Foundations of Complex-system Theories: In Economics, Evolutionary Biology, and Statistical Physics

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9780521778268: Foundations of Complex-system Theories: In Economics, Evolutionary Biology, and Statistical Physics
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Complex behavior can occur in any system made up of large numbers of interacting constituents, be they atoms in a solid, cells in a living organism, or consumers in a national economy. Analysis of this behavior often involves making important assumptions and approximations, the exact nature of which vary from subject to subject. Foundations of Complex-system Theories begins with a description of the general features of complexity and then examines a range of important concepts, such as theories of composite systems, collective phenomena, emergent properties, and stochastic processes. Each topic is discussed with reference to the fields of statistical physics, evolutionary biology, and economics, thereby highlighting recurrent themes in the study of complex systems. This detailed yet nontechnical book will appeal to anyone who wants to know more about complex systems and their behavior. It will also be of great interest to specialists studying complexity in the physical, biological, and social sciences.

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Foundations of Complex-system Theories analyzes, for the first time, the key concepts and general methods used in studying complexity in statistical physics, evolutionary biology, and economics. It highlights the features common to each area, and describes how we understand and deal with complexity.This detailed yet nontechnical book will appeal to anyone who wants to know more about complex systems and their behavior. It will also be of great interest to specialists studying complexity in the physical, biological, and social sciences.

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(From Preface) Einstein once said that "thinking without the positing of categories and of concepts in general would be as impossible as is breathing in a vacuum." His remark echoes a long tradition of Western philosophy arguing that our experience and knowledge are structured by a framework of categories or general concepts. The categorical framework contains our most basic and general presuppositions about the intelligible world and our status in it. It is not imposed externally but is already embodied in our objective thoughts as oxygen is integrated in the blood of breathing organisms. Since the categories subtly influence our thinking, it is as important to examine them as to test whether the air we breathe is polluted. Philosophers from Aristotle to Kant have made major efforts to abstract them from our actual thoughts, articulate and criticize them.

This book continues my effort to uncover the categorical framework of objective thought as it is embedded in scientific theories and common sense. Scientific theories contain some of our most refined thoughts. They do not merely represent the objective world, they represent it in ways intelligible to us. Thus while their objective contents illuminate the world, their conceptual frameworks also illustrate the general structure of theoretical reason, an important aspect of our mind.

As a physicist who turns to philosophize, I naturally started by examining relativity and quantum mechanics. Many general concepts, including the familiar notions of object and experience, space-time and causality, seem problematic when physics pushes beyond the form of human observation and analyzes matter to its simplest constitutive level. Quantum and relativistic theories have been used by many philosophers to argue for the impossibility of invariant categories. I contested their arguments in How is Quantum Field Possible? There I compared the conceptual frameworks of quantum field theory underlying elementary particle physics, general relativity for the large-scale structure of the universe, and our everyday thinking about the world. Their topics vary widely, but they share a common categorical structure. Modern physical theories reject many specific everyday opinions about particular objects and properties but retain the general common-sense notions of object and property. They do not abrogate the seemingly problematic categories but make the categories explicit and incorporate them within themselves, effectively clarifying and consolidating the general presuppositions that we tacitly understand and unreflectingly use in our daily discourse.

After quantum and relativistic physics, the next obvious stop is statistical mechanics. Most advancement in statistical mechanics occurs in condensed- matter physics, which investigates the microscopic structures of solids and liquids. A solid or a fluid is a many-body system, a complex system made up of a great many interacting constituents of similar status. The many- body theories in condensed-matter physics provide a conceptual framework that unites the microscopic and macroscopic descriptions of large composite systems without disparaging either.

Guided by the philosophical aim of seeking general patterns of thought, I realize that many-body theories address a major problem that has concerned philosophers since the debate between the Greek Eleatics and Atomists. How do we explicitly represent the composition of a large system while preserving the integrity of the system and the individuality of its constituents? The importance of the problem is evident from the diversity of circumstances in which it arises. Hobbes' Leviathan and Leibniz's Monadology offer disparate solutions in different contexts, and their answers have many competitors. The problem persists today, so does the polarity in solutions. Large-scale composition is highly complex. Crude models unable to handle the complexity conceptually sacrifice either the individual or the system. Even worse, the expedient sacrifice is sometimes interpreted as "scientific" justifications for various ideologies. Such simplistic models and interpretations have practical consequences besides undermining the credibility of science. The modern individualistic and egalitarian society is a many-body system, and the tension between the individual and the community lurks beneath the surface. What concepts we use to think about the situation affect our perception of ourselves and the society in which we participate, and our perception influences our action. We can clear up some conceptual confusion by a careful analysis of scientific theories to see how they represent composition and what assumptions they have made in their representations.

Many-body systems are the topics of many sciences, for they are ubiquitous in the physical, ecological, political, and socioeconomic spheres. If there is indeed a categorical framework in which we think about them, then it should not be confined to physics. To maintain the generality and broad perspective befitting philosophy, I decided to diversify. I looked for sciences of many- body systems that have developed reasonably comprehensive theories. After a little survey I chose to learn economics and evolutionary biology to sufficient depth so that I can analyze their theories, compare their conceptual structures to that of statistical physics, and extract the common categorical framework. I always have a strong interest in these fields and seize the opportunity to find out what their researchers are doing.

The parallel analysis of theories from economics, evolutionary biology, and statistical physics does not imply that the social and biological sciences ape physics or are reducible to it. Science is not like a skyscraper in which the upper floors rest on the lower; it is closer to an airport in which the concourses function as equals. I draw analogy among the sciences. Analogy is instructive not because it patterns the strange in terms of the familiar but because it prompts us to discern in the familiar case a general idea that is also applicable to unfamiliar situations. For example, the comparison of the perfectly-competitive market theory in microeconomics and the self- consistent field theory in physics does not explain consumers in terms of electrons or vice versa. It brings out a general theoretical strategy that approximately represents a complex system of interacting constituents as a more tractable system of noninteracting constituents with modified properties responding independently to a common situation jointly created by all. The theoretical strategy is widely used, but the rationale behind it is seldom explained in the social sciences. Consequently social theories using it often spawn ideological controversies over the nature of the independent individuals and their common situation. The controversies can be cleared up by drawing the analogy with physical theories in which the theoretical transformation between the original and approximate representations is explicitly carried out, so that we can see plainly the assumptions involved and the meaning of the resultant individuals.

A significant portion of this book is devoted to the presentation of scientific theories and models that serve as the data for conceptual analysis. Due to the complexity of many-body systems, the sciences rely heavily on idealization and approximation, and each splinters into a host of models addressing various aspects of the systems. I try to lay bare the assumptions and presuppositions behind the models so that the readers can assess their claims, which are often culturally influential. Besides clarifying general concepts, I hope the book will stimulate more dialogue among scientists in various fields, not only about what they are studying but how they are proceeding with it. Therefore I try hard to make the material intelligible to a general reader, presenting the conceptual structures of the sciences as plainly as I can, using as little jargon as possible, and explaining every technical term as it first appears. Since the book covers a wide range of material, I try to be concise, so that the major ideas stand out without the cluttering of details.

Cambridge, Massachusetts

From Chapter 1: According to our best experimentally confirmed physical theory, all known stable matter in the universe is made up of three kinds of elementary particle coupled via four kinds of fundamental interaction.[1] The homogeneity and simplicity at the elementary level imply that the infinite diversity and complexity of things we see around us can only be the result of the making up. Composition is not merely congregation; the constituents of a compound interact and the interaction generates complicated structures. Nor is it mere interaction; it conveys the additional idea of compounds as wholes with their own properties. Composition is as important to our understanding of the universe as the laws of elementary particles, and far more important to our understanding of ourselves, for each of us is a complex composite system and we participate in complex ecological, political, and socioeconomic systems. How does theoretical science grapple with the complexity of composition?

Large-scale composition is especially interesting because it produces high complexity and limitless possibility. Zillions of atoms coalesce into a material which, under certain conditions, transforms from solid to liquid. Millions of people cooperate in a national economy which, under certain conditions, plunges from prosperity into depression. More generally, myriad individuals organize themselves into a dynamic, volatile, and adaptive system which, although responsive to the external environment, evolves mainly according to its intricate internal structure generated by the relations among its constituents. In the sea of possibilities produced by large-scale composition, the scopes of even our most general theories are like vessels. Theories of large composite systems are complicated, specialized, and lack the sweeping generality characteristic of theories in fundamental physics. To explore their unique approach, structures, and results is the purpose of this book.

Large composite systems are variegated and full of surprises. Perhaps the most wonderful is that despite their complexity on the small scale, sometimes they crystallize into large-scale patterns that can be conceptualized rather simply, just as crazy swirls of colors crystallize into a meaningful picture when we step back from the wall and take a broader view of a mural. These salient patterns are the emergent properties of compounds. Emergent properties manifest not so much the material base of the compound but how the material are organized. Belonging to the structural rather than the material aspect, they are totally disparate from the properties of the constituents, and the concepts about them are paradoxical when applied to the constituents. Life emerges in inanimate matter; consciousness emerges in some animals; social organization emerges from individual actions. Less conspicuous but no less astonishing, the rigidity of solids and turbulence of fluids emerge from the intangible quantum phases of elementary particles; rigidity and turbulence are as foreign to elementary particles as beliefs and desires are to neurons. Without emergent properties, the world would be dull indeed, but then we would not be there to be bored.

One cannot see the patterns of a mural with his nose on the wall; he must step back. The nature of complex compounds and our ability to adopt different intellectual focuses and perspectives jointly enable various sciences to investigate the world's many levels of organization. Things in different organizational levels are so different each science has developed its own concepts and modes of description. What are the general conditions of our mind that enable us to develop various sciences that operate fairly autonomously but share an objective worldview? What are the general conditions of the world that make it possible for us to use disparate concepts to describe structures of the same stuff on various scales and organizational levels? Given that various organizational levels are causally related by composition, what are the theoretical relations among the corresponding descriptive levels? More specifically, what are the relations between theories for large composite systems and theories for their constituents, theoretical relations that give substance to the notion of composition?

This book tries to answer these questions by extracting, articulating, and comparing the conceptual structures of complex-system theories from several sciences specialized in connecting different organization levels. We examine economics; evolutionary biology, especially its theoretical core known as population genetics; statistical mechanics, especially its application to condensed-matter physics that studies the microscopic mechanisms underlying the macroscopic behaviors of solids and liquids. In addition, we investigate three mathematical theories that find extensive application in the three sciences and beyond: deterministic dynamics, the calculus of probability and stochastic processes, and the ergodic theory connecting the two. The sciences and mathematics have separately received much philosophical attention, but I know of no systematic comparison and few that focus on composition.[2]

Theories in economics, evolutionary biology, and statistical physics cover a wide range of topics, which is further extended by the applications of the mathematical theories. Our analysis focuses not so much on what the theories address but how they address them. Despite the diversity in topics, their theoretical treatments share an abstract commonality, which makes possible interdisciplinary workshops in which biologists, economists, and physicists work together and pick each others brain.[3] This book tries to show that the recent interdisciplinary exchange belongs only to the tip of an iceberg. Beneath, on a more abstract level, the commonality is foundational, for the subject matters of the sciences have a general similarity, and the scientists all share the general theoretical reason of human beings.

The subject matters of economics, evolutionary biology, and statistical physics are all complex systems made up of many interacting constituents: national economies made up of millions of consumers and producers bargaining and trading; evolving species comprising billions of organisms competing for resource; solids constituted by septillions of electrons and ions attracting and repelling each other. The sciences aim to study the properties of the systems as wholes and connect them to the properties of and relations among their constituents: the causal relations between the performance of an economy and the decisions of consumers; between the changing composition of a species and the adaptedness of organisms; between the ductility of a metal and atomic bonds. Economics, evolutionary biology, and statistical physics are not the only sciences of complex systems generated by large-scale composition. They are outstanding for being sufficiently theoretical to illustrate the structure of theoretical reason in accounting for the wholeness of large systems, the individuality of their consti...

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