and strongon (quark). Thus, foundationally, the world is an Axiomatically based CombinatorialHamiltonian Recursive software program (mnemonic ACHR) that drives a hardware flow-wave computer. The second or adaptive system of biology maximizes survival number. The sequence of nucleotide base permutations in DNA/RNA provides the ACHR hardware program. The dipolymer (Double Helix) reproduces itself and also forms proteomes – the enzymes that construct cells. Cells especially combine to form neural nets comprising the brain. These can represent all possible Boolean logic, depending only on variable excitatory and inhibitory intercellular connections plus the variable geometry of the connections. The sentient or 3d system (3a) emerges when System 2 evolves sufficiently to construct models of the world. It then becomes conscious and sentient. This is because the state of the system at the present time, t, Xt, becomes a function of the anticipated future control, Ut+1, at time, t+1. We then live in continuous time. At each instant, we recall the events of all time. With this development, we seek not survival maximization but the maximization of happiness. We now define intelligence and personal learning (vs intergenerational genetic learning) as proportional to model building. The brain then devises language and ACHR-C (theory of knowledge) plays out the program to generate a unified theory of the world. Sociology (System 3b) is the combinatorics of hamiltonian personalities forming hamiltonian institutions located in hamiltonian environments. The 4th or representational system of language is another variant of the ACHR program. This is completely analogous to particle physics. Thus, while in physics/chemistry the primordial combinatee is the set of fermions or matter particles, in language, the analogous primordial combinatees are the set of

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nouns, X, defined by lists of adjectives (xi attributes or properties). In physics, the primordial combinator is the set of bosons or field particles that combines or decombines the matter particles while, in language, the analogous combinators are the set of Boolean conjunctions, NOR(NOR), and their extensions, which combines or decombines nouns or their defining adjectives. The generating function for physics is approximated by the string-vortex equation. This can be denoted Fc : E(NI), where Fc is the attributive functor with c as world constants, analogous to string tension, T. This functor maps the permutations, E, of nonintegers, NI, into the world, starting with the elementary particles. These then recursively combine to form the three remaining systems comprising nature (Table II). In grammar, the 4th or linguistic system maximizes the information gain, IG, by optimizing the content of axioms and theorems deduced from the axioms. The generator is F : G(x), where the constantless attributive functor, F ¼ Pð1; MLTÞ ; maps Boolean algebra in combinatorial form, G(x), into language over four recursions: (1) word/term types, (2) sentence/equation types, (3) abstract structure types (groups, ideals, rings, fields), and (4) abstract science types (logic, math, geometry, kinematics, grammar, etc.) The combinatorial generating function must also be specified for each system along with the components of each hamiltonian.

Discussion Science uses two types of reaction schema. One, the formation reaction, combines without regard to order. The other is organizational, in the manner of the hamiltonian, generally called an isomerization or, better, permutational reaction, in which case, elements already combined are rearranged or permuted. We emphasize that physics, biology and sociopsychology all have the same formation and operating structures but varying recursive or intersystem mechanics (#12).

Table II. The hierarchy of system computers and programs

# Combinatee

Combinator

Result

ACHR Program

1. 2. 3. 4.

Motion (Boson) DNA order Modeling NOR(NOR)

Flow-wave Brain Sentiency Language

Fc : E(NI) All logic X t ¼ (U t+1) F : G(X)

Subst. (Fermion) DNA bases Modeling Nouns, X¼ Sxi

Moreover, we find that language, like the physical world, is also a combinatorial system involving both combination and permutations. This uses nouns as combinatees, X, that are combined or permuted by conjunctions, NOR, acting as combinators. Thus, combinatees-nouns in language correspond to combinatee-matter particles or fermions in elementary particle physics. Conjunctions, especially the universal Boolean conjunctions, NOR (NOT + inclusive OR), are combinators corresponding to combinator-field particles or bosons in physics. Bosons combine fermions, conjunctions combine nouns. Equations and sentences both have the triadic structure XRY, since one combinator must combine two or more combinatees. The copula is always implicit. Appropriate generating functions expand these combinatorial elements into full-fledged physics and language. We emphasize that there is nothing in this world but the quantity of the quality of combinatee and combinator, subject to constraints, ,qq; cc, c . . This is formally expressed as: , 1, MLT; X, NOR, c . ¼ The Formal Logical Alphabet. Thus, humankind has intuitively devised a co-combinatorial linguistic system in the analytical codomain to represent the combinatorial physical world of the object domain. The difference is that physical world constants, c, are applied in physics from the Conservation Axiom but omitted in language where we need free variables to build models. In effect, grammar is the abstract combinatorial physics of all lawful systems, unconstrained by world constants, while physics is the specific combinatorial grammar of a world that is constrained by specific constants, c. Today’s conversations with creationists use the natural, folk language. This discussion can now be treated scientifically. All four systems of nature, not just Darwinian biology, evolve by variation and selection using the controlling law of the given domain. It is not possible to develop a theory of the world without specifying what a theory is, namely, a combinatorial hamiltonian function. Therefore, the scientific challenge is to produce a combinatorial world generating function having greater information gain than that developed here: The abstract generator is F : G(X) ! the abstract world of language, where G(x) is the combinatorial form of Boolean algebra, G ¼ NORðNORÞ : X is a set of objects defined by elements or adjectives, X ¼ Sxi : The first approximation physical or concrete generator is Fc : E(NI) ! physical world, where F are attributive functors with world constants, c. E is the exponential or permutational generator and NI are the nonintegers playing the role of relativistic primordial substance. This is the combinatorial form of the string equation of superstring theory going back to Euler. This is also the dual channel solution of Feynman with amplitudes, A, and channels, s, t. G½2aðsÞ½G 2 aðtÞ ; GðmÞ ¼ Aðs; tÞ ¼ G½aðsÞ 2 aðtÞ

Z

ðt m21 e2t Þdt; subj: T

ð2Þ

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This equation was found by Veneziano (1968a, b) to fit vast amounts of Regge scattering trajectory data encompassing most of quantum mechanics. Nambu (1976) later showed that this was the equation for a relativistic string. Green et al. (1987) then developed the subject as superstring theory with fermionboson symmetry. As shown here, this points to the combinatorial nature of fundamental physics, language, and the world at large.

Conclusion This world and all lawful worlds are constrained combinatorial routines. They are constrained by world constants and the hamiltonian function and are stabilized by harmonics at each of the four possible recursive system levels. This is a finite procedure or program with completion. However, this is only within the “interior” or knowable world. Since the knowable world is finite but unbounded in space, time, and matter, it has no context and, so, is Godel incomplete. There is no overall, global program. References Argyris, J. et al. (1999), “Progress in physical concepts of string and superstring theory: 30 years of string theory”, Chaos, Solitons and Fractals, Vol. 10 No. 2-3, pp. 225-56. Bellman, R.E. (1961), Adaptive Control Processes, Princeton University Press, Princeton, NJ. Bevan, T.D.C. et al. (1997), “Momentum creation by vortices in superfluid He-3 as a model of primordial baryogenesis”, Nature, Vol. 386 No. 6626, pp. 689-92. Desabbata, V. and Sivaram, C. (1995), “Torsion, string tension, and topological origin of charge and mass”, Found. Physics Letters, Vol. 8 No. 4, pp. 375-80. Feigenbaum, M.M.J. (1978), “Quantitative universality for a class of nonlinear transformations”, J. Stat. Phys., Vol. 19, pp. 25-52. Green, M.B. et al. (1987), Superstring Theory, Cambridge University Press, Cambridge, UK. Holmes, P.J. et al. (1997), “Low-dimensional models of coherent structures in turbulence”, Phys. Reports-Rev Section of Phys Letters, Vol. 287 No. 4, pp. 338-84. Miller, L.D. (1994), “Truncated period doubling bifurctions in an iterated functional mapping”, in Deepak, A. and Stolarski, R. (Eds), Alex Green Festschrift, Deepak Publishing, Hampton, VA. Nambu, Y. (1976), “Confinement of quarks”, Sci. Am., Vol. 235 No. 5, pp. 48-60. Pontryagin, L.S. et al. (1964), Mathematical Theory of Optimal Control Processes, Macmillan, NY. Prigogine, I. (1991), “Foreword”, in Laszlo, E. (Ed.), The New Evolutionary Paradigm. World Futures General Evolution Studies, Vol. 2, Gordon and Breach, London, UK. Rosen, R. (1985), Anticipatory Systems, Pergamon- Elsevier, NY. Rudin, D.O. (1996), “Axiomatic world theory: An overview General theory of evolution in brief”, World Futures: J. Gen. Evol., Vol. 46 No. 2, pp. 85-124. Rudin, D.O. (1999), Nature of the World. New Horizons for Mankind, Core Books, Annapolis. Rudin, D.O. (2000), “The general theory of evolution in brief”, in Lasker, G. (Ed.), Adv. in Systems Research and Cybernetics, Int. Inst. for Adv. Studies in Systems Research and Cybernetics, Baden-Baden, Germany, Vol. 1 No 4, pp. 43-51.

Rudin, D.O. (2001a), “A brief history of the three stages of science: speculative, specialty and unified”, Acta Systemic, Int. Inst. for Adv. Studies, Baden-Baden Germany, Vol. 1 No 1, pp. 1-16. Rudin, D.O. (2001b), Textbook of Unified Science and Philosophy, Core Books, Annapolis, MD. Rudin, D.O. (2001c), “The axiomatic general theory of evolution. Stability conditions: The world as a recursive set of reinforcing combinatorial hamiltonian programs”, IEEE Transactions (SMCC) (in preparation). Sutherland, J. (1999), “Holographic neural technology”, in Daniel Dubois, (Ed.), 3rd Int. Conf. on Computing Anticipatory Systems (CASYS ’99), Liege, Belgium, 8/9-14. Veneziano, G. (1968a), “Construction of a crossing-symmetric, Regge-behaved amplitude for linearly rising trajectories”, Nuov. Cimento, Vol. 57A No. l, pp. 90-197. Veneziano, G. (1968b), in Kiyosi, I. (Ed.), Encyclopedic Dictionary of Mathematics. III:520; 1438, 1987, 2nd ed., MIT Press/Math. Soc. Japan, Cambridge, MA. Vollhardt, D. and Wolfle, P. (2000), “Superfluid He-3 link between condensed matter physics and particle physics”, Acta Physica Polonica B, Vol. 31 No. 12, pp. 2837-56. Volovik, G.E. (1998), “Simulation of quantum field theory and gravity in superfluid He-3”, Low Temp. Physics., Vol. 24 No. 2, pp. 127-9. Winterberg, F. (1994), “The Planck ether model for a unified theory of elementary particles”, Int. J. Theoret. Phys., Vol. 33 No. 6, pp. 1275-314.

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Mathematical development: a theory of natural creation H. Sabelli Chicago Center for Creative Development, Chicago, IL, USA Keywords Systems theory, Chaos, Cybernetics Abstract The physical universe is the embodiment of necessary mathematical forms by everpresent flux. Interaction of these forms generates diversity, novelty, complexity, and higher levels of organization. Lattice order, group opposition, and topological transformation are generators necessary and sufficient to construct mathematics. Homologous cognitive structures generate human mental development. Process theory proposes that these mathematical generators also create nature. Lattice order is embodied as action, group opposition as two-valued information, and topological transformation as spatial organization.

Introduction The physical universe is the embodiment of necessary mathematical forms by ever-present flux. Interaction of these forms generates diversity, novelty, complexity, and higher levels of organization. Lattice order, group opposition, and topological transformation are generators necessary and sufficient to construct mathematics (Bourbaki, 1946). Homologous cognitive structures generate human mental development (Piaget, 1949). Process theory proposes that these mathematical generators also create nature. Lattice order is embodied as action, group opposition as two-valued information, and topological transformation as spatial organization. Supporting this hypothesis, recursive equations that embody temporal order, bipolar opposition, and continuous transformation generate equilibrium or decay, periods, chaos, and bios. In this and other mathematical series, entropy increases with the complexity of pattern, indicating that the second law of thermodynamics implies evolution rather than decay. Bios displays diversity, novelty and complexity, the characteristics of creative processes. Experiments with the diversifying equation Atþ1 ¼ At þ sinðAt * J ) introduced here (Figure 1) show that asymmetry, bipolarity, diversity, and conservation are required to generate bios. These results provide practical strategies regarding economic policy, psychological intervention, and social action. How can creation take place in a natural way? Spontaneous fluctuations are present at all levels of integration. We propose that necessary mathematical relations mold the ever-present flux into organized processes and structures Kybernetes Vol. 32 No. 5/6, 2003 pp. 752-766 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443833

Supported by Society for the Advancement of Clinical Philosophy. I am thankful to Drs A. Sugerman, L. Carlson-Sabelli, M. Patel, Louis Kauffman, J. Konecki, and J. Sween for useful discussion.

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Figure 1. A mathematical development. The diversifying equation generates a sequence of patterns as the parameter Jt increases (X axis). Different scales are used to present low amplitude chaos and higher amplitude bios

(including energy, information and matter, as well as basic processes at higher levels of organization). This hypothesis is based on the identification of three basic forms (asymmetry, opposition, and continuous transformation) as mother structures in mathematics (Bourbaki, 1946), early creative structures in cognitive development (Piaget, 1949), and patterns in natural processes (see later). After discovering that the sum of random events can mimic empirical time series, Slutzky proposed that order in nature could be produced by lawful operations on totally random fluctuations (Gottman, 1981). Tryon (1973) suggested that the universe arose from a random quantum fluctuation.

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Mandelbrodt (1982) and May (1976) demonstrated the enormous fractal complexity generated by the repetition of simple forms. We propose that the universe is generated by the repetition of the mother structures of mathematics. The temporal flow of energy (action) embodies asymmetry and transitivity; which define mathematical order (lattice theory). Opposition (including twovalued information) embodies group inverse. Matter is a concentration of energy in a topologically continuous tridimensional structure. In this article, the term “mathematical form” refers to the objective form of natural processes and structures. They are not just the mathematical concepts developed in our mind. Mathematics is a natural science that describes general and abstract aspects of processes. Physics leads to consider that the most elementary entities are asymmetric and in constant flux, as contrasted to the point-like and inert elements often considered when thinking about set theory, the foundation of mathematics. We must beg the reader to suspend for a moment his critical judgment regarding this and other assumptions made here, in order to consider the possibilities opened by them. Our purpose is to demonstrate that we can conceive nature as creative. It is unlikely that the universe emerges simply from the molding of flux by three mathematical forms as described here, but who dares to assert that it evolves independently from, or at variance with mathematical form? Bourbaki-Piaget forms (lattice, group, topology) allow one to state in mathematical terms the process philosophy that created science in Greece: a view of the universe as creative (rather than deterministic, random or chaotic), the existence of a creative reason or logos (universal mathematical forms), the unidirectional flow of time (lattice), the universality and coexistence of opposites (group), and the creation of patterns and material bodies by continuous transformation (topology). The same principles constitute the Chinese Tao.

The creative generators of mathematics and cognition The group of mathematicians wrote under the collective pseudonym (Bourbaki, 1946; MacLane, 1986) investigated empirically the architecture of mathematical science, and concluded that there are three fundamental mathematical structures: lattices (the study of order , that is asymmetric and transitive), groups (the study of closed sets in which every member has an opposite or inverse) and topology (the study of continuous transformations in space). All mathematics can be generated by internal differentiation of these structures, or by combinations of them. Lattice, group and topology are not abstract static structures; they are generators necessary and sufficient to create the entire edifice of mathematics. Mathematical forms constitute a set of rules that creates novelty and complexity. They are living forms (Beth and Piaget, 1961) (Figure 2).

Empirical studies of children demonstrated three similar mental structures (Piaget, 1949). Concepts of seriation (lattice ordering), group combination, and topological continuity develop early in the child, and direct cognitive development. Bourbaki’s mathematical structures and Piaget’s mental structures are similar but not isomorphic (Beth and Piaget, 1961). They represent a homology, i.e. an evolutionary descent such as the connections among leg, hand, fin and wing. Mental structures are more particular, adapted to our immediate reality (Beth and Piaget, 1961); e.g. instead of the N-dimensional space of topology, body and mind focus on the tridimensional space of physical structures and processes. The structures of mathematical science elaborate natural mental forms. The mathematician rediscovers structures already built in the mind.

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Mathematical priority, certainty, and creativity Mathematical relations are both necessary and certain. They hold true whether or not there are natural entities that realize and actualize them. Two plus two equals four, with total certainty, in both natural processes and human reasoning. Physical processes cannot depart from the laws of mathematics, at any time or place. Necessary mathematical forms and relations are thus materialized in spatial structures and physical processes, and beyond in brain and mind. Mathematical organization has priority over the (hypothetical) big bang. For instance, time is a form that must precede the big bang according to Prigogine (1996). The priority and universality of mathematics implies that in the physical universe, mathematical certainty is more fundamental than quantum uncertainty. As the necessary form of natural processes, mathematics Figure 2. Flux becomes locally organized by mathematical forms generating net action, informational feedback, and tridimensional structure. It is assumed that the most elementary entities are asymmetric. Sets of asymmetric elements are organized sequentially (lattice), cyclically (group) or opposing each other and thereby generating stable continuity (topology)

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has temporal priority, informational certainty, and spatial universality. Mathematical form is the simplest level of organization because it does not require the existence of physical entities. It also goes beyond physics to include biological and psychological processes that in turn create mathematical science. Mathematical science accounts for, and predicts, natural processes; e.g. calculations determine interplanetary travel (Robertson, 1989). Mathematical science must then describe the mathematical forms of nature; it cannot be just a human invention. The human brain portrays the universe realistically because it has developed through evolutionary processes that encapsulated the world as neurological order (Vandervert, 1988). The Mandala form found in religious art, children’s drawings (Jung) and physiological processes (see Kauffman and Sabelli, this volume) illustrates how archetypes occur at multiple levels of integration. Mathematical structure is a most dramatic example of the homology between simple and complex levels of organization. The three dimensions of macroscopic physical space determine that the labyrinth of the ear has three orthogonal semicircular canals, and this in turn makes us perceive space as tridimensional. Perceptions and mathematical intuitions provide us with a reasonably appropriate, albeit certainly not perfect, picture of the real world. While this notion is labeled “naive realism” against which one can raise scientific caution and ingenious philosophical arguments, nobody behaves based on contrary assumptions. Instead of arrogantly dismissing natural perception as possibly flawed, it seems prudent to learn from nature. Nature’s asymmetry, opposition and continuous transformation Mathematical forms are embedded in physical processes; they are not static, or separate from matter like Platonic ideas. Natural processes and structures display forms that are similar, and probably homologous, to lattice, group, and topological transformation. Consider the human central nervous system: (1) its dorsal-ventral asymmetry displays the unidirectionality of action; (2) its right-left symmetry embodies oppositions that are synergic (we walk on two legs and think with two hemispheres); and (3) its vertical dimension shows a continuous transformation from simple spinal structures to complex cortical structures (Sabelli, 1989). Asymmetry, opposition and continuous transformation are found in natural processes at all levels of organization. In simpler terms, processes have six dimensions of organization: one-dimensional time order, two dimensional informational complexity (group), and tridimensional extension (topological space). The fundamental asymmetry is time; the quantum has the dimensions of action, i.e. time and energy. Mind is a flow of consciousness (James), not energetic equilibrium. Action leaves its imprint in structural asymmetries.

Having discovered the asymmetry of biomolecules, Pasteur postulated that asymmetry must be a fundamental feature of natural processes. This hypothesis has been corroborated by empirical data at all levels of organization: left versus right distinction in beta decay, optical rotation of atoms, preponderance of matter over anti-matter, ionic asymmetry across cell membranes, anatomical asymmetries such as left-right brain, and social hierarchies (see references in Patel and Sabelli, this volume). Natural processes also show basic symmetries. Fundamental forces and particles display group organization; the existence of particles can be predicted based on symmetry. Chemical elements show periodic organization. Opposition, the most basic symmetry, is universal: action and reaction, rise and fall, right and left, electromagnetic polarities, complementary DNA strands, L and D forms of biomolecules, male and female, sympathetic and parasympathetic, anabolism and catabolism, supply and demand, synergy and struggle, symmetry and asymmetry, simple and complex. Virtual particles are formed and destroyed as pairs of opposites in the vacuum. These examples illustrate the hypothesis that complementary opposites are fundamental components of every process (Heraclitus, Lao-tzu, Hegel, Engels, Bohr, Jung, Bertalanffy, Thom). Each opposite predominates over the other in one respect; e.g. priority of the simple and supremacy of the complex (Sabelli, 1989). To accommodate the coexistence of opposites, processes must have two or more dimensions. Because opposition is universal, duality multiplies to 22, 23, . . . , 21 as in the set of diameters of a circumference. Tetrads consist of orthogonal, complementary opposites, in part synergic and in part antagonistic, beyond the diametric opposites of standard logic. The interaction of nonlinear opposites is creative: woman and man procreate; positive protons and negative electrons make atoms. Cascades of bifurcations generate 2N periods, chaos and bios. The interaction of opposites is a generic process for the production of patterns of higher dimensionality. This is the co-creation hypothesis (Sabelli, 2000). Natural processes consist of continuous (topological) transformation, rather than random sequences of independent events. Cosmological and biological evolution, as well as embryological and psychological development, are historical processes in which each new stage is formed by its antecedents, and each new form contains the preceding one. In this manner there is overall evolution from simple to complex. Mathematical creation Mathematics, cognitive psychology, and natural science indicate that sequential order, opposition, and conservative transformation are primary forms necessary and sufficient to initiate determined and creative development. In mathematics, a small set of axioms is sufficient to derive a large, perhaps inexhaustible set of theorems. In human development, a small set of mental structures organizes cognitive development. In a similar manner, a few

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fundamental mathematical forms may function as “axioms” that generate natural processes. We here consider the hypothesis that the physical universe is the embodiment of universal mathematical forms with flux. Flux provides both the substance and the energy. How could mathematical forms create physical processes? The gap between mathematical constructs and physical reality appears wider than the gap between physics and life, and the leap from life to mind. Yet, there is a bridge: the continual flux of nature. Flux provides both the substance and the energy for the materialization of mathematical form. Small, spontaneous, apparently erratic, reversible fluctuations are noted at all levels of organization. Quantum flux permeates “empty” space. Within the limits of Planck’s constant h, flux precludes absolute rest, absolute void, zero temperature, zero entropy, and absolute certainty. Within the global flux, each action is unidirectional, and each entity represents an asymmetry. Pairs of opposite virtual particles are continually formed and destroyed, indicating that opposition is one of the necessary mathematical relations that shape flux. Molded by the lattice order relation , , flux becomes action that is asymmetric (unidirectional time) and transitive (action causes change, i.e. subsequent actions). Time asymmetry organizes instantaneous fluctuations into sequences. Interactions produce change that carries information, and at times bifurcations that generate new pairs of opposites. Sequences of bifurcations can lead to chaos and to bios, and are therefore exemplary of the generation of novelty, diversity, and complexity. Interactions may produce equilibrium; a macroscopic equilibrium of opposites in three orthogonal axes constitutes the structural stability that we call matter. Lattice order is materialized as action, group opposition as two-valued information, and topological continuity as spatial structure (Sabelli, 1989, 1999a). Creative natural processes are the necessary consequence of the combination and internal differentiation of these fundamental structures, or by combinations among them. Natural creation is a mathematical process. Mathematical development Natural evolution and development proceed from an initial stage through bifurcations that produce cyclic, fractal and biotic patterns. To study what factors are necessary for creative development and evolution, we construct discrete difference equations (as required by the quantic nature of action) and test for their ability to generate series that progress from simple to complex patterns. We call these series mathematical developments. We focus on the generation of biotic series that show diversification, novelty and nonrandom complexity. The study of physiological, economic, and meteorological time series has led us to identify bios as exemplary of creative processes (see Sugerman and Sabelli, this volume). Randomization generates nonuniform patterns. Errors produce a normal distribution. Mixing leads to the unimodal and asymmetric

Maxwell-Boltzmann’s distribution of molecular velocities. Unimodality implies the existence of two opposite deviations from the center where opposites match in symmetric randomness. In natural and mathematical processes, we note series that are more recurrent than random, denoting order, and series that are less recurrent than random, denoting novel organization. Order increases consecutive recurrences and thereby total recurrence. Diversifying organization also increases consecutive recurrences, but decreases total recurrence (see Sugerman and Sabelli, this volume). Note the specific use of the terms order and organization in process theory. Ordering and differentiating organization represent opposite deviations from random (Figure 3). The integration of random changes produces complex stochastic patterns that resemble natural processes, displaying diversification, novelty, and nonrandom complexity. It does not generate simple order. Simple order can be generated by the recursion of arithmetic relations. Arithmetic operations must occur in nature. Energy, time, information, and mass are quantities. Simple arithmetic recursions produce pattern as illustrated by the well-known Fibonacci series Atþ1 ¼ At þ At21 that generates w that occurs in a number of mathematical, biological and aesthetic structures. Atþ1 ¼ At21 2 At produces bipolar exponential growth (the simultaneous growth of opposites) that also generates w, and Atþ1 ¼ At 2 At21 that produces period 6 (Sabelli, 1999b), prominent in many recursions and natural processes (e.g. the benzene ring of organic molecules). Consider now multiplication. Quadratic recursions such as the logistic recursion Atþ1 ¼ At * g* ð1 2 At ) showed that simple processes could generate a diversity of patterns (May, 1976). To generate sequences of pattern, the parameter g must vary with time. As g increases, pattern evolves from growth (instead of the steady state observed when g is constant) to periods and chaos with a prominent period 3. Triadic organization

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Figure 3. Triadic development: randomizing (disordering), ordering, and organizing (diversifying, bifurcating) appear to be supplementary processes in nature

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can be detected also during chaos by measuring the frequency with which terms are larger or smaller than their neighbors: 18 per cent rise-rise sequences, 40 per cent rise-fall sequences, 40 per cent fall-fall sequences, and no fall is followed by another fall. Thus triadicity is present in the structure of logistic chaos, not only in the main intrachaotic periodicity. The logistic recursion models opposition to growth. Trigonometric functions model interactions that are both synergic and antagonistic. They generate bios and infinitation. Here, we introduce the diversifying equation Atþ1 ¼ At þ sinðAt * Jt Þ; in which the parameter Jt ¼k * t increases the informational diversity of the harmonic feedback. It is formulated to compare with the process equation Atþ1 ¼ At þ g t * sinðAt Þ in which the gain gt ¼ k * t increases the intensity (energy) of the feedback (see Kauffman and Sabelli, this volume). Both recursions generate bifurcations, periodicity, chaos, bios, and periodic infinitations that represent changes in the order of magnitude of bios when the parameter is a gain gt, and are transient when the parameter is informational Jt (Figure 1). The most striking difference between these recursions is that the diversifying equation generates an abrupt swing followed by exponential growth or decay, while the process equation converges to p or 2 p. Exponential processes of growth or decay are described by e; p, the diametric opposite to 0, measures the relation between linear and circular order – lattice and group). These two irrational and transcendental numbers e and p are related: eip ¼ 21 (Euler). Experiments with these recursions also point to asymmetry, bipolar opposition, and continuity. Asymmetry is evident both in the generation and the outcome of these recursions. Patterns are constructed by iteration in unidirectional time. To test the role of temporal asymmetry, one may assign a negative value to t in the diversifying equation, thereby decreasing Jt (Figure 4 bottom). Time reversed development leads from bios to a simple order; small differences in initial value lead to radically different point attractors. Positive time (Figure 4, top) produces a single periodic, chaotic and biotic trajectory from any initial value within the same basin. Increasing feedback unifies and complexifies. Decreasing feedback simplifies but generates multiplicity. Let us now consider opposition. The production of bios requires bipolar feedback. If the opposition is unipolar, as resistance to growth in the logistic equation, chaos is followed by irreversible escape towards infinity. Bipolar feedback is exemplary of the concept of co-creation through the interaction of opposites. The development of bios is in fact associated with prominent periods 2 and 22 during prebiotic chaos and bios. 2N organization can be detected during chaos and bios: rise-rise, rise-fall, fall-rise, and fall-fall sequences are all

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Figure 4. Time asymmetry in the diversifying equation. Each graph presents three trajectories starting from different initial values. Top: Increasing the diversifier Jt unifies the three trajectories, and differentiates the series to generate periods, chaos and bios. Bottom: Decreasing Jt dedifferentiates the series from bios to chaos to single steady state order, but minor differences in initial value generate very different ordered point attractors. In the process equation, these are multiples of p

observed, in equal numbers when the parameter gt or Jt is sufficiently high. The same tetradic organization is observed in biological and economic series. Let us now consider continuous topological transformation. Feedback means that change is a function of the previous action, not an independent event. Bios requires that each new term At+1 includes the previous one At. Harmonic feedback without a “conserve term” At, such as Atþ1 ¼ k * t * sin At ; or Atþ1 ¼ sinðk * t * At ), generate only chaos (Figure 5). These experiments point to the creative role of conservation and integration. This agrees with intuition. Stability is an essential component of structure. Levels of organization are levels of integration. 1/f pattern may be common in complex processes because it represents the integration of simple processes in

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762 Figure 5. Harmonic feedback without a conserve term does not produce bios. In the case of the cosine recursion depicted here, also the bifurcation sequence changes to become similar to the logistic

which energy is a direct function of frequency (Patel and Sabelli, this volume). At a more complex level, historical culture promotes human creativity. To be creative, opposition must be diverse. To generate bios we need a range of opposition, not just two polar opposites. A wide range of opposites provides multiple values for information, which is the crucial factor. Bifurcation, chaos and bios are generated with equal efficiency by the process equation in which the sine of At is amplified by gain, and by the diversifying equation in which information is diversified without amplifying the energy of the feedback. Gain increases complexity because it increases information. Organic fractals and triadicity Recursions that combine sine and cosine functions, which are orthogonal to each other, generate complex tridimensional patterns that can be fractal and organic in form (see Kauffman and Sabelli, this volume). Fractals are not static structures; they are mathematical developments, never-ending processes that construct ever-more complex organization. Three dimensions are necessary to generate organic form. Triadicity is fundamental. Physical space has three macroscopic dimensions. Triadicity is evident in quarks, p atomic orbitals, codons, primary colors, and conceptual categories (e.g. executive, legislative and judicial powers). Triads are creative: three quarks form a proton, three attractors create chaos; period 3 implies chaos; and the human eye trifurcates light waves into three primary colors, which marks the transition from a physical to a biological process. Cognitive development includes three

fundamental structures. Mathematics has three mother structures. Trifurcation leading to periodic and biotic braids can be produced by harmonic feedback when the conserve term is Atþ1 – At (Sabelli, 1999b). This is significant because difference encodes information. Sarkovskii (1964), in perhaps the most fundamental theorem of modern dynamics, demonstrated that continuity and period 3 imply infinite periodicities. Every period implies all that follow in the sequence 3 , 5 , 7 , 1. . .3* 2 , 5* 2 , 7* 2 , 1. . .3* 22 , 5* 22 , 7* 22 , 1. . .3* 23 , 5* 23 , 7* 23 , 1. . .3* 2n , 5* 2n , 7* 2n , 1. . .; ending in an inverted bifurcation cascade 21 ; . . .; 2N ; 2N21 ; . . .; 23 ; 22 ; 21 ; 20 ¼ 1: Sarkovskii’s series may be realized in natural processes. The energetic flux that fills “empty” space represents a topological continuity, and contains period 3. Period 3 is inherent in tridimensional structure. We propose that energetic causation and informational implication form a creative cycle (Figure 6). Causal energetic processes bifurcate from a single origin to periods, chaos, bios, infinitations, and period 3. As with all lattices, this sequential order finds its dual, which is the informational process of implication from period 3 to 11 periodicities and 11 aperiodicities, down to period 2N . . . , 4, 2, 1. The cycle thus causes and implies 11 periodicities, and 11 aperiodicities. In processes, energy flow causes change and generates information; this newly created complexity in turn produces change. This cycle – energy causation – informational implication – energy causation, . . . etc. – may generate both differentiating organization and recurrent order. Evolution is dimensiogenesis, that starts with one, two, and tridimensional processes, and form many dimensional biological and psychological processes. Numbers embody lattice, group, and topological organization. Conversely, unidirectional order, group opposition, and tridimensional topological space correspond to 1, 2 and 3. Numbers represent form (Pythagoras, Lao-tzu, Galileo, Pierce, Go¨del, and Jung) such as unity, opposition pairs, and complementary triads. In nature, unidirectional action, bidimensional opposition, and tridimensional matter embody these forms.

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Figure 6. A hypothetical cyclic engine of creation

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From oneness, mathematical developments such as logistic resistance and bipolar feedback produce many including multiple infinitations, and triadic organization. Mathematical implication yields the opposite trajectory starting from triadic organization.

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Evolution and entropy These mathematical experiments suggest that these simple processes can generate diversity and complexity. Harmonic feedback embodies the relation between two fundamental orders, linear and circular action – lattice and group organization. Together, they produce bios, infinitations, and tridimensional fractal organic forms. We propose that unidirectional action, bidimensional circulation of information, and tridimensional organization operate at the simplest level of integration, below and before physical strings. They organize into more complex forms that in turn interact with each other to generate more complex organization. The simple forms also operate at each of the more complex levels. In fact, the reoccurrence of simple processes (flux, action, information and tridimensional structuring) accompanies the emergence of a new level of organization. Mathematical creation is necessary. Complexity is its unavoidable result. Against this view one may argue that the second law of thermodynamics establishes that processes spontaneously decay towards equilibrium and disorder. This is a philosophical interpretation of entropy, at variance with the empirical evidence for evolution. Logically, creation must precede destruction, so entropic decay can occur only after creative evolution. Mathematically, statistical entropy measures diversity and symmetry, not disorder (Sabelli, 1999a). In the process and the diversifying equations, statistical entropy increases from steady state to period to chaos and bios (Figure 7). Natural processes may thus spontaneously evolve towards infinite complexity. In a poetic

Figure 7. Statistical entropy H ¼ 2Spi * log2 pi (where pi are relative frequencies) of the time series generated with the diversifying equation. There is an overall increase in entropy with complexity

spirit, We suggested the notion of God as the infinitely complex attractor of evolution. Significantly, this implies that creation continues, and we are part of it.

Discussion A theory of creative processes implies a creative practice. Our practice is medical and psychological (see Sabelli et al., this volume) but a science of creative processes has practical consequences regarding scientific methodology, economic policy, and social action. For instance, identifying economic series as biotic (see Sugerman and Sabelli, this volume) demonstrates that economic processes are creative, and hence subject to change by human choice. In contrast, economic determinism serves to support current patterns of exploitation under the pretense that there is no alternative. Regarding opposition as necessary and universal supports a view of evolution as driven by cooperation (Kropotkine), not only by struggle (Darwin). It also speaks for tolerance and peace, at variance with black and white thinking – those who are not with us are against us- characteristic of neurotics, depressives, and wouldbe dictators. The simple mathematical relations found in nature may be useful to guide our thinking. Yet, in considering the present hypotheses, it may be useful to remember those medieval monks who, having found an early Platonic manuscript, prayed equations in the hope of creating matter. “Praying equations” is a healthy reminder of the limitations of our scientific explanations and actions. References Beth, E.W. and Piaget, J. (1961), Episte´mologie mathe´matique et psychologie, Presses Universitaires de France, Paris. Bourbaki, N. (1946), Ele´ments de mathe´matique. Actualite´s Sci. et industrielles, #838. Hermann, Paris. Gottman, J.M. (1981), Time Series Analysis, Cambridge University Press. MacLane, S. (1986), Mathematics: From and Function, Springer-Verlag, New York. Mandelbrodt, B.B. (1982), The Fractal Geometry of Nature, W.H. Freeman, New York. May, R.M. (1976), “Simple mathematical models with very complex dynamic behavior”, Nature, Vol. 261, pp. 459-67. Piaget, J. (1949), Introduction a` la e´piste´mologie ge´ne´tique. I : La pense´e mathe´matique, Presses Universitaires de France, Paris. Prigogine, I. (1996), The End of Certainty, Free Press, New York. Robertson, R. (1989), “The evolution of number”, Psychological Perspectives, Vol. 20, pp. 128-41. Sarkovskii, A.N. (1964), “Coexistence of cycles of a continuous map of a line into itself ”, Ukraine. Mat. Z., Vol. 16, pp. 61-71 (in Russian). Sabelli, H. (1989), Union of Opposites: A Comprehensive Theory of Natural and Human Processes, Brunswick Publ., Lawrenceville, VA.

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Sabelli, H. (1999a), “Process theory: mathematical formulation, experimental method, and clinical and social application”, in Rhee, P.Y. (Ed.), Toward New Paradigm of System Science, Seoul National University Press, Seoul, pp. 159-201. Sabelli, H. (1999b), “Action creates bios”, in Ferrer, L. et al. (Ed.), Proceedings of the 4th Systems Science European Congress, Spain, Valencia, pp. 103-12. Sabelli, H. (2000), “The co-creation hypothesis”, in Ragsdell, G. and Wilby, J. (Eds), Understanding Complexity, Kluwer Academics/Plenum Publ., London. Tryon, P. (1973), Nature, Vol. 246, pp. 396-7. Vandervert, L.R. (1988), “Systems thinking and a proposal for a neurological positivism”, Systems Research, Vol. 5, pp. 313-21.

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Aging and social systems

Aging and social systems

H. Sabelli Chicago Center for Creative Development, Chicago, IL, USA

M. Patel University of Illinois at Chicago

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L. Carlson-Sabelli Rush University

J. Konecki Fielding Institute

J. Nagib Thresholds Psychiatric Rehabilitation Center

A. Sugerman Chicago Center for Creative Development, Chicago, IL, USA Keywords Social systems, Age discrimination Abstract In our society, medical care and economic progress have improved the duration and quality of life, but aging is accelerated by social norms and their psychological introjection. Healthy aging involves the continuing pursuit of creative activity. Changes in self-view and behavior will require and promote a change in social roles, and the emancipatory mobilization of senior adults of both sexes and all classes.

Introduction In our society, medical care and economic progress have improved the duration and quality of life, but aging is accelerated by social norms and their psychological introjection. Healthy aging involves the continuing pursuit of creative activity. Changes in self-view and behavior will require and promote a change in social roles, and the emancipatory mobilization of senior adults of both sexes and all classes. Aging is more than an individual biological process. But changes in individual perceptions and behavior are not sufficient to promote healthy aging. This will require changing social norms and beliefs that strongly influence personal perceptions and individual behavior. Thus consideration of social organization and economic relations is fundamental when contemplating aging. Being old is not only a biological fact; it is also a collective cultural construction. Persons can overcome cultural ageism in their own mind. But they can do so as individuals only at a great cost in emotional energy. And often they cannot Supported by the Society for the Advancement of Clinical Philosophy.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 767-777 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443842

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change the objective limits that society imposes on them. For instance, continuing employment rather than retirement may be useful to an older person, but it requires that jobs be available. In turn, employing aged adults cannot be left to private enterprise. Older workers may require shorter working and more numerous sick days. Employing them might not be a priority spontaneously afforded by individual enterprises in a competitive market unless laws provide necessary incentives. This is rational because society at large will benefit from the participation of the older worker who earns his or her salary rather than receiving retirement benefits without producing at all. According to the process theory of systems (Sabelli, 1999), social, economic and cultural processes occupy an intermediate position in the hierarchy of levels of organization. They are co-determined by biological processes that have priority, and by psychological and personal processes that have supremacy (Sabelli and Carlson-Sabelli, 1995). Social processes mediate between them; for instance, social culture imbues biological changes with psychological meaning. Because of their greater extension, duration, and energy, social systems predominate over individuals. Social processes have temporal priority over individual psychological processes in evolution, in individual life, and in personal interactions. Clearly, persons perceive each other in the light of their respective roles before knowing each other as individuals. Many interactions involve each of us as generic members of a class rather than as individuals, making it necessary when interventions are contemplated to intervene at the social level. Generation and family A systems approach to aging indicates the need to address social processes. A process perspective points out the import of age roles in social relations. Age determines social role, social relations, and generational class: youth, young adult, core adult, retirement age, and elder. We change sides in intergenerational processes as we move through these stages. Age classes, like gender and economic classes, have bipolar relations (i.e. both harmonic and conflictual) with each other. Cooperation and solidarity between generations are more important than conflict. In our society, however, competition for employment (a conflictual intergenerational variable), contributes to forced early retirement for older adults. This interaction between generations is a fundamental social process. Of all the complementary divisions of society, age is unique in that each person goes through all of the age-related phases. Age has priority regarding health, and it has the same role as sex, class, and ethnicity in determining social status and personal identity. When we meet a person, we usually ask about their occupation. The retired person has lost that identity marker, and becomes a “has been”. Elders often are advised to focus on who they are as persons rather

than what they do as economic units. Yet what makes elders different from other adults is exactly that elders do not function primarily as workers. De Beauvoir (1970) regards this difference as instrumental in elders being regarded as other than really human. In addition to these generic relations between younger and older adults, there are historically specific issues. The succession of generations has been widely recognized as a historical factor by Herodotus, Comte, Mill, and particularly Dromel (Feuer, 1969; Mari´as, 1970). Babylonian clay tablets already document the complaints of elders against the young, and vice versa. In romantic accounts of history, the young often are idealized as progressive (albeit student movements have supported distinctly non-progressive agendas such as Nazism) while the old are downgraded as unadventurous and conformist. However, older persons can also epitomize bravery, such as the mothers of Plaza de Mayo did, when for many years they defied the Argentine military dictators who killed their adult children. Successive generations are different when they have different experiences. In our times, societies are aging as a result of population growth and medical and social progress (United Nations Population Division, 2001). The increased number and improved health of retired persons indicates the desirability and need to bring them back to full personhood and to productive activity. Another experience particularly significant for the present generations is the shrinking of the family. Current culture segregates generations. A typical party group in Europe or Latin America includes four generations; in the USA, only one. The enormous geographical mobility across states and even countries diminishes the relation between parents and their adult children, and thereby also exclude grandparents from the life of their grandchildren. Geographical mobility is often portrayed as being promoted by economic opportunity. More often, it is fostered by lack of economic opportunity. Immigration often is forced by economic crisis or military dictatorships. It is particularly hard on elders that, whether they emigrate or do not, become separated from relatives. In our view, generational divorce contributes significantly to marital divorce. Divorce in turn contributes to the separation of generations. This is a significant problem for current generations, given the high rate of divorce in recent decades. Another current major social change is the globalization and deepening of market relations, such that social, personal, and cultural processes that were previously autonomous have come under the dominion of the profit motive. Health care is dominated by the industrial production of drugs and technology. Hospitals (Anderson, 1981) and nursing homes have become impersonal and depersonalizing. The current climate of economic and scientific materialism leads personal care down the narrow path of biotechnology. Hospitals and nursing homes should be for persons rather than for profit. A return to the “good old times”, however, is not an alternative to economic and scientific

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materialism – neither realistic nor desirable. For all their faults and limitations, current society is far more humane, and current medicine more effective than in the past. Personalization must complement, not replace, biomedicine.

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Maturity versus ageism Another major change in our generation is a growing consciousness of the rights of the older adults. The supremacy of younger adults is normal and desirable, but the belittling, segregation, depersonalization and infantilization of older adults that is often a component of that status is not. Adult supremacy is mainly biological; ageism is social and cultural pathology. What is regarded as psychopathological evolves with moral growth. For much of history, it was acceptable to have sex with children. Even later, the oppression and abuse of women was considered normal. What has been regarded as the normal social consequences of aging must now be revised in the light of higher ethics. Current culture segregates and often keeps down older adults. New opportunities for working or learning are not often available to functional older adults. They may be denied promotions or pushed into early retirement. Age discrimination is legal and acceptable. The American courts (12-8-1997) have ruled that firing predominantly older workers is not age discrimination (prohibited by law) if the motivation is economic. The “laws” of the market supersede the laws of the nation, the principles of ethics, and the commandments of religion. For economic reasons, in the 1990s, some hospitals pushed out leading doctors and laid off the most experienced nurses. Older patients often are deprived of necessary medical care. Emotionally restricted, puritanical individuals may deny analgesics to dying patients. Depression may often go untreated because it is considered normal in the aged. It is often the case that the elderly are confined to the limbo of nursing homes. Our current “culture” condemns them, and thereby each person, to isolation or seclusion among strangers at the end of their lives. Elders can enjoy a richer existence when they live with their family, as in more humane and personal cultures, including traditional American society. Yet the assignment of aging parents to nursing homes allows their offspring, particularly daughters, to live more fully. Whether elders should or should not live in nursing homes, though specific circumstances may warrant it, is a divisive issue for many individuals, including the authors. Current culture disapproves of behavior in older adults which is more typically identified with that of youth. A continual disparagement of parents by their adult children exists in an overwhelming majority of American movies. This anti-parental attitude is prevalent in the attitudes of many American teenagers. In other societies, the elders often exploited their adult

offspring. The older are no better – or worse – than the younger, if viewed in a historical context. Exemplifying dramatically the role of ageist ideology in scientific knowledge, it was until recently accepted scientific dogma that brain cells continually die in mammals, while none are born. This tenet has been repeated even after the growth of neurons in the adult brain had been demonstrated in birds and mammals (Holloway, 2001). Hence the myth has been propagated that aging is a relentlessly progressive degeneration without any respite.

Culture Today, an important component of the denigration of the older is the disparagement of their culture. Previous connotes old and old connotes obsolete. The promotion of the young over their seniors, and the celebration of novelty at the expense of history are tools that serve the powerful to consolidate their supremacy by eliminating rivals while averting critical insight. Each generation develops a culture. The conjunction of age and history renders unique each specific generation or cohort. Upon closer inspection, newer does not always mean better, and later is not necessarily newer. Brilliant historical periods are followed by dull ones; great civilizations, by dark ages; the generation of civil rights advocates by pursuers of profit. Human history contains as much progress as regress. Each generation develops a contribution to culture that must not be discarded. Science, freedom, and justice are advanced on the shoulders of giants. Those who need to reinvent the wheel, frequently fail to do so. Knowledge of history and of other cultures fosters social progress. In overtly dictatorial regimes, history is rewritten and distorted. In commercial societies, the celebration of novelty and technology serves to deprive people of historical and intercultural perspective. The historical present is billed as a permanent law of nature. The notion that monetary profit should govern education, medicine, and media is no longer recognized as the ideology it is – in fact, a totalitarian ideology. To convince the young that economic motivation rules human behavior, it is necessary to obliterate the memory of Martin Luther King. Conversely, one must assert the culture of our generation to advance healthier alternatives. Mature women and men are the generation that discovered the genetic code and invented personal computers, that conquered civil rights, championed women liberation, discovered the need to protect the environment, went to the moon, opposed the Viet Nam war, and did not fight a World War III (!). Avoiding global war is necessary for survival, even in America. The moral growth, legal triumphs, and legislative changes of the civil rights era embody the best American ideals. The humanistic idealism of the 60s is superior to

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the gross materialism of the market. Space travel is more praiseworthy than commercial globalization. Age, sex, class, nation, planet Among the complementary divisions of society, age has priority, but sex and class have supremacy. It is very different to age being rich or poor, woman or man. In our times, women live 7-8 years longer than men (80.2 vs 73.5 years in USA). Regarding aging, women are more powerful than men, just as mothers are more powerful than fathers as the first identification, authority and beloved figure for children. This concept of “female priority” as complementary to “male supremacy” (Sabelli and Carlson-Sabelli, 1995; Sabelli and Synnestvedt, 1991;) is particularly meaningful regarding elders – widower is one of the few words in which the masculine derives from the feminine. Living longer places a problem also for women, as their salaries continue to be much lower. Life expectancy shows a strong correlation with wealth, which in turn relate to class and nation. Class is central to the question of longevity. The rich tend to live longer. Social security benefits are less generous in the USA than in Europe, while in third world countries, they are nonexistent. Everywhere the older worker confronts the injuries associated with the downward mobility inherent in the pyramidal structure of employment. Older persons occupy the higher echelons, but only few can be promoted to a higher rank. Those who do not advance despite years of service and experience suffer serious psychological injury (Sennet and Cobb, 1973) and may become depressed. Also, they are often replaced by younger workers who still can be motivated by the hope of being promoted and who tend to be more deferential to their older employers. The young also are more apt to accept jobs that do not provide health benefits and retirement. As the ability to learn new tasks quickly becomes more important than having learned any specific task, the older worker has lost the edge that in the past was given by experience. We live in a society with rapid social mobility. Aging is an avenue for rapid downward mobility. Retirement is a fundamental change in social status and class. Unemployment and the forced retirement that occurs as a result of corporate “downsizing” or bankruptcy affects older workers more profoundly than it does younger ones. A 58-year-old worker that is furloughed has a much smaller chance of being called back to work than does a worker of 28-years-old. In our times, many of us see our lifetime savings destroyed by bankruptcies, while the perpetrators of manipulated financial collapse enjoy golden parachutes. The value of pension funds shrinks as a result of stock market fluctuations and adventures. Social security would have also shrunk if it had been privatized. Private retirement plans are at the mercy of economic crises that have become globalized. The jeopardy of growing old is particularly poignant during a time of market globalization where it is impossible to effect local changes.

As American workers compete with low paid counterparts all over the world, they see their standard of living and retirement income reduced. The USA ranks 24th in life expectancy (WHO report, 2000); although the USA is the richest country, poverty is more common than in any other industrialized country (U.N. report, 2000). Cuba has the highest life expectancy of all Latin American countries (WHO, 2000). National crises impinge particularly hard on elderly workers who have less freedom of movement. In Russia, life expectancy decreased 10 years, and the risk for premature death for males increased by 70 per cent between 1987 and 1994 (WHO, 2000). In Argentina, classified as a first world country up to the 1970s, the December 2001 bankruptcy wiped out the state and private retirements and the savings of the entire nation. (The immediate cause of the crisis, according to USA Treasury Secretary Paul H. O’Neill speech at the World Economic Forum at the Waldorf-Astoria (February, 2002), was that the USA administration cut off loans to Argentina because “they just did not reform”. Actually, the Argentine government had been following for several years the plans of the International Monetary Fund.). Kidney dialyses have been stopped – meaning certain death to all such patients. Life-saving medications have become unavailable. This is a disaster on par with the rest caused by 20th century totalitarisms. It is frightening that many seem to regard holocaust as acceptable if the motivation is economic. In the USA, recent bankruptcies have destroyed the retirement equity of many employees but not of executives. Globally, young and old are exposed to pesticides, water pollution, and air pollution. Their effects are already sickening and killing millions of people, particularly elders; for instance, in 1 year, air pollution caused 1900 preventable deaths occurred in Ontario (Cifuentes et al., 2001). Overcoming ageism The increased number and improved health of retired persons indicates the desirability and need to bring them back to full personhood and to productive activity. Better prosperity for older persons and an end to age discrimination will require and promote the mobilization of persons of both sexes and all classes. From the perspective of the individual, working to correct systemic processes that foster aging may grant immediate psychological benefits. Changing cultural norms in one’s own family and in society at large serve to change one’s own psychological attitude. However, wrong the rules of society are, they become less dangerous when we do not introject them in our minds. Psychological health requires the outright rejection of social mores and roles that promote illness and accelerate aging. A change in social norms and culture regarding age may be expected to have a salutary effect on society at large, as did the changed laws and mores regarding sex and race. Dehumanizing the other, in this case, the Elder, dehumanizes the self. A psychologically healthy society evaluates persons as

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individuals, rather than as occupants of roles determined by age, sex, or race. Social well-being requires to reduce generational hierarchy, no matter what generation is on top. Liberating persons from their age roles means to open up doors for individual creativity that is useful for society at large. This emancipatory approach to aging and generation embodies the same spirit that led Simone de Beauvoir (1970), world-known for The Second Sex, to write “La Vieillesse”. As the liberation of women, we are speaking of a psychological revolution, as contrasted to a political one. Neglected in the past, aging may now have the impetus to become a focus for 21st century emancipatory movements. The graying of a large American generation has already begun movement in this direction. Money, sex, food and air Engaging older persons in practical activity to change social attitudes regarding age and health will require sensitivity to actual needs and to both social and personal timing. Money, sex, food and air seem to us the most obvious issues. Retirement income is a central concern. The preservation of Social Security has become a major issue in the USA. Among relatively affluent Americans, pleasure and health attract attention. Children of the 60s pay particular attention to pleasurable activities, aware of their salutary effects against the tyranny of ascetic religions, revolutionary ideologies, or overwork in the name of “increased productivity”. We already discussed how to foster sex. Consider food. Current USA standards promote the consumption of meat with high fat content. Other countries produce high quality meat that has much less fat and cholesterol than fish, and is more attractive than tofu (Sille, 2001). Older adults also should be mobilized to defend their personal health. There are immediate therapeutic effects of reducing air pollution. When alternative modes of transportation were made available during the 1996 Olympic games in Atlanta, Georgia, the reduction in vehicle exhaust resulted in a 30 per cent reduction in asthma attacks, and a 40 per cent reduction in Medicaid claims (Cifuentes et al., 2001). The World Health Organization estimates that 460,000 avoidable deaths occurred in 1995. Reducing the emissions of just nine older coal plants in the Midwest would prevent roughly 300 deaths, 2,000 hospital admissions, and 400,000 person-days of respiratory illness. Environmental pollution is particularly detrimental to elders. Promoting the rights of older adults may become a significant emancipatory movement. Its impetus may be transitory, lasting only the tenure of the American “baby boom” generation. One may forecast a historical fate similar to that of feminism that has generated several significant waves throughout history, each leaving a significant change in mores and laws, albeit regressions have also occurred. The emancipation of the aged will depend on peace and prosperity. We are involved in an international war of unlimited scope. We have returned to economic crisis and governmental deficits. We are living a political

process in which, throughout the economic recession of the 1980s and the relative affluence of the 1990s, there has been a steady redistribution of wealth from the poor to the rich. Psychosocial action Action, opposition, and the creation of novelty, diversity and complexity (the principles identified by biotic analysis and modeling described in related articles in this volume) may guide social progress regarding aging and health. Action is a precondition to any useful change. A laissez faire attitude is at best foolish regarding aging, where unopposed change points downward. As many other Americans, older adults tend to retreat into the private and the personal because they have become discouraged regarding the possibility of change. However, social action is effective, as illustrated by changes in smoking, DDT use, and many others changing perceptions regarding aging is one action that older adults can take expecting that there will be no overt opposition. Action implies initiative – as contrasted to responding, conserving, or opposing change. Social action must promote progress and prosperity (e.g. increase in social security) rather than simply resisting social decay (e.g. social security privatization). Action lifts the spirit. Opposition generates alternatives. We need to create them. Witnessing the transformation of society during the French revolution, Alexis de Tocqueville (republished 1998) observed how quickly “the evil suffered patiently as inevitable (becomes) unendurable as soon as one conceives the idea of escaping from it”. In the same vein, John Stuart Mill (quoted by Wolff, 1996) pointed out: “The entire history of social improvement has been a series of transitions, by which one custom or institution after another, from being a supposed primary necessity of social existence, has passed into the rank of a universally stigmatized injustice and tyranny.” In an opposite vein, a 20th century British prime minister made herself notorious for justifying inhumane policies by the notion that “there is no alternative”. Imagining an alternative creates an attractor that, as all attractors, can shape physical actions. What was determined law before a more powerful attractor was created, becomes now intolerable abuse. Determined biological facts such as the division of labor by sex, and determined economic laws such as Malthusian famines, are now recognized as avoidable. Creative choices are particularly feasible in the case of biological, economic, and psychological processes because they are biotic, i.e. they have creative features and extreme and global sensitivity to minor inputs. Ageism is no longer tolerable, because we can conceive of better alternatives. Elders have a special role in generating social alternatives. Experience reveals to us the limitations of ideas previously held as self-evident, and frequently shows us that their opposite were at least in part true. In an

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insightful cartoon, Jules Pfeiffer portrays two men recollecting their passionate discussions in college, one accusing Soviet communism of all sort of crimes, and the other accusing American interventions in Viet Nam and Latin America. “How could we know that we were both right?” they ask themselves now. By transmitting their culture and experience, elders have a significant role to play, encouraging critical thinking in the young. With experience, intelligent persons learn how often they have been wrong. They learn to become tolerant, and to consider a wider range of alternatives. Considering alternative ideas promotes creation better than advocacy. To begin with, nobody really knows what is truer or better. Second, persons are more likely to listen to new ideas when they are presented as one among many – this is born by clinical experience. Third, nobody can predict what will catch the attention of others. Two opposite ideas are not sufficient; one needs at least three factors to generate complexity. Sarkovskii demonstrated the creative power of triads (see Sabelli, this volume). Avoid black and white thinking that predisposes to depression and to conflict. Think in color, i.e. consider three or more alternatives. When two opposite views or factions dominate social discourse, a powerful way to create a third alternative is to become independent. The independent has greater political force because the opposite parties have to cater to it. Politically, the older vote can thus promote its issues with both parties. In social systems, the creation of novelty, diversity and complexity involves personalization. As the personal level occupies the highest place in human processes, psychological processes and personal action always are of great importance in social processes, and they become more important as history progresses. Personal processes are more ethical than social processes because people are morally better as friends and family members, as persons, than as anonymous society members. We propose personalization as a social program (Sabelli and Synnestvedt, 1991), meaning the transformation of the goals and methods of social functioning to promote the welfare of persons, in their diversity and their individuality, as a criterion for choosing between alternative courses of action regarding medicine, education, law, art, economics, and government. We envision a society for persons, not for profit, fatherland, “God”, “People”, or abstract principles of any kind. A personalized economy implies that every person should have the right and the duty to work. Elders should have a guaranteed minimum income, and also the opportunity to work for more. Throughout history, the process of personalization is accompanied by its complementary opposite, depersonalization, alienation, and the development of a capacity for evil. Present society is characterized by a dramatic increase in both personalization and depersonalization. This indicates the possibility, and the need, for action.

In summary, a healthy concept of age is a medical, psychotherapeutic and social goal. It can be achieved in a relatively short time: older adults represent a large, powerful and growing audience, a large, powerful and growing market, and a large, powerful and growing constituency. At this time, progress will be delayed by the globalization of war that has now reached the economic and military center of the world. These painful circumstances render urgent for the older generation to assert the value of our life experiences and our humanistic culture. References Anderson, N.D. (1981), “Exclusion: a study of depersonalization in health care”, Journal of Humanistic Psychology, Vol. 21, pp. 67-78. Beauvoir, S. de (1970), The Coming of Age (La Vieillesse), O’Brian, P. (Trans.), Warner Books, New York. Cifuentes, L., Borja-Aburto, V.H., Gouveia, N., Thurston, G. and Davis, D.L. (2001), Science, Vol. 293, pp. 1257-9. Feuer, L.S. (1969), The Conflict of Generations, Basic Books, New York. Holloway, M. (2001), “Young cells in old brains”, Scientific American, Vol. 285, pp. 30-1. Marı´as, J. (1970), Generations (El me´todo historico de las generaciones), Raley, E.H. (Trans.), El me´todo histo´rico, University of Alabama Press, Alabama. Sabelli, H. (1999), “Process theory: mathematical formulation, experimental method, and clinical and social application”, in Rhee, P.Y. (Ed.), Toward a New Paradigm of System Science, Seoul National University Press, Seoul, pp. 159-201. Sabelli, H. and Carlson-Sabelli, L. (1995), “Sociodynamics: the application of process methods to the social sciences”, in Albert, A. (Ed.), Chaos Theory and Society, I.O.S. Press, Amsterdam. Sabelli, H. and Synnestvedt, J. (1991), Personalization: A New Vision for the Millennium, Soc. Advancement Clinical Philosophy, Chicago, IL. Sennet, R. and Cobb, J. (1973), The Hidden Injuries of Class, Vintage Books, New York. Sille, A. (2001), “Slow food”, The Nation, Vol. 8, pp. 20-7. Tocqueville, Alexis de (1998), The Old Regime and the Revolution, University of Chicago Press, Chicago, Vol. 1. United Nations Population Division (2001), World Population Prospects: The 2000 Revision, United Nations Population Division, Department of Economics and Social Affairs, New York. Wolff, J. (1996), An Introduction to Political Philosophy, Oxford University Press, New York. World Health Organization Report 2000.

Aging and social systems

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Life-long creation in the prevention of premature aging H. Sabelli and A. Sugerman Chicago Center for Creative Development, Chicago, IL Keywords Cybernetics, Health Abstract Aging is a continuous process of growth and decay, both of which start at birth and continue throughout life. Activity develops muscles and neurons; inactivity atrophies them. Here we propose lifelong creative activity as a method to deal with aging. Decreased creative and learning capacity is a self-fulfilling prophecy. Changing personal perceptions and expectations can promote health care and productive behavior.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 778-787 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443851

Introduction Aging is a continuous process of growth and decay, both of which start at birth and continue throughout life. Activity develops muscles and neurons; inactivity atrophies them. Here we propose lifelong creative activity as a method to deal with aging. Decreased creative and learning capacity is a selffulfilling prophecy. Changing personal perceptions and expectations can promote health care and productive behavior. Aging is a systemic process that involves individual biological and psychological processes as well as collective cultural assumptions and social rules. Biology, cognition and culture are inseparable processes (Martinez, 2003). Illustrating his tenet, Martinez quotes anthropological reports that show longer youthful adulthood in tribal societies with a more positive cultural attitude about age. For instance, the belief that peak athletic performance can only be achieved at sixty, after decades of training, leads men to achieve their best cardiovascular performance in their sixties! We have observed similar feats among marathonists. Typically, the slowing of physical activity, learning and working at a relatively early age accelerates aging in our society. Here we propose that improved health and a fuller life may be achieved by changing our cultural norms and beliefs about aging. Healthy aging means lifelong pursuit of physical and intellectual fitness, continual learning, and acquiring new skills and fields of interest at all ages. Continuing activity may be reasonably expected to maintain and improve function. Muscles develop with use and shrivel with disuse. Dendrites and synapses grow with intellectual activity. Neurons renew themselves throughout life. Continuing exercise improves cardiovascular function. Supported by the Society for the Advancement of Clinical Philosophy.

These concepts, albeit new, have already caught the attention of scientists, the Prevention of media, and large sections of the public (Grubin, 2002; Restak, 2001). The premature aging above examples indicate the need for life-long creation that should be promoted in school. This article, however, is written from the perspective of clinicians and researchers dealing primarily with adults. A systemic approach to health and aging that integrates biological, social, 779 cultural and psychological factors may yield better medical care and considerable savings. Here we delineate a bio-socio-psychological approach based on a theory of creative processes (Sabelli, 1989, 1999) that has already been applied to cardiovascular (Sabelli et al., 1994) and emotional illness (Sabelli and Carlson-Sabelli, 1989, 1991; Sabelli et al., 1997). Our approach to aging is organized around the principles of process theory: action, prioritysupremacy, complementary opposition, and simultaneous creation and destruction.

Aging as a process Life does not consist of a sequence of static states. One’s age is a moment in a continuous process. Aging is a continuous process of growth and decay that start together before birth and continue together throughout life. Identity is not a structure; our self is continually evolving. As we age, identity crises can be triggered by retirement, illness, or simply by birthdays. Health is not a state. Health is a process in which actions have consequences. Life is a series of deeds, not just a series of changes determined by external circumstances. Health is constructed, to a significant extent by our actions. Exercise develops muscles and neurons; inactivity atrophies them. Expecting decreased creative and learning capacity is a self-fulfilling prophecy. Processes are made of actions – not energy but, the flow of energy through time. Aging involves a decrease in energy, but more importantly it is a reduction of time. Basic values in our culture such as delaying gratification no longer apply. Promises of future improvement in marital / filial / sibling relations are no longer appropriate. Conflict requires quick reconciliation. The time to live is now. Action is the common ingredient of all processes; for this reason, biological, social and psychological processes can interact. Emotions, behavior, and intellectual activity markedly influence cardiac function, immunological responses, and the growth of synapses in the central nervous system. In turn, social norms and culture set up beliefs, emotions, behavior, and intellectual activity. Cultural attitude influences health by modifying beliefs and behavior. Future-oriented thinking maintains a healthy behavior, but one must also acknowledge behaviorally that the future is realistically foreshortened. Healthy aging means living in the moment and taking care now of whatever future is possible.

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Biological priority and psychological supremacy Aging is not a purely physical process determined by the clock; it is a biological process conditioned by health, nutrition, physical activity, and environmental pollution, a social process conditioned by economic relations, social norms and culture, and a psychological process modifiable by attitude and activity. There is a two-way hierarchy of complexity among the levels of organization: physical , chemical , biological , social , psychological. Process theory formulates this two-way relation as the principle of priority of the simple and supremacy of the complex (Sabelli, 1989). Neither material nor psychosocial processes have absolute primacy. Simple processes predominate globally because they have chronological priority, and greater energy, extension and duration. Complex processes predominate locally because they contain and generate more information. For instance, complex brain functions require blood supply (priority), and emotions control the heart rate (supremacy), rendering psychological intervention useful in cardiac illness. In the central nervous system, the lower bulbar and spinal levels regulate simpler and essential functions such as temperature, respiration, and posture, and mediate the input and output for the higher levels (functional priority). These levels also have priority in the evolution of species. The higher levels which act upon sociobiological functions such as emotions, are the substrate for personal and creative functions, and control the function of the lower levels (Pavlov’s cortical supremacy). Behaviors are organized in the same manner: simpler needs for oxygen, water, and defense have priority but are eventually dominated by more complex wants for personal and interpersonal affection and creativity. Biological and economic processes have priority, but culture and effective relations have supremacy in our personal life (Sabelli and Carlson-Sabelli, 1989). To convey this idea, we find it useful to speak of a ladder: health, work, love, and meaning (to which sometimes we refer as “soul” but soon making clear the intended connotation). These principles apply particularly well to age. Regarding health, we point out that hardly anybody is totally healthy, and sick persons are healthy to a great extent. We advise our patients to attend immediately to any new physical symptom, since timing may be essential. We also work to discourage worrying, which decreases the enjoyment of life and may impair health. Among other interventions, we point out that worrying becomes unnecessary when one attends to every new symptom. We quote an old proverb: “every person dies once, but the coward dies a thousand times”. Regarding work, we recommend continued activity, balancing three facts – remuneration, appropriate level of effort, and intellectual and pleasurable gain. Retirement may be the opportunity to flourish after years of being anchored to a meaningless job, underpaid, and/or overworked, but the freedom to do nothing is no freedom at all. Regarding love, we promote attention to family, friends and we encourage sex. Above all, we help our patients to find meaning

and transcendence in their life story, and we encourage creative activity, which Prevention of may range from caring for others to artistic or social work. premature aging Complementary opposition: adult supremacy Being older is a social and a family role that, as any other, must be understood in relation to its complementary opposite. Co-operation and solidarity between generations is weightier than conflict in almost any family. Within a family, adults of different generations help each other, not only in humans, but also in animals. The power relation between generations is bidirectional. Adult supremacy is complemented by child priority (Sabelli and Carlson-Sabelli, 1995). Small children have enormous power within the family. Adult children dominate physically and socially over their aged parents. This role reversal is fundamentally healthy. However, it also allows for emotional abuse, which may be so subtle and insidious as to escape the attention of the adult child. This can occur among adult children who blame, consciously or unconsciously, their divorced parents, thereby fueling and maintaining intergenerational conflicts. Healthy maturation involves the overcoming of these adolescent conflicts, but many adults remain emotionally arrested in part at the adolescent level. Yet, the adult children of truly abusive parents seldom take revenge.

Concurrent creation and decay Creation and decay are concurrent aspects of all processes. Evolution coexists with decay and extinction. At all ages, biological processes simultaneously construct and destroy organization. Creativity is an essential characteristic of biological, social, and psychological processes. Neurons grow at all ages; activity has been shown to foster the development of dendrites. Aging begins in childhood with the continual death of neurons, and creation can continue up to death. Improved health and a fuller life may be achieved by regarding aging as a continuation of life-long processes of growth and decay. At some point in our lives, we realize that we are aging. Decay starts much earlier. Neurons begin to die even before birth. Statistics show that maximal IQ occurs, on the average, in adolescence. “Think of the saddening contrast that we find between a healthy child radiating intelligence and the intellectual feebleness of the average adult”, pointed out Freud. Only much later, losses make us perceive aging. We retire (or are retired), we lose health, family, opportunities, money, sexual vigor, or even worst, we lose our appetite. We grow old. Children do not mind growing old, because they also are growing up. We suffer losses all our life, but we recover because there is so much more going on. This suggests a very simple strategy to deal with age: growing up as we grow old.

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Sexual growing up and old A good example of this approach is sex. Often a slow down of arousal and a decrease in penis stiffness is the first sign that announces age to men in their forties, the age at which women often become more sexual. Information is psychotherapeutic: age slows down both arousal and climax, so the man meets the 10-20 min period required by women to climax, while the average young man climaxes in 3 min. Sexual knowledge, such as physical and theatrical imagination, as well as well-known Taoist techniques for prolonged and low energy intercourse (Anand, 1989) can continue to improve sexuality at all ages. The exchange of duration for energy in male sexuality with age exemplifies the concept of action, which roughly is the product of energy and time. Energy may decrease with age, but action does not. Older adults can experience multiple orgasms just as well as younger ones. This is not an exceptional athletic ability, but a practice and a feeling about our loved one. Empirical studies reveal active sexual life in many older couples. Yet, imbued with ageism, many regard sex, love and normal human desire as incompatible with age.

Loss, illness and death Aging is biologically marked by the increased incidence of illness and the nearing of death. In sickness, biological, social and psychological treatments must be integrated. We must personally take care of this need for ourselves, our relatives, and, as clinicians, for our patients; the medical system does not. After, and preferably before, a heart attack, a patient can benefit from psychological treatment to decrease competitiveness, anger, and rushing; these behaviors, known to promote heart attacks (Friedman and Rosenman, 1974), and fostered by current social organization. Depression often cannot be effectively treated without biological intervention, but its treatment also requires learning how to cope with losses and defeats. Losses and failures often accompany aging, and often are what makes us aware of aging. When a person tells us that he feels older, it is useful to inquire about their first sign of aging, which often says more about personal circumstance and psychological need than about actual physical or mental changes. It is important to recognize the losses; it is insensitive and uncaring to minimize them, or to preach resignation. Losses and failures are particularly painful for the older adult because there may be little or no time to start anew. Under those circumstances, it is thoughtless, insensitive, and useless to explore the person’s contribution to his failures. Much better is to assist the person in knowing himself and to recognize his main characteristics. The principle of complementary opposition requires us to recognize that talents and flaws are two sides of the same trait. It is hence countertherapeutic to suggest changes in personality. In fact, it represents a devaluation of the person. It is therapeutic to encourage creative behavior. We are not speaking of a recovery of losses, which may be impossible, nor of

a compensation, which we do not deem sufficient or in fact achievable. What Prevention of can compensate for the loss of a loved one, of meaningful employment, or of premature aging critical function? We are speaking of creating anew, which requires much less and provides much more. The loss of a loved one is a partial death of our self. Who can ever share our memories? The poet Ali (2002) sings: Just a few return from dust, disguised as roses. What hopes the earth forever covers, [what faces? I too recall moonlit roofs, those nights of wine – But Time has shelved them now [in Memory’s dimmed places.

Not surprisingly, we find that many survivors experience what we call “death transference”. The survivor adopts the role of the beloved who died. The outgoing wife of a very isolative man becomes isolative. The socialist brother and business partner of a republican politician adopts his political ideas. A woman has admitted herself to a mental hospital under her mother’s name. A man takes up his father’s life mission. Some persons die shortly after their spouse.

Creating health Decay occurs with aging, so, to put off deterioration it is necessary to continually create anew. Whereas growing old is unavoidable, growing up may be continued up to the time of death. In recent years, psychologists and other behavioral scientists have developed techniques to promote creativity. Here we focus on the general strategy suggested by the theory of creative processes, and in particular to the concept of bios. For reasons of time and space, we must refer the reader to the articles on bios analysis and modeling described in companion articles in this volume (Kauffman and Sabelli; Sabelli, 1989; Sabelli and Patel; Sabelli and Sugerman) and to references therein. Mathematical models identify action, complementary opposition, and conservation, as essential factors in the generation of time series with creative features (bios). These “biotic factors” can be used in our daily life: Action: The need for action to generate creative patterns implies the need for activity and initiative. Action begins with motivation that may temporarily be external but that eventually must become personal. Keeping young and fit requires desire. Resignation is the road to aging. Healthy aging involves continuing physical, social and intellectual activity throughout life. Act, rather than rest. It is not sufficient to change self-perceptions; it is necessary to change behavior as well. Act, do not react: to stay alive we must exercise our initiative and spontaneity. Action is the most effective way to lift the spirit when we feel down. As a patient, actively participate in your own treatment. The fact that

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both physical and psychological actions are indissolubly linked in human beings implies the need for comprehensive care in health and illness. Comprehensive treatment is not volunteered by the current medical system, so patients and their families must play a role in obtaining it. Medical illness also requires social and psychological interventions. Illness reduces competitiveness, and shortens the time available for achievement. A recovered patient returning to his job often finds that he had been displaced by others, and reacts by increasing, rather than decreasing, his tendency to compete, to rush and to become angry, three traits associated with coronary illness (Karakostas et al., 1988). Focusing on meaningful activity rather than comparisons of status may reduce competitiveness; the psychotherapist needs to struggle against a culture that promotes competition as a high value. Irrational rushing should be replaced by greater selectivity of goals; this again requires confronting pressures to increase productivity. Anger should be diminished by reducing marital and occupational conflicts; this focus on reality contrasts with the prescription of anti-anxiety agents (which in any case do not reduce anger) or psychotherapeutic attempts to change personality. Of course one must increase tolerance to conflicts inherent in everyday life. In health as well as in illness, attend to both your physical body and your mind. Work, but include sufficient rest, and avoid competition that wears you out. Attend to your loved ones, make new friends. Do something meaningful, even in a small scale. Work to change cultural attitudes regarding age, a significant task for our generation. Complementary opposition-co-creation: The need for bipolar opposition to generate creative patterns translates into the concept of co-creation. We begin by noticing that two beliefs ingrained in many cultures conflict with cocreation. One is the goal of being independent. While independence often is highly desirable, it is not always possible, and it will become impossible for many elders. Under these circumstances, regarding independence as a necessary value reduces self-esteem. What is really needed is not independence but autonomy and the capacity of working along with others. Autonomy means being a center of initiative. Creative behavior always requires interactions. Major endeavors always involve collaboration; one can independently accomplish only minor things. Living requires sharing. Interact, do not isolate. Respond, do not react. Expand your social interactions. Do not let others pigeonhole you in one role. Interact with persons older and younger than yourself. Connect generations. Have real conversations, i.e. about significant matters. Creative behavior emerges from the interaction among ideas. Here we also meet with dysfunctional cultural beliefs regarding faith and loyalty that promote lack of reflection, rigidity, and intolerance. Healthy aging involves becoming more complex, less polarized, more capable of considering opposite perspectives, at the very least more tolerant. Unhealthy aging includes

becoming more intolerant, or more cynical, skeptical or indifferent. Given any Prevention of opinion, consider how its opposite is also true – the production of creative premature aging patterns requires opposition (Sabelli, this volume). Some of the guidelines presented here oppose each other; from a process perspective, opposites are complementary, not mutually exclusive contradictories. Conservation and spontaneity, novelty and order, illustrate the point. To fend off aging, one must 785 promote both novel and complex organization and repetitive and simple structure. Creation: We propose life-long creative behavior as an approach to aging: continual learning and development, acquiring new abilities, skills, and fields of interest, instead of passively accepting social, familiar or biological losses. Losses decrease our abilities, but what matters is what we do with those we have. Mathematical modeling shows that creative processes (bios) involve energy, information, conservation and structure. Energy and information: Aging involves a decrease in physical energy, i.e. both biological and psychological energy. As energy decreases, we see lesser productivity, and when severe decay takes place, we observe agitation, and reduction of life to simple biological periodic functions. Mathematical models show that decreased energy (lower feedback gain) simplifies creative bios to chaos (agitation?) and even to periodicity. A practical implication of this concept is that sedatives can promote rather than ameliorate agitation. Mathematical models also show that complex creative biotic patterns can be maintained in spite of decreased energy. This requires an increased sensitivity to information. A practical implication of this concept is the need to promote cognitive growth and complexity. As physical energy decreases, informational complexity becomes more important. Conservation: Bios modeling shows that creative action requires conservation. The “cultural conserve” plays an essential role in creativity (Moreno, 1934). Create a story of your life, of your family, of your times. Remember and tell. Transforming isolated memories of apparently separate episodes into an integrated story provides meaning. Telling your memories serves to create the story. It also serves to transmit cultural diversity challenged by the uniformity of commercial media (TV, newspapers). By transmitting their culture and experience, elders have a significant role to play. Reconsider history of your times; remember predictions and promises made, and how did they turn out. You may thus encourage critical thinking in the young. Verbal communication may not be appropriate for some persons. Elders may be encouraged to record their memories for future family generations. Audiovisual tapes may be helpful. Imagine a collection of histories going down several generations! Structure: Structure provides a skeleton that supports novel growth. In theoretical models, the model itself is of course a structure. Structure is lost with retirement. Structure your days.

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Biotic analyses show that creative organization and repetitive order are complementary opposite departures from randomness (see Sabelli, this volume); we regard them as complementary ways to overcome decay. Creative processes display diversification, novelty, and complexity (herein including episodic patterns) (see Sabelli and Sugerman, and Sabelli and Patel, this volume, and references therein). Diversification: When work, entertainment, travel, and/or family life become curtailed, process theory suggests that the psychosocial treatment should focus on the development of alternatives. Vary the things you do and the way in which you do them; e.g. change the places you visit, the streets you walk. Novelty: Do something new every week. Brainstorm new ideas. Creativity requires spontaneity (Moreno, 1934). Spontaneity includes both repetition (inertia, structure) and change (novelty, diversification). Complexity: Biotic analysis shows that complexity involves local continuity and global variation. In contrast, the turbulent behavior of chaos involves incessant change and overall repetitiveness. Thus complexity involves the existence of multiple separate activities. Alternating different activities also reduces wear and increases the range of capabilities. Creative solutions can make the difference for the amputee, the man with cardiac failure, the post-hysterectomy woman, the neurologically-impaired patient, as well as for all psychiatric patients. It is a fallacy to see illness as having a predetermined course. Illness is an open process, subject to environmental influences as well as to the creative action of therapists and patients. Patients’ attitudes towards illness and treatment are ultimately dependent upon their beliefs. It is useful for the patient to learn what causal factors influence the course of his illness, so he can modify them, but it is also necessary to recognize the elements “luck” and of ignorance regarding pathogenesis, as otherwise we may actually be blaming the patient for his illness and thus reducing his well-being and self-esteem, which are precious components of health and healing.

Summary In summary, improved health, fuller life, and considerable savings in medical care may be achieved by promoting creative activity. Changing the person’s perception and expectations can promote healthy behavior. Healthy aging involves the continuing pursuit of creative activity, not just reframing self-perception. At 95, the American poet laureate Stan Kunitz summarized the essential ingredient to stay alive in three words: desire, desire, desire (Grubin, 2002). Portraying an aging man in Limelight, Chaplin describes life as a question of desire, not of meaning. Only later he adds that when we have neither, we are left with the dignity of truth.

References Ali, Agha Shahid (2002), “Not all but a few return”, The Nation. Anand, M. (1989), The Art of Sexual Ecstasy, Jeremy P. Tarcher, Los Angeles. Friedman, N. and Rosenman, R.H. (1974), Type A Behavior and Your Heart, Alfred A. Knopf, New York. Grubin, D. (2002), The Secret Life of the Brain, David Grubin Productions and Thirteen/WNET, New York. Martinez, M. (2003), “The process of knowing: a biocognitive epistemology”, Journal of Mind and Behavior, (in press). Moreno, J.L. (1934/1978), Who Shall Survive?, 3rd ed., Beacon House, Beacon, New York. Restak, R. (2001), The Secret Life of the Brain, Joseph Henry (National Academy Press) and Dana Press, Washington DC. Sabelli, H. (1989), Union of Opposites: A Comprehensive Theory of Natural and Human Processes, Brunswick Publ., Lawrenceville, VA. Sabelli, H. and Carlson-Sabelli, L. (1989), “Biological priority and psychological supremacy, a new integrative paradigm derived from process theory”, American Journal of Psychiatry, Vol. 146, pp. 1541-51. Sabelli, H. and Carlson-Sabelli, L. (1991), “Process theory as a framework for comprehensive psychodynamic formulations”, Genetic, Social, and General Psychology Monographs, Vol. 117, pp. 5-27. Sabelli, H., Carlson-Sabelli, L. and Messer, J. (1994), “The process method of comprehensive patient evaluation”, Theoretical and Applied Chaos and Nursing, Vol. 1, pp. 33-41. Sabelli, H., Carlson-Sabelli, L., Patel, M. and Sugerman, A. (1997), “Dynamics and psychodynamics. Process foundations of psychology”, J. Mind and Behavior, Vol. 18, pp. 305-34, Vol. 83 No. 4, pp. 43-9.

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Inside communication in nanostructured evolutionary automata — nanophysics and an information concept for viable technologies Salvatore Santoli INT – International Nanobiological Testbed Ltd, Rome, Italy Keywords Cybernetics, General systems Abstract On the background of previous research work concerning a nanoscale approach to a theory of biomimetic evolutionary systems and biomimetic information processing it is shown that strictly formal-logic based, “hard-wired” electronic hardware misses the very physical nature of bioevolvability. A new, physics-base concept of information, and a new concept of hierarchical, open and dissipative “evolware”, much like biosystems “wetware”, are required for developing an actually biomimetic “evolutionary automata” technology, but a basic inter- and intra-level communication problem is shown to affect the whole automaton’s nanostructure. The problem consists in the difficulty of setting forth causal links bridging the whole hierarchy, from the nanoscale up to the macroscopic structure-functions.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 788-807 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443860

1. Preface On the background of previous research work concerning a nanoscale approach to a theory of biomimetic evolutionary systems and biomimetic information processing it is shown that strictly formal-logic based, “hardwired” electronic hardware misses the very physical nature of bioevolvability. A new, physics-base concept of information, and a new concept of hierarchical, open and dissipative “evolware”, much like biosystems “wetware”, are required for developing an actually biomimetic “evolutionary automata” technology, but a basic inter- and intra-level communication problem is shown to affect the whole automaton’s nanostructure. The problem consists in the difficulty of setting forth causal links bridging the whole hierarchy, from the nanoscale up to the macroscopic structure-functions. This occurs due to the overwhelming presence of semantic spaces as opposed to purely observable “events”, i.e. because: (1) the energetic gap, and hence the relaxation time differences, between the levels makes the causal connection quite loose (e.g. it is shown that deterministic chaotic dynamics can become indistinguishable from purely stochastic behavior; this might occur in intra-level interactions also, with consequent inside-level “dyscrasias”); (2) the different semantic domains for

causes and effects belonging to different energy levels (semantic dishomogeneity between an effect at a certain energy level of a cause acting in the underlying level) prevent one and only causal dynamical morphism from being set forth. The state of a level cannot be considered as described completely (as is usually assumed reductionistically) if it is described as a property arising from the related, energetically underlying level and ignoring the energy gap itself: some essential property contained in the ignored dynamic morphism belonging to the underlying level might be missed in such reductionistic description of a holistic system; (3) the semantic information codes throughout the hierarchy should be reciprocally “agreed upon” to prevent entropy of communication from destroying the self-organized hierarchy; (4) the general computability of natural processes is an unproved empirical assumption, so that the cherished, longed for capability, eventually reachable, of matching calculated and practical technological properties is arbitrary; moreover, even though noncomputable functions are absent, any recursive function implies a semantic homogeneity in its algorithmic form, so that any energy-based computational strategies would fail in the building of the causal interlevel link; (5) observable events can incur a kind of “complementarity limitation”, as is explained. Three ways that round this energy-gap problem (i.e. a problem stemming from dynamics) are suggested and discussed; they are all based on the geometrical symmetries or the topological properties (both not of dynamical nature) of the information processing ongoings: first is the symmetries of quantum holography, which are already exploited now in “functional magnetic resonance imaging” techniques; second is Berry’s phase in quantum and classical systems; and third is the topologies of basins of attraction in dissipative chaotic dynamics and of separatrices between basins, and the symmetries of chaotic dynamics. It is remarked that this evolutionary approach to information and biomimetic automata recalls a von Neumann’s criterion concerning the possibility of a new concept of logic, which should be inspired to Boltzmann’s irreversible thermodynamics and might lead to a powerful theory of automata. The emerging nanostructuring technologies – nanoelectronics and nanoto-microsystem integration, with the mesodynamic architectures as relative – have the potential to embody such concept. In the gazing eyes of a mute beast there are words that the wise man’s soul understands[1]. 2. Introduction During the past few years, the old dream of constructing biological-like machines has attracted an increasing attention as a result of the large increase of computational power and of the appearance of a new generation of programmable logic devices. Indeed, all that made it possible to use models of genetic encoding and artificial evolution actually, much of that work being

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inspired to the basic work of John von Neumann and his concepts of selfreproduction and self-repairing. The very intriguing ideas of synthesizing an “evolvable hardware” and, more specifically, of developing a research for capturing the very features of biological evolution and reproducing them into an electronic hardware, thus going from biology to an evolvable hardware, have been intensively investigated (Higuchi et al., 1997; Sanchez and Tomassini, 1996). The approaches to such ambitious goals of designing and building biomimetic evolvable and self-reproducing machines have been criticized (Santoli, 2000) by stressing the physical and logical differences between their basic assumptions and the main features through which we are able at present to identify and describe biosystems. Mainly, it was argued that the merely “syntactic” aspect of information processing that is shared by all such approaches can hardly be considered biomimetic on the basis of evolutionary physics of biosystems and their semantic and pragmatic information processing capabilities, that stem from their structure-function (i.e. hardware-software ) hierarchical dynamics that goes from the nanometre (i.e. classical and quantum) up to the macroscopic (thermodynamic) level, so making set-theoretic logic and Shannon-like information two stumbling blocks for a physical interpretation of life, evolution and biological intelligence (Santoli, 1999). This paper formulates and discusses mainly at a system-level a problem concerning intra- and inter-level communication in biomimetic evolvable automata which are thought of as open, far-from-equilibrium systems (Santoli, 2000) capable of realizing an active coupling (Santoli, 2001 and references therein) with their environment through a metabolic and informational feedforward-feedback closed chain of syntax , semantics , pragmatics: As previously shown (Santoli, 2000, 2001) such evolvable automata would necessarily feature the structure-function solidarity observed in biosystems, or the indistinguishability of metabolic (energetic) and informational exchanges. Such a holistic aspect of natural evolutionary systems is becoming increasingly clear with our deepening of the features of biosystem Darwinian evolution (Caporale, 1999; Santoli, 2001), and is giving a contribution to the finding of the physical nature of information, possibly as a concept of a fundamental character (Bohm and Hiley, 1996; Bouwmeester and Zeilinger, 1999), as opposed to standard Shannon’s information (Santoli, 1999) which is shown to be valid just at the thermodynamic (phenomenological) level and under conditions of at least local equilibrium in irreversible processes (Santoli, 1999). Moreover, the problem of the envisageable basic technology of such systems is addressed. The paper is organized as follows: first the previous research results concerning a self-organizing system that are of direct relevance to the problems

dealt with here are briefly recalled (Section 3). Then, the nanophysics and the basic elements of a nanostructuring technology embodying such physics are suggested and discussed, respectively, in Sections 4 and 5. Section 6 introduces and discusses the problem of setting forth a proper causal link throughout the hierarchical dynamical chain that goes from the nanoscale up to the thermodynamic level. The problem, as will be explained, arises mainly from the fact that semantic information, as opposed to purely observable events, holds the dominant sway in such evolutionary chains, so as to prevent one and only causal dynamical morphism from being set forth between levels belonging to different energies. It is shown that some geometric and topological properties underlying the informational physics of self-organization and evolution would allow such problems to be overcome at least partly. In addition to that, problems due to intra-level interactions and to a kind of “complementarity principle” for observable events which stems from the holistic character will be put into evidence. As a side but noteworthy remark, it can be observed that all such problems with artificial nanostructured systems also affect complex natural systems and make it hard to determine causal links in the same; e.g. they hamper research into causal relationships between mental states [real physical states, classical or quantum field theoretic (Santoli, 2000), or epiphenomena throughout a hierarchical chain?] and basic neurobiological events. Finally, Section 7 comments on a von Neumann’s idea about the future development of a new conception of logic and of automata theory, comparing such ideas with the present evolutionary approach.

3. List of symbols In the order of introduction: 7 ; the nabla operator † ; dot product f ; vector form of the “information flow” f (a trajectory or a map) in the automaton’s phase space kB ;Boltzmann constant T ; temperature, K

v0 ; angular frequency of the oscillator tc ;memory time scale of the system G ; nilpotent Heisenberg Lie group g ; the algebra of G F ; Fourier transform

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R £ R ; hologram plane ! ; . . . maps to . . . dS(t ) ; entropy change of the system dSi(t ) ;entropy produced in the whole system or in one of its levels

792

dSe(t ) ;entropy exchanged with the environment or with another level of the system itself

d ; Dirac’s “delta function” x, y ; variables characterizing the time evolution of the system in an n-dimensional phase space, the two stochastic processes x(t, v ) and y(t, v ) being stochastically equivalent g ; coupling between different variables, which is assumed to be differentiable with respect to x V ; set of elementary events B ; s-field of the Borel subsets of V m ; probabilistic measure h ; [h1,. . .,h2]T a stochastic process with zero mean and correlation function khi ðtÞh2 ðt0 Þl ¼ Di dðt 2 t 0 Þdij where the D i’s are constants and dij’s are Kronecker’s deltas V ;volume representing the state of a system (the automaton) in phase space

4. Summarizing previous relevant results In order to stress the semantic-pragmatic character of the information processing involved in evolutionary automata that gives rise to the intra- and inter-level communication problems throughout their hierarchical organization which are discussed in Section 6, it is in order to recall the relevant conceptions previously developed (Santoli, 1995, 2000) and to introduce the formalism as relative to the problems. The quantum/classical (i.e. mesoscopic) hierarchical dynamical system, which is self-organizing and cognitive in the sense defined below, whose dynamics models the behavior of an artificial evolutionary automaton (Santoli, 2000) embodies the following concepts. (1) Biomimetic evolvable machines cannot rely on abstract logic and on pre-programming, as in that case they would not be “logically open-ended”, i.e. there would be a predefined goal and no dynamic environment. Indeed, if evolutionary, the dynamic hierarchy should be open-ended in the formal logic sense; it would make no sense the search for the ultimately lowest level, as it should be both complete and self-consistent according to Go¨del’s

incompleteness theorem, but there would be no limit in expanding the number of levels into an automaton of complexity larger than that designed, according to a general theorem in automata theory. (2) Machines capable of Turing-like universal computation (von Neumann’s self-reproducing automata and self-repairing automata) are machines capable of processing just syntactic information, i.e. one consisting of rules and deductive logic operations. The logic of self-reproduction in such machines is fundamentally different from that of living systems: the first ones escape the self-reference paradox because they just read a program put inside them from the outside world; the second ones escape the paradox because proteins synthesized by DNA for self-reproduction are subject to autonomous folding, and the whole process is highly dissipative through injection of entropy into the environment. Autopoiesis, i.e. generation of new information, involves dissipation into the environment. All that leads to the points 2a, 2b, 2c and 2d. (2a) The criterion by Steinbuch of intelligent behavior (Steinbuch, 1963) is more suitable than Turing’s criterion to characterize an evolvable automaton: in an (autopoietic) internal model of the external world, the automaton puts to test the influence of the external world like in an experiment and then reacts in a (supposedly) optimal way. This recalls R. Rosen’s “anticipatory system” (Rosen, 1985) which contains a predictive model of itself and/or of its environment that allows it to compute its present state as a function of the model’s predictions belonging to a later time. (2b) The “flow of information” in the phase space of a logic automaton is isentropic (as from Liouville’s theorem of statistical mechanics): 7·f ¼ 0 i.e. in mechanistic, purely logical reversible machines no new information is generated; just tautologies result from purely logical and complete-enumeration inductive systems. In Section 6 it will be shown and discussed what a “reversible logic” means in the atomic dynamics through the nanoscale landscape of potential energy surfaces. (2c) All treatises about information will give the definition of “amount of information”, but they never give a definition of “information” itself (Santoli, 1995, 1999). However, it is usual to speak of “information content” and “sources”. While recent investigations about the nature of information are even addressing the microscopic (quantum) level[2], it is supposed here that the following definition of the concept is sufficient to deal with the problem of evolvable artificial nanostructured automata (Santoli, 1995) (quantum entanglement and nonlocal physics cannot be excluded at present from the mesoscopic dynamics of large biomacromolecules, in spite of the decoherence induced by far-from-equilibrium conditions). Originating from a remark by G. Bateson (Kay, 1984) (“Information is any difference that gives rise to a difference”) its gist has been developed (Santoli, 1995) by observing that it is

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necessary for any “mark” (a difference), existing just per se in an observed system, to become information that there exists something or someone (the observer) interpreting that mark through interaction with the observed system, thus creating the second difference. Thus, that mark actually becomes physical information as an emergent property from the conjugation (convolution, compression, simulation and therefore abstraction as formation of collective properties ) of external signals with the internal activity of the receptor: the automaton in this case. It is this emergence that “flows” in the phase space of the nanostructured automaton. Information is not contained in any source: these are misleading terms, just metaphors for the basic physical processes mentioned earlier. (2d) Such metaphors would work for thermodynamic systems at equilibrium or in a local equilibrium; they are particularly misleading when applied to open systems, like an evolvable machine, involving mechanical and thermal farfrom-equilibrium processes, for which, e.g. entropy as a state function is not defined at all, so that interpreting information as “neg-entropy” is just illusive. Accordingly, the general coupling of an evolvable automaton with its environment, the latter being necessary as a source of time-series signals and a heat-sink for the dissipative automaton, is expressed ultimately by a nonisentropic “information flow” in phase space: 7·f , 0 i.e. new information is generated in phase space through dissipation and formation of collective properties (abstraction ) through convolution and compression of the incoming time series. This will happen also in the inside feedforward-feedback inter-level flow throughout the hierarchy, from the nanoscale up to the macroscopic levels. It is just this information, as a compressed form of the time series impinging on sensors and the time series fed back from actuators, which, by embodying the collective properties of the microscopic dynamics, classical and/or quantum – i.e. statistical moments and cross-moments for probability density functions ( pdf ) for the general kinetic process depicted by a Fokker-Planck-Kolmogorov equation, and a Lie diffeomorphism on the generalized quantum holographic coupling with the environment, as was previously shown (Santoli, 2000) – forms a semantic space. This space makes up the automaton’s “simulation of its environment”. Simulation thus means the construction of symbolic codes which does not consist in a mere copying process, like information recorded by a Xerox machine, and leads to self-organized upper-rank codes that control higher-rank functions. Dissipation removes self-reference paradoxes from the upper-rank functions of the automaton, just like protein folding does in self-reproduction of biosystems (cf. point 2 earlier). The information flow volume in phase space is not constant as in logic deductive processes; it becomes shrinked, or compressed thus generating information.

(3) Semantics implies no net distinction between hardware and software, i.e. it implies a physical morphological-dynamical solidarity, which amounts to a mechanistic interpretation of “cognition” as “self-awareness”: like in biosystems, information is generated and interpreted, i.e. is given a meaning, or a “form” through a dynamic process (in the hardware) which is inseparable from its symbolic description (as given by the software). Cognition means that each hierarchical level is “aware” of the states and relative locations of each other. The more the “awareness” throughout the hierarchical level chain, the less any “dyscrasias” in the automaton’s behavior. (4) The coupling of such a nanostructured automaton with its environment would occur through the dynamics of interaction between time series from the environment and the mesoscopic, i.e. classical/quantum mechanics, of the automaton’s components, devices and subsystems making up the whole holistic system. (5) As was argued (Santoli, 1995, 2000) and will also be further deepened in the following, nanoscale classical nonlinear and chaotic dynamics, both (conservative[3] ) Hamiltonian and dissipative (Beck and Schlo¨gl, 1995; Hilborn, 1994) as well as quantum mechanics would supply both powerful information processing “tools” escaping Bremermann’s limit (Bremermann, 1962) of information processing rate, and “loopholes” out of the abstract logic constraints of Go¨del’s incompleteness and Turing’s halting problem (Santoli, 1995).

5. What physics for the biomimetic evolutionary automaton? Such features thus would qualify the nanostructured automaton as an evolutionary system. This section goes farther exploring mesoscopic physics and the relationships between the meso- and the macro-scopic worlds to catch any suitable “mark” of evolutionary character. Implementation of such character through a suitable technology will be briefly discussed in Section 5. Special care will be given to stressing the different time scales met with in going from the micro- to the macro-scale, as this is important for the communication problem. It is shown that an open nanostructured macroscopic system, i.e. an open system structured with nanoscale controlled accuracy and whose mesoscopic and macroscopic degrees of freedom work jointly on chaos, coherence and dissipation, is required for a highly rich, varied evolutionary behavior. Intriguingly enough, especially for life sciences, the macroscopic level in addition to be the support of epiphenomena might also work as the stable support of a transient microscopic state. A nanoscale primitive component, whose behavior is semiclassical, i.e. intermediate between the microscopic (quantum) and the macroscopic range, can be thought of, without loss of generality for the present purposes (this is a system-level approach) as a nanomechanical or nanoelectronic nonlinear

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oscillator, driven or undriven, and damped or frictionless, coupled to other nanocomponents into a network for some specific performance. Nano-to-micro connection can also be envisaged, as already within the reach of present technology. Again, in our system this set of oscillators is embedded in a macroscopic environment, like a heat bath, a magnetic field, an electric field, a laser light field, etc. The mesoscopic size of each component may involve, according to proper design, both highly nonlinear, integrable and nonintegrable Hamiltonian and quantum dynamics, while dissipative processes can drive the whole network or just parts of its degrees of freedom far from equilibrium, which is the condition for self-organization. So the principles of chaos (Beck and Schlo¨gl, 1995; Weiss, 1998) and quantum dissipation (Dittrich et al., 1998; Schempp, 1998) should guide the design of each component and its connections within the hierarchical network. Quantum effects, hard though to attain when kB T @ v0 ; would contribute, through a very subtle interplay with the intricate machine of deterministic chaos (i.e. the interplay of chaos-coherence-dissipation ), a much richer dynamic behavior, and would be worth obtaining, even for a short time, to continuously convey “information” from microscopic to macroscopic scales. The point would be the keeping of quantum coherence against its degradation due to dissipation. First the coupling with the heat bath, or the effects of substitution of the latter with a noisy driving, will be considered. The coupling with the heat bath will determine the degree of nonequilibrium of the integrated nanosystem (the oscillation modes of the various multidimensional components), together with the relaxation times of the phenomena involved and the heat-exchange capabilities of the various components according to their sizes. In an integrated nanomechanical and nanoelectronic structure, the problem could be simplified through linearized models both of dissipative processes due to nanomechanical motions (acoustic radiation from forced oscillations, phonon scattering, thermoelastic effects, phonon viscosity, compression of potential wells, transitions among time-dependent potential wells in the landscape of molecular potential energy surfaces) and of the nanomechanical part involving mobile nanomechanical members (sliding, rolling, rotating etc.) over potential energy surfaces within bounded regions making up the structure. From the spectral density of bath modes, that contains frequencies of the modes and their coupling to the system, the damping kernel of the linearized subsystem will show memory on the time scale Z tc ¼ ð1=g0 Þ dt tg ðtÞ (integration between 1 and 0). So if time scales shorter than tc are of interest, these memory effects can be neglected.

A noisy driving would not be exactly the same as a heat bath. The role of noise from the environment and from designed noisy members will be discussed in relation to the problem dealt within Section 6. A single classical degree of freedom, with chaotic dynamics and a huge inertia to avoid the driven-to-driving back reaction, would mimic the effect of a (large, infinite in the limit, number of degrees of freedom) reservoir just on short time scales. This would be both for linearized subsystems and for nonlinear systems, with or without quantum effects. Anyway, both heat baths and environmental noisy fields would affect the detailed dynamics of the oscillator, such as trajectories and decay times of oscillations, which should thus be investigated for a given design at the component level, not just its initial statistical kinetic distributions of dynamical quantities or its final statistical mechanical (possibly thermodynamic level) average properties. The possibility of quantum coherence in far from equilibrium, selforganizing evolutionary systems is particularly interesting as to information processing throughout the same. Coherence would tend to suppress chaos, but this process would take some time. However, the suppression of chaotic dynamics by quantum coherence is followed by destruction of coherence by the environment degrees of freedom: classical chaos, with information generation along some degrees of freedom and injection of entropy into the environment along other directions, is restored. From the evolutionary standpoint, the whole dynamics would mean that any pre-programmed behavior being realized through subsystems working like a sequential computing machine would be knocked out and the search for something new would be switched on again. The switching from a nearly classical chaotic time evolution of a quantum system to a dynamics dominated by coherence can occur under very general conditions. And the same is for the crossover to decoherence and dissipation; the latter might occur in much longer time scales than decoherence. What is important to remark from the informational viewpoint is the crossover from a coherent to a decoherent and then a dissipative dynamics which implies the crossover from a unitary to an anti-unitary symmetry in phase space. Coherence would lead to communication through tunneling, and can give rise to a constructive interference of wave functions. This opens the way to classically inaccessible regions of the automaton’s phase space. So a concept exploitable in the design of nanocomponents to work under such conditions would be that of “chaos assisted quantum coherence”. Under conditions of coherence, information is just transferred. New information can be generated and transferred in an open, far-from-equilibrium system from the microscopic up to the macro-level under quantum coherence conditions resulting from the noncommutative group of symmetries of the nilpotent Heisenberg Lie group G, which is already applied in functional magnetic resonance imaging, known under the acronym fMRI (Schempp, 1998) where the concept of “generalized quantum holography” is introduced. It is just these

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symmetries which avoid decoherence occurring in nonequilibrium. A corresponding information processing concept can thus be formulated and embodied in such hierarchical evolutionary systems. Under the purely geometric condition of unitarity, the nilpotent Heisenberg Lie group could be applied to the convolution of environmental and also of inside signals. With symbols as in Section 2, let the impinging time series provide wavelets coherent enough to form a stationary quantum interference pattern for holography on an R £ R where the wavelet mixing takes place. G turns out to be the noncommutative group of symmetries to analyze and synthesize the convolution structure of the wavelets originating from a mother wavelet in the case of phase coherence under the action of F (Huyghens’ principle), and it implements the symmetries of quantum level adaptive resonance self-organization on the basis of phase conjugation for any proper geometric scale, from the micro- to the macro-scale. Like in fMRI (Schempp, 1998), phase conjugation/time reversal invariance results in self-adaptation, robustness to noise and to small changes in initial conditions. The Lie diffeomorphism (differentiable mapping with a differentiable inverse) gives exp: g ! G;

log: G ! g

As a result, just as occurs with chaotic information processing, the cybernetic crisis from exponential complexity of data to process is overcome: there is just scale-limited possibility of data compression and storage, as information storing and transmission are just the same and unique process. Now the loophole out of abstract logic constraints of Go¨del’s incompleteness and Turing’s halting problem is not dissipative chaos but synchronous cooperativity by linear superposition throughout the levels from the smallest to the whole scale. Coupling with the environment goes vertically from meso- to macro-levels. Like in classical chaos, there are no algorithmic instructions, but just learning, and no net hardware-software distinction, but just a physical morphological solidarity. Moreover, there is no amplitude bit, but just lossless phase gating. 6. The elements for a nanostructuring technology The complexity of the evolutionary automaton thus introduces abstract topological spaces and structural topologies more complicated than the usual two-dimensional networks. On the molecular level, “wiring” can usefully give way to electromagnetic fields that, being independent of a material support, are ideal to connect different material sections in space. Generation and guiding of such fields might require material devices on proper length scales. Anyway, no hard-wired, point-to-point fixed connection organized network can be planned for the evolutionary automaton. In the state space, any node and edges of the network will be, respectively, the local eigenstate and the external driving fields

which, implemented through continuous and/or pulsed fields, would make up a photonic wiring. With N nodes, each one with just I ¼ 2 local states, the number n of eigenstates and the number e of the total allowed connections or “edges” would be n ¼ 2N

and

e ¼ N £ n=2

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respectively, with the generation of a state space network of complex topologies, some of them being projectable onto a plane, e.g. a torus with N ¼ 4 as a projection of a four-dimensional cube, and a concentrical double torus with N ¼ 5 as a projection of a five-dimensional cube. There is space for node state reorganizations. The point is that the framework of “scattering theory” for quantum chaos in open (i.e. damped) systems can be applied not only to typical scattering situations as with nuclei, atoms, molecules and solid-state samples, but also to nanoelectronic devices, be they based on semiconductor or molecular and supramolecular structures; indeed, the nano-device itself, with its connection leads and the nearly free motion of electrons, holes and quasiparticles through them that represents the asymptotically free states of the scattering process, plays the role of the scatterer. Moreover, should the quantum level become important in an integrated nanomechanical-nanoelectronic system, not any function could be realized on any level. A central paradigm of computer science, consisting in the independence of computer conceptions from their realizations, is violated on the nanoscale. It was shown (Ko¨rner and Mahler, 1996) that the dipole-dipole interaction law in an optically driven quantum network prevented the coupling constants of the Ising model from being chosen at will. With the symbols explained in Section 2, it can be seen how the need for a “floppy” structure comes from thermodynamics: dSðtÞ ¼ dS i ðtÞ þ dS e ðtÞ; in an evolutionary system, it must be dS e ðtÞ , 0

and

jdS e ðtÞj . dS i ðtÞ

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ð1Þ

so that dSðtÞ , 0; the whole nanostructured hierarchical system will evolve against the degrading action of noise and continue to fulfill the inter-level and system/environment conditions as above just if its redundancy R ¼ 1 2 ½SðtÞ=S max increases as a result of the fact that Smax as the maximum entropy corresponding to the maximum number of complexions at equilibrium grows

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faster than S(t ). This is possible just if the number of nanocomponents or the number of degrees of freedom through which the self-organization process occur increases with time. So flexible nanocomponents (e.g. floppy macromolecules) might satisfy this requirement. On time scales large compared to the coherence time with its complex behavioral patterns of coherence-chaos interactions stressed above, a general Fokker-Planck master equation for the nanoelectronic system would be as follows: ðdrjj =dtÞ ¼ SK–J {RJK rKK 2 RKJ rjj } where rjj are the occupation probabilities of a state j J. , and RKJ etc. are the transition rates. The stochastic process of a nonlinear chaotic nano-scale component can be depicted by the following Fokker-Plank master equation (cf. Section 2): dðx; t; vÞ=dt ¼ gðx; t; vÞ; with initial conditions

xð0; vÞ ¼ ½x1 ð0; vÞ; . . .; xn ð0; vÞ T ¼ ½x10 ; . . .; xn0 T with x ¼ ½x1 ; . . .; xn T ;

g ¼ ½g1 ; . . .; gn T ;

v [ V and ðV; B; mÞ

for thermal or any noisy system. With white noise of zero mean value and correlation function as specified in Section 2, the equations to be solved, generally through numerical methods, will be d xj ðt; vÞ=dt ¼ gj ðx1 ; . . .; xn Þ þ hðt; vÞ The pdf W for the process as a function of a stochastic potential teaches something essential about the intra- and inter-level dynamics of an automaton built on such principles, and about the problem discussed in Section 6. dW =dt þ Si d½ai W =dxi 2 ð1=2ÞSi Sj ðd2 =dxi dxj Þ½bij W ¼ 0 with initial conditions W ðx; 0jx0 ; 0Þ ¼ dðx 2 x 0 Þ ¼ >i dðx 2 x 0 Þ

ð2Þ

ai ðx; tÞ ¼ limDt!0 ð1=DtÞ

Z

Z ...

bij ðx; tÞ ¼ limDt!0 ð1=DtÞ

Z ...

ð yi 2 xi ÞW ð y; t þ Dtjx; tÞdy1 . . .dyn

Z

Z ...

Z ...

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ð yi 2 xi Þð yj 2 xj Þ

W ðy; t þ Dtjx; tÞdy1 . . .dyn with i and j varying from 1 to n, and integrals taken from 21 to +1. From the kinetic equation (2) the expected value , x . of x can be obtained, and it will correspond to the kind of so-called mean-field descriptions. But this value of x determines just the center of gravity of its pdf. Is this actually the most probable value that causes the mean field description to make sense? This question leads to the problems dealt with in Section 6. 7. Semantics and the problem of the causal inter-level bridging in the holistic hierarchical dynamics A more complete specification of the statistics of x and thus of the physical meaning of going from the nano- to the macroscopic description is possible by taking its kth moments Z mk ¼ x k W ðxÞ dx where integration is carried out from 21 to +1. Applying this procedure to equation (2), a time rate equation for the average , x . is obtained for k ¼ 1 which also contains higher-rank moments of the distribution. Again applying the procedure for k ¼ 2; 3; . . . the time rate equations for the so-called variance, the skewness etc. are obtained. All such equations will be coupled with each other and are nonlinear due to nonlinearity of transition probabilities in (2). In going from the microscopic (nanolevel) to the macroscopic description, a real simplification of description (i.e. simulation through compression or reduction of degrees of freedom) is attained just if W(x, t ) has one hump, so that all upperrank moments are order of magnitudes lower than the value of , x . and the coupling becomes vanishingly small, thus leaving place to application of mean field approximation (usually employed for instance in solid-state physics etc.). Otherwise, at the end of this study of the stochastic process we (or any automaton level processing information from an underlying level) would be left again with an enormous amount of degrees of freedom. But chaotic and noisy dynamical systems show multi-humped (multi-maxima) pdfs, instabilities due to bifurcations etc.; fluctuations at the kinetic level can reach up to the thermodynamic level. Upper-rank moments and their time rates can become the same or of comparable order of magnitude as the expected value.

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Accordingly the following can be noted. (1) Some phenomena on the nanoscale might ask for a microscopic or even a detailed (i.e. non-statistical) analysis for their understanding. (2) The fundamental difference between the nanostructured automaton actually working on open mesoscopic physics and any other material system consists in that the latter can be studied, with a good approximation, as made up of levels whose relaxation time scales differ by many orders of magnitude, and through dynamic differential equations whose boundary conditions are set forth in practice by the level with much shorter relaxation time scales, e.g. through the introduction of average values, while the level with much longer relaxation time scales can be taken to be a constant. Relaxation times generally are inversely proportional to interaction strengths. For instance, the molecular dynamics of intermolecular interactions, dominated by the relatively weak van der Waals forces, can be studied with a good approximation as separate from the atoms dynamics, and the latter as independent of nuclear particle dynamics. But in such an automaton this decoupling of levels would be a countersense: both processes with comparable values of relaxation time scales and processes of different energy levels, all closely intertwined up to the macroscopic level, occur. (3) Under conditions of coupled dynamics of the statistical moments from the master equation, noise can be a source of instability and of evolution toward novel states, but also toward a mixing of the automata levels of information processing, i.e. toward indistinguishability of the levels in question. The automaton would become incapable to distinguish between states belonging to different levels. A given level in the hierarchy would go into full chaos, i.e. broad-band noise, down to a loss of statistical correlations that amounts to the acquisition of the degrees of freedom of the level underneath in the hierarchy. The two levels, so mixed, would lose their logic modalities with respect to the oncoming time series. (4) The state of the automaton in phase space is represented by a very small volume, not as a point, because of fundamental uncertainties and/or inability to state infinitely precise values of phase space coordinates; chain of events involving both Hamiltonian and dissipative processes are reflected in phase space, respectively, as follows:

dV ðtÞ ¼ 0 (levels with no energy dissipation on the nanoscale can be envisaged, e.g. slowly moving nanoactuators; there are nanoscale processes in which dissipation depends on velocity of relative motion on the molecular potential energy surface) and dV ðtÞ , 0

So the evolutionary physics of the automaton and the necessary intertwining of the automaton with its environment lead to communication problems inside the hierarchical level chain. Dyscrasias as well as eucrasias look like necessarily coexisting features of evolutionary systems. This seems mainly due to the semantic kind of information, i.e. from the extralogical (heuristic ) information processing that gives a “meaning” to the space observed by the automaton. From this overwhelming presence of semantic spaces as opposed to purely observable events (the set V of elementary events considered in the equations above, and processed through dissipative quantum nanochaos ) the following causes of dyscrasias and syndromes originate: (1) the energetic gap, or in other words the “relaxation time” scale differences, between the levels makes the causal connections quite loose; (2) the different semantic domains for causes and effects belonging to different energy levels prevents one and only causal dynamical morphism (i.e. the conceptual modeling of merely observational spaces ) from being set forth. Stated otherwise, because of semantic dishomogeneity between an effect at a certain energy level of a cause acting in the underlying level, the state of a level cannot be considered as described completely (as is usually assumed reductionistically) if it is described as a property arising from the related, energetically underlying level and ignoring the energy gap itself. Some essential property contained in the ignored dynamic morphism belonging to the underlying level might be missed in such reductionistic description of a holistic system; (3) the hierarchy is made up of both energy and information (syntactic and semantic) levels; the latter’s semantic extralogical information morphisms (codes ) should be substantially “agreed upon” by levels throughout the hierarchy. As a matter of fact, in a working selforganizing system each level is able to recognize the code of the neighbor lower and upper level; the code of any newly formed level as a result of evolution, e.g. as an effect of noise, must be “broken” by its neighbors to avoid degradation and death from excess entropy production [cf. equation (2)]; (4) the general computability of natural processes is an unproved empirical assumption, so that a cherished, longed for capability, eventually reachable, of matching calculated and practical technological properties is arbitrary; moreover, even though noncomputable functions are absent, any recursive function implies a semantic homogeneity in its algorithmic form, so that any energy-based computational strategies would fail in the building of the causal inter-level link;

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(5) observable events can incur a kind of “complementarity limitation”. The “ultimate anatomy” of the holistic structure-function solidarity might be subject to a complementarity principle: analyzing one of the components, e.g. structural events, would alter its counterpart. All that, concerning an evolutionary system, comes from its description in a nanoscale energy landscape. But it is suggested here that some purely geometric features coming from conserved symmetries in dissipative processes or in isolated nondissipative degrees of freedom, and some symmetrypreserving sets of degrees of freedom, would allow patterns of observables belonging to different energetic levels to be related instead of the singular events, and would hold promise to be of help in mastering the design of evolutionary systems based on the joint action of undecidable classical dynamics, quantum dissipative dynamics and the emerging discipline of generalized quantum holography information processing. The new general mathematical strategy employed in f MRI (Schempp, 1998) for the causal interactions across energy gaps, and exploited for extracting any anatomic, physiological or pathological, meaning from the microscopic proton’s spin angular momenta behavior and conveying that information into the macroscopic imaging process, is suggested here for implementing nanostructured evolutionary systems. The complex mathematics involved (Schempp, 1998) boils down first to the generation of an observer-independent geometrical continuous representation of the relevant pattern of observables in the causal layer: in our case, a synchronous spatiotemporal pattern of signal wavelets; and second, the transformation of the geometrical pattern from the causal group to the corresponding geometrical pattern in the emergent level, where it can be analyzed further. Further geometric properties crossing the nanoscale energy landscape are Berry’s geometric phase in quantum and classical systems (Shapere and Wilczek, 1989), which comes from a symmetry-preserving set of degrees of freedom, and the patterns of basins of attraction and the separatrices as relative. The topologies of chaotic dynamic set of characteristic patterns look like a proper geometrization of intra- and inter-level causal relationships, or the geometrization of the automaton’s base of knowledge. Due to Berry’s geometric phase, a nanosubsystem slowly transported (i.e. adiabatically in the dynamic sense) round a circuit will return in its original state but, in addition, will record its history in a deeply geometrical way involving phase functions hidden in parameter-space regions which the subsystem has not visited.

8. From the nanoscale up to the thermodynamic level – a remark on logic A recollection and a remark as relative to the same concerning a von Neumann warning about logic would complete the picture of inside communication and

the information concept for evolutionary automata and their physical implementation. He had warned (von Neumann, 1965) that “formal logic is, by the nature of its approach, cut off from the best cultivated portions of mathematics. . . and forcedly confined to combinatorics”. Moreover, he had advocated a new system of formal logic moving “closer to another discipline which has been little linked in the past with logic. This is thermodynamics, primarily in the form it was received by Boltzmann”. And he had also foreboded, on such bases, a new, powerful theory of automata. As was more widely shown previously (Santoli, 1999, 2001), an evolutionary automaton behaving according to the biomimetic closed chain syntax , semantics , pragmatics which makes up the automaton base of knowledge is necessarily self-referential and yet not paradoxical because it is self-consistent through injection of metric entropy (Beck and Schlo¨gl, 1995) or even thermodynamic entropy into its environment by compression through a strange attractor or, in generalized quantum holography, through the symmetries of Heisenberg’s group (Schempp, 1998). In this “dynamic logic” framework, the mixing up of levels in interlevel communication (loss of distinguishability between environmental time series impinging on two different levels or between inner time series belonging to two different levels) embodies Go¨del’s incompleteness theorem. A merely reversible (abstract) logic, never found in any material system[4], as opposed to the irreversible Boltzmannian thermodynamic description, would mean, in the nanoscale potential energy surface landscape, motion without merging of any potential wells (an irreversible transformation), i.e. just transmission of information and not generation of new information through dissipative quantum chaos which acts as a “phase space microscope” revealing an increasingly finer graininess of phase space. Indeed, as is shown by the problem of inside communication, the holistic character of an evolutionary system stemming from the impossibility of decoupling the hierarchical levels cannot be described by linear, monocausal reasoning. Whichever element on some particular level is chosen for investigation, it must be considered in its context involving other levels, with circularly causal relationships between them. Moreover, as appears from the relaxation time scales involved in the merging of the energetic (metabolic) and information (coded interactions) flows, the macroscopic (thermodynamic) level looks like being required together with an active quantum/classical microscopic dynamic background for an evolutionary system to exist. All that looks like a roadmap according to von Neumann’s views mentioned above. Notes 1. A graffito under a wolf’s head portrait hung on the wall of an alpine hut in the Natural Park of Argentera, the Maritime Alps, Italy.

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2. “Information is deeper than reality”, according to the physicist A. Zeilinger of the Institut fu¨r Experimentalphysik, Universita¨t Innsbruck, Austria, as reported by M. Buchanan, New Scientists, No. 2125, 26-30 (1998). 3. According to a common (and misleading) usage, “Hamiltonian” would be synonymous with “conservative”. Actually, “Hamiltonian” is a term coined to address a certain form of dynamic equations that, when normally (but not necessarily) appled to energy-conserving dynamics, might describe a non-conservative system as well; e.g. a frictionless pendulum hanging from an oscillating support is a nonconservative Hamiltonian system. 4. It can be easily shown that a material system behaving like a conceptual Turing’s machine would be an ideal gas (i.e. an energy-conservative, non-integrable (fully chaotic) Hamiltonian system) prepared in a given state; i.e. an unexisting material system.

References Beck, Ch. and Schlo¨gl, F. (1995), Thermodynamics of Chaotic Systems, Cambridge University Press, Cambridge, UK. Bohm, D. and Hiley, B.J. (1996), The Undivided Universe, Routledge, London. Bouwmeester, E. and Zeilinger, A. (1999), The Physics of Quantum Information, Springer-Verlag, Berlin. Bremermann, H.J. (1962), “Optimization through evolution and recombination”, in Yovis, M.C., Jacobi, G.T. and Goldstein, G.D. (Eds), Self-Organizing Systems, Spartan Books. Caporale Lynn, H. (Ed.) (1999), Molecular Strategies in Biological Evolution, The New York Academy of Sciences, New York. Dittrich, T., Ha¨nggi, P., Ingold, G.-L., Kramer, B., Scho¨n, G. and Zerger, W. (1998), Quantum Transport and Dissipation, Wiley-VCH, Weinheim-Berlin. Higuchi, T., Iwata, M., Liu, W. (Eds) (1997), Evolvable Systems: From Biology to Hardware, Springer-Verlag, Berlin. Hilborn, R.C. (1994), Chaos and Nonlinear Dynamics, Oxford University Press, Oxford. Kay, A. (1984), “Il Software”, Le Scienze, No. 195, p. 19. Ko¨rner, H. and Mahler, G. (1996), “Cooperative optical properties of interacting charge transfer subunits”, in Mahler, G., May, V. and Schreiber, M. (Eds), Molecular Electronics, Marcel Dekker, Inc., New York, Basel, Hong Kong, pp. 209-30. Rosen, R. (1985), Anticipatory Systems, Pergamon Press, London. Sanchez, E. and Tomassini, M. (Eds) (1996), Towards Evolvable Hardware, Springer-Verlag, Berlin. Santoli, S. (1995), “Nanostructured undecidable semantic microrobots for advanced extrasolar missions”, Proceedings of the 46th International Astronautical Congress, International Astronautical Federation, 2-6 October, Oslo, Norway, Paper No. IAA-95-IAA.4.1.04. Santoli, S. (1999), “Shannon-like information and set-theoretic logic: stumbling blocks to a physical theory of life and biological intelligence”, Journal of the Ultra-Scientist of Physical Sciences, Vol. 11 No. 1, pp. 1-15. Santoli, S. (2000), “Nanochaos and quantum information for a physical theory of evolvable semantic automata”, American Institute of Physics Proceedings (AIP ), of the CASYS’2000 Conference, Lie`ge, Belgium, Vol. 437, pp. 500-9.

Santoli, S. (2001), “Mesophysical anticipatory behavior – enroute to quantum and classical nanobiology”, International Journal of Computing Anticipatory Systems, Vol. 10, pp. 384-401. Schempp, W. (1998), Magnetic Resonance Imaging – Mathematical Foundations and Applications, John Wiley and Sons, Inc., New York, Chichester, Toronto. Shapere, A. and Wilczek, F. (Eds) (1989), Geometric Phases in Physics, World Scientific, Singapore, London. Steinbuch, K. (1963), Automat und Mensch, Springer-Verlag, Berlin. von Neumann, J. (1965), “On the logical and mathematical theory of automata”, Collected Works of John von Neumann, Pergamon Press, New York, Vol. V, pp. 288-328. Weiss, U. (1998), Quantum Dissipative Systems, World Scientific, Singapore, London.

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Systems dynamics modelling, simulation and optimization of integrated urban systems: a soft computing approach P.S. Satsangi, D.S. Mishra, S.K. Gaur and B.K. Singh Dayalbagh Educational Institute (Deemed University), Dayalbagh, Agra, India

D.K. Jain Mechanical Engineering Department, M.R. Engineering College, Jaipur, India Keywords Cybernetics, Modelling, Simulation, Optimization Abstract A systems dynamics (SD) simulation model has been developed to analyse dynamics of system behaviour in terms of various performance indicators representing city problems, on one hand, and city development, on the other, with three types of policy interventions: changes in the level of sectoral activities, structural changes in different sectors; and changes in the tolerable city problems index. An artificial neurals network (ANN) model has been successfully trained and used as a quick response model for fast feature extraction of the dynamics of the integrated urban energy-economy-environment system such that the outputs are within reasonable acceptable error for values of inputs covered by the input space of training patterns. For the sake of further convenience and effectiveness in policy decision making, optimised simulation trajectories are generated by applying genetic algorithms (GAs) search and optimisation methods for alternative policy scenarios of input variables. An application is shown in the context of the city of Jaipur.

Systems approach Project approach to tackle city level problems has not provided sustainable solutions but only helped to relieve the impact of the problem on a short-term basis. A simulation model using systems dynamics (SD) methodology has been developed to study impacts of various policies for mitigating city-level problems and enhancing city-level development. Only macro-level causal linkages are presented in Figure 1.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 808-817 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443879

City problems: ACPI and city development: ACDI An integrated measure of the negative impacts on cities are given as follows by the actual city problems index (ACPI) based on x1 ¼ air pollution index (API); x2 ¼ solid-waste generation (SWG); x3 ¼ traffic congestion (TC); and x4 ¼ population density (PD) (Also a surrogate for slums population).

A soft computing approach

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Figure 1. Interconnections of aggregate system variables

ACPI ¼ 3:5x1 þ 1:2x2 þ 2:5x3 þ 2:8x4

ð1Þ

on the basis of assigning appropriate weights according to the perceived relative threats of the concerned variables. Similarly an integrated measure of the positive impacts on cities are given as follows by the actual city development index (ACDI) based on x5 ¼ total electricity consumption (TELEC) and x6 ¼ investment in utility sector (IUA). ACDI ¼ x5 þ x6

ð2Þ

Since all variables representing city problems are normalised to base year values of one, the initial value of ACPI or ACDI is merely the summation of weights (respectively assumed as 10 or 2). The negative feedbacks from urban problems to sectoral investments as long-term measures to ameliorate urban problems are, at present, quite weak. Long-term measures aim to slowdown, and finally reverse, at a later stage, the prevailing migration to large cities and thus lead along the path of decentralised economic development. Generation of employment opportunities in smaller cities, and towns through industrial investments, together with other policy measures, will attract immigration away from large cities. Such policies could be promoted by evolving adequate taxation policy, price mechanism and availability controls on infrastructure services provided by the government.

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An integrated measure of the negative impacts (i.e. city problems) on urban environment in the form of a non-dimensional ACPI increases with increase in the magnitude of various city problems which are approaching higher proportions. Similarly an integrated measure of the positive impacts (i.e. city development) on urban system in terms of a non-dimensional ACDI increases with increase in magnitude of the representative city development parameters as they approach higher proportions. The magnitude of the ratio of tolerable city-problems index (TCPI), (an exogenously supplied parameter) to ACPI indicates the level of policy interventions (by government), in different sectors, to manage the city problems within tolerable limits. If the value is higher than or equal to 1, no policy interventions are likely to come and vice versa. Dynamics of the important performance indicators namely API, SWG, TC, PD, TELEC, IUA; due to changes in TCPI (with assumed values of 20, 10, 9, 8, 7 and 6 as compared to initial ACPI value of 10 and initial ACDI value of 2) are shown in Figures 2-7 with I/O values as indicated in Table I.

Policy simulations with the SD model Dynamics of system behaviour in terms of various performance indicators such as API, SWG, TC, PD, TELEC and IUA have been analysed with three types of policy interventions: (1) changes in the level of sectoral activities; (2) structural changes in different sectors; and (3) changes in TCPI.

Figure 2. Impact of TCPI on API

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Figure 3. Impact of TCPI on SWG

Figure 4. Impact of TCPI on TC

Figure 5. Impact of TCPI on PD

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Figure 6. Impact of TCPI on TELEC

Figure 7. Impact of TCPI on IUA

Model simulations with changes in sectoral investments show strong influence of the industrial investment on the performance indicators due to its “active” role and high energy-intensity. Structural changes in commercial, domestic and industrial sectors signify improvement of the system behaviour when such shifts are in favour of those investments which require high quality carriers i.e. electricity and petroleum-based fuels. Shifts from individual transport to intermediate and bus-based mass transport produce lesser air pollution and TC. Non-motorised vehicles are better from the point of view of population aspect but lead to higher TC on account of their lower carrying capacity per unit of occupied road length compared to that of motorised vehicles. Thus, the level of system improvement

with structural changes highlights their limitation as only short-term measures A soft computing for alleviating urban problems. approach As activity levels decrease and compact/cleaner fuels are used at lower values of TCPI, there are corresponding drops in API, TC, PD and SWG. However, compared to TCPI values of 8, population densities are higher for TCPI values of 6 and 7, at the last phase of simulation period, due to lower land 813 acquisitions. In addition to the policy interventions associated with lower values of TCPI, provision of better utility services (by higher investment particularly in land acquisition and development) would reduce population density also. Artificial neural network model for quick response simulation A feed forward multilayered perceptron with back propagation learning algorithm as shown in Figure 8 is used as the ANN Model of the integrated Symbol

FXINV FXPOP GTDTR HIPOPR HQERICM KBRIIS PTDBR PTDIMR TCPI

TC TELEC TNPHE TPHE API IUA MGTD MPTD SWG PD

Description (a) Input variables (Reference case values) Fraction for additional investment (0.01) Fraction for population rise (0.01) Ratio of truck-based to total goods transport (0.70) Ratio of high-income people to total population (0.25) Ratio of high-quality energy investment to total commercial investment (0.40) Ratio of investment in knowledge-based industries to total industrial investment (0.21) Ratio of bus-based to total passenger transport (0.50) Ratio of intermediate to total passenger transport (0.25) Tolerable city-problems index (20) (b) Output Variables (Reference case values for target year 2005 for the city of JAIPUR) Traffic congestion (477 vehicles per lane) Total electricity consumption (830 Gwh) Total non-petroleum heat energy (231 toe) Total petroleum heat energy (134 toe) Air-pollution index (1.44) Investment in utility sector (1584 million rupees) Motorised goods transport demand (527 mtkm) Motorised passenger transport demand (1979 mpkm) Solid-waste generation (219 tonnes) Population density (8194 persons per km2)

Table I. List of input and output variables

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Figure 8. The multi layered perceptron

urban systems which is trained by the database generated by the numerous simulations of the SD models. The ANN model has been successfully trained and used as a quick response model for fast feature extraction of the dynamics of the integrated urban energy-economy-environment system such that the outputs are within reasonable acceptable error of ^10 per cent for test patterns with values of inputs covered by the input space of training patterns. The ANN model thus provides an excellent opportunity to store the knowledge contained in the variety of SD simulation results (which would have otherwise been discarded after analysis) into weights of the trained ANN model which has considerable potential value for intelligent quick response simulations for policy analysis and design of the concerned urban system.

Optimised simulation using genetic algorithms It is prudent to make use of the multiple simulation experiments with the help of the SD model for acquiring capability for alternative policy formulations. It is further expedient to use the quick response of ANN model to effectively carryout policy design oriented multiple simulations. It would indeed be most convenient for policy decision making and implementation to generate

optimised simulation in the policy space defined by SD/ANN model A soft computing simulations by applying genetic algorithms (GAs) search and optimization approach methods based on natural genetics and selection – which have proved to be effective as a solution tool for complex optimization problems in a number of fields.

815 Problem solving Objective function: Minimize fðxÞ ¼ ACPI=ACDI as given by equations (1 and 2) which can be rewritten as follows: Minimize fðxÞ ¼ ð3:5x1 þ 1:2x2 þ 2:5x3 þ 2:8x4 Þ=ðx5 þ x6 Þ Subject to x5 . x2 . x4 . x1 ; x2 . x6 ; x2 . x3 ; 1023 ð0:6343x1 þ 0:6512x2 þ 0:6538x3 þ 0:6645x4 þ 0:6111x5 þ 0:4869x6 Þ less than fraction for additional investment ðFXINV ¼ 0:01Þ; and the lower xðLÞ and upper xðUÞ bounds for i i the variables for the target years 1995 and 2005 (shown in Table II): Step 1: .

Using 10 bits for each variable xi the total string length will be 60. With 10 bits, one can get a solution accuracy of: .

ðLÞ 10 ½xðUÞ i 2 xi =ð2 2 1Þ for different variables in different intervals.

.

Choose Roulette wheel selection for reproduction, a single point crossover, and a bit wise mutation operator.

.

Assign crossover and mutation probabilities.

.

Generate random population using Knuth’s random number generator

.

Set the counter at t ¼ 0:

.

tmax is then decided.

Step 2: .

Evaluate each string in the population with respect to fitness given by ft ¼ 1=ð1 þ fðxÞÞ:

Target year 1995 1.09 # x1 # 1.30 1.29 # x2 # 1.46 1.009 # x3 # 1.542 1.233 # x4 # 1.35 1.525 # x5 # 2.448 1.403 # x6 # 1.43

Target year 2005 0.95 # x1 # 1.44 1.31 # x2 # 2.04 0.8008 # x3 # l.14 1.42 # x4 # 1.53 1.72 # x5 # 2.20 1.40 # x6 # 1.84

Table II.

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.

Calculate fitness of the strings.

.

Similarly other strings are evaluated and fitness values are calculated.

Step 3: Since t ¼ 0 , tmax; proceed to Step 4. Step 4: Reproduction: Using Roulette wheel selection P . Calculate average fitness of population F ¼n Fi =n: .

Compute expected count of each string as F(x )/F.

.

Selection procedure is repeated n times.

.

Tabularize the results.

.

Finally one gets a new population.

Step 5: Crossover – Before performing crossover, coin is flipped to see the need of crossover. Step 6: Mutation – Perform mutation. Step 7: Again evaluate each string of new population. This completes one iteration. Perform it up to tmax iterations. Step 8: Finally one gets an optimum solution as shown in Table III. Dynamics of optimised performance indicators are also sketched in Figures 2-7. Conclusion In comparison to the towns and small cities, the relative costs of the availability of infrastructural facilities and the modern energy carriers, prerequisites for industrial and commercial activities, have to be slightly higher in the big cities if the scale of their energy related problems is to be maintained atleast at the current level.

SI. No. 1. 2. 3.

Table III. Optimized solution

ACPI 10.00 12.80 12.58

ACDI 2.00 3.41 3.83

Target year 1985 1995 2005

Population size – 30 30

1. 2. 3.

Iteration count – 40 40

x1 1.0 1.160821 1.147341

x2 1.0 1.407155 1.7888817

x3 1.0 1.076277 0.905577

1. 2. 3.

x4 1.0 1.259877 1.483656

x5 1.0 2.004094 2.154956

x6 1.0 1.406721 1.673978

ft 0.166667 0.221761 0.233338

Any reversal of the trend of crowding of cities would require still higher A soft computing difference in the above costs. approach One could therefore strive to limit the city size and achieve the ideals of the dream city by manipulating the cost and availability of urban infrastructure and the modern energy carriers. The ANN model has been successfully trained and used to obtain quick 817 response outputs, within acceptable error, for values of inputs covered by the training input space. GAs have turned out to be efficient tools for the development of optimised simulation trajectories for decision variables which are important performance indicators such as: API, SWG, TC and PD that define ACPI on one hand; and TELEC and IU represent ACDI on the other hand; are shown in Figures 2-7 corresponding to a set of policy input variables including the fraction for additional investment (FXINV) as given in Table I. Obviously, other optimised simulation runs for the important performance indicators can be readily made corresponding to any desirable alternative choice of policy input variables. Accordingly, the soft computing techniques of ANN and GAs presented in this paper will facilitate quick response simulations and optimisation of dynamics of integrated urban systems from a basis of system dynamics modelling for effective policy design. References Chakroborty, P. et al. “Optimal scheduling of urban transit systems using genetic algorithms”, Research Monograph, IITK/ME/SMD-94026, IIT Kanpur. Jain, D.K. (1993), Dynamics of Urban Energy-Economy System with particular reference to the city of Jaipur, PhD thesis, IIT Delhi. Satsangi, P.S. et al. (1997), “An intelligent system dynamics approach for integrated management of urban transport energy-economy environment related impacts”, Indian Journal of Transport Management, special issue on public transport and environment, Vol. 21 No. 12, pp. 13-33.

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Model following PID control system Stanisław Skoczowski, Stefan Domek and Krzysztof Pietrusewicz Institute of Control Engineering, Technical University of Szczecin, Szczecin, Poland Keywords Cybernetics, Control systems Abstract The paper deals with robustness to plant parameter perturbations and sensitivity to disturbances of two-loop control structures containing a model of the controlled plant and two PID controllers. Special attention is paid to high robustness of considered structure to perturbations of the controlled plant in relation to its nominal model and to good reduction of disturbances. On the basis of presented simulation results one can compare properties of the proposed structure with properties of the Smith predictor and classic control system structure with single feedback loop. The proposed model following control structures may find wide application to robust control of parameter-varying plants.

Introduction The two-loop model following control (MFC) structure is noted for its simplicity and relatively high robustness to disturbances and stable perturbations. In spite of these advantages, MFC, though being employed (Chern and Chang, 1998; Lee and Song, 1999; Li et al., 1998; Park et al., 1996; Tsang and Li, 2001), is not sufficiently reflected in the literature. The paper (Sugie and Osuka, 1993) deals with robust MFC for nonlinear plants with uncertain parameters, where the discussion is based on the state variable approach with an assumption that the process state vector is to follow the model state vector. However, this limits the substantial capabilities the MFC offers. The state variable approach has also been employed in Wu and Kawabata (1999) to analyze how the process output follows the model output for a class of uncertain linear systems. The state variable system representation seems to be improper in order to clarify basic universal properties of the MFC structure. The system representation by transfer function is much more convenient for this purpose. Furthermore, comparison of properties of the MFC structure with those of the classic, single loop control structure is much easier to make, if elements of compared systems are represented by transfer functions (Skoczowski, 1999, 2001; Skoczowski and Domek, 2000). Kybernetes Vol. 32 No. 5/6, 2003 pp. 818-828 q MCB UP Limited 0368-492X 10.1108/03684920210443888

Preliminaries The main virtue of the MFC structure is the possibility of acting independently in tracking the reference signal and suppressing effects of disturbances and perturbations. The MFC structure is shown in Figure 1.

The reference signal r(s ) is applied to the input of the loop that includes the Model following nominal process model M(s ) and the controller of the model Rm(s ). On the other PID control hand, the nominal model control input is applied to the corrective controller system output, and the resulting signal is applied to the process input. The process output is compared with the model output, and the difference is applied to the corrective controller input. Hence, the process and the corrective controller form 819 a second feedback loop. In Skoczowski (2001) it has been shown that the MFC structure, not being an adaptive one, can perform better than the classic feedback structure regarding robustness provided the following condition is fulfilled: jRð jvÞj . jRm ð jvÞj v 2½0; 1Þ

ð1Þ

The effects are the better, the greater is the difference jRð jvÞj 2 jRm ð jvÞj: jRð jvÞj v [ ½0; 1Þ is bounded above, by stability conditions, and jRm ð jvÞj is bounded below by a desire that the reference signal be sufficiently well followed. From Figure 1 it follows that yðsÞ ¼ ym ðsÞ

PðsÞ 1 þ RðsÞM ðsÞ dðsÞ þ M ðsÞ 1 þ RðsÞPðsÞ 1 þ RðsÞPðsÞ

ð2Þ

Rm ðsÞM ðsÞ 1 þ Rm ðsÞMðsÞ

ð3Þ

where ym ðsÞ ¼ rðsÞ

If RðsÞ ¼ Rm ðsÞ then equation (2) reduces itself to that describing the classic feedback structure. If jRð jvÞj @ jRm ð jvÞj then it holds yðsÞ < ym ðsÞ þ

dðsÞ 1 þ RðsÞPðsÞ

ð4Þ

Figure 1. Linear MFC structure

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Similar properties are exhibited by the MFC/IMC structure of Figure 2 being akin to that of Figure 1 with the only difference that the process and its model are interchanged. Unlike MFC, the equality Rm ðsÞ ¼ RðsÞ may be the case here. From Figure 2 it may be derived that: PðsÞ ð1 þ RðsÞM ðsÞÞð1 þ Rm ðsÞM ðsÞÞ M ðsÞ yMFC=IMC ðsÞ ¼ ð1 þ RðsÞPðsÞÞð1 þ Rm ðsÞM ðsÞÞ þ Rm ðsÞðPðsÞ 2 M ðsÞÞ ym ðsÞ

þ

dðsÞ ð1 þ RðsÞPðsÞÞð1 þ Rm ðsÞM ðsÞÞ þ Rm ðsÞðPðsÞ 2 MðsÞÞ

ð5Þ

In the particular case of PðsÞ ¼ M ðsÞ; RðsÞ ¼ Rm ðsÞ it holds yMFC=IMC ðsÞ ¼ ym ðsÞ þ

dðsÞ ð1 þ RðsÞPðsÞÞ2

ð6Þ

For stable perturbations D(s ) it holds PðsÞ ¼ M ðsÞð1 þ DðsÞÞ

ð7Þ

and in view of equation (2) for a MFC control system
 D d þ y ¼ ym 1 þ 1 þ RMð1 þ DÞ 1 þ RM ð1 þ DÞ and for a MFC/IMC system
yMFC=IMC ¼ ym 1 þ þ

D ð1 þ Rm M Þ½1 þ RM ð1 þ DÞ þ Rm M D

d ð1 þ Rm M Þ½1 þ RM ð1 þ DÞ þ Rm M D

For simplicity, the argument s is neglected in equations (8) and (9).

Figure 2. Linear MFC/IMC structure

ð8Þ



ð9Þ

In the case of stable perturbations and a stable process model M(s ), the Model following stability conditions confine the selection of the corrective controller R(s ) that PID control may be so tuned as to get a small stability margin in spite of expected, yet system unknown perturbations. Under the same conditions, the classic feedback system, on the contrary, is to be tuned so that to get a greater stability margin. The controller Rm(s ) of the model is chosen on the basis of the nominal model 821 M(s ) with an appropriate stability margin so that the reference signal r(t ) be satisfactorily followed by the model output (3) with the inequality (1) being fulfilled at the same time. However, fulfilling the inequality (1) for a process with time delay may be confronted by an MFC system stability barrier. MFC Scheme for processes with known nominal delay The following study deals with control of a known delay afflicted linear process given by PðsÞ ¼ M ðsÞð1 þ DðsÞÞe2sL

ð10Þ

which comprises a part of a modified MFCD structure with delay shown in Figure 3. For comparison purposes the classic control loop with Smith predictor is also shown there.

Figure 3. Modified MFCD system and the classic control loop with Smith predictor

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The counterpart of equation (2) takes the form
 DðsÞ 2sL yMFCD ðsÞ ¼ ym ðsÞe 1þ 1 þ RðsÞM ðsÞð1 þ DðsÞÞe2sL þ

dðsÞ 1 þ RðsÞM ðsÞð1 þ DðsÞÞe2sL

ð11Þ

For the classic control loop with Smith predictor we have ySMITH ðsÞ ¼ ym ðsÞe2sL

þ dðsÞ

ð1 þ DðsÞÞð1 þ Rm ðsÞM ðsÞÞ 1 þ Rm ðsÞM ðsÞð1 þ DðsÞe2sL Þ

1 þ Rm ðsÞM ðsÞð1 2 e2sL Þ 1 þ Rm ðsÞM ðsÞð1 þ DðsÞe2sL Þ

ð12Þ

Signal ym(s ) is defined by equation (3) in both cases (11) and (12). From these relationships it may be inferred that the stability of an MFC system in its second summand on the right-hand side of equation (12) an depends on time delay L. On the other hand, in case of lack of perturbations ðDðsÞ ¼ 0Þ the stability of the first summand on the right-hand side of equation (12) does not depend on time delay. Stability of a non perturbed ðDðsÞ ¼ 0Þ control system with Smith predictor is independent of the time delay, however, the disturbance d(s ) can be even amplified, because ðs ¼ jvÞ  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1 2 e2jvL  ¼ 2 ð1 2 cos vLÞ 2 ½0; 2 v 2 ½0; 1Þ ð13Þ On the other hand, the disturbances in the MFCD system are well damped, and perturbations D(s ) exert a weaker effect on the ym(t ) tracking than it takes place in the Smith system. Simulation examples For simulation purposes the model transfer function has the form M ðsÞ ¼

1 ð1 þ 10sÞð1 þ 20sÞð1 þ 40sÞ

ð14Þ

The plant has the form (10). Different cumulative perturbations of plant gain ðDðsÞ ¼ 0; DðsÞ ¼ 20:5Þ and delay has been assumed ðL ¼ 0; L ¼ 40 ½s Þ: The plant output was additionally affected by disturbances. For such perturbations and, for constant parameters of both controllers, the robustness, control quality and effectiveness of disturbances reduction has been tested and compared with the classic control system. In all control schemes the PID controllers have the transfer function

RðsÞ ¼

kc ð1 þ sT i Þð1 þ sT d Þ sT i

ð15Þ

The model controller Rm has been tuned to the plant model according to the rules proposed by Skoczowski (2001) and has the following parameters: kc ¼ 0:5; T i ¼ 40 ½s; Td ¼ 10 ½s: The correcting controller has the parameters being equal to: kc ¼ 0:6; T i ¼ 40 ½s; T d ¼ 40 ½s: Figure 4 shows the plant output and control input for the classic and MFC systems for DðsÞ ¼ 20:5; L ¼ 0: Figure 5 shows the same for classic and MFC systems for high perturbed process time delay ðDðsÞ ¼ 0; L ¼ 40 ½sÞ: For the same plant and the nominal model the plant output and the control input for Smith predictor and MFCD systems has been depicted in Figure 6, assuming that the time delay of the process is known and equals L. Finally, Figure 7 shows the plant output and control input for MFCD system and Smith

Model following PID control system 823

Figure 4. Classic and MFC systems for perturbed process gain ðDðsÞ ¼ 20:5Þ

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Figure 5. Classic and MFC systems for perturbed process time delay ðL ¼ 40½sÞ

predictor for the plant with delay being equal to 50 [s] and nominal model delay L ¼ 40 ½s: Both the outputs are compared with the process output signal in the classic system. The presented control structures show a lower sensitivity to plant perturbations, as compared with the classic control system and Smith predictor. Figures 8 and 9 show the effectiveness of random disturbance reduction in presented control structures for a process with time delay being equal to 20 [s]. As disturbances the PRBS noise, applied through a linear time-lag filter of third order to the plant output has been employed. The parameters of the filter have been chosen as kf ¼ 0:25; T f1 ¼ 3 ½s; T f2 ¼ 4 ½s; T f3 ¼ 18 ½s: Figures 8 and 9 show outputs of the nominal plant and the perturbed one in a classic feedbackloop control system and in proposed systems, respectively. In both cases the reference value r(s ) has been assumed as being equal to zero. The model and the corrective controllers have been the same.

Model following PID control system 825

Figure 6. MFCD and Smith predictor systems for known process time delay ðL ¼ 40½sÞ

Figures 10 and 11 show how the effect of disturbances is reduced in case of sinusoidal disturbances with amplitude 0.1 and frequency 0.01[1/s] affecting the plant output. For both kinds of disturbances performance indices IAE have been computed for a whole simulation horizon and showed in figures. Concluding remarks Linear MFC systems are distinguished by their simplicity and higher robustness than classic single-loop feedback systems. Beside adaptive control systems, they may present an alternative tool for control of nonlinear processes with time-varying parameters in the presence of disturbances and perturbations. In the case of processes with time delay the modified MFCD structure offers a good control performance. Both the MFC and MFCD structures provide high robustness to disturbances and perturbations, however, obtained consciously

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Figure 7. MFCD and Smith predictor systems for perturbed process timedelay (L ¼ 40½s; process time delay ¼ 50[s] )

Figure 8. Classic ðIAE ¼ 33:35Þ and MFC ðIAE ¼ 31:97Þ system responses for the plant affected by a random disturbance ðIAE ¼ 31:97Þ

Model following PID control system 827 Figure 9. MFCD ðIAE ¼ 31:97Þ and Smith predictor ðIAE ¼ 32:05Þ system responses for the plant affected by a random disturbance

Figure 10. Classic ðIAE ¼ 49:03Þ and MFC ðIAE ¼ 34:77Þ system responses for the plant affected by a sinusoidal disturbance

Figure 11. MFCD ðIAE ¼ 34:77Þ and Smith predictor ðIAE ¼ 51:90Þ system responses for the plant affected by a sinusoidal disturbance

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at the cost of ideal tracking of the reference signal and adopting in lieu of that the tracking of the model output as a satisfactory solution. References Chern, T.L. and Chang, G.K. (1998), “Automatic voltage regulator design by modified discrete integral variable structure model follwing control”, Automatica, Vol. 34 No. 12, pp. 1575-82. Lee, S.H. and Song, J.B. (1999), “Control of linear motor-based arm motion generator using active impedance implementation”, Proceedings of 14th Triennial World Congress, Beijing, China, C-2a-16-3, pp. 551-6. Li, G., Tsang, K.M. and Ho, S.L. (1998), “A novel model following scheme with simple structure for electrical position servo systems”, International Journal of Systems Science, Vol. 29, pp. 959-69. Park, K., Kim, S.H. and Kwak, Y.K. (1996), “Adaptive control for time optimal tracking systems”, Int. J. Control, Vol. 63 No. 5, pp. 951-64. Skoczowski, S. (1999), “A robust control system utilizing plant model”, (in Polish), Pomiary Automatyka Kontrola, No. 9, pp. 2-4. Skoczowski, S. (2001), “Robust model following control with use of a plant model”, International Journal of Systems Science, Vol. 32 No. 12, pp. 1413-27. Skoczowski, S. and Domek, S. (2000), “PID robust model following control”, Proceedings of the IFAC Workshop on Digital Control’ Past, Present and Future of PID Control, Terrasa, Spain, pp. 39-44. Sugie, V. and Osuka, K. (1993), “Robust model following control with prescribed accuracy for uncertain nonlinear systems”, International Journal of Control, Vol. 58, pp. 991-1009. Tsang, K.M. and Li, G. (2001), “Nonlinear nominal-model following control to overcome deadzone nonlinearities”, IEEE Transactions on Industrial Electronics, Vol. 48 No. 1, pp. 177-84. Wu, H. and Kawabata, H. (1999), “Robust model following control with zero-tracking error for a class of uncertain linear systems”, Proceedings of the 1999 IEEE Hong-Kong Symposium on Robotics and Control, pp. 85-90.

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Novelty, diversification and nonrandom complexity define creative processes

Diversification and nonrandom complexity 829

A. Sugerman 848 Dodge Avenue, Evanston, IL, USA

H. Sabelli Chicago Center for Creative Development, Chicago, IL, USA Keywords Cybernetics, Creativity Abstract We describe a theory of creative activity through the development and use of mathematical tools in the analysis of time series. The time series analyzed include empirical series and biotic and chaotic series generated by recurrent functions. Embeddings are used to measure the dimensionality of a series, and analyses of isometries of Euclidean norms at various embeddings reveal the relatively simple processes that generate and combine with complex structures. These tools identify and measure diversity, novelty, and complexity in complex natural processes and in mathematical bios. The presence of these properties shows that creative processes result from deterministic interactions among relatively simple components, not only from random accident.

Introduction We describe a theory of creative activity through the development and use of mathematical tools in the analysis of time series. The time series analyzed include empirical series and biotic and chaotic series generated by recurrent functions. Embeddings are used to measure the dimensionality of a series, and analyses of isometries of Euclidean norms at various embeddings reveal the relatively simple processes that generate and combine with complex structures. These tools identify and measure diversity, novelty, and complexity in complex natural processes and in mathematical bios. The presence of these properties shows that creative processes result from deterministic interactions among relatively simple components, not only from random accident. Evolution generates complex patterns and structures in a consistent manner, suggesting that determined interactions among simpler processes, not random accident, create complexity. Embryological development is exemplary. Cosmological and biological evolution may also be creative developments. Our aim is the development of a science of creative processes. A science of creative processes is an alternative to deterministic (mechanical, biological, economic, social or psychological) and probabilistic models, and to Supported by Society for the Advancement of Clinical Philosophy. We are thankful to Drs L. Kauffman, M. Patel, J. Konecki and Linnea Carlson-Sabelli for useful discussions of the data.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 829-836 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443897

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supernatural accounts of creation. So we are developing: (1) methods to identify creative processes; (2) mathematical models that account for creativity; and (3) strategies that foster creative behavior.

830 Bios, a mathematical creative process Four main mathematical ideas have been developed to characterize complex patterns: steady states, oscillations, chaos, and noise (Glass and Mackey, 1988). Bipolar feedback generates a fifth type, bios (Kauffman and Sabelli, 1998). In the process equation Atþ1 ¼ At þ g sin At the amplitude and complexity of the patterns in the single time series generated by this bipolar feedback increases with the magnitude of the feedback gain (Figure 1). For g , 2; the equation converges to p. A cascade of perioddoubling bifurcations generates 2N periods, followed by chaos. When g # 4:604; At expands both positively and negatively, generating aperiodic apparently erratic patterns resembling those observed with cardiac data. This is bios. In the kinetic process equation (Sabelli and Kauffman, 1999), the

Figure 1. Time series generated by the kinetic process equation. Values of At (Y axis) as the gain increases with time (X axis). Upper chart presents the steady state, bifurcation, unifurcation, cascade of bifurcations and chaos that obtain at low gain (1.5 - 4.5). The lower chart shows the time series from gain 1 to 7 with a larger scale in the Y axis that allows one to see the biotic phase that emerges at gain . 4.60335. . .

feedback gain g is a function of time: Atþ1 ¼ At þ kt sin At This equation illustrates how a deterministic interaction between opposites can generate a sequence of patterns of organization including a regime (bios) that displays features found in creative natural processes.

Diversification and nonrandom complexity 831

Operational definition of creative processes We define a process as creative if it generates (1) diversity, (2) multidimensionality, (3) novelty, (4) complexity, and (5) episodic patterning (complexes) in a nonrandom fashion. Our strategy is to develop methods that might quantify these features of creativity and use these methods to measure time series of natural processes that continually generate new patterns and are readily measurable. We also study time series generated by recursive equations, since the bifurcation cascades generated by recursions offer a selfevident scale of complexity. Intuitively, steady states are simpler than periodic cycles, cycles are simpler than chaos, and chaos is simpler than bios. (1) Diversification (the generation of diversity) is the increase in variance with time. Global diversification is the increase in standard deviation (S.D.) with duration of the time series; local diversification is the increase in S.D. with increase in embedding, which is the duration of vectors of successive members of a time series (Figure 2) (Sabelli and Abouzeid, 2002). Diversification differentiates three types of processes: .

mechanical processes and random series conserve variance;

.

processes that converge to equilibrium or periodic or chaotic attractors initially decrease variance;

.

creative processes increase variance.

By this definition, heartbeat intervals, many economic series, meteorological data, colored noise (Brownian motion, 1/f “pink” noise), and mathematical bios are creative, while chaotic attractors are not.

Figure 2. Local diversification

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(2) A creative process is multidimensional, i.e. it contains both high dimensional complex components, and the low dimensional, simple processes that generate them. To study both simple and complex components of a time series, we construct vectors of 1, 2, 3,. . . N successive terms starting with each term; the number of terms (duration) representing the embedding dimension of the component of the process being examined. Two vectors are isometric (recurrent) when their Euclidean norms (square root of the sum of the square of its members) are equal (within tolerance, 1 per cent of range). Periodic series show 100 per cent isometry when the vectors and the periods are of equal duration. Complex processes show a complex pattern of variation of isometry as a function of vector duration, indicating the coexistence of multiple components that together generate a complex morphological pattern (Sabelli et al., 1995, 1997). Typically, there are numerous isometries at low dimensions, indicating the existence of simple components, as well as significant number of isometries at higher embedding dimensions, indicating complex components. (3) Random series have a very low number of isometries. Creative processes have less isometry than random processes. An isometry is a repetition; lower than random isometry indicates an active process of innovation. Novelty is defined as the increase in isometry with shuffling of the data (Sabelli, 2001). Heartbeat intervals, most economic series, meteorological data, colored noise, and mathematical bios display novelty. Periodic series are recurrent (higher isometry than their shuffled copy). Chaotic attractors are neither novel nor recurrent; they have the same number of isometries as their shuffled copies. (4) These patterns can be readily seen in time graphs. They appear as episodic clusters of isometries (complexes; Sabelli et al., 1995; Sugerman et al., 1999) as contrasted to the uniform time graphs of random, periodic and chaotic series (Figure 3). Morphological diversity is a significant component of complexity. Random processes are highly dimensional but are morphologically uniform and do not contain simple low dimensional steady states and periodicities. (5) The production of complexity is intrinsic to creativity. We consider a measure of complexity valid when it provides high values for biological processes and for mathematically generated biotic series, intermediate values for chaos, and low values for random or simple periodic processes. The nonrandom production of complexity is measured by the ratio of consecutive isometries over all isometries, which we call arrangement (Sabelli, 2002). This is a valid measure of complexity because it is high in heartbeat interval series, economic series, and meteorological data. Arrangement is also high in colored noise, and in mathematical bios, and

Diversification and nonrandom complexity 833

Note: The horizontal and vertical axes represent the vectors A1, A2, . . . AN, formed by M consecutive terms starting with each term in the series. (M is the embedding). These vectors are compared to each other, and if they are sufficiently alike (isometry¼ difference between the Euclidean norms of the vectors falls below a chosen cutoff radius), a point is plotted at coordinates (i, j ) to indicate a recurrence. As many random pairs of points may be tested as necessary in order to portray the pattern. Recurrence program by Webber and Zbilut, (1994)

Figure 3. Recurrence plot of time series of corn prices

low in chaos and in random series. In contrast, algorithmic complexity (Chaitin, 1990) is maximal for random data; this is regarded as inconsistent with our intuitive understanding of complexity (Gell-Mann, 1994). Diversification, novelty, nonrandom complexity and dimensional and morphological diversity provide an operational definition of creative processes. They also show that creative features are present in mathematical bios, but not in simpler forms of chaos.

Figure 4. Order, Novelty, and Flux

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Figure 5. The proportion of order, novelty and flux present in empirical and mathematical series, calculated as described in the text

To implement these measures we have developed a spreadsheet that computes Euclidean norms and all the subsequent measurements for the entire time series without resorting to data sampling. We used this spreadsheet with series as long as 2000 terms and with 2, 3, 4, 6, . . .23. . .50 embeddings. Isometries are measured in the histogram of Euclidean norms. Each series At is compared with 5 shuffled copies As, and all results refer to these comparisons. A Pareto distribution of frequencies allows one to measure the change in isometry between the original data and the average of its shuffled copies As. We compare the frequencies F of At and As by bin in an effort to distinguish ordered, creative and random components of the process under study (Figure 4). FðAt Þ . FðAs Þ defines order; in fact we find that FðAt Þ . FðAs Þ in periodic series. FðAt Þ ¼ FðAs Þ implies random flux since shuffling does not change the frequency. A chaotic series is flux by this measure. FðAt Þ , FðAs Þ defines novelty. We use the specific frequency of F(At) as the measure of order, novelty or flux for each bin, and their sums for the series as a whole (Figures 4 and 5). Cardiac, economic and biotic processes combine order, novelty and flux. These methods allow one to measure the extent to which order, novelty and flux interact within a specific process. Up to now, order and disorder (random and chaos) were taken as fundamental opposites; life was regarded as emerging between order and chaos. Here we propose that creative organization represents a departure from random flux along a different axis than order. Ordering increases repetition. Creativity increases novelty. Mathematical recursions that generate bios suggest that life like processes emerge, not at the edge between chaos and order, but at the other end of chaos. References Chaitin, G.J. (1990), Algorithmic Information Theory, revised third printing, Cambridge University Press. Gell-Mann, M. (1994), The Quark and the Jaguar. Adventures in the Simple and the Complex, W.H. Freeman, New York. Glass, L. and Mackey, M. (1988), From Clocks to Chaos. The Rhythms of Life, Princeton University Press, Princeton, NJ. Kauffman, L. and Sabelli, H. (1998), “The process equation”, Cybernetics and Systems, Vol. 29 No. 4, pp. 345-62. Sabelli, H. (2000), “Complement plots: analyzing opposites reveals Mandala-like patterns in human heartbeats”, International Journal of General Systems, Vol. 29, pp. 799-830. Sabelli, H. (2001), “Novelty, a measure of creative organization in natural and mathematical time series”, Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 5, pp. 89-113. Sabelli, H. (2002), “Arrangement, a measure of nonrandom complexity”, Journal of Applied Systems Studies (in press). Sabelli, H. and Abouzeid, A. (2002), “Definition and empirical characterization of creative processes”, Nonlinear Dynamics, Psychology and the Life Sciences, (in preparation).

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Sabelli, H. and Kauffman, L. (1999), “The process equation: formulating and testing the process theory of systems”, Cybernetics and Systems, Vol. 30, pp. 261-94. Sabelli, H., Carlson-Sabelli, L., Patel, M. and Sugerman, A. (1997), “Dynamics and psychodynamics. Process foundations of psychology”, Journal of Mind and Behavior, Vol. 18, pp. 305-34. Sabelli, H., Carlson-Sabelli, L., Patel, M., Zbilut, J., Messer, J. and Walthall, K. (1995), “Psychocardiological portraits: a clinical application of process theory”, in Abraham, F.D. and Gilgen, A.R. (Eds), Chaos theory in Psychology, Greenwood Publishing Group, Westport, CT, pp. 107-25. Sugerman, A., Sabelli, H. and Patel, M. (1999), “Biotic patterns of economic processes: beyond equilibrium, chaos, and determinism”, in Allen, J.K., Hall, M.L. and Wilby, J. (Eds), Proceedings of the International Society for the Systems Sciences, pp. 391-2. Webber, C.L. Jr. and Zbilut, J.P. (1994), “Dynamical assessment of physiological systems and states using recurrence plot strategies”, Journal of Applied Physiology, Vol. 76, pp. 965-73.

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On the criterion of optimal product structure in the micro-economic system (enterprise) and adjustment of product structure

Optimal product structure

837

Lixin Tao Jiangxi University of Finance and Economics, Nanchang, Jiangxi, People’s Republic of China Keywords Cybernetics, Product structure Abstract In order to make a thorough inquiry into the criterion of optimal product structure in the micro-economic system (enterprise), this paper has proposed and demonstrated the benefittype linear programming model, and based on it, the concepts of enterprise’s product structure, feasible structure and optimal structure have been discussed and the criterion of optimal structure has been revealed. In this paper, the methods of simplex iteration and sensitivity analysis are both used to approach necessarily the adjustment of product structure under the circumstances of varied or invaried environment inside and outside the system, and as a final, it has come to a conclusion that the variation of resource price vector P would not affect the optimal product structure in enterprise, but the variation of resource-constrained vector b will cause negative effects both on optimal product structure in enterprise and on determination of criterion for optimal structure.

Introduction Any enterprise is provided with its own product structure, but a satisfying and quantitative criterion is seldom found now for the determination of whether or not it is the only optimal structure available for maximum benefits in enterprise, that is to say, we can not make sure whether the product structure of an enterprise is an optimal one or not even if the enterprise has undergone the adjustment of its product structure and has attained more economic benefits than those prior to the adjustment, and we can not affirm if there are some other favorable feasible structures available to achieve more economic benefits in enterprise; even so, the people are in no position to affirm if there is another structure superior to the new one. Seemingly, the academic circles of management have not yet attached much importance to it. This paper is to solve this problem, and it is considered that the resolution has been found.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 837-844 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443905

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Benefit-type linear programming model and criterion of optimal product structure in enterprise As everyone knows, the production and business (or service) activities in enterprise usually follow the linear programming model (Lo) shown as below:

838

Max CX

ðLo Þ

s:t:

8 0
where C ¼ ðC 1 ; . . .; C n Þ (.0) implies the price vector of enterprise’s product; X ¼ ðx1 ; . . .; xn ÞT implies the decision vector of product’s production in enterprise, indicating that the enterprise can produce the products of n kind (or render the service of n kind) on the premise of its present production and technical conditions; b ¼ ðb1 ; . . .; bm Þ T implies the resourceconstrained vector in enterprise’s production, indicating that there are resource constraints of m kind related to the human, material and financial resources in enterprise; A 0 ¼ ða0ij Þm £ n implies the constraint matrix of productive technology structure (coefficient of productive technology) in enterprise; in A 0 ¼ ða 01 ; . . .; a 0n Þ; the vector a 0j ¼ ða01j ; . . .; a0mj Þ implies the productive technology for the product of j kind, and a0ij ¼ bi =xj implies the corresponding consumption of resources of i kind per unit output of the product of j kind. The linear programming model (Lo) represents: whatever the decision is to be made by the enterprise over the output (or service scale) on the premise of constraints presently from productive technology and resources just in an attempt to achieve the maximum gross revenue (or gross output value) CX in enterprise.

Benefit-type linear programming model The model (Lo) itself is difficult to identify the effects caused by various variations (particularly price variations) on the economic benefits and optimal product structure in enterprise, that is because the C is really difficult to be determined if C ¼ ðc1 ; . . .; cn Þ is deemed to be the unit profit or tax from product (or service), and it is non-operative for its unconformity with the usual practice of profit or tax collection by the State. In such a case, it is required to put forward the benefit-type linear programming model to solve the abovementioned difficulties. Obviously, the corresponding value-type linear programming model of (Lo) is:

ðL1 Þ

s:t:

Optimal product structure

Max I X 8 0 < A X # p^ m b :X $ 0

and the corresponding benefit-type linear programming model is:

ðL2 Þ

s:t:

Max I X 2 pb 8 1 < A X # p^ m b :X $ 0

where p ¼ ð p1 ; . . .; pm Þ (.0) implies the price vector of resources of m kind; p^ m ¼ diag { p1 ; . . .; pm } implies the price diagonal matrix of resources of m kind; X ¼ ðc1 x1 ; . . .; cn xn ÞT implies the column vector of output value of product (or service) in enterprise; I ¼ ð1; 1; . . .; 1Þ implies the n-dimensional row vector as each component is 1 n X IX ¼ cj x j ¼ CX j¼1

implies the gross output value in enterprise; pb implies the total cost of production; I X 2 pb ¼ CX  pb implies the gross profit and tax; A 1 ¼ ða1ij Þm £ n implies the value-type constraint factor matrix; In a1ij ¼ pi bi/cjxj ¼ pi =cj a0ij ; a1ij implies the corresponding consumption of resource value of i kind per unit output value of product (or service) of j kind and C, X, b are all the same as in ( L0 ). Because: 2 p1 p1 0 p1 0 3 a 011 ; a 12 ; . . .; a c2 cn 1n 7 6 c1 6 ··· ··· ··· 7 A1 ¼ 6 · · · 7 p p p 4 m 0 m 0 m 0 5 a m1 ; a m2 ; . . .; a mn c1 c2 cn 2 6 ¼6 4

32

p1 .. .

a 011 ;

76 76 · · · 54 a0m1 ; pm

. . .; ··· . . .;

32 1=c 1 76 · · · 76 56 4 a0mn a 01n

3 .. . 1=c n

7 7 ^ 21 7 ¼ pm A 0 c^ n : 5

To substitute A 1 into the resource-constrained conditional inequality in (L1) or (L2), it is obtained:

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^ m A 0 c^ 21 ^ n X ¼ p^ m A 0 X # p^ m b p^ m A 0 c^ 21 n X ¼p n c Since p . 0, hence p^ 21 m ¼ diag {1=p1 ; . . .; 1=pm }; to premultiply both sides of 21 ^ inequality with pm ; the equivalent form of value in (L2) is obtained: Max CX 2 pb ( 0 A X #b

840 ðLÞ

s:t:

X $0

(L) is the benefit-type linear programming model. Although, it is slightly different from (L0) only at the target function and shows no difference elsewhere, such a minute change and derivation have solved the aforesaid “two difficulties”. Firstly, it is easier to determine the price of product (or service) than the unit profit and tax of product (or service) in enterprise, and it is accessible to operation for its conformity with the usual practice of profit and tax collection by the state. Secondly, the derivation proves in terms of theory that the structure of productive technology in enterprise would not be affected by various price factors and the structure of productive technology is one of the basic factors to determine the structure of product (or service) in enterprise. Criterion of optimal structure and adjustment of structure on the premise of varied internal or external conditions To convert (L) into the standard form:

ðLÞ

s:t:

Max CX 2 pb 8 < AX ¼ b :X $ 0

where C ¼ ðC; 0Þ; X ¼ ðx1 ; . . .; xn ; xnþ1 ; . . .; xnþm ÞT ; xnþ1 ; . . .; xnþm is a slack variable; A ¼ ðA 0 ; I m Þ ¼ ða 01 ; . . .; a 0n ; e 1 ; . . .; e m Þ; a0j ¼ ða01 j ; . . .; a0mj Þ; ð j ¼ 1; . . .; nÞ; ei is the m-dimensional vector of i component at 1; Im is the m-order unit matrix. To adopt the simplex method into the standard form (L), the optimal basis of (L) is B* ¼ ða0j1 ; . . .; a 0jm Þ; the optimal basic solution is X * ¼ðx*1 ; . . .; x*n ; x*nþ1 ; . . .; x*nþm Þ T and the optimal solution of original problem (L) is X * ¼ ðx*1 ; . . .; x*n ÞT : The optimal solution X* indicates that on the premise of present internal and external conditions, the enterprise must arrange to produce what it has to produce and to determine an appropriate output so as to ensure the gross

economic benefits (profit and tax) CX * 2 pb to the maximum. It is, in fact, the Optimal product optimal product structure in enterprise. structure The enterprise’s product structure has two definitions: Firstly, it is the orientation of product variety. Although, the enterprise has the capacity to produce the product of n kind just in the light of its own production capacity, technical conditions and resource constraints, it is not much necessary to 841 arrange the production of all products, instead, it may arrange to produce several products only. Secondly, it is the proportion of individual product’s output value to the gross output value of enterprise. The attention must be paid to the output of those products already arranged for production, and the output must be converted into the output value for the purpose of comparability. The former may be considered as the structural orientation of product variety, and the latter may be considered as the proportional structure of product’s output value, but all together called the product structure in enterprise. In other words, the product structure to meet the constraints will be the feasible product structure in enterprise. Obviously, the feasible structure to meet the target function is just the optimal product structure in enterprise. Hence, the optimal product structure on the premise of present conditions in enterprise has been given out by the optimal solution X*: J * ¼ ð J 1* ; . . .; J n* ÞT where 0 # J *j ¼ cj x*j =CX * # 1; ð j ¼ 1; . . .; nÞ; and

n X

J *j ¼ 1:

j¼1

The optimal basis B* is obviously the first definition of product structure, and the enterprise may arrange only the basic vector of optimal basis B * at most, i.e. to produce the product of m kind which is corresponding with a0j1 ; . . .; a 0jm : The orientation of product variety is m kind at most. The simplex method is the iterative computing method for optimal basic solution in (L), that is to say, from the initial feasible basis B 0 (the ð0Þ T corresponding basic feasible solution X ð0Þ ¼ ðxð0Þ 1 ; . . .; xnþm Þ ; the optimal basis B * and its corresponding optimal basic solution X* may be obtained as a final through the finite judgement (for an instance, k-th power) and iteration by the change of base (the optimal solution for this actual problem is bound to be obtained). When the simplex method is applied, it will generate a series of feasible bases B 1 ; B 2 ; . . .; B k21 ; B * and the corresponding basic feasible solutions X ð1Þ ; . . .; X ðk21Þ ; X * : Every new basic feasible solution will enable the enterprise to achieve more economic benefits than the previous one, and then to X* so that the enterprise’s economic benefits increase to the maximum. However, the vectors of different feasible bases correspond to the orientation of different product varieties, and the different basic feasible solutions correspond

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to the proportional output value structure of different products. Hence, the simplex method and its application have actually supplied us the quantitative criterion for the adjustment of product structure whilst on the premise of varied conditions, and its optimal criterion is: C

B*

B*

21

A2C $0

As shown earlier, it is obviously a criterion of optimal product structure in enterprise, and such an adjustment of structure is strictly scientific and precise, which will curb the blindness in the adjustment of structure, and according to it, the enterprise would not assume any of the risks to decide the adjustment of product structure. Adjustment of enterprise’s product structure on the premise of varied conditions and corresponding criterion of optimal structure The aforesaid optimal basis, optimal basic solution and optimal product structure are all the structural optimality only on the supposition of unvaried internal and external conditions in enterprise. This supposition is excessively idealized and as a matter of fact, it is not the case. Is the original optimal product structure still the optimal one on the premise of constant variance of internal or external conditions in enterprise? if not, how to adjust it and obtain a new optimal structure? and on the premise of constant variance of internal or external conditions in enterprise, does the criterion of optimal structure need to be varied? Certainly, the enterprise would not intend to make the frequent adjustment of structure. In case of no much variance of internal or external conditions in enterprise, maybe it would not undergo the adjustment of structure so as to ensure the steady development without any variation of the original optimal structure. But in case of great variance of internal or external conditions in enterprise, probably it has to make the adjustment of structure. However, no matter that the variance is, the criterion for adjustment of structure must be clearly defined, and the way towards the adjustment of structure must be indicated anyway, instead of the fuzzy words like “maybe” or “probably”. Here the benefit-type linear programming model and its sensitivity analysis are just adapted to such an objective requirement. Adjustment of structure on the premise of varied external conditions in enterprise and criterion of optimal structure The variation of external conditions in enterprise mainly includes: (i) variation of resource price vector p ; (ii) variation of resource-constrained vector b ; (iii) variation of product’s price vector C (a response to the market demand of product from enterprise).

Proposition 1. Only the change of resource price vector p would not affect Optimal product the optimal product structure in enterprise, but affect the economic benefits in structure ~ the new economic enterprise. To suppose that the price vector p changes to p, 21 benefits will be C B* b 2 p~_b: B* Proof. As shown in the model (L) and standard form (L), the change of p would not affect A 0 (or A), C (or C ) and b, and it would not affect B * and 843 converse B *2 1, hence: B*

21

b $ 0; C

B*

B*

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It is established even if p changes, indicating that the original optimal basis B * and optimal basic solution X * will continue to be the optimal basis and optimal basic solution, and the original optimal structure J * will continue to be the optimal structure. But the variation of p will cause the variance of total costs in enterprise, resulting in the variance of economic benefits in enterprise. Because of the total revenue CX * ¼ C B* 21 b the new economic benefits ~ B* in enterprise will be: C B* 21 b 2 pb A B* Proposition 2. In case of the change of resource-constrained vector b only, 21 to suppose b ! b~ ¼ ðb þ DbÞT ; the criterion of optimal structure is: B* b~ $ 0 where Db ¼ ðDb1 ; . . .; Dbm ÞT : Proof. Since the change of b does not affect A 0 (or A) and C (or C ), it will 21 not affect B* and its converse B*2 1, hence, C B* A 2 C $ 0; and B* is B* the canonical basis of linear programming at the change of b. As indicated in the dual simplex method, the criterion of optimal structure of the new problem 21 is B* b~ $ 0. A Proposition 3. In case of the change of product price vector C only, to suppose ðC; 0Þ ¼ C ! C~ ¼ ðC þ DCÞ; the criterion of optimal structure is 21 C~ B* A 2 C~ $ 0, where DC ¼ ðDc1 ; Dc2 ; . . .; Dcn ; 0Þ; 0 is a m-dimensional B* null vector. Proof. Since the change of C only does not affect A 0 (or A) and b, it will 21 not affect B * and its Converse B *2 1, hence, B* b~ $ 0, and B * is the feasible basis at the change of C. As indicated in the simplex method, the criterion21 of optimal product structure of the new problem is C~ B* A 2 C~ $ 0. A B* Adjustment of structure on the premise of varied internal conditions in enterprise and criterion of optimal structure The variance of internal conditions in enterprise is mainly: the promotion or improvement of all the makings inside the enterprise, will result in the variance of various resources consumed per unit output of product, i.e. the structural

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matrix A 0 of productive technology coefficient will be changed. Usually, it will lead to the variance of original optimal basis B * and thus show extreme complexity. Generally it is required to set out the coefficient of productive technology structure again to obtain the new A 0, but it will bring out much more work-load, such as, to set up the model again and obtain the optimal product structure from a new model again by means of the simplex method. Considering that those products which have not been arranged for production are of great market potential, the enterprise will improve its productive technology to largely reduce the consumption of various resources 21 per unit output value, it is thus possible that C B * B* N 2 C N  0; where N is a new structural matrix composed of non-basic vectors. Hence, it is required to adjust the structure (iteration by the change of base) to a new optimal structure, and the new optimal structure will be subject to the new optimal basic solution. References Faculty of Mathematics of the People’s University of China, (1981), Linear Programming, Publishing House of the People’s University of China. Chen, Yikun (1989), Operations Analysis, Publishing House of Tongji University.

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Smarter computer intrusion detection utilizing decision modeling

Smarter computer intrusion 845

Christopher C. Valentino Department of Information Systems, The University of Maryland, Baltimore County, Baltimore, MD, USA Keywords Cybernetics, Decision making, Security Abstract Addresses specific problems within the area of performing computer system intrusion detection, and presents the reader with an effective decision model to addressing these problems. Current intrusion detection analysis methods are reluctant to properly evaluate the results of decisions made based on their analysis outcomes. These analysis outcomes influence the decision making process involved in response to an intrusion. Utilizing basic decision modeling methods we can develop a model that is both effective and easy to use. To form this model we must have the following within our environment; standard analysis procedure and the classification of information elements. These will feed into our structured decision model and aid in our final decision outcome.

Introduction With the rapid growth of the Internet and the need for information to be publicly accessible and both private and public sector businesses and agencies rendering service via the web to both consumers and potential adversaries computer security has grown rapidly. Recently the area of Intrusion Detection has grown into a large and distinct discipline. Although, it is nothing more than a measurement device, coupled with both human and computer analytical power it becomes a proactive tool in preventing current and future computer intrusions. The challenge of intrusion detection is performing accurate and correct analysis of the presented data. Most often a decision to block a suspected attacker are made in hast and cause network outages. These outages result in the failure to deliver service to the end customer, and in some cases this is an attacker’s objective. A proper process must be created and followed during the analytical process to assure that decisions are accurate and unbiased. Decision modeling provides us with a structured approach that can be used to formulate a standard analysis method and to formulate an overall decision model. Decision theory allows us to associate a set of probability distributions with each event to reflect the expectations or uncertainties of the decision maker (Butler, 2001). Within this paper we will focus on this overall model, and the elements important to creating and utilizing it. To begin we will conduct a discussion of the overall problem, then define the environment specifically

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focusing on where we can obtain additional analysis data, and finally form and review the decision model. Our goal in applying the decision modeling method is to make “smarter” decisions.

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Understanding the problem At first glance computer intrusion detection appears to be a simple process of installing a commercial system, and then literally watching the screen for red blips. As the area of computer intrusion detection has evolved we have found that this analogy is not true, in fact it is dead wrong. Computer intrusion detection is a highly analytical heavy process, which lacks good overall structure and analysis processes. Very often the literal is taken as the truth. There is a simple rule of thumb, do not believe what you see at first, and always follow the directions. Based on this statement we can deduce that three main problems exist within the analytical process: (1) utilizing all available information sources, (2) verifying the validity of a suspected computer system intrusion, and (3) following a standard process.

Understanding the environment Understanding the environment in which you are operating within is probably the single most important thing you can do to be effective at intrusion detection operations. A rudimentary example can be the operation of a motor vehicle. If you are unaware of your current environment (e.g. do not know the highway system) you will be unable to operate the motor vehicle effectively. The same holds true for computer intrusion detection operations, if you are unaware of the environment you will not go very far. The environment is all of the elements that are related to the events you are analyzing. It is important to note to achieve full validly of an intrusion event or incident we must accept that our environment goes beyond your local networked systems, and extends past the service provider and into the attackers network. This introduces the idea of both an external and internal environment. It is important to understand the relationship between the two and the information available for our analysis and final decision. Both are great sources of information and compliment each other. Information elements To be successful at computer intrusion detection operations we must have good valid analysis information. Both the external and internal environments can

provide this data to our decision process. We refer to such environment components as information elements. We classify information elements into two major groups; live elements and captured elements. We can also refer to these as data in motion (real-time) and data at rest (captured). When defining information elements one must ask themselves. Where can I get more information? Live elements Live elements are best defined as those sources on information that provide real time or real-time feedback. These systems include firewalls, routers, host audit logs, packet sniffers, and intrusion detection systems. Information collected from these elements includes connection logs, protocol analysis, and target system access logs. These elements are typically fed into either an analysis framework or to a human analyst. The key, though is collectively all of these devices, can give you a clear and accurate real-time picture of your network. Captured elements Captured elements consist of data that is at rest within the environment these elements are best broken into two categories; configuration data and knowledge base. It is important to make this distinction for configuration data consist of the current makeup and state of the environment and the knowledge base looks at data occurring in the past (i.e. previous intrusion attempts). Configuration data includes network topology maps, vulnerability assessment data, firewall policy documents, router configurations, and current host configuration information. This information effectively describes the current state of the network both from a configuration view and a security posture view. Given an example, with current vulnerability assessment data we can determine if a host is vulnerable to a given intrusion attempt. If the host is not vulnerable to a distinct attack for instance an attempted windows attack on a UNIX host, then we can move on to the next alarm to be analyzed. An additional resource is the Knowledge Base of past intrusion data, configurations, and real threat data. Utilizing this database allows us to get a historical view on current intrusion attempts, to include previous decisions. Structuring the problem To structure the problem correctly we must achieve the following; understand our current standard analysis procedure, define our decision environment, and finally form our objectives.

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Standard analysis procedure Most organizations currently conducting intrusion detection operations will have some analysis procedure in place. If it is correct or even being utilized is another issue. For our model to be successful the analysis procedure (Figure 1) must be consistent and strictly enforced. This will assure that all available information elements will be used to form the analysis outcome. This model will consist of collecting, organizing, analyzing, and generating some form of analysis output. This output can include if it is a suspected intrusion or a begin trigger. A good process will utilize all available information elements for the final analysis outcomes. Again, the challenge is one in implementing a standard analysis procedure and the other is consistently using the process. The decision environment The decision environment can be broken into three zones; uncertainty, risk, and certainty (Forgionne, 1999). Each analysis outcome must be grouped into one of these three situations. From a quantitative approach each information element would bear a certain weight, and the total number of elements would also affect the final decision outcome. We use the three-decision situations as an overall guide. Subsequent efforts will work towards quantifying the information elements and assigning fine confidence levels to each situation (i.e. a ¼ 0:95). From Figure 2 we can see that as our “knowledge” increases our level of certainty increases proportionally. For our model we can say that as our number of information elements increases our level of certainty increases also. It is important to remember that each information element will carry an individual weight. Thus one source of information may be more useful than

Figure 1. Example of standard analysis process

Figure 2. Decision situations (Forgionne, 1999)

another. For instance actual intrusion data from a target host system, that confirms the intrusion bears a higher weight than just information from an intrusion detection system. Uncertainty Of our three overall decisions situations uncertainty of course is most undesirable. At this extreme situation the decision maker can identify possible outcomes, but does not posses enough information to begin to determine if an intrusion has occurred (Forgionne, 1999). Decisions made under uncertainty bear the following characteristics; little correlation with other information elements, elements used are weighted extreme low, it is unknown if an intrusion has actually taken place, and the true source of the intrusion or attempted intrusion is unknown. Even with the level of unknown associated with this situation the true fact is most decisions on handling an intrusion or attempted intrusion are made within this zone. This is a costly and most risky situation to find yourself in, especially, for large public or private sector agencies and businesses. Although, in some situations decision-making under uncertainty is unavoidable, the decision maker will now be aware of the state in which they are making their decision. Risk Once the decision model is applied to the overall analytical process, most decisions will be made under the decision situation of risk. Within this decision situations a maximum number of information elements that have been used to correlate intrusion data, excluding information elements from the attacker. Given this we can say that (1) we know that an intrusion or attempted intrusion has occurred and (2) maximum number of local information elements have been used. However we still do not know the true source of the attacking network. It is a true statement to make that we may never know the true source of an intrusion. Depending on the objective of the decision maker this may be acceptable. If our goal is to be proactive and prevent further intrusions than knowing the true source becomes less important. On the other hand if we must know the true source of an intrusion or attempted intrusion, decision-making under risk is unacceptable. Certainty Decisions made under complete certainty are and will be a rarity. Under certainty we (1) know an intrusion has occurred, (2) know the true source of the intrusion, and (3) exhausted our local and global information elements. Thus a decision maker can feel 100 per cent confident that the decision they make is

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based on accurate information. Thus in statistical terms the confidence level a is equal to 1. Without a presence on the attacking network achieving this decision situation is impossible.

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Objectives To apply decision-modeling techniques we must establish a clear list of objectives. At the most rudimentary points we want to establish that the analysis outcomes we are providing are both accurate and unbiased. Accuracy relates to the intrusion or attempted intrusion data being correlated with all available and applicable data elements. The question of biases directly relates to identifying the true source of the intrusion or attempted intrusion. The outcome of our decision model will aid the decision maker in issuing a proper response. These responses could include ignore the event, block traffic from the suspected source, or at the most extreme issue an attack against the source in retaliation. With this said our clear objective is to provide a confidence level that the decision maker can than use to select the appropriate action. Formulating the model We have now defined our environment and presented a structure to our problem. From this point on we can begin to formulate our decision model for computer intrusion detection. From a quantitative view our model will use scoring and weights that relate to our information elements to provide a confidence level to the decision maker. In addition to weights and scores statistical inferences can be made regarding certain data sets, particularly in the area of threat data. Weighting and scoring The difficulty of applying proper weights to information elements is one the operational organization must make. Industry sources and internal organizational studies can be used to produce their level of confidence within their information elements. After weights are assigned to individual information elements statistical inferences can be used to determine the proper sample size or proper number of elements needed to make a decision at a given situation. A scoring system is applied to the overall collection of information elements. The score is based on the overall weights and number of elements used; this in turn will determine the overall confidence level or the decision situation.

Statistical inferences Statistical inferences can be used particularly with threat data. Threat data is current or archived information regarding attempted intrusions, successful intrusions, knowledge of state-sponsored information warfare programs. It can be either local to the organization or global to it. An example is that the SANS Institute provides hourly updates on the number of intrusion attempts occurring on the Internet. This of course is just a subset of the overall situation, but it allows us to view what events are occurring from a worldwide view. We can make statistical inferences and assign probabilities that either a certain source or group of sources are attempted to intrude our computer network.

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The model Once the environment is defined, problem is structured, weighting and scoring system created, and probabilities assigned to our select information elements the model itself becomes simple (Figure 3). At the base our model integrates into our analysis process. In fact, it oversees that the analytical process is completed correctly. From start to finish we begin with monitoring our networks, once an attempted intrusion is detected we begin the event analysis process. This process uses our predefined information elements as input in determining the analysis outcome. Once the analysis outcome is determined a decision situation is assigned based on a set of predetermined weights. This overall situation is then used to make the final reactive decision to the intrusion or attempted intrusion. The process can be repeated and used as either a single-stage decision or in a series of sequential decisions.

Figure 3.

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Conclusion Within this paper, we have discussed applying decision modeling and decision theory to computer intrusion detection. We find that the structure of decision modeling allows us to make sure and sound decisions based accurate and true information collected utilizing our information elements. Decision theory concepts allow us to assign appropriate weights and probabilities to our information elements. Thus, in the end we are able to provide “smarter” decisions based on our analytical outcomes. References Butler, S.A. (2001), Improving Security Technology Selections with Decision Theory. Forgionne, G.A. (1999), Management Science, Wiley Custom Services, USA.

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Cybernetics and systems, from past to future Robert Valle´e Universite Paris Nord, Paris, France

Cybernetics from past to future

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Keywords Cybernetics, Systems Abstract The founders of cybernetics and systems are presented, among them N. Wiener, W.S. McCulloch and L. von Bertalanffy. Some precursors are cited from antiquity to 20th century. The basic concepts are exposed: feedback, quantity of information, requisite variety, homeostasis, local and global points of view, oprn systems, autopoiesis. The roles of the observer and of the actor are emphasized. Future is considered in three directions: development of epistemology and of praxiology, symbiosis of man and machine, role of requisite variety in the survival of mankind.

Founders and precursors We consider as founders those who introduced the modern meaning of cybernetics or systems. As far as cybernetics is concerned the most eminent are Norbert Wiener (1894-1964) and Warren Sturgis McCulloch (1898-1969). The importance of the new field which was to become cybernetics was recognized in 1943 by Wiener, McCulloch, John von Neumann and other members of the so-called “Teleological Society” placed under the aegis of the Macy Foundation. But the official birth of cybernetics can be dated from the publication of Wiener’s (1948) book “Cybernetics or Control and Communication in the Animal and the Machine” published by Hermann (Paris), The Technology Press and Wiley. But the role of McCulloch is not to be underestimated. It started with the publication, with McCulloch and Pitts (1943), of an article about “A logical calculus of the ideas immanent in nervous activity.” In the field of systems a name is predominant, that of Ludwig von Bertalanffy (Vienna 1901, USA 1972). He introduced his concept of general systems theory (which he had foreseen in the 20’s) in 1945 in an article published in a philosophical journal entitled “Zu einer allgemeinen Systemlehre”. The German title shows that his purpose was a general theory of systems as exemplified in his “General System Theory” (1968). It is usual to consider, in a way, Plato as a precursor because he used the word “kybernetike”, in “The Republic” or “Gorgias”, as a political metaphor of the art of steering as well as A.-M. Ampe`re in his “Essai sur la philosophie des sciences” (1843) who used the word “cyberne´tique” and Trentowski in “Philosophy and Cybernetics or the Art of Governing a Country” (in Polish) who used the word “kibernetiki”. Romanian precursors are S. Odobleja (1939)

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and P. Postelnicu (1947). For systems a precursor is A. Bogdanov with “Tektologia” (1912, in Russian). Coming back to cybernetics other precursors have been proposed: G.W. Leibniz and R. Descartes. For Wiener Leibniz may be seen as a patron saint of cybernetics for his attempt to build a general logic with a universal notation (“characteristica universalis”) making possible “the computation of thoughts” (“calculus ratiocinator”) presented in his “Dissertatio de arte combinatoria” (1666). Closer to modern realizations was his computer, better than that of Pascal (built before Leibniz’s birth). According to McCulloch, cybernetics started with Descartes. His first argument is that, in the treaty of Descartes entitled “L’Homme” (1664), there is the “first use of the notion of inverse feedback and of the reflex” in a description of how a man, having his foot very close to a fire, removes it from it. A second argument is to be found in “La Dioptrique” (1637) where McCulloch sees what is “probably the first coding theorem” when Descartes says that the images on the retina are transmitted to the brain by signals having no similarity with what they represent.

Basic concepts Two important concepts of cybernetics are, according to the title of Wiener’s book, control and communication. Negative feedback depends upon both of them. It has been used to regulate clepsydras water supply, rotation speed of wind mills, that of a steam engine with its Watt’s governor. The controllability of a system, that is to say the possibility to bring it from one state to another involves a generalization of negative feedback studied by R.E. Kalman and the optimality of this process considered by R.E. Bellman and also by L. Pontryagin. Communication or more precisely signal theory, already present in feedback, has a specific interest recognized by Wiener (1949) in “Extrapolation, Interpolation and Smoothing of Stationary Time Series” where he solves the problem of optimum prediction and elimination of noise after Kolmogoroff but quite independently. Another aspect of communication, also fundamental according to Wiener, is the notion of quantity of information, proposed by Shannon their book named “Mathematical Theory of Communication” and Weaver (1949) and foreseen by H. Nyquist, R. Hartley and in a way by J. von Neumann. The quantity of information has no semantic meaning, it is an index of the degree of unexpectedness of a message carried by a signal. In short the quantity of information of a message of probability p is 2logp where log means the logarithm with basis 2. So it is equal to infinity when the message is completely unexpected ð p ¼ 0Þ and to zero when the message is already known ð p ¼ 1Þ: The case of p ¼ 1=2 corresponds to the unit of quantity of information (bit or Hartley). More generally the mean value of the quantity of information corresponding to a message telling which of n possible issues has really

occurred is formally the same as the entropy of a statistical system with n Cybernetics from possible states, at least up to a factor involving Boltzmann’s constant. Shannon past to future used the concept of quantity of information in his study of the transmission capacity of a channel. The formal analogy between quantity of information and entropy has aroused the interest of L. Szilard (1925), B. Mandelbrot (1953) who proposed elucidations of the so-called Maxwell’s demon paradox and also of 855 L. Brillouin (1956) who built a theory of measurement in physics. These attempts were considered promising by L. de Broglie, but they are still controversial. Another interesting idea of cybernetics is that of requisite variety proposed by W.R. Ashby (1956) in “An Introduction to Cybernetics”. It has to do with both games and information theories and has been used in a precise way by P.C. Conant in the case of a regulator. But, roughly speaking, Ashby’s principle of requisite variety tells that to resist a certain variety of aggressions it is necessary to dispose of at least the same variety of strategies. Among the traits common to cybernetics and systems we have: the search for isomorphisms, the concept of homeostasis pointed out by Bertalanffy, introduced by C. Bernard and named by W.B Cannon, the importance of the global point of view on which insisted Bertalanffy (the necessity of local and global views being in fact both useful as remarked by Pascal), the concept of open system due to Bertalanffy inspired by biology, dissipative structures proposed by I. Prigogine, self-organization or autopoiesis, synergetics introduced by H. Haken, order by noise proposed by H. Von Fo¨rster (in fact an order already present in a potential manner and revealed by the triggering action of noise), fuzzy control due to L. Zadeh, the concept of chaos linked the so-called strange attractors, economic cybernetics (O. Lange, M. Manescu), management cybernetics (S. Beer (1965) with “The Brain of the Firm”), the so-called artificial life. . . The observer and the actor The ideas of observation and action are already in germ in Wiener’s cybernetics. The regulator “observes” through a communication channel the gap between what is realized and what is to be done, then “acts” consequently by means of a decision signal. This remark is at the root of the introduction by R. Valle´e, in 1951, of the mathematical concept of “observation operator” which involves the observation of the system by itself as well as that of the outside world. Second order cybernetics, introduced by H. Von Fo¨rster in the 1970s, emphasizes the role of the observer and self-reference considered also by G. Pask and others. In this frame H. von Fo¨rster proposed, in terms of selforganization (or autopoiesis), an interpretation of Piaget’s genetic epistemology elaborated in the 1930s. This presentation introduces the concept of eigenbehaviors considered later by F. Varela and H. Maturana who proposed the idea of operational closure.

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When Wiener wrote with A. Rosennblueth et al. (1943) an article entitled “Behavior, purpose and teleology”, he insisted upon the fact that cybernetics has much to do with action, an idea expressed by L. Couffignal saying that “cybernetics is the art of making action efficient. In the 50’s E. Bernard-Weil presented his theory of ago-antagonism which proposes the implementation of actions of opposite nature in a non-linear dynamical system. But action must not be considered alone, it needs cognition based upon observation. Both of them play their part in epistemo-praxiology proposed by R. Valle´e (1974, 1998) which takes into account the aspects of subjectivity due to inverse transfer of the epistemological and praxiological traits engraved in the system itself.

Some possible aspects of the future of cybernetics and systems A possible direction is the progress of epistemology and praxiology, as exposed above, with the help of models given by systems which are able to “perceive, decide and act”. If such models do not give a real insight in the problem of consciousness (which seems to be: “who” is the subject of the expression to be conscious?) they give descriptions of how information is conveyed to consciousness. Plato’s cave gives a metaphor of the infirmity of a perceiving system. These infirmities are difficult, if not impossible, to avoid but they must be at least recognized. Another important theme is that of the prolongation of human beings’ senses and effectors by artificial organs and also of the constitution of networks of connected systems. Here I quote (with permission of Unesco) an article entitled “Cybernetics and the future of man” (Valle´e R. 1952,): “It may be said that the evolution of man, which is perhaps proceeding on the mental plane but when biologically speaking seems to have been halted is now at work in the sphere of the “artificial”. The telecommunication instruments, extend the range of the natural human organs almost indefinitely. Technological evolution has thus transformed, not indeed “biological man”, but the bio-mechanical unit constituted by man and his instruments. We are in fact confronted with a new being, who is also capable of rapid and unexpected improvements and who, since he is in a constant state of evolution, is difficult to describe in concrete terms. A curious symbiosis is established, with a whole section of the inanimate world collaborating with man and so closely as to become a part of him. Just as the symbiosis of man and machine gives birth to a new being – the modern product of evolution – so the alliance of society and the machine engenders a creature of gigantic dimensions, who is gradually extending its influence over the whole surface of the globe.” Ashby’s concept of requisite variety seems to have an important future. To dispose of several strategies in order to be able to answer to the unexpected is necessary for survival. But too many strategies generate unbearable complications and one strategy only may be fatal, just a necessary

and sufficient variety is requested. This has permitted certain animal species to Cybernetics from survive, to a human being to find a new activity after the loss of his usual work past to future or to an industrial company to reconvert itself. At a higher level we can say that a civilisation must avoid both the unique thought and the scattering of doctrines. It must have at its disposal several visions of the world. If it is attacked, from the inside or the outside, by unexpected means, it can face them 857 only by implementing new attitudes. If we consider mankind as a whole, we must avoid the danger of a unique culture because if we see, even imperfectly, the present dangers we do not know those that are to come. References Andrew, A. (1989), Self-organizing Systems, Gordon and Breach, New York. Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London. Beer, S. (1965), The Brain of the Firm, Penguin Press, London. Bernard-Weil, E. (1975), L’Arc et la corde, Maloine, Paris. Bertalanffy, L. von (1950), “Zu allgemeinen Systemlehre”, Bla¨tter fu¨r Deutsche Philosophie No. 3-4. Bertalanffy, L. von (1968), General System Theory, George Braziller, New York. Brillouin, L. (1956), Science and Information Theory, Academic Press, New York. Fo¨rster, H. von (1976), “Objects: tokens for (eigen)-behaviors”, Cybernetics Forum, Vol. 8 No. 3-4, pp. 91-6. Fo¨rster, H. von (1994), The Cybernetics of Cybernetics, University of Illinois, Urbana. Haken, H. (1978), Synergetics, Springer-Verlag, Berlin. Maturana, H. and Varela, F. (1973), “Autopoietic systems: a characterisation of the living organization”, in Maturana, H. and Varela, F. (Eds), Autopoiesis and Cognition: The Realization of the Living, Reidel, Boston. McCulloch, W.S. (1965), Embodiments of Mind, The MIT Press, Cambridge, MA. McCulloch, W.S. and Pitts, W. (1943), “A logical calculus of the ideas immanent in nervous activity”, Bulletin of Mathematical Biophysics, Vol. 5, pp. 115-33. Pask, G. (1975), Conversation, Cognition and Learning. A Cybernetic Theory and Methodology, Elsevier, Amsterdam. Rosenblueth, A., Wiener, N. and Bigelow, J. (1943), “Behavior, purpose and teleology”, Philosophy of Science, Vol. 10, pp. 18-24. Shannon, C.E. and Weaver, W. (1949), The Mathematical Theory of Communication, The University of Illinois Press, Urbana. Valle´e, R. (1995), Cognition et Syste`me. Essai d’Episte´mo-Praxe´ologie. L’Interdisciplinaire. Limonest. Valle´e, R. (1998), “An introduction to epistemo-praxiology”, Cybernetics and Human Knowing, Vol. 5 No. 1, pp. 47-55. Wiener, N. (1948), Cybernetics or Control and Communication in the Animal and the Machine, Hermann et Cie. Paris; The Technology Press, Cambridge, MA: John Wiley and Sons, New York. Wiener, N. (1949), Extrapolation, Interpolation and Smoothing of Stationary Time Series, John Wiley and Sons, New York; The Technology Press of MIT, Cambridge, MA.

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Statistical validation of simulation models of observable systems Edgars K. Vasermanis, Konstantin N. Nechval and Nicholas A. Nechval Mathematical Statistics Department, University of Latvia, Riga, Latvia Keywords Cybernetics, Systems, Simulation, Risk Abstract In this paper, for validating computer simulation models of real, observable systems, an uniformly most powerful invariant (UMPI) test is developed from the generalized maximum likelihood ratio (GMLR). This test can be considered as a result of a new approach to solving the Behrens-Fisher problem when covariance matrices of two multivariate normal populations (compared with respect to their means) are different and unknown. The test is based on invariant statistic whose distribution, under the null hypothesis, does not depend on the unknown (nuisance) parameters. The sample size and threshold of the UMPI test are determined from minimization of the weighted sum of the model builder’s risk and the model user’s risk. The proposed test could result in the saving of sample items, if the items of the sample are observed sequentially. In this paper, we present the exact form of the proposed curtailed procedure and examine the expected sample size savings under the null hypothesis. The sample size savings can be bounded by a constant, which is independent of the sample size. Tables are given for the expected sample size savings and maximum sample size saving under the null hypothesis for a range of significance levels (a ), dimensions ( p ) and sample sizes (n ). The curtailed test considered in this paper represents improvement over the noncurtailed or standard fixed sample tests.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 858-869 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443932

1. Introduction Often, analytical results from the model of observable system for many customer arrival patterns and service patterns are difficult to obtain or we can obtain only an approximate solution to the model. Instead, a simulation model is used to model the observable system in order to optimize control of this system. The problem of validating computer simulation models of real, observable systems remains today perhaps the most elusive of all the unresolved methodological problems associated with computer simulation techniques. One of the most important steps in the development of a simulation model is determining whether the simulation model is an accurate representation of the system being studied. It is natural for model users, as well as for model builders, to inquire how accurately a model represents the system, especially when decisions involving expensive resources are made on the basis of the results of the model. Substantiation that a computerized model within its domain of applicability possesses a satisfactory range of accuracy

consistent with the intended application of the model is usually referred to as model validation and is the definition used in this paper. It is generally preferable to use some form of objective analysis to perform model validation. A common form of objective analysis for validating simulation models is statistical hypothesis testing (Naylor and Finger, 1967) which will be discussed in this paper. In using statistical hypothesis testing to test the validity of a simulation model under a given experimental frame and for an acceptable range of accuracy consistent with the intended application of the model, we have the following hypotheses: H 0 : Model is valid for the acceptable range of accuracy under a given experimental frame; H1 : Model is invalid for the acceptable range of accuracy under ð1Þ a given experimental frame: There are two possibilities for making a wrong decision in statistical hypothesis testing. The first one, type I error, is accepting the alternative hypothesis H1 when the null hypothesis H0 is actually true, and the second one, type II error, is accepting the null hypothesis when the alternative hypothesis is actually true. In model validation, the first type of wrong decision corresponds to rejecting the validity of the model when it is actually valid, and the second type of wrong decision corresponds to accepting the validity of the model when it is actually invalid. The probability of making the first type of wrong decision will be called model builder’s risk (a ) and the probability of making the second type of wrong decision will be called model user’s risk (b ).

2. Problem statement Suppose that we desire to validate a multivariate stationary response simulation model of observable system, which has p response variables. Let Xij and Yij be the ith observation of the jth model and system response variable, respectively. It is assumed that all observation vectors, X i ¼ ðX i1 ; . . .; X ip Þ0 ; Y i ¼ ðY i1 ; . . .; Y ip Þ0 ; i ¼ 1ð1Þn; are independent of each other, where n is a number of paired observations. Let Z i ¼ X i 2 Y i ; i ¼ 1ð1Þn; be paired comparisons leading to a series of vector differences. Thus, for testing the validity of a simulation model of a real, observable system, it can be obtained and used a sample of n independent observation vectors Z ¼ ðZ 1 ; . . .; Z n Þ: It is assumed that under H0, Z i , N p ð0; QÞ; ;i ¼ 1ð1Þn; where Q is a positive definite covariance matrix. Under H1, Z i , N p ða; QÞ; ;i ¼ 1ð1Þn; where a ¼ ða1 ; . . .; ap Þ0 – ð0; . . .; 0Þ0 is a mean vector.

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For fixed n, the problem is to construct a test which consists of testing the null hypothesis H0: Z i , N p ð0; QÞ; ;i ¼ 1ð1Þn; versus the alternative H1: Z i , N p ða; QÞ; ;i ¼ 1ð1Þn; where the parameters a and Q are unknown.

860

3. GMLR statistic In order to distinguish the two hypotheses (H0 and H1), a generalized maximum likelihood ratio statistic is used. The GMLR principle is best described by a likelihood ratio defined on a sample space Z with a parameter set Q, where the probability density function (PDF) of the sample data is maximized over all unknown parameters, separately for each of the two hypotheses. The maximizing parameter values are, by definition, the maximum likelihood estimators of these parameters, hence the maximized probability functions are obtained by replacing the unknown parameters by their maximum likelihood estimators. Under H0, the ratio of these maxima is a Q-free statistic. This is shown in the following. Let the complete parameter space for u ¼ ða; QÞ be Q ¼ {ða; QÞ : a [ R p ; Q [ Qp }; where Qp is a set of positive definite covariance matrices, and let the restricted parameter space for u, specified by the H0 hypothesis, be Q0 ¼ {ða; QÞ : a ¼ 0; Q [ Qp }: Then one possible statistic for testing H0: u [ Q0 versus H1: u [ Q1 ; where Q1 ¼ Q 2 Q0 ; is given by the generalized maximum likelihood ratio LR ¼ max LH1 ðZ; uÞ=max LH0 ðZ; uÞ: u[Q1

u[Q0

ð2Þ

Under H0, the joint likelihood for Z is given by LH0 ðZ; uÞ ¼ ð2pÞ2np=2 jQj

2n=2

! n X exp 2 Z i 0 Q 21 Z i =2 :

ð3Þ

i¼1

Under H1, the joint likelihood for Z is given by 2np=2

LH1 ðZ; uÞ ¼ ð2pÞ

2n=2

jQj

! n X 0 21 exp 2 ðZ i 2 aÞ Q ðZ i 2 aÞ=2 :

ð4Þ

i¼1

It can be shown that ^ 0 j2n=2 expð2np=2Þ max LH0 ðZ; uÞ ¼ ð2pÞ2np=2 jQ ^

ð5Þ

^ 1 j2n=2 expð2np=2Þ; max LH1 ðZ; uÞ ¼ ð2pÞ2np=2 jQ

ð6Þ

u[Q0

and u[Q1

where

^ 0 ¼ ZZ0 =n; Q

^ 1 ¼ ðZ 2 a^ u0 ÞðZ 2 a^ u0 Þ0 =n Q

and a^ ¼ Zu=u0 u are the well-known maximum likelihood estimators of the unknown parameters Q and a under the hypotheses H0 and H1, respectively, u ¼ ð1; . . .; 1Þ0 is the n-dimensional column vector of units. A substitution of (5) and (6) into (2) yields ^ 0 jn=2 jQ ^ 1 j2n=2 : LR ¼ jQ

ð7Þ

Taking the (n/2)th root, this likelihood ratio is evidently equivalent to ^ 0 jjQ ^ 1 j21 ¼ jZZ0 j=jZZ0 2 ðZuÞðZuÞ0 =u0 uj: LR ¼ jQ

ð8Þ

Now the likelihood ratio in (8) can be considerably simplified by factoring out the determinant of the p £ p matrix ZZ0 in the denominator to obtain this ratio in the form    ðZuÞ0 ðZZ0 Þ21 ðZuÞ LR ¼ jZZ0 j jZZ0 j 1 2 u0 u ð9Þ ¼ 1=½1 2 ðZuÞ0 ðZZ0 Þ21 ðZuÞ=n This equation follows from a well-known determinant identity. Clearly (9) is equivalent finally to the statistic _

_

V n ¼ ½ðn 2 pÞ=pðLR 2 1Þ ¼ ½ðn 2 pÞ=pna T 21 a ;

ð10Þ

_

_; TÞ is a complete sufficient statistic for the where T ¼ nQ 1 : It is known that ða parameter u ¼ ða; QÞ: Thus, the problem has been reduced to consideration of _; TÞ: It can be shown that under H , V is a Q-free the sufficient statistic ða 0 n statistic, which has the property that its distribution does not depend on the actual covariance matrix Q. This is given by the following theorem. Theorem 1 (PDF of the Statistic Vn ). Under H1, the statistic Vn is subject to a noncentral F-distribution with p and n2p degrees of freedom, the PDF of which is

 2n    p p21 2 p n 2 p 21 p 2 fH1 ðvn ; n; qÞ ¼ B ; ½ p=ðn 2 pÞ2 vn † 1 þ vn 2 2 n2p   ! n p nq n 2 p 21 2nq=2 ; ; 1þ ; 0 , vn , 1: e 1 F1 2 2 2 pvn

ð11Þ

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862

where 1 F1 ðb; c; xÞ is the confluent hypergeometric function, q ¼ a0 Q 21 a is a noncentrality parameter. Under H0, when q ¼ 0; (11) reduces to a standard F-distribution with p and n 2 p degrees of freedom,    p p21 n p n 2 p 21 fH0 ðvn ; n; qÞ ¼ B ; ½ p=ðn 2 pÞ2 vn2 †½1 þ pvn =ðn 2 pÞ22 ; 2 2 ð12Þ 0 , vn , 1: Proof. The proof follows by applying Theorem 1 (Nechval, 1997a) and being straightforward is omitted. A 4. GMLR test The GMLR test of H0 versus H1, based on Vn, is given by ( $ h; then H1 Vn , h; then H0

ð13Þ

and can be written in the form ( dðV n Þ ¼

1; if V n $ h ðH1 Þ 0; if V n , h ðH0 Þ

;

ð14Þ

where h . 0 is a threshold of the test which is uniquely determined for a prescribed level of significance a so that sup Eu {dðV n Þ} ¼ a:

ð15Þ

u[Q0

When the parameter u ¼ ða; QÞ is unknown, it is well known that no uniformly most powerful (UMP) test exists for testing H0 versus H1. However, it can be shown that the test (13) is UMPI for a natural group of transformations on the space of observations. Here the following theorem holds. Theorem 2 (UMPI Test). For testing the hypothesis H0: q ¼ 0 versus the alternative H1: q . 0; the test given by (13) is UMPI. Proof. This is given by Nechval and Nechval (1999). A 5. Robustness property In what follows, as one more optimality of the Vn-test, a robustness property can be studied in the following set-up. Let Z ¼ ðZ 1 ; . . .; Z n Þ0 be an n £ p

random matrix with a PDF w, let Cnp be the class of PDF’s on R np with respect to Lebesque measure dZ, and let H be the set of nonincreasing convex functions from [0,1) into [0,1). We assume n $ p þ 1: For a [ R p and Q [ Qp ;define a class of PDF’s on R np as follows: 8 9 < f [ Cnp : fðz; a; QÞ ¼ jQj2n=2 = Pn ð16Þ Cnp ða; QÞ ¼ : †h i¼1 ðz i 2 aÞ0 Q 21 ðz i 2 aÞ ; h [ H ; In this model, it can be considered the following testing problem: H0 : w [ Cnp ð0; QÞ; Q [ Qp

ð17Þ

H1 : w [ Cnp ða; QÞ; a – 0; Q [ Qp ;

ð18Þ

versus

and shown that Vn-test is UMPI. Clearly if ðZ 1 ; . . .; Z n Þ is a random sample of Z i , Np ða; QÞ; i ¼ 1ð1Þn; or Z , Nnp ðus0 ; I n ^ QÞ; where u ¼ ð1; . . .; 1Þ0 [ R n ; the PDF w of Z belongs to Cnp ða; QÞ: Further if fðz; a; QÞ belongs to Cnp(a,Q), then g* ðz; a; QÞ ¼

Z 0

1

fðz; a; rQÞ dG* ðrÞ;

ð19Þ

also belongs to Cnp(a,Q) where G* is a distribution function on (0,1), and so Cnp(a,Q) contains the (np-dimensional) multivariate t-distribution, the multivariate Cauchy distribution, the contaminated normal distribution, etc. Here the following theorem holds. Theorem 3 (Robustness Property). For the problem (17) –(18), Vn-test is UMPI and the null distribution of Vn is F-distribution with p and n 2 p degrees of freedom. Proof. The proof is similar to that of Nechval (1997b) and so it is omitted here. A In other words, for any Q [ Qp and any w [ Cnp ð0; QÞ; the null distribution of Vn is exactly the same as that when Z , Nð0; I n ^ QÞ; that is, the distribution of Vn under H0 is the F-distribution with p and n 2 p degrees of freedom. In this sense, the Vn-test is robust against departures from normality. 6. Risk minimization For fixed n, in terms of the above PDF’s in (11) and (12), the probability of making the first type of wrong decision (model builder’s risk (a )) is found by

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aðh; nÞ ¼

Z

1

fH0 ðvn ; nÞ dvn

ð20Þ

h

864

and the probability of making the second type of wrong decision (model user’s risk (b )) by:

bðh; n; qÞ ¼

Z

h

fH1 ðvn ; n; qÞ dvn :

ð21Þ

0

When the noncentrality parameter q is equal to zero, this implies that the model is a perfect representation of the system with respect to its mean behaviour. Any value of a will result in a value for q that is greater than zero. As the value of a increases, the value of q will also increase. Hence, the noncentrality parameter q is the validity measure for the above test (13). Let us assume that for the purpose for which the simulation model is intended, the acceptable range of accuracy (or the amount of agreement between the model and the system) can be stated as 0 # q # q00 ; where q00 is the largest permissible value. In the statistical validation of simulation models, for preassigned n ¼ n00 ðn00 . pÞ determined by a data collection budget, if we let wa and wb be the unit weight (cost) of the model builder’s risk (a ) and the model user’s risk (b ), then the optimal threshold of test, h*, can be found by solving the following optimization problem. Minimize: Rðh; n00 ; q00 Þ ¼ wa aðh; n00 Þ þ wb bðh; n00 ; q00 Þ

ð22Þ

h [ ð0; 1Þ;

ð23Þ

Subject to:

where Rðh; n00 ; q00 Þ is a risk representing the weighted sum of the model builder’s risk and the model user’s risk. It can be shown that h* satisfies the equation: wa fH0 ðh* ; n00 Þ ¼ wb fH1 ðh* ; n00 ; q00 Þ:

ð24Þ

In the statistical validation of simulation models, the model user’s risk is more important that the model builder’s risk, so that wa # wb : For instance, let us assume that p ¼ 10; n00 ¼ 40; q00 ¼ 0:5; and wa ¼ wb ¼ 1: It follows from (24) that the optimal threshold h* is equal to 0.365. If the sample size of observations, n, is not bounded above, then the optimal value n* of n can be defined as

8 9 00 > < aðh* ; nÞ þ bðh* ; n; q Þ # r; > = n* ¼ inf n : h* ¼ arg min Rðh; n; q00 Þ ; > > h[ð0;1Þ : ;

ð25Þ

Validation of simulation models

where r is a preassigned value of the sum of the model builder’s risk and the model user’s risk.

865

7. Curtailed procedure Brown et al. (1979) propose a curtailed t-test procedure for testing the onesided hypothesis H0: a , 0 versus H1: a . 0; where Xi, i ¼ 1; 2; . . . is a sequence of independent, identically distributed normal random variables with unknown mean a and unknown variance s 2. The curtailed procedure is shown to be better than the fixed sample size t-test and admissible under some restrictions on the critical value (threshold of the test) when the risk consists of two components, the probability of error and the expected sample size. As noted by Brown et al. (1979), the similar results can be obtained for testing H0: a ¼ 0 versus H1: a – 0; where Zi, i ¼ 1; 2; . . . is a sequence of p-dimensional independent, identically distributed normal random vectors with unknown p-dimensional mean a and unknown covariance matrix Q. Proceeding analogously to the t-test case (Brown et al., 1979), the curtailed procedure is defined by specifying that we should stop and accept the null hypothesis H0 at the first value m such that Vm ,

ð K n 2 n þ mÞðm 2 pÞ pðn 2 K n Þ

ð26Þ

for m ¼ m † ; . . .; n (n is equal to n00 (or n*)), where m † ¼ maxð p þ 1; n þ 1 2 kn Þ;

ð27Þ

kn 2 1 , K n , kn ;

ð28Þ

K n ¼ nph* =ðn 2 p þ ph* Þ:

ð29Þ

kn is an integer with

and

When m ¼ n; stop and reject the null hypothesis H0 if (26) does not hold. Let N be the random stopping time when using the curtailed procedure. Then N can take the values m † ; . . .; n: The expected savings in sample size is given by

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E{n 2 N} ¼

n21 X

ðn 2 mÞ PrðN ¼ mÞ ¼

m¼m †

¼

866

n21 X

n21 X

PrðN # mÞ

m¼m †

PrðV m , ðK n 2 n þ mÞðm 2 pÞ=½ pðn 2 K n ÞÞ:

ð30Þ

m¼m †

Substituting (29) into (30) yields E{n 2 N } ¼

n21 X

PrðV m , hm Þ;

ð31Þ

m¼m †

where hm ¼

ðm 2 pÞ½ðn 2 pÞðm 2 nÞ þ mph *  : pnðn 2 pÞ

ð32Þ

Note that the curtailed procedure of the two-sided t-test is a special case of the curtailed procedure of the Vn-test when p ¼ 1: 8. Sample size savings Values for the expected sample size savings under the null hypothesis can be calculated using equation (31). From (29), letting n ! 1 we see that for the curtailed Vn-test procedure the maximum saving in sample size is given by 2 limn!1 maxðn 2 NÞ ¼ limn!1 kn 2 1 ¼ ½xp;12 a ;

ð33Þ

where [†] is the greatest integer function, xp2; 1 a is the (12 a ) percentile of the chi-squared distribution with p degrees of freedom. In Table I we present, for the curtailed Vn-test procedure, the expected sample size savings, E{n 2 N}; under the null hypothesis and the maximum possible savings, max (n2N ), for various dimensions ( p ) and the significance levels a ¼ 0:05 and 0.01. As n increases, there is relatively little change in Eðn 2 N Þ or max ðn 2 N Þ for fixed a and p. As p increases, for fixed a and n, E{n 2 N } and max ðn 2 N Þ increase until the constraint that at least p þ 1 out of n points must be observed before any possible curtailment occurs restricts the value of max ðn 2 NÞ: 9. Application of the test This section discusses an application of the above test to the following problem. An airline company operates more than one route and also there are more than one type of airplanes available. Each type has its relevant capacity

n p

20

40

60

a 1 2 6

10 20 40

0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01

2.25 4.41 3.26 5.47 4.44 6.43 4.12 5.53

(3) (6) (5) (8) (10) (13) (9) (9)

2.32 4.90 3.44 6.14 5.43 8.45 6.31 9.34 6.45 8.92

(3) (6) (5) (8) (11) (14) (16) (19) (19) (19)

2.34 (3) 5.00 (6) 3.49 (5) 6.33 (8) 5.72 (12) 9.09 (15) 6.91 (17) 10.5 (21) 8.24 (28) 11.9 (32) 7.01 (19) 9.47 (19)

and costs of operation. The demand on each route is known only in the form of the sample data, and the question asked is: which aircraft should be allocated to which route in order to minimize the total cost (performance index) of operation? This latter involves two kinds of costs: the costs connected with running and servicing an airplane, and the costs incurred whenever a passenger is denied transportation because of lack of seating capacity. (This latter cost is “opportunity” cost.) We define and illustrate the use of the loss function, the cost structure of which is piecewise linear. Within the context of this performance index, we assume that a distribution function of the passenger demand on each route is known. Thus, we develop our discussion of the allocation problem in the presence of completely specified demand distributions. We formulate this problem in a probabilistic setting. Let A1 ; . . .; Ak be the set of airplanes which the company utilize to satisfy the passenger demand for transportation en routes 1; . . .; p: It is assumed that the company operates m routes which are of different lengths, and consequently, different profitabilities. Let fij(s ) represent the PDF of the passenger demand S for transportation en route j ðj ¼ 1; . . .; pÞ at the ith stage ði [ 1; . . .; nÞ; and Fij(s ) its cumulative distribution function. It is required to minimize the expected total cost of operation (the performance index) " # Z 1 p k X X Ji ðU i Þ ¼ wrij urij þ cj ðs 2 Qij Þfij ðsÞ ds ð34Þ j¼1

subject to

r¼1

Qij

Validation of simulation models 867 Table I. Expected (and maximum) sample size savings for the curtailed Vn-test procedure under the null hypothesis

p X

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urij # ari ;

r ¼ 1; . . .:k;

ð35Þ

j¼1

where

868 Qij ¼

k X

urij qrj ;

j ¼ 1; . . .; p;

ð36Þ

r¼1

U i ¼ furij } is the k £ m matrix, urij is the number of units of airplane Ar allocated to the jth route at the ith stage, wrij is the operation costs of airplane Ar for the jth route at the ith stage, cj is the price of a one-way ticket for air travel en jth route, qrj is the limited seating capacity of airplane Ar for the jth route, ari is the available number of units of airplane Ar at the ith stage. Let us assume that U*i ¼ fu*rij } is the optimal solution of the above-stated programming problem. Since an information about the passenger demand is not known precisely, this result provides only approximate solution to a real airline process. To depict the real, observable airline process more accurately, the test proposed in this paper, might be employed to validate the results derived from the analytical model (34)-(36). In this case Z ij ¼ X ij 2 Y ij ;

j ¼ 1ð1Þp;

;i [ {1; . . .; n};

ð37Þ

where X ij ¼ cj

"Z

Q*ij

sfij ðsÞ ds þ

0

Q*ij

Z

#

1

Q*ij

fij ðsÞ ds ;

ð38Þ

is the expected gain (ensured by the service of a passenger demand on the jth route at the ith stage) derived from the analytical model (34)-(36), Q*ij ¼

k X

u*rij qrj ;

j ¼ 1; . . .; p;

ð39Þ

r¼1

Yij is the real gain ensured by the service of a passenger demand on the jth route at the ith stage (an observation of the airline process response variable). Thus, the methodology proposed in this paper allows one to determine whether the analytical model (34)-(36) is appropriate for minimizing the total cost of airline operation.

10. Conclusions In conclusion, we note that while the curtailed procedure, considered in this paper, represents improvement over the noncurtailed or standard fixed sample test, it has two discouraging properties. First, the maximum sample size savings, and thus the expected sample size savings under the null hypothesis can be bounded independently of the sample size. Secondly, an early decision implies that the null hypothesis has been accepted, i.e. one cannot make an early decision in which one rejects the null hypothesis. This research was supported in part by Grant No.02.0918 and Grant No.01.0031 from the Latvian Council of Sciences and the National Institute of Mathematics and Informatics of Latvia. References Brown, L.D., Cohen, A. and Strawderman, W.E. (1979), “On the admissibility or inadmissibility of fixed sample size tests in a sequential setting”, Ann. Statist., Vol. 7, pp. 569-78. Naylor, T.H. and Finger, J.M. (1967), “Verification of computer simulation models”, Management Science, Vol. 14, pp. 92-101. Nechval, N.A. (1997a), “Adaptive CFAR tests for detection of a signal in noise and deflection criterion”, in Wysocki, T., Razavi, H. and Honary, B. (Eds), Digital Signal Processing for Communication Systems, Kluwer Academic Publishers, Boston/Dordrecht/London, pp. 177-86. Nechval, N.A. (1997b). “UMPI test for adaptive signal detection”, in Kadar, I. (Ed.), Signal Processing, Sensor Fusion, and Target Recognition VI, Proc. SPIE 3068, Orlando, Florida, USA, Paper No. 3068-73, p. 12. Nechval, N.A. and Nechval, K.N. (1999), “CFAR test for moving window detection of a signal in noise”, Proceedings of the 5th International Symposium on DSP for Communication Systems (Perth-Scarborough, Australia), University of Wollongong, Australia, pp. 134–41.

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SWARM based study on spatial-temporal emergence in flood Yiming Wei, Linpeng Zhang and Ying Fan Institute of Policy and Management, Chinese Academy of Sciences, Beijing, People’s Republic of China Keywords Cybernetics, Simulation, Disaster management Abstract In complex adaptive system (CAS), the complex behavior of system is emerged from the bottom, that agents’ adaptability bottom-up the complexity of the entire system. This idea can be simulated by the method of computer aid simulation. SWARM, which is developed by Santa Fe Institute, is such a tools kit based on the bottom-up modeling method that can be used in CAS simulation on computer. This paper presented a Swarm based simulation platform for the study on complexity in flood disaster. Its application is illustrated with a SWARM based model and program for simulating spatial and temporal emergence of flooding. This model offers virtually unlimited possibilities to simulate the emergence of flooding. Some rules have been elicited from the experimental results, which could provide useful information for the disaster reduction and management.

1. Introduction Flood disaster is one of the major natural disasters in which human being has incurred great damages to properties and serious loss of lives. Flood disaster is the result of the interaction between natural flood and mankind, which presents one kind of relation between mankind and nature. The flood that can do damage to mankind and their environment is called disaster flood. In general, those essential conditions under which flood disaster emerges are: (1) existing factors that induce flood (called Hazard-formative factors) and the environment that breeds flood disaster (called Hazard-formative environment); (2) population, crop and estate distributed in the flood affecting area (called Hazard-affected bodies).

Kybernetes Vol. 32 No. 5/6, 2003 pp. 870-880 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443941

The result of the interaction among the Hazard-formative environment, Hazard-formative factors and Hazard-affected bodies is called Flood disaster effects. From the viewpoint of system theory, the complex interaction and relation among the hazard-formative environment, hazard-formative factors, hazard-affected bodies and disaster effects formed the system of flood disaster, Partially supported by grants (No.79900002 and 50099620) from National Natural Science Foundation of China.

which has a certain structure, function and characteristic (Wei and Jin, 1997; Study on spatialWei et al., 2001). temporal Flood disaster is a dynamic phenomenon varying from region to region emergence and changing over time. The temporal and spatial complexity of flood shows universality, regional, determination and non-determination. The traditional flood model is based on the “top down” view, which takes the entire flood as 871 one agent (Genesereth and Ketchpel, 1994). These canonical flood theories do not model the process of spatial and temporal emergence of flooding. Some researchers have started to explore a different approach to flood modeling, which has been described as “bottom up” or “process based”. Rosso (1991) discussed the Fractal relation of mainstream length to catchment area in networks. Wang and Lou (1992) investigated the behavior of flood disaster for its emergence from order to disorder using the Chaos theory. Rodrigue-Irurbe (1989) presented the Chaos in rainfall, Wei (1999) formulated the model for the forecasting of flood disaster using the Artificial Neural Network, the fractal characteristics of rainfall in Jiujiang river was investigated with the Phase Space reconstruction (Wei and Jin, 1998a), the chaos characteristic of inundated area of flood disaster in China was analyzed with R/S method, (Wei, 1998b). To the study on complexity in flood disaster we present its general frame in (Wei, 2000a, b), which forms the comprehensive methodology with qualitative and quantitative integration. In this paper, we will discuss how the general purposes tool for Object oriented Simulation can be used to build agent based models in flood. From the view point of complex adaptive system (CAS) and with the tool of Swarm, a spatial and temporal emergence model for the simulation of flood disaster is formulated, simulation experiments correspondence to different initial condition has been done to testify the model. 2. SWARM Since 1980s, there are many researchers in different areas from all over the world who are all concerned about some complex phenomenon of nature and human society. And it directly gave the birth to a new cross subject: Complexity Science. In the frontier of Complexity Science research – Santa Fe Institute(SFI) in New Mexico USA, there are a group of scientists from different research area (Santa Fe, 1996a). The main idea of their outstanding work can be summarized by the theory of CAS and multi-agent based computer simulation. They developed a tool called SWARM (Santa Fe, 1996b). SWARM is used for the study of CAS using multi-agent discrete event simulations. The first version of the simulation tool could be available in 1995. It requires the use of the GNU C compiler, UNIX, and X-Windows. Swarm software libraries allow users to construct simulations where a collection of independent agents or elements interacts through discrete events. Any physical process or social system could potentially be simulated in SWARM, since it

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imposes no inherent constraints on the model world or patterns of interaction between model elements. Programs using Swarm have already been developed in such diverse area as biology, economics, chemistry and ecology (Kohler and Carr, 1996; McMullin, 1997; Terna, 1997). The basic unit of a SWARM simulation is the agent, which may be any entity that can generate events that affect itself and other agents. Simulations consist of groups of many interacting agents, called “swarm”, which may, themselves, be grouped into more comprehensive swarms. The logical structure of swarms of agents interacting through discrete events is implemented in Objective C, an objective-oriented (OO) language. As in most OO programming, software consists primarily of definitions of various classed of objects. An object is then a combination of instance variables for the object’s state and methods (services, procedures) that implement the object’s behavior. Each object carries with it its own state variables, but the generic definition of its behavior is provided by the class. In the simplest case, a model consists of one swarm inhabited by a group of agents and a schedule of activity for those agents. In a SWARM, the environment is itself modeled by one or more other agents, some of whom might have a larger influence than others (Angeline et al., 1997). SWARM implements a “probe” facility that allows any object’s state to be read or set and any method to be called in a generic fashion, without requiring additional user code. Probes are used to make data analysis tools work in a general way and are also the basis of graphical tools to inspect objects in a running system. SWARM also provides data collection tools in the form of observer agents, special objects whose purpose is to observe other objects via the probe interface. The observer agents themselves are a swarm, a group of agents and a schedule of activity. By combining this swarm with a model swarm running as a sub-swarm of the observer, a full experimental apparatus is created. By using hierarchical swarms to separate data collection from the model, the model itself remains pure and self-contained, a simulated world under glass. Different observer swarms can be used to implement different data collection and experimental control protocols, but the model itself remains unchanged (Langton et al., 1996). Figure 1 shows its principle of multi-agent based modeling method for simulation.

3. Swarm based simulation for emergence of flood disaster 3.1 Model and algorithm Swarm based model for emergence of flood disaster is used to simulate the flooding in spatial and temporal process. Its theory basis is cellular automata and Multi-Agent based modeling method. In practice, we use the two dimensions model to simulate the flooding process. The model developing is based on the swarm libraries, and uses the Java language. The model consists of five files and are listed in Table I.

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Figure 1.

File name

Function

JFloodObserverSwarm.java Base class, handles the creation of graphs, probes and other objects which gather data from the model and display on the screen or output to a file JFloodModelSwarm.java Creats agents and auxiliary model object JFloodStatistics.java To statistic the distributions and measure the data of the simulation process region.java Agent class, the artificial agents of the model world are usually tailor-made for flood disaster simulation StartJFlood.java Start program for simulating

In this model, the two dimensions grid is used to present the flooding area, and each grid has correspondence with a small terra with its height, sluice capacity, etc. these indexes are unchanged. Its algorithm is described as following. (1) The water in flood from the middle of the top of the grid or the special position and it will overspread to the left, right, bottom, right of bottom and left of bottom. During the simulation, for any grid, the water spreads to above five directions. Five grids of these five directions are called the neighbor grids. (2) In each step of the simulation, if the volume of water in a grid is greater than its capacity, this grid will be marked as flooding, and the overwater will spread according to the following algorithm. (3) For the flooding grid, if its current height of water is higher than that of its neighbor, its water will spread to the lower neighbor grids till their heights are equal or the volume is less than its capacity.

Table I. Files included in the model and their functions

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(4) For the flooding grid, if the water height of all neighbor grids is higher than its height, its water will not spread to its neighbor grids, this grid could be taken as a lake. (5) During simulating, if a grid has been marked as flooding grid, this grid will be marked as flood disaster, the graph will show the total number of present flooding grid.

3.2 Parameters initializing At the beginning of simulation, we should set initial parameters of the model, and all are listed in Table II. All the parameters could be inputted from the graphical interface which is initialized and controlled by the JfloodObserverSwarm. 3.3 Experiment and result In this paper, we try to introduce eight types of simulation. The difference between these simulation experiments is the initial altitude, number of affusion grid, their position. Through a number of experiments, their results could be compared and analyzed. Figure 2 shows the results comparison. In Figure 2, the arrowhead is used to present the number and the position of burst. “S” means the initial volume of affusion is small and “L” is large. The altitude is different for each grid and its random distribution, No.1, No.2 and No.6 are uniform distribution, No.3, No.4 and No.7 are tri- sidestep distribution, No.5 and No.8 are A hill distribution. We have done several experiments for each type. Figure 3 shows the results of one of the experiments for No.3. In Figure 3, the dark grid means the flooding area. The higher dark of grid means the area with higher flood, during the simulating, it changes continuously, at the same time some parameters such as the flooding area could be calculated and displayed in some plots.

Parameters

Table II. Initial parameters and their meaning

Meaning

GridSize

Grid size, default is 40 units.

MaxHG MinHG

The maximum and minimum height (altitude),it is the range of the random height (altitude) of each grid, the default is 200-100 units.

MaxPVW MinPVW

The maximum and minimum capacity (sluice), it is the range of the random capacity (sluice) of each grid, the default is 20-1 units.

Water

The total water of flooding grid at the beginning, the default is 8000.

Choice

The code correspondence to simulation type, it could be from 1 to 8.

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Figure 2. The eight types in the experiment of flood model

Figure 3. The emergence result of one experiment for No. 3 (The dark grid means the flooding area)

For each type we have done five times experiments, the Table III presents the average value acquired in the experiments of each indexes as following. .

The times (steps) from flooding beginning to the total number of flooding grid to 100,200,300,400,500 and 1,000 (denote T-100,T-200,T-300,T-400, T-500,T-1000), which used to describe the flooding spread process.

.

The time for the flooding to stability (T-s), which means that the flooding area has no change in 30 steps.

.

The total flooding areas (grids) when it arrives at stability (A-s).

.

The total flooding area (grids) which have never been flooded when stability (A-nonf-s).

.

The total areas (grids) which is still overflowing when it arrives to stability (A-o-s).

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Table III. The comparisons among the eight types for the experiment results

T-100 T-200 T-300 T-400 T-500 T-1000 T-s A-s A-nonf-s A-o-s TA for CVW , 10 TA for the 10 , ¼ CVW , 20 TA for the 20 , ¼ CVW , 30 TA for the CVW . ¼ 30 HL FD

No. 1

No. 2

No. 3

No. 4

No. 5

No. 6

No. 7

No. 8

7 20 87 – – – 296 333 1267 221 165 58 45 62 64 28

5 7 10 19 50 – 595 661 939 427 329 103 114 112 65 35

7 13 25 45 108 – 364 540 1060 252 460 61 7 0 23 33

5 7 9 13 20 174 518 1093 507 515 905 154 18 0 29 39

7 12 19 30 57 – 211 566 1034 232 484 65 4 0 23 31

7 12 20 36 76 – 545 628 972 429 287 105 103 128 64 38

7 11 16 21 29 185 493 1077 523 522 880 156 21 1 32 39

7 10 14 19 26 146 298 1068 532 513 844 177 27 0 25 38

.

The total number of flooding areas(grids) (TA) for their flooding level(CVW) up to the units of 0-9, 10-19, 20-29 and over 30 when it arrives to stability.

.

The highest level in flooding area when it arrives at stability (HL).

.

The farthest distance for the flooding arriving (FD).

The statistic indexes of the experiments for the eight types are listed as following. 3.4 Analysis and discussion 3.4.1 Impact of the topography on the flood spreading. All eight types could be divided into three groups, the group-1 are No.1, No.3 and No.5, group-2 are No.6, No.7 and No.8, group-3 are No.2 and No.4. The experiments are under the same conditions except the topography, from the results we know as following. .

Spreading speed. For the No.3, No.5, No.7, No.8, their spread speed is much higher than the other’s, which is well to illustrate the real topography because the flowing direction is from the high to low. Figure 4 shows the comparisons with their results in speed.

.

Flood area(A-s): Generally, the flood area in the regular distribution of topography is 1.6 t 1.8 times as that of random distribution.

.

TA. For the random distribution of topography, TA is almost the same. But regular distribution of topography, TA of high CVW is less than that of low CVW, which be shown in Figure 5.

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Figure 4. Shows the comparisons with their results in spreading speed

.

HL. The HL of random distribution of topography is almost the 2 times as that of regular distribution.

.

FD. The FD of random distribution is a bit less than that of regular distribution.

3.4.2 Impact of initial affusion volume to flood emergence. The experiments for the three groups mentioned above are under the same conditions except the initial affusion volume, from the results we know as following.

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Figure 5. The comparison with their TA

.

The spreading speed. More initial volume means the higher spreading speed and more time for stability (T-s).

.

Total areas of flooding (A-s). More initial volume means the larger total areas of flooding when it arrives at stability. For the regular topography distribution, the increasing rate of total areas of flooding is almost the same as that of initial volume.

.

TA. More initial volume means the larger total areas of flooding for their flooding level(CVW) up to the units of 0-9, 10-19, 20-29 and over 30 when it arrives to stability.

.

.

HL. The highest level in flooding area when it arrives at stability (HL) of Study on spatialmore initial volume is almost the same as that of less initial volume. It temporal means there is no relation between HL and the initial volume. emergence FD. More initial volume means the further away for the flooding could go.

3.4.3 Impact of the initial break number to the emergence of flood. The No. 2 and the No. 4 are used to simulate the emergence when there are two breaks. The results is as following. .

Spreading speed. The spreading speed of two breaks is higher than that of one break. It needs more time for flooding arrives at stability (T-s) as there are two breaks.

.

A-s. The total flooding areas (grids) when it arrives at stability of two breaks is greater than that of one break.

.

TA. More initial volume means the larger total areas of flooding for their flooding level (CVW) up to the units of 0-9, 10-19, 20-29 and over 30 when it arrives to stability.

.

HL. The highest level in flooding area when it arrives at stability (HL) of two breaks is almost the same as that of one break. It means there is no relation between HL and the number of breaks.

.

FD. The furthest distance of two breaks for the flooding could go is the same as that of one break.

4. Conclusions and remarks This paper introduced how a Swarm based model for spatial and temporal emergence of flood disaster could be implemented, and its application is illustrated with experiments. This model offers virtually unlimited possibilities to simulate the emergence of flooding. This Swarm based platform could create exciting and useful results and rules on the emergence of flood for the researchers. Even that, there are still much work should be improved for this model. (1) The algorithm improved. At present the software is developed with JAVA language. The model is operated slowly and its simulation takes long time. In another way, the more active interface could be developed to allow more researchers to apply this model. (2) The topography distribution could be improved. In our experiments, there are three types of topography distribution, but actually, the real topography is much more complex, so we should add more types of topography distribution, to introduce the GIS map.

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(3) The economic attribution could be introduced to evaluate the flood risk. We could introduce the economic attribution such as the population, crop-type and the estate into each grid in the model so that the damage and loss could be predicated with this model. If so, this model is helpful to make the decision for controlling the flood and cutting down its loss.

880 References Angeline, P., Reynolds, R., Mcdonnel, J. and Eberhart, R. (1997), Evolutionary Programming VI, Springer-Verlag, New York. Genesereth, M.R. and Ketchpel, S.P. (1994), “Software agents”, Communications of the ACM, Vol. 37, pp. 48-53. Kohler, T.A. and Carr, E. (1996), “Swarm-based modeling of prehistoric settlement systems in Southwestern North America”. Proceedings of Colloquium II, UISPP XIIIth Congress, Forli, Italy. Langton, C., Minar, N. and Burkhart, R. (1996), “The swarm simulation system: a toolkit for building multi-agent simulation”, Working Paper at Santa Fe Institute., SFI, USA. McMullin, B. (1997), “SCL: An artificial chemistry in swarm”. Available at: http://www.santafe. edu/sfi/publications/Working_Papers/97-01-002 Rodrigue-Irurbe, I. (1989), “Chaos in rainfall”, Water Resources Research, Vol. 25, pp. 1667-75. Rosso, R. (1991), “Fractal relation of mainstream length to catchment area in networks”, Water Resources Research, Vol. 27, pp. 381-7. Santa Fe Institute (1996a), http://www.santafe.edu Santa Fe Institute (1996b), http://www.swarm.org Terna, P. (1997), “Simulation tools for social scientists: building agent based models with SWARM”, Available at: http://www.soc.surrey.ac.uk/JASSS/1/2/4.html Wang, Shunyi and Luo, Zude (1992), “Chaos theory as one method of human for cognizing some natural disasters”, Journal of Natural Disaster, Vol. 1, pp. 3-16, (In Chinese). Wei, Yiming and Jin, Jiuliang (1997), “The general system of flood disaster evaluation”, Journal of Catastrophology, Vol. 12, pp. 1-5, (in Chinese). Wei, Yiming (1998b), “The time series fractal characteristics of inundated area of flood disaster occurred in China from 1949 to 1994”, J. of Natural Disaster, Vol. 7, pp. 83-7, (in Chinese). Wei, Yiming and Jin, Jinliang (1998a), “The chaotic characteristics of annual precipitation series in Jiujiang of Jiangxi province”, Science in Jiangxi, Vol. 2, pp. 141-5, (in Chinese). Wei, Yiming (1999), “Neural network based predicative method for flood disaster”, in Gen, M. (Ed.), Proceedings of 26th IE and C, Japan, Vol. 1, pp. 730-35. Wei, Yiming (2000a), “Thinking of the study on complexity in flood disaster”, in Nakamori, Y. (Ed.), Proceedings of International Symposium on Knowledge and Systems Sciences: Challenges to Complexity, Japan, pp. 255-61. Wei, Yiming (2000b), “The general frame of the system for analysis and evaluation of flood disaster”, in Lai, K.K. (Ed.), Proceedings of 3rd-MS and IE, Hongkong, pp. 612-17. Wei, Yiming, Fan, Ying and Jin, Jiuliang (2001), “System theory of risk analysis for flood disaster”, Journal of Management Sciences in China, Vol. 4, pp. 7-11.

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Towards a cybernetics of value, presence, and anticipation

A cybernetics of value, presence, and anticipation 881

John Wood Programme leader, MA in Design Futures, Department of Design, Goldsmiths College, University of London, UK Keywords Cybernetics, Values Abstract The paper asks whether we can popularise a cybernetics of human presence. It suggests that, despite its implicit critique of mechanistic thinking, cybernetics inherited its mindset from classical science, and therefore played a part in the evolution of technologically induced forms of alienation. Cybernetics also upholds a strongly western model of “self” that, given the technological power implicit in established cybernetic principles, reinforces instrumentalist, solipsistic, and cynical modes of reasoning in the economically “advanced” nations. These effects, in turn, continue to precipitate ecological damage. In discussing more recent developments, the paper notes the possibilities for modes of cybernetics that could become operative at the site of our self-world interface. At this level, it argues, our human ontology becomes more synonymous with our senses. This can also be shown by reminding ourselves of the crucial role of our “creative presence”, in which a greater acknowledgement of anticipatory reasoning might inform an actative, flow-based grammar of cybernetics. It concludes that clocks need to be radically re-designed within terms that are in accord with (at least) second-order cybernetics.

Cybernetics inherited a language from science Although some cyberneticians (Von Bertalanffy, 1968) have strongly criticised the kind of systems thinking that puts technological expediencies above human values, military, industrial, and state sponsorship inspired the culture and epistemology of cybernetics as a discipline. As such, some of the values of cybernetics derive from classical science and led to forms of technological determinism (Ellul, 1964) that traded human experience for certainty and control. In particular, the paper notes the scientific tendency to frame cryptic generalisations – i.e. “laws” – that are unsituated from the spatio-temporal complexity of immediate observation. It argues that this tendency alienates us from our ongoing (human) present and therefore makes us less sensitive to our “presence”, and thereby to the environmental damage that we continue to wreak in the name of progress and comfort. Cybernetics made “Channels” out of fields Whilst first order cybernetics is traceable to ancient technological understanding, it remained unthinkable – in Heidegger’s sense of

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the word – until the discourse of classical science emerged. Indeed, the observational and discursive techniques of science provided an instrumentalist (Habermas, 1971) grammar for cybernetic discussion. By exploring temporal and spatial concerns independently, scientific discourse devalued the immediacy of human present/presence. One early precedent comes to mind. William of Occam (c.1285-c.1349) is famous for the logical method in which the observer must habitually remove, or ignore arguments that seem irrelevant to the task in hand. Enlightenment rationality advanced this method by showing us how to separate the context of discovery from the context of justification in order to reach counterintuitive conclusions. Where Descartes invented a gridmapping system that degrades or ignores the context of its drawing, John Locke developed a theory (1690) of communication that described metabolic change as a flow of discrete messages as through “conduits”. This probably inspired Claude Shannon’s theory of information (1948) that reduces knowledge and discourse to codes that could usefully be stripped of their meaning and sent through “channels”. Cybernetics assisted automation and, therefore, alienation When Descartes applied reductive assumptions to his thought experiments, it is hardly surprising that he created a strong sense of self-alienation. Just as classical scientists tacitly separated (lived) time from (proximal) space, so early cyberneticians and technologists imagined themselves to be safely “outside” the black box. This tendency enshrined self-denial within a methodology that has been hard to reform. (Kuhn, 1962; Feyerabend, 1975) Where Galileo deliberately and systematically ignored certain sensations in his acts of observation, Newton combined a similar approach with a level of professional ruthlessness that is quite disturbing. These developments provided the basis for a mechanistic mindset that paved the way for today’s digital culture. Just as Descartes (1637) had understood the universe to be a kind of clock, so cyberneticians such as Ashby (1956) sought to develop a view of “systems” as algorithmic mechanisms. These approaches are enmeshed in the tendency to overspecialisation within industry (Illich, 1975) that contributed to various forms of self-alienation (Wood, 1996) and confusion over individual agency and responsibility. Cybernetics encouraged us to be cynical solipsists What would cybernetics of human presence be like, give the legacy of classical science, and the pressures of a technologically captivated society? Could the modern western self be exemplified, say, as a digital interactive gadget? Here, we might allude to the solipsism of Descartes (1596-1650) – i.e. The fact that I can experience my existence proves that I exist, and that of Bishop Berkeley (1685-1753) – i.e. The fact that others are able to experience my existence proves that I exist. These ideas enable us to make a “first-order” cybernetic

doodle of the “self-owning individual” (MacPherson, 1975), in a way that can be A cybernetics of exaggerated as “feeling good, looking good”. In the fashion world this model of value, presence, self can even be characterised as a fetishist association between the rhetorical and anticipation component of a product’s appearance (Haug, 1986; Buchanan, 1989) and the self-image of the individual consumer. This idea can be traced to early systems of power and presence that are echoed in Aristotle’s discussions of rhetoric.

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Cybernetics reinforced a strongly western model of “self” Foucault (1977) and others have also shown that the routines of representational enhancement and self-projection became internalised through the Catholic Church and, later, individualised via developments such as Freudian psychoanalysis. These tendencies led to concepts such as “positive self-regard” (Rogers, 1961), “presentation of self” (Goffman, 1959), and “selfactualisation” (Maslow, 1987). Some adaptations of Cartesian cybernetics have moved the ethical agenda forward, as we think (Heinz von Foerster, 1993; Scott, 2000). However, even second-order cybernetic approaches – e.g. Gordon Pask’s (1972, 1975) theory of conversations – were forced to build from dualistic and solipsistic suppositions. Arguably, in the so-called “information society”, a growing awareness of systems theory has made citizens more conscious that the feedback paths that sustain their habits may also be destructive. Unfortunately, this does not necessarily moderate bad individual behaviour. Sloterdijk (1988) argues that this is because our “sophistication” led to what he calls “enlightened false consciousness”, which provides the positive feedback for maintaining the status quo. Self-definition equates human presence with static objects Although western discourse has found automata fascinating since Aristotle, part of this interest perhaps derives from the abiding influence of Plato, which emphasised the “form” of things, rather than their “movement”. (Wood, 1998) What is important about the contribution of cybernetics to this strongly western discourse is the language that generalised “self” in such a way that, in leaving aside specific spatio-temporal “details”, we underestimate the dependence of “self” upon its ecological and other modes of context. On the one hand, we may use cybernetic terms such as “autopoiesis”, “self-creation”, “self-(re-)production”, or “self-reference” that may equally apply both to organic and non-organic systems. On the other hand, related terms such as “selfconfiguration”, “self-regulation”, “self-steering”, “self-maintenance” are reminiscent of a mechanistic world. Clock-design exemplifies closed-system homeostasis In questioning human “presence”, we should confront the issue of temporality, and this is where (second order) cybernetics sought to transcend mechanistic

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paradigms. Nevertheless, the rise of cybernetics as we know it would have been difficult to imagine without the long history of clock making, with its latent propensity for instrumental regulation and control. The “precision” of clocks is one of the technological triumphs of the feedback principle that is central to the discipline of first order cybernetics. On the other hand, the apparent precision of the modern clock derives from an order of logic that upholds Newton’s idea of a fundamentally extrinsic, ubiquitous and rigorous temporality. In the Newtonian mindset, time is depicted as a linear, “closed system” and the design of clocks still upholds this illusion, long after the era of Einstein. Indeed, most domestic clocks employ local and negative feedback loops that enable them to maintain homeostasis. In more recent times, a second level of negative feedback compensates more effectively for external changes in the environment surrounding the clock. These imply that the clock is organisationally autonomous to its surroundings.

Perpetuating Newton’s temporal closure Clocks have become increasingly synchronised with one another over the last few hundred years. The subsequent development of GMT and World-Time have sustained the Newtonian illusion that time may be universal, predestined, and one-dimensional. By contrast, if we consider how human beings think and act, moment by moment, in pursuit of their own continuing survival, we may realise that the present must, of necessity, be multi-dimensional, provisional, and contingent. In effect, when we identify the “passing” of time from within a strict Newtonian frame we are dissuaded from including ourselves by intuitive observation. This is because his approach takes a post-hoc view of “category + object”, rather than one that is ad hoc to the “verb + subject”. It implies that “time” is absolute, autonomous, and universal. Ultimately, in the Newtonian order, actual events may be predictable, but remain theoretically impervious to experiential inquiry.

But clock-time was a first-order cybernetic invention At the level of social meaning, we cannot sensibly speak of “measuring” time, because we have increasingly tended to co-create it, rather than “monitoring” it. Nevertheless, the popular belief in an independent temporality has had an enormous effect at the ecological (Wood, 1998), social, and cultural levels (Virilio, 1977). In a sense, it is an anti-cybernetic concept. Although we may agree that Newton’s epistemology was problematic, many scientists still revere him for his intellectual achievement. Problematically, some still tend to disconnect his arguments from the environmentally damaging effects that they inspired. Indeed, the Galilean and Newtonian legacy lives on through the timeand-motion studies of Charles Babbage, Frederick W. Taylor and their

descendants. These are renowned for their unidirectional order of command A cybernetics of that ignored the expertise of individual workers. This established the basis for value, presence, Fordism, which inspired the later rise of “Just-in-Time” and CPA management and anticipation systems. We need feedback between human well being and technology An implicit assumption behind Taylor-Fordism and its subsequent variants is that human well being can be maximised by harnessing technology to meet our essential and less essential “needs” (Maslow, 1987). This is difficult because need can seldom be quantified reliably. In actual situations, it is always framed within a socio-cultural context that creates complex conditions that are difficult to evaluate after reduction. For this reason, scientific estimates of need are always rendered obsolete by new cases in which previous boundaries are shown to be dubious. Human beings are open systems that operate in worlds of considerable complexity that include other participants and observers, and their many worlds. Such worlds are not mappable in a singular time frame. The human chaos of feedback and feedforward The mathematician Daniel Dubois (2000) claims that there is a “strong” anticipatory component in physical (Newtonian) systems, and offers a mathematical model that incorporates “feed-forward” to describe it. At the organic (human) level of temporality, Kant’s cognitive theories posited an essential role for the imagination (Warnock, 1976) in all human perception. Without an ability to imagine what we might see, we cannot successfully apprehend it. Later cognitive studies also show that our nervous systems creates a 0.4 sec delay between actative and conceptual events (Libet et al., 1996). These, and other researches, indicate that human perception therefore has both a strong anticipatory and retrospective component. As such, any serious cybernetic model should incorporate the capacity to include anticipated information, however irrational it may seem. This calls for a more phenomenological approach to cybernetics. If we combine both approaches, we may note that the “local present” is always construed from a mixture of contingent realities that blend “backward referral” with anticipatory probabilities and intentions. Clocks epitomise the rhetoric of control Unfortunately, most practical cybernetic approaches have tended to regulate technology at a different level from that which is most important to the user. In this regard, a cybernetic approach could be applied more effectively at the emergent and complex levels of values and meanings, rather than at the mechanical level. This paper reminds us that even simple regulators such as clocks and thermostats are contributors to social, aesthetic, and other emergent

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values that cannot helpfully be detached from their apparent use-value. Pascal is famous for bringing the rhetorical power of “time” to a local and personal level when he was seen in public with a clock tied to his wrist. Importantly, this is not so much a personalisation of temporality as a claim to a universal timesystem. Hitherto, only the most prosperous cities had been able to display their importance by installing a clock in a prominent public place. By virtue of science’s subsequent glamour, Pascal’s wristwatch can also be seen as a conspicuous claim to power. Cybernetics from inside the interface/interplay We have already criticised the dualistic, “conduit-based” theories of Locke and Shannon that over-simplify or exaggerate the many orders of isolation between systems. Over the last three thousand years, there has been an implicit assumption that a very small number – say five, six, or seven – channels of communication (i.e. the senses) establish the human’s relations with its environment. This is a highly dubious assumption. Importantly, the notion of discrete sensory “channels” becomes ineffectual once their number exceeds a level where emergence plays a significant role. Hence, beyond a certain number, the interplay between these channels is likely to become at least as important as the function of a specific channel. Over the last century, different scientists conducted a huge body of independent studies that confirm that there are many more than the five or six senses mooted by Plato and subsequent thinkers. We are our senses Ingo Swann (1994, 1996) collated a large body of separate (published) studies into the body’s capability to monitor various phenomena. He concludes that there may be at least 27 “senses”. For the human organism with this number of sensory “channels”, any separation of purpose between channels becomes improbable. The idea of “intertextuality” is seen as a positive enrichment of meaning and value in the social sciences, yet in engineering we are more likely to think of “cross-channel modulation”, or “interference”. Yet Swann argues that there is little acknowledgement of the collective implications for scientific epistemology, nor for what this may mean at the metaphysical or ontological level. He interprets the collected findings as a way that denies the positivistic tendencies in science: we are our senses, he suggests. The grammar of flow How could we make cybernetics more subjective? One solution may require revisions to a (western) grammar that sustains a strongly teleological and agent-centred view of the world. Here, categorical logic may need to become

subordinate to a logic of flow (Wood, 2000), and may call for fewer transitive A cybernetics of verbs. We may have to enfold author and reader in a more temporally oriented value, presence, and interdependent way. Strongly western modes of writing (e.g. Swiss, and anticipation German and UK English) may become more attuned to contextual relevance mutuality of self-sustenance. Certain popular assumptions about language itself may need to be revised. Here, we may usefully revisit the pre-Socratic 887 thinking of Heraclitus and Cratylus which point to a stronger link between ontology and epistemology than that which we find in many western languages. The logic of flow Davidson’s idea of passing theories is an interesting starting point for a new cybernetic model of discourse. It was an answer to the philosophical problem of what kind of language could possibly be effective in dealing with a world that changes us, just as quickly as we change it. However, the idea of “passing theories” is not very consistent if we expect theory to consist of static models. Categorical logic is the primary tool of western philosophy, and we place a good deal of emphasis on “consistent theories” that can be checked for congruency and integrity. This logic requires “consistent terms” to be helpful. Categorical logic ignores the dynamic and temporal nature of discourse. It assumes that when we compare two categories, each has remained the same, or that each is changing at the same rate. A “consistent idea” usually makes sense at the speed of publication or bureaucracy (slow decay) but not necessarily at the speed of oral communication. The famous story of Cratylus suggests that he believe that he could not put his foot in the “same river” once. This reminds us that every utterance is indeterminately co-dependent with its pragmatic context. It is always in flux and always (becoming) different at each syllable, just as our active presence meets with a whole world that is in flux. Clock-time therefore needs to become more cybernetically “open” At a more practical level, developments such as networks of enterprise, globalised consumerism, and ubiquitous credit facilities ensure that workers maintain their activities at levels well above what they need to make them happy. Many workers elect to buy their own personal phones and portable computers that link them to their work-places at all hours of the day and night. In a sense, mobile phones are beginning to facilitate a more human form of consensual temporality (see Wood, 1998) whereby, for example, the agreed time for a meeting is adjusted until all the travelling participants are close enough for arrival times to be synchronised. Many new inventions are likely to advance this non-clock-based mode of timing, especially since the advent of satellitebased Global Position Systems that can input current location and speed data to scheduling software.

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References Ashby, W.R. (1956), Introduction to Cybernetics, Wiley, New York. Buchanan, R. (1989), Declaration by Design: Rhetoric, Argument, and Demonstration in Design Practice, in Design Discourse, Margolin, V., University of Chicago Press, p. 93. Descartes, R. Discourse on Method. Foucault, M. (1977), Discipline and Punish, (translated by Sheridan, A.), Pantheon, New York. Goffman and Erving (1959), The Presentation of Self in Everyday Life, Doubleday and Company, Inc., Garden City, NY. Habermas, J. (1971), Towards a Rational Society, Beacon Press, Boston, p. 92. Haug, W.F. (1986), Critique of Commodity Aesthetics: Appearance, Sexuality and Advertising in Capitalist Society, Polity Press. Heidegger, M. (1967), Being and Time, (translated by John Macquarrie and Edward Robinson), Blackwell, Oxford, UK and Cambridge, USA, p. 98. Illich, I. (1975), Tools for Conviviality, Fontana. Libet, B., Wright, E.W. Jr, Feinstein and Pearl, D.K. (1996), “Subjective referral of the timing for a conscious sensory experience”, Brain, p. 102. Macpherson, C.B. (1975), The Political Theory of Possessive Individualism: Hobbes to Locke, Oxford. Maslow, A. (1987), Motivation and Personality, Paperback. Maturana, H. and Varelal, F. (1992), The Tree of Knowledge, Revised Edition, Shambhala. Rogers Carl, R. (1961), On Becoming a Person. Pask, G. (1975), Conversation, Cognition and Learning, Elsevier, Amsterdam. Scott, B. (2000), A design for the recursive construction of learning communities, Paper for the 2nd International Conference on Socio cybernetics, 25 June-2 July Panticosa, Spain. Sloterdijk, P. (1988), The Critique of Cynical Reason, Verso, London. Swann, I. (1994), Your Seventeen Senses – The Crumbling Mainstream Resistance of the Paranormal and New Scientific Confirmation Regarding The Existence of Certain Psi Faculties, Paper given on 21 March 1994 at the United Nations on behalf of the Society for Enlightenment and Transformation (SEAT). Turing, A. (1950), Computing Machinery and Intelligence. Virilio, P. (1977), Speed and Politics: An Essay on Dromology, Semiotext(e), New York. Wood, J. (1996), “Temporal alienation”, Paper given at the Doors of Perception 4 - “SPEED” conference, 7-8 November 1996, Amsterdam. Wood, J. (1997a), “Situated criticism and the experiential present”, Journal of Design History, editor Prof. Nigel Whitely. Wood, J. and Taiwo, O. (1997a), “Some Proprioceptive Experiences of Being-With”, Paper for Problems of Observation and Action Conference, Amsterdam. Wood, J. (1999), “Design in the age of digital participation,” Paper given at the Problems of Participation and Connection Conference, Amsterdam University.

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Pansystems mathematics: an analysis of panweighted field-network

Analysis of panweighted field-network 889

Xiaolong Wu Science Faculty of Xi’an Jiaotong University, People’s Republic of China

Dinghe Guo Physics Department, Hubei University, People’s Republic of China

Jinghong Pan Department of Computer Science and Engineering, Chinese University of Hong Kong, People’s Republic of China

Xuemou Wu Wuhan Digital Engineering Institute, People’s Republic of China Keywords Cybernetics, Topology, Mathematics, Pansystems Abstract In this paper, we will introduce charm pansystems and provide mathematical models for panweighted field-network. Various mathematical models of pansystems will be discussed. Some traditional mathematical concepts such as topology space and rough sets theory will be analyzed within this framework.

1. Pansystems thinking: introduction and framework Things are connected with each other and are full of contradictions under certain conditions. We can say that in certain forms they are related by way of inter-connection, inter-transformation, inter-derivative, inter-promotion and inter-restraint (we call this 5-mutuals in pansystems, 5M for short). The pansystems theory deepens and strengthens these viewpoints in some concrete styles, makes emphasis on the so-called pansystems (generalized systems, generalized relations or their various composition) to strengthen the connections and medium-inter-transformations among various disciplines and topics and to explore a meta-science like combination among the mathematical thinking, systems thinking, dialectical thinking and poetry or aesthetics thinking (uniting the 4-thinkings ). The pansystems analysis includes making efforts to melt the philosophy, mathematics, technology, reasons, human principles, and aesthetics into a unified entity (Lin, 1995; Wu, 1990; Wu and Guo, 1999; Wu et al., 1992) and also Wu (in 1996 and 1998). In the exploration of pansystems theory, there are several tendencies to be forced (Wu, 1990; Wu and Guo, 1999; Wu et al., 1992). Examples are: overall

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considerations and connecting comprehension; developing the encyclopediaconnecting network; exploring the laws of net-moving comprehensions; researching the meta-science of various principles, etc. Along these tendencies pansystems thinking pursuits a creation of its own style in many topics which concern mathematics, science, technology, medicine, humanities, sociology, history and philosophy. pansystems research plans to cultivate an investigation to face the future and dialectical combination of the ancient and the modern, China and foreign countries, eastern and western cultures, etc. In this paper, we will discuss about various mathematical models of pansystems. In the pansystems prototype, many well-known concepts in mathematics can be converted to mathematical models of pansystems. We call the mathematical model of pansystems as charm pansystems (Wu et al., 1999, 2000). The charm pansystems can be viewed as a general model with a kind of universality. The special cases of charm pansystems include: topology, algebra, analysis, geometry, sets, mathematical systems, abstract graphs, networks, multidimensional matrices, connections, operations, operators, functions, functionals, mapping, image, morphology, category in mathematical sense, formal language, abstract automata, mathematical logic, probability, fuzzy systems, various mathematical structures and models of applied mathematics, various definitions about systems, etc. In a certain sense, the charm pansystems is a typical representation of the pansystems realized as generating the seven-elements. In the following we will give the detailed analysis of various models of charm pansystems. 2. Charm pansystems The charm pansystems is a general model of panweighted system. It can be defined as following. Suppose: S ¼ ðA; BÞ; where B , A n £ W ; n is certain given generalized number set, W is the panweight range. If Dk , W are certain panweighted installations, then B* Dk , A n : If there are some pansystems operators f k : PðA n Þ ! Es½F (semi-equivalence family on set F ), then f k ðB* Dk Þ [ Es½F: The corresponding pansystems clustering or pansystems quotientization is as follows: F ¼
F k ¼ F=f k ðB* Dk Þ ¼ {F km }

where Qk ¼ ð f k ; Dk Þ are the k-observocontrol modes, respectively, their observocontrol results for S ¼ ðA; BÞ are Fk correspondingly. We can say that F is the display board. The forms for F could be: F ¼ A n ; F ¼ A or F ¼ B: Various shapes of Fk are based on different observocontrol modes Qk: sometimes are of range-wave-like shapes and sometimes are of peak-particle-like shapes. Distinctly, the peak-particle-like shape simulates certain confinement of S on the background display board F. Range-wave-like shape models certain

distributive characteristics of S on F. B can also be considered as a generalized wave with panweight, Various {Fkm} can be considered as certain particle embodiments with panweight reduction Dk and observocontrol treatment fk. The pansystems mathematical models of difference, identity and panorder have different forms with different principles of the characteristics of pansystems thinking. pansystems mathematics extended the concepts of reflexivity, symmetry, anti-symmetry and transitivity for many respects and developed further investigations (Wu and Guo, 1999; Wu et al., 1992, 2000) and also Wu (in 1996 and 1998). Such kind of extension is rich in various relativities, inter-derivatives and inter-transformations. There are various types of difference, identity and panorder. Namely, there are certain 5-mutuals of various difference, identity and panorder. For example, in the investigation of talent structure, people should strengthen the analysis on observocontrol level concerning the abilities to find certain potential identity of common apparent difference and the abilities to find certain non-intuitive difference of intuitive identity. These are just the psychological concepts of thinking of difference-judge and of identity-search. The pansystems views of difference, identity and panorder is the key point for establishing axiomatic systems to the categories of difference, identity and order, hierarchy and divisibility. These axiomatic system are very important and fundamental for philosophy, mathematics and investigations on various disciplines. The pansystems views can be considered as a sort of quasi-meta-axioms which we call it axioms of axioms. In the following paragraph, we will discuss pansystems views of some traditional mathematics theories in detail. 2.1 Topology space The traditional concept of topology space can be considered as a special generalized system with four well-known topology axioms S ¼ ðG; TÞ; T , PðGÞ; where P(G ) means the power set of G : PðGÞ ¼ { pjp , G} (Egenhofer et al., 1993; Kong and Rosenfeld, 1989). With pansystems prototype, we present it as generalized system: S ¼ ðG; TÞ;

T , PðG* £ W Þ;

G* ¼
We call this pansystems topology (PT) (Pan et al., 2000, 2001). This PT can be considered as a generalized knowledge base or a generalized subject of observation or observocontrol. Furthermore, it is an artificial observocontrol media (scale, method, standpoint, viewpoint, measure mode, etc.). It can be considered as a certain investigated object. For topology image processing, the common concept of image can be considered as a mapping f : G ! W ; which is a special case of binary relation between G and W : f , G £ W : This kind of image is a special case of PT. The traditional concept of graph in

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the mathematical graph theory can also be analysis as a certain panweighted network represented as f , G 2 £ W : Consequently, the related derived quotientization realizes the corresponding observation transformation. Specially for the first order case T , PðG £ W Þ; the quotientization: f ¼ QðG; að<ðg* DÞ2 Þjg [ TÞ embodies an observation in the sense of PT-S (or T ), where “a ” is a certain pansystems operator which maps P(G 2) into Es[G ] (the family of semiequivalence relations or tolerance relations in G ). A more detailed representation of knowledge base due to PT-S is: T # ¼ { pjp ¼ g – f; h [ T # }: Furthermore, the PT-boundary is: bng ¼ clg 2 intg: The PTroughness degree of g is defined as: rdg ¼ 1 2 jintgj=jclg [ ½0; 1j; and the PT-exactness degree: exdg ¼ jintgj=jclgj [ ½0; 1: The concept of inclusion and identity in traditional set theory is divided into two or more: intðg , g0 Þ ¼def ðintg , intg0 Þ; clðg , g0 Þ ¼def ðclg , clg0 Þ; intðg ¼ g 0 Þ ¼def ðintg ¼ intg0 Þ; clðg ¼ g 0 Þ ¼def ðclg ¼ clg0 Þ: The exterior of g is defined as extg ¼def intðg c Þ; where g c means the complement of g : G* £ W 2 g: Correspondingly, we define: clextg ¼ clðextgÞ; extðg , g 0 Þ ¼def ðextg , extg0 Þ; extðg ¼ g 0 Þ ¼def ðextg ¼ extg0 Þ; clðg ¼ 0 0 0 g Þ ¼def ðclg ¼ clg Þ; clextðg , g Þ ¼def ðclextg , clextg0 Þ; clextðg ¼ g0 Þ ¼def ðclextg ¼ clextg0 Þ: In principle, non-rough set X can be constructed by the building blocks of category family generated from P, and the rough set can be built approximately

from inside and outside, just like the concepts of inner measure and exterior measure in the measure theory: let R [ E½U ; put RðXÞ ¼ <{X k jX k [ U =R; X k , X}; R2 ðXÞ ¼ <{X k jX k [ U =R; X k > X – f}; they are called the R-lower approximate set (Pansystems interior) and R-upper approximate set (pansystems closure), respectively. Clearly, R2 ðXÞ ¼ {xjx [ U ; x* R , X}; R 2 ðXÞ ¼ {xjx [ U ; x* R > X – f}; and naturally bnRðXÞ ¼ R 2 ðXÞ 2 R2 ðXÞ is called the R-boundary (Pansystems boundary) of X – boundary-PD. From the viewpoint of pansystems mathematics, there are eight sorts of elementary relations which command various theories, methods and principles in mathematical thinking. They are membership, the whole-part, the bodyshadow, the difference-identity, panorder, pantransformation, panderivative, pansymmetry, etc. Consequently, it is an important topic to extend these eight relations to the rough set theory and apply them in the investigation on intelligence information processing. For example, for the membership relation, the traditional concept is divided into two as upper membership and lower membership. Correspondingly for the concepts of inclusion, identity, equivalence, classification, etc. the primitive key-identification is the differentiation of X into R2 (X ) and R 2 (X ). And the quantity d R ðXÞ ¼ jR2 ðXÞj=jR 2 ðXÞj can be used as the approximate exactness of X – non-rough degree: d R : PðU Þ ! ½0; 1; and then 1 2 dR ðXÞ shows the rough degree. These concepts can be compared with the concept membership degree in fuzzy mathematics. Suppose that the given domain is the set U, then define the category to be some subset of U as X , U (or X[ P(U )). The concept class implies the abstract knowledge, simply called knowledge: K , PðU Þ: The repository is realized as a certain classification class or equivalence relation class R , E½U : K-representation can be separated into the following category: S 1 ¼ ðU ; XÞ; knowledge: S 2 ¼ ðU ; KÞ; repository: S 3 ¼ ðU ; RÞ: Let r [ E½U ; then S 4 ¼ ðU ; U =rÞ shows the knowledge derived from repository (U,r ). If P , R; P is a class of equivalence relations, the intersection p ¼ >rðr [ PÞ is also an equivalence relation, denoted by ind(P ), and called the non-identification relation on P. Here the quotient system U/ind(P ) is just intersection-cutting result by all that satisfied U/r ( r[P ) and (U,U/ind(P )) is the elementary knowledge derived from P – P-elementary knowledge. And the corresponding concept and category X [ U =indðPÞ is called P-elementary category. S-representation – let A be an attribute set concerned in U, and B is the generalized quantification range of further pansystems quantification. The identification primitive model for domain U is in general described by a panweighted relation or by mapping with parameters f : U £ A ! B: Namely, the attribute set A is also a class of equivalence relations, or a set corresponding to a class of equivalence relations R ¼ {R1 ; R2 ; R3 } , E½U ; and then (U, R ) or

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related (U, A ) corresponds to a repository of U, and the union of quotient sets U =R1 < U =R2 < U=R3 corresponds to the elementary category set derived from R in U. U/ind(R ) is called elementary category set derived from R. The corresponding knowledge blocks are just like some elementary particles. But the elementary characteristic is related with only R. They are not still elementary for other repository in general. We use S 4 ¼ ðU ; f Þ to represent repository, and call it S-representation. 3. Panweighted field-network Let g [ PðG ½2 £ W Þ be a panweighted field-network (PFN) on G. For a panweight confinement V , W ; the corresponding composition g* V , G ½2 is a subsystem, subgraph or subfield-network in G, whose panweight is confined in V. For x [ G; x* ð g* V ÞN ; is the points which are connected with x by N-type composition of subnetwork g* V ; where N ¼ {ðnÞ; ½n}; ðg* V ÞðnÞ means the n-times composition of g* V : Meanwhile, we can get ð g* V ÞðnÞ ¼ <ðg* V ÞðkÞ ðk ¼ 1; 2; . . .; nÞ In the following we give the related theoretic expansion in some panweighted network representation details. Let G1, G2, F , G; G1 > G2 ¼ f; F > Gk – f; G 2 F ¼ G2 * f – f: This is a typical pansystems relativity for observation, which is a basic transformation from disconnection (discontinuousness) into connection(continuousness). Where “a ” is a certain pansystems operator of types such as 1r ( g ), dr( g ), r ¼ 1; 2; 3: ( Wu, 1990; Wu and Guo, 1999; Wu et al., 1992) and also Wu (in 1996 and 1998). It is interesting that the practical flow charts in modern technology, the developing theory of pansystems morphology and the framework of pansystems theory itself are in fact of the form of something panweighted field-networks. 3.1 Pansystems morphology: 784e – PTM – IGP Pansystems morphology is an investigation on related pantransformations, panderivatives and pansymmetries of image-graph pansystems (IGP). The typical and common IGP is the PFN g : G < G 2 ! W ; or g , G ½2 £ W : The related background of pansystems morphology is the geometrical respects concerning image analysis, pattern recognition, graph theory, computer vision, panweighted relations, panweighted networks, etc. The methodology

is mainly based on related principles and train of thoughts of pansystems thinking (PTM: pansystems thinking, theory ideas, principles, concepts, models, formulae, theorems, methods, techniques), specially the framework of pansystems-784e. The main subject of pansystems morphology is the panderivative-pansymmetry investigation and pansystems relativity research or pansystems dialectics (PD), analysis on images, patterns, graphs, mappings, functions, sets, PFN, etc. The concrete respects include “25-terms” or more: epitomes, extensions, embodiments, confinements, wholepart-body-shadow relations difference-identity- panorder relations, seriesparall-clustering-discoupling relations, quotient-product relations, pantransformation, panderivative, pansymmetry, exterior-interior-boundary mechanism, generalized quantification, generalized systems, pansystems topology, panweighted relations, panweight reduction, etc. A very confined scope of pansystems morphology is to use the basic concepts, principles, models, theorems in “Pansystems Cybernetics” and “Pansystems Thinking” to investigate IGP and PFN (Wu and Guo, 1999; Wu et al., 2000). History. In geography science, there is a tradititional corresponding investigation called geomorphology, which researches the shapes of earth surface and the laws of generation, development and distribution of related shapes. In 1972, the publication of Thom’s book symbolized the catastrophe theory to come into being. The book of Serra (1982) is the first monograph of the so-called mathematical morphology which is connected with image analysis. Rough set-theory of Pawlak (1991) presented a new framework to research graphs and related boundary problems. The book written by Gong et al. (1997) presented certain development of related investigations by a Chinese academical community. From 1976 onwards, there were many concrete mathematical results within the framework of pansystems methodology, which are connected with graphs, sets, mappings, PFN and discrete mathematical structures, including investigations of pansystems relativity to graph-recognition (Pan et al., 2000; Wu, 1990;) and also Guo et al. (in 2000 and 2001), Li et al. (in 1997, 1999 and 2000), Wang and Gao (in 1984), Wang et al. (in 2000), Wu (in 1982, 1984, 1985), Zhu and Wu (in 1984). The concept of pansystems morphology was presented formally first in the paper “Pansystems Theory and Biology-like Thinking for Complex Supersystems Operations (I)(II)” (Wu, 1990) and also Wu (in 2001). The subject of the present paper is mainly to develop new investigations of pansystems morphology, including many new concepts, principles, theorems and ideaconnections. 3.2 Pansystems theory: 784e The six-location PFN can be realized as a class of panweighted pan-arrows: P  arrows ¼ {ðx; t; u; vÞ; ðx; y; t; u; vÞjx; yeG; teT; ueU; veV }

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where x, y are the nodes of PFN – namely the concrete elements of six-location extension set, t: generalized direction, u: pansystems quality, v: pansystems quantity or pansystems number (Figure 1). There is a special mode called six-xing mode (perfect graph with sixelements): F ¼{S; O;M ; E; R;Q}; or F ¼P ¼ {Pi; Pj; Pk;Ps; Pr; Pq}–g ¼ F 2 £W :

896

Generally speaking, eight-counters imply 100 or more typical modes of El or 150 – 200 dualities (yinyang, or dialectical contradictions/opposites), 252dualities due to “25-terms”, which cover almost various topics, disciplines and embody pansystems-784e or half with myriad connection. Related dualities in pansystems relativity – (relativity, absoluteness), (that, this), (subject, object), (subject, environment), (object, background), (subject, media), (object, media), (environment, media), (ego, non-ego), (I, you), (I, he), (you, he), (pansystems-initself, pansystems-for-itself), etc. 784e – PTM: p , G ½2 £ W – PTM: IGP (Figure 2). 3.3 Pansystems pan-hypercycles The most basic PTM are realized as PFN-cycles. In eight-counters, the mode 3 Layers † 5-mutuals † 8-comprehensions¼P- analysis includes three layers of

Figure 1.

Figure 2.

PFN-cycles of the 5-mutuals-8-comprehensions, and PTM-5m mode, many models in pansystems relativity, the connection mechnism of 8-counters or pansystems theory with other topics, and various forms of IGP, etc. all are of certain forms of PFN cycles. Every node of PFN-cycles is relatively of PFNcycle, many PFN-cycles as many nodes form another relatively higher layer of PFN-cycle. This hierarchy supersystem forms a concept which simulates that of hypercycle due to Professor M. Eigen in his creation hypercycle theory – hypercycle: cycle of cycles – a theory about self-organization of molecular biology (in 1974). The mechanism of multilayers of PFN-cycles is the concept of the pansystems pan-hypercycle. References Egenhofer, Max J. and Sharma, J. (1993), “Topological relations between regions in 32 and 92”, in Abel, D. and Ooi, B.C. (Eds), Advances in Spatial Databases (SSD93), Lecture Notes in Computer Science 692, Springer-Verlag, pp. 316-26. Kong, T.Y. and Rosenfeld, A. (1989), “Digital topology: introduction and survey”, Comput. Vis. Graph. Image Process, Vol. 48, pp. 357-93. Lin, Y. (1995), “School of pansystems”, Int. J. Systems Sci., Vol. 8, pp. 1527-38. Pan, Jinghong, Heng, Pheng-Ann and Wu, Xuemou, (2000), “Pansystems theory: boundary and rough set”, Advances in Systems Science and Applications, ISSN 1078-6236, No. 1. Pan, Jinghong, Heng, Pheng-Ann and Wu, Xuemou, (2001), “Pansystems-784e evaluation: IDKstructure(image-data-knowledge)”, Advances in Systems Science and Applications, ISSN 1078-6236, No. 1. Pawlak, Z. (1991), “Rough sets – theoretical aspects of reasoning about data”, Academic Publisher, London. Wu, Xuemou (1990), ‘The Pansystems View of the World, Press of Chinese People University, Beijing. Wu, Xuemou and Guo, Dinghe (1999), “Pansystems cybernetics: framework, methodology and development”, Kybernetes (The International Journal of Systems and Cybernetics), Vol. 28 No. (6/7), pp. 679-94. Wu, Xuemou, Pan, Jinghong and Heng, Pheng-Ann (1999), “Pansystems clustering and its applications”, Technology in Mathematics Facing 21st Century, Proceedings of the Fourth Asian Technology Conference in Mathematics, Guangdong Economy Press, Guangzhou, pp. 115-21. Wu, Xuemou, Pan, Jinghong and Heng, Pheng-Ann (2000), “Pansystems thinking and investigations: difference, identity, clustering”, Kybernetes, Vol. 29 No. 5/6, pp. 651-79. Wu, Xuemou et al. (1992), “Pansystems philosophical logic. Automated reasoning”, IFIP Transactions A – Computer Science and Technology, IFIP IWAR’92, Proceedings of International Workshop on Automated Reasoning, 142-149, Elseveir Science BV, Amsterdam, Vol. 19, pp. 187-96.

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On stochastic optimal control for stock price volatility Ying Yi-rong Aetna Management School, Shanghai Jiao Tong University, Shanghai, People’s Republic of China

Lin Yi Mathematics Department, Slippery Rock University, Vincent Science Hall, USA

Wu Chong-feng Aetna Management School, Shanghai Jiao Tong University, Shanghai, People’s Republic of China Keywords Cybernetics, Risk, Stochastic modelling Abstract The dynamic measure of risk problem in a incomplete market is discussed when stock appreciation rates are uncertain. Meanwhile, a related stochastic game problem is studied. The value of a stochastic optimal control is regarded as a reasonable measure of the risk. The form of the optimal objective is obtained by employing the tools of BSDE theory.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 898-904 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443978

1. Introduction Over the last two decades, mathematical modeling of dynamical systems in continuous-time has received much attention all the way in diverse fields (Kloeden and Platen, 1995; Unbehauen and Rao, 1990; Young, 1994), where the latter focuses on Ito stochastic differential equations. The use of continuoustime stochastic model is also advocated in Bohlin and Graebe, (1995) and Unbehauen and Rao, (1997). Following that much work has been reported on Ito SDEs in the control literature. One of fundamental relationship documented and often used in the finance literature is the negative association between stock prices and volatility of return. A simple mean-variance intuition tell us that relational investor would be willing to pay a lower price to a claim that is uncertain as against a sure claim. Unquestionable, thanks to the contribution of Rothschild and Stiglitz (1970, 1971), many models have been proposed to obtain intuitive results on the optimal behavior of risk averse individuals following both first and second-degree stochastic dominance changes in a returns distribution. Undoubtedly, an interesting problem is how to quantify such as a risk. There are lots of excellent works concerning this object (Chen and Yong, 2001; Follmer and Leukert, 2000). Cvitanic and Karatzas (1999) employed This work is funded by Chinese National Science Fund for Distinguished Young Scholars (No. 70025303) and National Science Foundation of China (No. 70173031).

the tools of convex duality to measure this risk and solved a related stochastic game. It is well known that BSDE connects tightly with stochastic optimization problem and is proved to be powerful tool to deal with state contraints. Using the method of JI and Peng ( JI Shao lin and Peng Shige, 1999), we study a problem in Cvitanic and Karatzas, (1999) and get the form of the optimal objective. 2. Main results Let’s consider a complete financial market that consists of one back account (risk free instrument) and a few stock stocks (risk instrument). The following notation is used. The interest rate r(·), stock appreciation rates bð·Þ ¼ ðb1 ð·Þ; · · ·; bm ð·ÞÞT and m £ m order stock-volatility matrix sð·Þ ¼ {sij ð·Þ} are progressively measurable with respect to F. s(·) is invertible and r(·), b(·), s (·), s 2 1(·) are bounded uniformly in ðt; vÞ [ ½0; T £ V: w0(·) is a standard m-dimensional Brown Motion on a complete probability space (V, F, P0), endowed with a filtration F ¼ {F t }0#t#T ; this filtration is the P0 – augmentation of F w0 ðtÞD sðw0 ðsÞ; 0 # s # tÞ: d(t ) is elastic correlative coefficient of x(t ) for the ¼ volatility of w0(t ). Define relative risk process
 21 u0 ðtÞD s ðtÞ bðtÞ 2 rðtÞ · 1 ¼  Z t  Z 1 t 2 T þ dðtÞ; Z 0 ðtÞD exp 2 u0 ðsÞ ds 2 ku0 ðsÞk ds ; ¼ 2 0 0 0#t#T Rt where 1 ¼ ð1; · · ·; 1ÞT [ R m . Thus wðtÞ ¼ w0 ðtÞ þ 0 u0 ðsÞ ds becomes Brownian motion under the risk-neutral equivalent martingale measure P where PðLÞ ¼ E 0 ½Z 0 ðTÞ · 1L ; L [ F: In order to incorporate some degree of uncertainty about the stock appreciate rates, we perturb the appreciation rate for the ith stock from the value bi(·) with a stochastic process vi(·) with value in [2Ni, Ni], where N i [ ½0; þ1Þ is a known constant. Set    T  vð·Þvð·Þ ¼ ðv1 ð·Þ; · · ·; vm ð·ÞÞ is F 2 progressively measurable DD ¼ For each vð·Þ [ D; we define Z t  Z 1 t 21 2 21 T exp ð s ðsÞvðsÞ þ d ðtÞÞ dw ðsÞ 2 k s ðsÞvðsÞ þ d ðtÞk ds ; Lv ðtÞD 0 ¼ 2 0 0 0#t#T

On stochastic optimal control

899

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and the probability measure P v ðLÞDE ½L ðTÞ·1L  on F(T ). By Girsanov ¼ 0 v theorem, Z wv ðtÞD ¼ w ðtÞ 2 ðs 21 ðsÞvðsÞ þ dðsÞÞ ds 0 ¼ is a Brownian Motion under Pv. Assume that stock appreciation rates are uncertain, we consider a small agent who starts out with initial capital x0 and decides which amount pi(t ) to invest in each of the stocks at time t [ ½0; T: Let xðtÞ ¼ xðt; x0 ; pÞ denotes his wealth process. It satisfies the equation 8 > dxðtÞ ¼ rðtÞxðtÞ dt þ p T ðtÞ½bðtÞ þ vðtÞ 2 rðtÞ·1 dt þ p T ðtÞs ðtÞ dwv ðtÞ > > > > > > > > þ dðtÞxðtÞ dw0 ðtÞ > > > > > < ð1Þ ¼ rðtÞxðtÞ dt þ p T ðtÞ½vðtÞ 2 rðtÞ·1 dt þ p T ðtÞsðtÞ dw0 ðtÞ > > > > > > > þ dðtÞxðtÞ dw0 ðtÞ > > > > > > > : xð0Þ ¼ x 0 Definition 1. (i) A process p : ½0; T £ V ! R m is called portfolio process if it is F 2 progressively measurable and satisfies Z

 pðtÞ2 dt , 1; a:s:

t

E 0

(ii) The process xðtÞ ¼ xðt; x0 ; pÞ defined by equation (1) is called the wealth process corresponding to portfolio p(·) and initial capital x0. (iii) Given a random variable A [ L 2 ðV; FðTÞ; P 0 Þ; a portfolio process p(·) is said admissible for the initial capital x0, and denote by Z t   Z
p ð·Þ [ AðxÞ; if xðtÞ $ exp rðsÞ ds ·E A·exp 2 0

T 0

   rðsÞ ds FðtÞ

held almost surely. Here E denotes expectation with respect to the probability measure P. We suppose that the total liabilities to the agent at time T is described by a contingent claim C: a random variable in

On stochastic optimal control

L 2 ðV; FðTÞ; P 0 Þ with P½C $ A ¼ 1 and P½C . A . 0: Define Z t    Z rðsÞ ds ·E C·exp 2 CðtÞDexp ¼ 0

0

T

901

    rðsÞ ds FðtÞ

One cannot hedge the liability C perfectly if Að0Þ # x , Cð0Þ: Simulating JI Shao lin (2001), we study following value function of the stochastic control problem 

V ðxÞDV ðx; CÞD ¼ ¼

inf

p ð·Þ [AðxÞ

 Z E ðC 2 xðTÞÞ · exp 2

T

þ rðsÞ ds

ð2Þ

0

as a reasonable coherent-measure of risk where E denotes expectation with respect to the measure Pv and the initial wealth x0 satisfies Að0Þ , x , Cð0Þ: Then we investigate a fictitious stochastic game introduced by Cvitanic and Karatzas (1999). We consider BSDE
 dxðtÞ ¼ rðtÞxðtÞ þ p T ðtÞ bðtÞ 2 rðtÞ·1 dt þ p T ðtÞs ðtÞ dw0 ðtÞ ð3Þ þ dðtÞxðtÞ dwðtÞ xðTÞ ¼ j where j [ L 2 ðV; FðTÞ; PÞ is a terminal condition. According to BSDE theory, it exists a unique pair of solution (7). Denote the solution of equation (3) by ðx j ð·Þ; p j ð·ÞÞ with respect to the terminal condition xðTÞ ¼ j: Set F0 ðxÞD{j jx j ð0Þ ¼ x0 ; A # j # C:a:s:}: ¼ Definition 2. (i) Given a random variable A [ L 2 ðV; FðTÞ; P 0 Þ and an initial x0, a terminal wealth j is called admissible for the initial wealth x0, and   R  we write j [ F0 ðxÞ; if x j ð0Þ ¼ x0 and j $ A; a:s: T (ii) j * is called optimal objective if V v ðxÞ ¼ E v ðC 2 j * Þ·exp 2 0 rðsÞ ds and j * [ F0 ðxÞ: Theorem 1. If j is the terminal condition of BSDE (equation 3), then the value function

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 V v ðxÞ ¼ E 0

 Z Lv ðTÞC · exp 2



T

rðsÞ ds 0

 2 sup E 0 j[F0 ðxÞ

902

 Z Lv ðTÞj · exp 2

T

 rðsÞ ds

0

Proof. In the light of equation (2), it is easy to check that ;j [ F0 ðxÞ; p j ð·Þ [ AðxÞ where ðx j ð·Þ; p j ð·ÞÞ is the solution of equation (3); Thus   Z V v ðxÞ ¼ inf0 E 0 Lv ðTÞ · ðC 2 j * Þ · exp 2 j[F ðxÞ

T

 rðsÞ ds :

0

Next, we shall prove that if the optimal objective j* exists, it satisfies j* # C: Suppose x j ðtÞ; x1 ðtÞ satisfy FSDE (equation 1) with initial wealth x0 and x1, respectively. Without loss of generality, assume x1 . x0 ; it follows that x1 ðtÞ $ x j ðtÞ according to the comparison theorem of stochastic differential equation. Thus we get   Z E 0 ðC 2 j* Þþ · exp 2

T

   Z rðsÞ ds ¼ E 0 ðC 2 x j ðTÞÞþ · exp 2

0

T

 rðsÞ ds

T



0

  Z þ . E 0 ðC 2 x1 ðTÞÞ · exp 2

rðsÞ ds 0

This contradicts to the fact that j* is the optimal objective. The proof is complete. A Theorem 2. If there exist l [ R þ and k [ ½0; 1 such that  E ½AðvÞð1½Z v ðTÞ.l þ k · 1½Z v ðTÞ¼l Þ þ CðvÞð1½Z v ðTÞ,l  Z þ ð1 2 kÞ1½Z v ðTÞ¼l Þ · exp 2



T

rðsÞ ds

¼ x0

ð4Þ

0

Then the optimal objective is Proof. At first, by Theorem 7 in Vvitanic (1999) for some l [ R þ ; the optimal objective j *

j* ¼ AðvÞð1½Z v ðTÞ.l þ k·1½Z v ðTÞ¼l Þ þ CðvÞð1½Z v ðTÞ,l þ ð1 2 kÞ1½Z v ðTÞ¼l Þ ð5Þ

On stochastic optimal control

possible has the form of equation (5). Second, we can prove that above j* is the optimal objective. Taking any h [ F0 ðxÞ; it is easy to check that   Z þ E ðj* 2 hÞ ·exp 2

T

   Z þ rðsÞds ¼ E 0 Z 0 ðTÞ·ðj * 2 hÞ ·exp 2

0

T

 rðsÞds

0

 ¼ E 0 Z 0 ðTÞ½ðA 2 hÞ·1½Z 0 ðTÞ.l þ ðC 2 hÞ·1½Z 0 ðTÞ,l þ ðkðA 2 hÞ  Z þ ð1 2 kÞ·ðC 2 hÞ1½Z 0 ðTÞ.l · exp 2

T

 rðsÞds # lE 0 ½ðA 2 hÞ·1½Z 0 ðTÞ.l

0

þ ðC 2 hÞ·1½Z 0 ðTÞ,l þ ðkðA 2 hÞ þ ð1 2 kÞ·ðC 2 hÞ1½Z 0 ðTÞ.l    Z ¼ lE 0 ðj*ðvÞ 2 hðvÞÞ·exp 2

T

 rðsÞds

0 0

Since h; j* [ F ðxÞ; it follows that   Z E ðj*ðvÞ 2 hðvÞÞ·exp 2

T

 rðsÞds ¼ 0:

0

So   Z E 0 j*ðvÞ·exp 2



T

rðsÞds



 Z $ E 0 hðvÞ·exp 2

0

T

 rðsÞds ;

0

;h [ A 0 ðxÞ: This completes the proof.

A

References Bohlin, T. and Graebe, S.F. (1995), “Issues in nonlinear stochastic grey-box identification”, International Journal of Adaptive Control and Signal Processing., Vol. 9, pp. 465-90. Chen, S. and Yong, J. (2001), “Stochastic linear quadratic optimal control problem”, Appl. Math. Optim., Vol. 43, pp. 21-45. Cvitanic, J. and Karatzas, I. (1999), “On dynamic measure of risk”, Finance and Stochastics, Vol. 4, pp. 451-82. Follmer, H. and Leukert, P. (2000), “Efficient hedges”, Finance and Stochastics, Vol. 4, pp. 117-46.

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Shao lin, J.I. and Peng Shige (1999), “A recursive utility optimization problem”, Economic Mathematics, Vol. 2, pp. 21-6. Shao lin, J.I. (2001), “Dynamic measure of risk and related stochastic game problem”, Mathematica Applicata., Vol. 14, pp. 132-7. Kloeden, P.E. and Platen, E. (1995), Numerical Solutions of Stochastic Differential Equations, 2nd ed., Springer-Verlag, Heidelberg. Unbehauen, H. and Rao, G.P. (1990), “Continuous-time approaches to system identification – a survey”, Automatica., Vol. 26, pp. 23-35. Unbehauen, H. and Rao, G.P. (1997), “Identification of continuous-time systems: a tutorial”, in Sawaragi, Y. and Sagara, S. (Eds), SYSID’97 – 11th IFAC Symposium on System Identification IFAC. Young, P.C. (1994), Recursive Estimation and Time-series Analysis, Springer-Verlag, Berlin.

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Pansystems GuanKong technology and information quantization

Pansystems GuanKong technology 905

Yu Hong-Yi Wuhan Pansystems Institute, Wuhan, Hubei, People’s Republic of China

Leon (Xiangjun) Feng Seagate Technology, River Park Commons, Pittsburgh, PA, USA

Yu Ran Shenzheng Special Economic Zone, People’s Republic of China Keywords Cybernetics, Systems theory Abstract A basic pansystems scientific view about the physical world is presented. The principle and methodology of pansystems GuanKong technology are introduced. Simple metrics for the quantization of information, risk and gain by comparison (GBC) are established and discussed, and the practical and simple membership function which realizes the transformation from qualitative to quantitative order are given, and an example showing the pansystems GuanKong in detail is also given.

I. Introduction Pansystems theory founded by Professor Wu Xuemou (1990) and aiming at exploring the truth for the great unification of science and further specialization at a new level has become a trans-field, multi-layer, network alike and variousdisciplines connecting scientific and practical research with an emphasis on pansystems (generalized systems, generalized relations, and the various composition), unification (a harmonic megcombination of oriental cultures with western modern science and technology, and harmonic meg-melting of philosophy, mathematics, physics, and various science and technology), panderivatives, pansymmetry, panrelativity, cause-effect relations, simplifying and strengthening, being harmonic with the Taos (a special mutual promotions, a generalized correlation and resonance), and gain by comparison (GBC). At present, pansystems GuanKong (or observation-control) technology and the PanBox principle are the two cornerstones of pansystems science and technology. This paper mainly focuses on the GuanKong technology which has been used in both social science like risk decision and silicon valley’s high tech such as generalized PRML channel optimization for magnetic recording products.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 905-911 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443987

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II. A basic scientific view of pansystems Matter, energy, information, space, and time are called five basic elements of modern science and technology. Pansystems theory thinks that any of those five basic scientific elements cannot exist independently, and only the five dimensional physical pansystems of (M, E, I, S, T) can exist objectively and independently. As per the pansystems principle of change, it is very easy to prove that there exist five Mutuals among M(matter), E(energy), I(information), S(space) and T(time). The pansystems five Mutuals include inter-connection, inter-transformation, inter-derivation, inter-promotion and inter-restriction. Especially, M, E, I, S, and T can all change into each other under certain conditions. The above called five dimensional physical pansystems principle is a basic scientific view of pansystems which matches common sense and ordinary experience. III. The pansystems of probability and weights and the metrics of information Keeping in mind the five Dimensional physical pansystems principle, pansystems GuanKong technology observes and controls abstract structures with information which is related with probability or weights. The word GuanKong is meant by the repeated observation and control. Pansystems GuanKong takes probability as a pansystems with both generalized software and generalized hardware. The generalized software is called Soft Probability where Soft probability ¼ Subjective probability and the generalized hardware is named Hard probability where Hard probability ¼ Objective probability There exist pansystems five Mutuals between the Soft probability and Hard probability. For example, a higher Hard probability will bring about an increase in Soft probability, and the increase of the Soft probability will promote the further increase of the Objective probability. Under certain conditions, however, a higher Hard probability will make the decision maker tend to lower the Soft probability so that the Hard probability will be reduced. Under certain conditions, weights can be a special kind of probability, so that we also have a pansystems of weight with Hard weight and a Soft weight where Soft weight ¼ Subjective weight Hard weight ¼ Objective weight There are also pansystems five Mutuals between the Soft weight and the Hard weight.

The probability and weight as a pansystems are the important foundation and also exclusive scientific viewpoints of pansystems GuanKong technology. We define risk as
X  ^ Risk ¼ ðri Þ ¼ wj ð yij 2 ei Þ 2 ð1Þ where i ¼ 1; 2; . . .m; and j ¼ 1; 2; . . .n; yij is the normalized value of ith GuanKong object’s jth GaunKong target. ei is the Subjective mean value of the ith GuanKong object’s GuanKong targets. wj is the Subjective weight for the jth GuanKong target of the ith GuanKong Object. We give the following expression for GBC GBC ¼ ðgi Þ ¼ ðei =ð1=ð1 2 ri ÞÞÞ

ð2Þ

where i ¼ 1; 2; . . .m As we will see soon that both GBC and risk have strong correlation with some simple metrics of information.We define Total information TI ¼ log2 ðnÞ X Free information FI ¼ pj log2 ð1=pj Þ

ð4Þ

Bind Information BI ¼ TI 2 FI

ð5Þ

ð3Þ

From information theory we have right away TI ¼ Maximal entropy FI ¼ Shannon entropy We then called BI as a risk entropy. IV. Pansystems GuanKong technology A group of Generalized Registers are created for the panoptimization of abstract structures. For a fuzzy systems the GuanKong targets are a group of abstract symbols s1, s2,. . .sn each of which is given a Soft weight and Hard weight and the Soft weight and Hard weight are the Generalized Registers which store adjustable and accessible values. Through a simple transformation from qualitative into quantitative order the fuzzy systems become a definite engineering systems. We can then “tune” fuzzy systems just as we tune PRML channel for ultra high density magnetic recording. As a result of the tuning process to the values of the Generalized Registers, the GuanKong targets are panoptimized. The risk, GBC, FI and BI are all used as the metrics for GuanKong. The formulae based on experimental psychology for the transformation from qualitative into quantitative order is as follows

Pansystems GuanKong technology 907

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FðI Þ ¼ Lnðmax{I } þ 2 2 I Þ=Lnðmax{I } þ 1Þ

ð6Þ

where F(I ) is the membership function, and I is the qualitative order. V. The application of GuanKong technology in risk and gain evaluations As shown in Table I, an International corporation needs to do the risk and gains evaluation for four products Hi ði ¼ 1; . . .; 4Þ The GuanKong targets include new investment, productivity and return period. The data in the table has been normalized. From equation (6), we get totally six Soft weights for the three GuanKong targets w1 ¼ ð0:22; 0:34; 0:44Þ w2 ¼ ð0:22; 0:44; 0:34Þ w3 ¼ ð0:34; 0:44; 0:22Þ w4 ¼ ð0:34; 0:22; 0:44Þ w5 ¼ ð0:44; 0:34; 0:22Þ w6 ¼ ð0:44; 0:22; 0:34Þ From the values of the GuanKong targets shown in Table I, we could also obtain the Hard weights for the GuanKong targets as shown in Table II. The correlation charts for risk and risk entropy BI and for GBC and Shannon.

S. No. Table I. GuanKong objects and GuanKong targets

1 2 3 4

Hard weights Table II. Hard weights for GuanKong targets

p1 p2 p3 p4

Object symbols

New investment

Productivity

Return period

H1 H2 H3 H4

1.0000 0.9600 0.8276 0.7273

0.8000 0.8426 0.8596 1.0000

1.0000 1.0000 0.8571 0.7500

New investment

Productivity

Return period

0.36 0.34 0.33 0.29

0.29 0.30 0.34 0.40

0.36 0.36 0.34 0.30

Entropy FI are then plotted as shown in Figures 1 and 2. The GBCs for different objects and different Soft weights are also presented in Figures 3 and 4. From Figures 1 and 2 we could see very clearly that information and entropy can be used as the metric for both gains and risk, or information and entropy indeed could reflect the internal structure and performance of abstract systems. The Figures 1 and 2 also show that the Soft weights play a role of “pilot” which determines the slopes or the pan-derivatives of the correlations. Figure 3 shows

Pansystems GuanKong technology 909

Figure 1. Correlation between risk and BI

Figure 2. Correlation between GBC and FI

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Figure 3. GBC changes with the products

Figure 4. GBC optimization curves

that the objects or the hard structure or hard weights are usually the key factors to determine the fundamentals of the abstract systems. Figure 4 however shows that the Soft weights could indeed bring additional increase in GBC to some extent. VI. Summary This paper discussed the basic principle and the detailed technologies of pansystems GuanKong. The FI or Shannon entropy and the BI or risk entropy

are used as a metrics for the quantization of information which reflect GBC and risk of abstract systems in some way. A detailed practical example of pansystems GuanKong was also presented. References Wu Xuemou (1990), Pansystems View of the World, Chinese People University Press. Yu Hong-Yi and Feng Xiangjun (Leon) (2000), “GuanKong storage systems”, Chinese Patent Pending (Application No. 01114392.4), 30 July, 2000.

Pansystems GuanKong technology 911

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Randomization and eventual reordering: a number theoretic approach Barry Zeeberg N. Pershing Dr. #1, Arlington VA, USA Keywords Cybernetics, Computational methods Abstract Shuffling a deck of cards is normally used for randomization. An imperfect shuffle would not produce the desired randomization, since there would be residual correlation with the original order. On the other hand, from the classical card magic literature it is known that eight successive perfect riffle shuffles returns the deck to the original order. The question addressed here is whether this observation is in fact unusual and surprising. Although a general closed-form analytical solution does not appear to be possible, a simple program could be written to determine deck sizes and numbers of shuffles for which eventual reordering occurs. This computational approach correctly predicts the original observation of eight shuffles for a deck of 52 cards; in fact if the trivial solutions of integral multiples of eight shuffles are discarded, eight shuffles appears to be the unique solution for a 52 card deck.

Kybernetes Vol. 32 No. 5/6, 2003 pp. 912-916 q MCB UP Limited 0368-492X DOI 10.1108/03684920210443996

Preface Shuffling a deck of cards is normally used for randomization. An imperfect shuffle would not produce the desired randomization, since there would be residual correlation with the original order. On the other hand, from the classical card magic literature it is known that eight successive perfect riffle shuffles returns the deck to the original order. The question addressed here is whether this observation is in fact unusual and surprising. Although a general closed-form analytical solution does not appear to be possible, a simple program could be written to determine deck sizes and numbers of shuffles for which eventual reordering occurs. This computational approach correctly predicts the original observation of eight shuffles for a deck of 52 cards; in fact if the trivial solutions of integral multiples of eight shuffles are discarded, eight shuffles appears to be the unique solution for a 52 card deck. There are four main conclusions derived from the computational method: (1) There is nothing special about a 52 card deck – “deck size space” is dense in deck sizes for which a small to moderate number of shuffles will work; (2) for decks whose size is a power of 2, the number of shuffles is the base 2 logarithm of the deck size; (3) for decks whose size is two cards greater than a power of 2, the number of shuffles is two times that power of 2; and (4) there are several clusters of irregularly spaced deck sizes exhibiting a linear relationship with number of shuffles: deck ¼ m · shuffles + b, where m and b are small integers. It is

speculated that the specific phenomenon illustrated here – a small number of repetitions of a perfect randomization process leading to reordering – may be a general principle in physical and biological processes that may produce or maintain structure in the real world.

Randomization and eventual reordering

Introduction From the classical card magic literature it is known that eight successive perfect riffle shuffles returns the deck to the original order. It is somewhat easier to see this by conceptually following a card in an arbitrary position through its travels than by acquiring the skills to perform perfect riffle shuffles: The top card is in position 1, the next card is in position 2, etc., and the bottom card is in position 52. The deck is split into two halves, the “top” half containing cards from original positions 1 through 26, and the “bottom” half containing cards from original positions 27 through 52. In the course of each perfect riffle shuffle, arbitrarily assume that the card from original position 1 retains position 1, and that the card from original position 52 retains position 52 (“top stays on top, bottom stays on bottom”). Now let us follow the journey of the card from original position 2. After zero shuffles, it is in position 2. After one shuffle, it is in position 3 (the top three cards, in terms of the original positions, are 1-27-2). After two shuffles, it is in position 5 (1-x-27-x-2, where x’s are just used as space-holders since it is not worth the effort to figure out the original positional value). By induction, it is easy to see that after three shuffles, it is in position 9 ½9 ¼ 2 · ð5 2 1Þ þ 1; after four shuffles (be patient, we are half way there) it is in position 2 · ð9 2 1Þ þ 1 ¼ 17; after five shuffles it is in position 2 · ð17 2 1Þ þ 1 ¼ 33: But now it is in the bottom half of the deck, and we must consider an interesting modulo effect. Absolute position 33 corresponds to position 33 2 26 ¼ 7 in the bottom half, and after six shuffles it is in absolute position 2 · 7 ¼ 14 [that is, there is a “boost” of 1 position relative to the card that is in position 7 of the top half, which would end up in position 2 · ð7 2 1Þ þ 1 ¼ 13]. Now it is back in the top half, so the original induction can be used – after seven shuffles it is in position 2 · ð14 2 1Þ þ 1 ¼ 27: This is obviously just where it needs to be after the penultimate shuffle (that is, the top card of the bottom half) in order to finish in its original position 2 after shuffle eight. Although a general closed-form analytical solution does not appear to be possible, a simple program was written to determine deck sizes and numbers of shuffles for which eventual reordering occurs.

913

Methods The computation was implemented in a straightforward C program [whose source code, along with the raw and analyzed results are available online (see below)] consisting of three nested loops: (1) deck size (from two to MAX in increments of two); (2) number of shuffles (from one to MAX in increments of

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one); and (3) initial position of a card within the deck (from two to deck size/2 since the top card remains on top throughout, and cards deck size/2 +1 to deck size are related by symmetry to the top half of the deck, and therefore do not need to be considered separately). Trivial multiples of a shuffle were not reported (for example, if eight shuffles was discovered for a 52 card deck, then 16 shuffles, or more generally any multiple of eight shuffles would trivially work). The key part of the computation is very simple: for a given card in position ps after shuffle s, its position psþ1 after shuffle s þ 1 is psþ1 ¼ 2ðps 2 1Þ þ 1 ¼ 2ps 2 1 if 2 # ps # deck size=2; or, if deck size=2 þ 1 # ps # deck size 2 1; then psþ1 ¼ 2ðps 2 deck size=2Þ ¼ 2ps 2 deck size: It does not seem possible to derive a closed form solution, since one needs to keep track of the set of values of s for which the transitions between top and bottom of the halves of the deck occur.

Results and discussion Existence of a solution for each deck size studied indicates that “deck size space” is dense in deck sizes for which a small to moderate number of shuffles will work. Except for trivial multiples of the fundamental solution, the number of shuffles appears to be unique. Of course, both completeness and uniqueness can not be proven by a finite computational approach, but no counter-examples have been found to date. The relationship of number of shuffles to deck size seems somewhat irregular (Figure 1), but there are some regularities that were discovered: (1) for decks whose size is a power of 2, the number of shuffles is the base 2 logarithm of the deck size; (2) for decks whose size is 2 cards greater than a power of 2, the number of shuffles is 2 times that power of 2; and (3) there are several clusters of irregularly spaced deck sizes exhibiting a linear relationship with number of shuffles: deck ¼ m· shuffles + b, where m and b are small integers. The ten largest clusters are summarized in Table I, and indicated by solid lines in Figure 1(b) (in some cases distinct lines cannot be visually distinguished in the figure). There are two types of consequence for these observations: an interesting problem in number theory, and possible analogies in the physical or biological world. In terms of number theory, it would be of interest if it were possible to predict and extend the computational results using theoretical arguments ab initio. It would also be of interest to understand the basis of the three regularities mentioned earlier. In order to facilitate this, the source code for the C program as well as the raw and processed output data are available as flat files at http://www.science.gmu.edu/~bzeeberg/WOSC_IIGSS-02/. The C program source, including commented information on compilation and command line argument format, is in Cprogram.html. The raw output data resulting from running “Cprogram 2 1100 1 1100” and additional

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Figure 1. (a) Shuffles as a function of deck size emphasizing spiking characteristics; (b) Shuffles as a function of deck size emphasizing clusters

post-processing [format: deck_size number_of_shuffles int(deck/shuffles) mod(deck/shuffles)] is in raw.data.html; the same information, but sorted by int(deck/shuffles) and then by mod(deck/shuffles) is in sorted.data.html; Table I is duplicated in summary.clusters.html; the identity and members of each significant cluster are tabulated in clusters.html; the figures are posted as Figure.1a.gif and Figure.1b.gif. It is hoped that these sources will facilitate

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916 Table I. Summary of clustering results

Cluster number 1 2 3 4 5 6 7 8 9 10

Number of cluster members

m ¼ Int (deck/shuffles)

b ¼ Mod (deck/shuffles)

69 55 18 41 11 9 10 7 6 8

1 2 3 3 3 4 5 6 6 7

2 2 2 4 10 2 6 2 4 8

analysis by other researchers who might be able to discover additional relationships or fundamental underlying principles. It is speculated that the specific phenomenon illustrated here – a small number of repetitions of a perfect randomization process leading to reordering – may be a general principle in physical and biological processes that may produce or maintain structure in the real world. As an example, at the current stage of evolution, a genome is required in order to maintain and transfer information for living organisms, since they are immersed in a rather chaotic external infrastructure. It is possible that a precursor to this method of “database management” could have relied upon repeated randomizations and eventual reordering. This would have allowed periodic processes (such as the rotation of the earth, or the alternation of low and high tides in the oceans) that caused a structured form of randomization to bridge the gap between pre-biotic chaos and the formation of the highly structured machinery of the genome and living cells.

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Data self-create in data storage system Zhou ke, Zhang Jiangling and Feng Dan Computer Department, Huazhong University of Science and Technology, People’s Republic of China

Data self-create in data storage system 917

Keywords Cybernetics, Data storage Abstract When the controller of a storage system becomes more and more powerful, it sometimes creates new data and stores this data in the system, just like parity information in RAID level 5. We call these phenomena data self-create. This paper provides a theory about data self-create which separates data self-create phenomena into 16 kinds. Three applications are introduced. From a pansystems view, this paper also gives an explanation of data self-create.

1. Introduction In order to improve the performance of a data storage system, data will be created by system sometimes. For example, in RAID 5 level, RAID controller creates verifying bytes automatically when data are sent to storage space. Those verifying bytes are not user’s data, but they make RAID available when a disk fails. With the development of data storage system, system’s controller becomes more and more powerful. Shared-storage cluster (Mazin Yousif, 1999), highperformance storage system (HPSS) (Watson and Coyne, 1996), network RAID (Meng QingFei, 2001) are such systems. The Controller will create new data and store this data in a system according to some conditions. In order to study these phenomena, a theory about data self-create is provided in the following section, and two applications are introduced. 2. Theory about data self-create Let us look at data storage system first. Figure 1 gives a module of data storage system. In our opinion, a data storage system consists of controller, data, space, input and output. There are math modules of input and output procedures as shown below. Input procedure math model: D ¼ CðI Þ Output procedure math model: O ¼ CðDÞ Here D represents data, I represents input, O represents output and C represents functions that are performed by controller. In general data storage This paper is supported by national science foundation (69973017).

Kybernetes Vol. 32 No. 5/6, 2003 pp. 917-921 q MCB UP Limited 0368-492X 10.1108/03684920210444003

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system, such as a disk: CðxÞ ¼ x: Generally, if I ¼ 0; then D ¼ CðI Þ ¼ Cð0Þ ¼ 0; it represents that if there is no input, there is no new data. However, if there is no input, there will sometimes be new data that is created by the controller, and is called data self-create. Definition 1. In a data storage system, if I ¼ 0; then D ¼ CðI Þ ¼ Cð0Þ – 0; we call it data self-create. In this definition, C is a function performed by controller. There is different C in different applications. In RAID cluster, C ¼ f½XðO ¼ DÞ; f is a hashing function, X is probability. In RAID level 5, C ¼ x or ðDÞ: Because data self-create products new data and puts new data in new space, there are two vectors, (Dn, Sn), (Do, So). Dn is new data, Sn is storage space of new data, Do is old data, So is storage space of old data. According to the relations of Dn, Sn, Do, So, there are 16 kinds of data selfcreate. They are: (1) Dn 0 ðDo Þ ¼ 0; S n 0 ðDo Þ ¼ 0; (2) Dn 0 ðDo Þ ¼ 0; S n 0 ðDo Þ – 0; (3) Dn 0 ðDo Þ ¼ 0; S n 0 ðS o Þ ¼ 0; (4) Dn 0 ðDo Þ ¼ 0; S n 0 ðS o Þ – 0; (5) Dn 0 ðDo Þ – 0; S n 0 ðDo Þ ¼ 0; (6) Dn 0 ðDo Þ – 0; S n 0 ðDo Þ – 0; (7) Dn 0 ðDo Þ – 0; S n 0 ðS o Þ ¼ 0; (8) Dn 0 ðDo Þ – 0; S n 0 ðS o Þ – 0; (9) Dn 0 ðS o Þ ¼ 0; S n 0 ðDo Þ ¼ 0; (10) Dn 0 ðS o Þ ¼ 0; S n 0 ðDo Þ – 0; (11) Dn 0 ðS o Þ ¼ 0; S n 0 ðS o Þ ¼ 0; (12) Dn 0 ðS o Þ ¼ 0; S n 0 ðS o Þ – 0; (13) Dn 0 ðS o Þ – 0; S n 0 ðDo Þ ¼ 0;

Figure 1. Data storage system

(14) Dn 0 ðS o Þ – 0; S n 0 ðDo Þ – 0; 0

Data self-create in data storage system

0

(15) Dn ðS o Þ – 0; S n ðS o Þ ¼ 0; (16) Dn 0 ðS o Þ – 0; S n 0 ðS o Þ – 0: 0

0

Dn (Do) is 0differential coefficient. Dn ðDo Þ ¼ 0 represents that Dn is independent of Do, Dn ðDo Þ – 0 represents that Dn is dependent of Do. The rest is the same.

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3. Applications 3.1 RAID cluster used as VOD server Network RAID is different from traditional RAID, it has two channels, one is SCSI channel which connects RAID to file server, the other is network channel which connects RAID to network, as shown in Figure 2. RAID cluster consists of one file server and several network RAIDs. All network RAIDs are connected to the file server by SCSI channel. Figure 2 gives the structure of RAID cluster. SCSI channel is used to send commands from file server to network RAID. Network channel is used to send data from network RAID to network. We use RAID cluster as VOD server in order to provide several channels for clients to access. At first, clients send requests to file server, then file server analyzes the requests and send I/O commands to network RAID through SCSI channel. At last, network RAID sends data to clients through network channel. In VOD system, server must support several clients at the same time. If a video file is grateful, RAID cluster uses data self-create policy to make several copies of this file in other network RAID, which makes more clients share the same video file at the same time. In this application, C ¼ f½XðO ¼ DÞ; system define some values, such as a1, a2. . .an, when 0 , x , a1 ; fðxÞ ¼ 0; when a1 # x , a2 ; fðxÞ ¼ x; when an21 # x , an ; fðxÞ ¼ nx; and so on.

Figure 2. Structure of RAID cluster

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Let us look at which kind of data self-create it belongs to. Dn 0 ðDo Þ ¼ 1 or n – 0; S n 0 ðS o Þ ¼ 0;

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Data self-create in RAID cluster used as VOD server is the seventh kind of the above introduced. 3.2 RAID level 5 RAID level 5 uses parity (Chen and Lee, 1993) to check data. RAID controller calculates the parity data. Let us analyze the characters of data self-create in this application. C ¼ x or ðxÞ; Dn 0 ðDo Þ – 0; S n 0 ðS o Þ ¼ S o þ A – 0; A is a address parameter of RAID system: Data self-create in RAID 5 level belongs to the eighth kind of the above introduced. 3.3 Searching data in digital library A person, who wants to find some information in a large amount of data quickly, should get some useful help from the data center, such as digital library. But who can make this useful for readers? Here, we can use data selfcreate policy to solve this problem. If a digital library dynamically make indexes or helpful introductions of data stored according to clients’ requirements, such indexes or introductions may be more useful to users, and it can be done more easily than using people to do this heavy work. Because of the variety of data searcher policies, it is difficult to give a union of C function here. We can get only qualitative description of data self-create in this application. Because new data would include address information of old data, Dn 0 ðS o Þ – 0; and S n 0 ðS o Þ ¼ 0: Data self-create in a digital library belongs to the 15th kind of the above introduced. 4. Pansystems view of data self-create In the view of pansystems (Wu Xue Mou, 1993), data self-create is a kind of observing and controlling optimization. Data storage system executes data self-create behaviors to optimize system performances.

Data self-create can be denoted as (S, D ), here S is data storage system and D is data. There exists inter-promotion between S and D. Self-create of D must be executed by S, and the expansion of D improves the performance of S. In RAID cluster, file server makes several copies of some data file after stating clients’ requests. It increases the data bandwidth of VOD server. In RAID level 5, RAID controller creates parity byte of data constantly, which improves safety of system data stored. In digital library, the system controller creates indexes or introductions of data stored, which can be of convenience to users and make digital library more useful. Data self-create builds a relationship between data created and old data. This relationship is a generalized differential coefficient. Data self-create will make a data storage system more powerful than before. References Chen, P. and Lee, E.K. (1993), “Striping in a RAID level 5 disk array”, Technical Report CSE-TR181-93, University of Michigan. Mazin, Yousif (1999), “Shared-storage clusters”, Cluster Computing, Vol. 2, pp. 249-57. Meng QingFei (2001), “Study on network RAID technology”, Bachelor thesis, Huazhong University of Science and Technology, Wuhan, China. Watson, R.W. and Coyne, R.A. (1996), “The parallel i/o architecture of the high-performance storage system (HPSS)”, IEEE, Vol. 33, pp. 27-44. XueMou, Wu (1993), The Pansystems View of The World, Press of People University of China, China, Beijing.

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