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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.
- Sales Rank: #2006547 in Books
- Brand: Brand: Cambridge University Press
- Published on: 1999-08-28
- Original language: English
- Number of items: 1
- Dimensions: 9.72" h x .87" w x 6.85" l, 1.60 pounds
- Binding: Paperback
- 420 pages
- Used Book in Good Condition
Review
"...gives a refreshing and general look at methods for studying complex systems." Journal of Statistical Physics
"This is a marvelous book....Auyang repeatedly points out how a rigorous examination of the nature of human knowledge reveals a collection of highly competent parts, which appear to be beyond integration or perhaps even beyond consistency." Mathematical Reviews
About the Author
Auyang has been a research scientist for 20 years wiht MIT where she received her Ph.D. in physics.
Excerpt. © Reprinted by permission. All rights reserved.
(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 constituents, and the maze of causal relations fusing the system and its constituents. Hence they are the benchmark for thinking about more complicated phenomena of composition that have so far eluded theorization. A fuller introduction to the sciences is given in the remaining sections of this chapter.
Properly generalized, the idea of composition applies to the mathematical theories we investigate. The probability calculus essentially studies the structures of certain types of large composite system, for instance long sequences made up of the repeated independent tossing of a coin, given the characteristics of a single toss. It provides a conceptual framework for us to grasp a sequence of coin tosses as a whole, to enumerate all its possible states, and to compute the frequencies of possible states with certain gross configurations. The synthetic view of the whole gives the calculus much of its analytic power. It is widely employed in the sciences of composite systems and contributes much to their success.
A dynamic process consisting many stages is a kind of one-dimensional composite system. In a deterministic process, the successive stages follow one another according to the iteration of a rule, akin to the constituents in a compound interacting with each other according to certain laws. Unlike classical dynamic theory, which is satisfied to find the behavior of a particular process given a specific initial condition, the modern formulation of deterministic dynamics grasps entire processes and studies the general features of classes of process. It again proves the power of the synthetic view of wholes. Chaos, bifurcation, attractor, and strange attractor are properties of processes as wholes. Chaos is an emergent character of deterministic dynamics. The contrast between a chaotic process and the determinate succession of its stages illustrates the disparity between the emergent concepts for wholes and the concepts for their parts. Such disparity is common in the theories for large composite systems.
Contrary to popular opinion, deterministic and stochastic dynamics are not the antagonistic dominions of law and chance. Ergodic theory, which has its root in the foundational research on statistical mechanics, shows that the two can be the fine-grained and the coarse-grained descriptions of the same process. By filtering out insignificant details, coarse graining often brings emergent properties into relief. The distinction and relation between fine- grained and coarse-grained descriptions pervade all the sciences we examine: mechanics and thermodynamics, microeconomics and macroeconomics, population genetics and macroevolution. They illustrate the importance of multiple focuses and perspectives in scientific investigation. Furthermore, when the theoretical relations among various perspectives are obscure, illusions such as a mysterious force of chance can occur.
The subject matter of the sciences and mathematics we examine covers physical, biological, social, and abstract systems. When we cut through the diversity of their topics, however, we discover a common synthetic microanalytic approach. Synthetic microanalysis institutes a broad theoretical framework in which concepts describing constituents and composite systems join forces to explain the complexity of large-scale composition. It stands in contrast to microreductionism, whose narrow theoretical framework has no room for system concepts.
Microreductionism is part of an influential philosophy that conceives ideal science as a seamless web of logic based on a few universal laws, from which all knowledge can be deduced. Focusing on composition, microreductionism assumes that once we know the laws and concepts for the constituents, mathematical prowess and large computers are all we need in principle for the complete knowledge of everything the constituents make up, no matter how complex they are. Concepts and theories about systems as wholes are reducible, which means in principle dispensable, because they are nothing but the logical consequences or definitions in terms of constituent concepts. Emergent properties, whose descriptions require system concepts, should therefore be outlawed from science.
The bottom-up reductive method is very successful for small and simple systems. In universalizing it, microreductionism tacitly assumes that large systems are simply more of the same and can be treated by the same theoretical framework and method. This assumption, encapsulated in the slogan "The whole is nothing but the sum of its parts," is correct if the parts do not interact, but unrelated constituents make trivial systems. Interaction and relation among the constituents make the whole more than the sum of its parts so that a larger whole is not merely a larger sum. They form structures, generate varieties, produce complexity, and make composition important. Microreductionism thinks that interactive effects can be accounted for by the addition of "and relations" in its slogan. Without pausing to explain how relations are summed, the breezy addition is a self deception that blinds it to the effort of many sciences, including the largest branch of physics. The theoretical treatment of structure formation in large composite systems with interacting constituents is tremendously difficult. It introduces a whole new ball game in science.
Systems with a few million interacting constituents are not magnified versions of systems with a few constituents. Their structures differ not only quantitatively but qualitatively. Consequently they engender different kinds of question and ways of theoretical thinking. We can adequately describe the solar system in terms of individual planetary motions, but we cannot comprehend a galaxy with billions of stars solely in terms of individual stellar motions. To understand galaxies we need new theoretical apparatus, including galactic notions such as spiral arms.
Small compounds share the same organizational level as their constituents; large systems constitute a higher organizational level. That makes a big difference. Entities on a single level are characterized by a single set of concepts; entities on different levels are often characterized by different concepts. Thus theories connecting two levels differ greatly from theories for a single level. This point is missed by microreductionism, which admits only single-level theories and assumes their adequacy in interlevel explanations. The assumption is unwarranted. Interlevel explanations require a theoretical framework that simultaneously accounts for the behaviors of systems on one organizational level, the behaviors of their constituents on a lower level, and the relations between them. This is the framework of synthetic microanalysis, which connects the descriptive levels for the system and the constituents, not by discarding system concepts but by enlisting them to join constituent concepts in explaining composition.
The laws governing the constituents are important, but knowledge of them is only a small part of the knowledge about large compounds. The immediate effects of the laws pertain to the tiny forces among individual constituents, which form an intractably complex network of mutual interaction. Constituent concepts focus on the minute details of the network, which quickly become overwhelming and obscuring. We overlook or average over the details and shift our attention to the network's salient structures.
What are the structures worthy of attention? Because the number of possible configurations generated in large-scale composition is overwhelming, it is humanly impossible to predict many system structures by the pure bottom- up method stipulated by microreductionism. Unpredictability, however, is not inexplicability, for explication has the help of hindsight. We can first observe the system structures and then microanalyze them in terms of the laws of the constituents plus suitable idealization and approximation. For this we need a top-down view of the whole. The holistic perspective is provided by the conceptual framework of synthetic microanalysis, in which scientists intellectually leap to the system level, perform experiments to find out nature's emergent properties, delineate macroscopic phenomena with system concepts, then reach down to find their underlying micromechanisms.
In studying large-scale composition, scientists microanalyze complex wholes instead of putting together myriad parts. They seek the constituent behaviors responsible for specific system properties, not the system patterns resulting from specific constituent behaviors. Synthetic microanalysis still uses bottom-up deduction, but guides it by the top-down view of composite systems as wholes. The system and constituent views, each confirmed by its own experiments, inform scientists about the approximations, idealizations, and possible contingent factors required for connecting them. Without this intelligence, blind deduction from constituent laws can never bulldoze its way through the jungle of complexity in large-scale composition.
Perhaps the best example of synthetic microanalysis is statistical mechanics, which is not simply a flexing of muscle by particle mechanics but a new theory with a elaborate conceptual structure developed specially to connect the mechanics and thermodynamics levels of description. Thermodynamics and particle mechanics are single-level theories; the former describes a composite system on the macroscopic level, the latter the microscopic level. Statistical mechanics is an interlevel theory. It employs the probability calculus, not to reduce thermodynamics to a province in the empire of particle mechanics, but to integrate the two in the federation of physics. The probabilistic framework and the postulates justifying its employment in physics are not derivable from the laws of classical or quantum mechanics. They are the irreducible theoretical contribution of statistical mechanics. Without the probabilistic framework, physicists would be unable to invoke the laws of mechanics in the substantive explanations of thermodynamic phenomena. Since the idea of a composite system as a whole is fundamental to the probabilistic framework, definitions made within the framework do not make system concepts dispensable.
Synthetic microanalysis and microreductionism differ in their views on the roles of experiment and mathematics, the unity of science, and the nature of human reason. The laws governing the constituents of solids are well known. If all solid-state phenomena are nothing but their mathematical consequences, then experiments would be mere rubber-stamps for verifying the derived results. Nothing can be further from the truth. Many interesting solid-state phenomena are experimentally discovered before they are theoretically explained. Important factors, for instance, the lattice structures of crystals, are experimentally measured and then put into theoretical models "by hand" for the prediction of other phenomena. Experiments often lead theories in research. Scientists, realizing that nature is subtler than they are, design experiments to elicit hints on what complex systems can achieve. These experiments and their results secure the top- down view in synthetic microanalysis.
When microreductionists say that all phenomena are mathematically derivable from certain laws, they usually regard mathematics as a mere calculational tool. Mathematics is a mighty calculational tool, but the calculational capacity hardly exhausts the meaning of Galileo Galilei's remark that the grand book of nature is written in the language of mathematics, nor of Willard Gibbs's remark that "mathematics is a language," which Paul Samuelson chose as the epigraph of his classic economics treatise. More important than calculation is the power of mathematics to abstract and articulate precisely significant ideas with wide implications, to construct complicated conceptual structures, and to analyze exactly the interconnection of their elements. This conceptual capacity of mathematics is fully utilized in the sciences, for instance, in microeconomics to spell out clearly the ideal conditions underlying the feasibility of a perfectly decentralized economy.
The history of science witnesses not the successive reduction of theoretical structures by the expulsion of concepts but the successive introduction of more encompassing synthetic conceptual frameworks that facilitate analysis of complex problems. The move of mathematics to higher abstract construction, which started in the nineteenth century, yielded many large conceptual structures that find applications in twentieth-century scientific theories. Differential geometry, which underlies general relativity, and group theory, which is fundamental to elementary particle theories, are examples of synthetic frameworks beyond the scope of this book. Another example is the modern formulation of dynamics, which underlies the study of chaos by including the notions of both dynamic processes as wholes and their successive stages. Our conceptual structures expand, but their expansion rates are much slower than the explosive rate increases in the number of phenomena that they explain. The disparity in rates of expansion, not the purging of ideas, manifests the unifying power of theoretical reason.
Synthetic microanalysis unites without reducing, achieving a federal unity of science in whose broad constitutional framework both system and constituent theories enjoy a certain degree of autonomy. It contrasts with the imperial unity advocated by microreductionism that, by dispensing with systems concepts in the description of composite systems, subject everything under the authority of constituent theories.
Galileo distinguished "scientists" from "calculators." Calculators care only about grinding out the mathematical consequences of given laws; scientists aim to understand the world. People often say that scientists solve problems. They do, but the universe is not a university and scientists are not students assigned homework problems. Scientists have to frame the questions themselves. To discern phenomena, to judge their importance, and to introduce appropriate concepts that represent them as definite problems are the most important steps in the frontier of research. A phenomenon totally opaque in one theoretical representation may become obvious in another; the Copernican revolution exemplifies the difference made by a model from a better perspective. Synthetic microanalysis, in which scientists jump ahead to discover and delineate important system behaviors whose micromechanisms need explanation, provides the freedom in representation that microreductionism stifles.
Microreductionism extols instrumental reason, which is engrossed in deduction and calculation. Theoretical reason, which drives science, goes way beyond proficiency in technical procedures. We will see in the following chapters how scientists maneuver their positions, shift their viewpoints, idealize judiciously, postulate creatively, discard irrelevant details about individual constituents, introduce novel concepts to represent organizations of wholes, and repeatedly reformulate their problems to make them more manageable. In the process of synthetic microanalysis they use logical reasoning and mathematical deduction, but they also think realistically and intuitively, trading off between detail and generality, authenticity and tractability. They rely on robust common sense, familiarity with the subject matter, active observation, and experimentation on the objective world. This informal and creative thinking marks theoretical reason from mere instrumental reason.
Outline of the book: This book is organized around the interrelated categories of individual and time, which are respectively extracted from the equilibrium and dynamic models of complex-system theories. The two are united by the category of possibility. Whether an individual is a system or a constituent, it is formulated in scientific theories in terms of its possibilities, represented by the state space that encompasses all its possible states. The state space is often the most important postulate of a scientific theory, for it defines the subject matter under investigation. It unifies equilibrium and dynamic models; the evolution of a system traces a path in its state space. The number of possible states explodes exponentially as a many-body system increases in size. The asymmetry between the enormity of possibilities and the scarcity of actualities underlies the concepts of probability, contingency, temporal irreversibility, and the uncertainty of the future.
Part I examines equilibrium models. Chapter 2 lays out the conceptual structure of many-body theories, concentrating on how it harnesses incongruous micro- and macroconcepts in the account of composition. It argues that their approach is synthetic analytic, which emphasizes the analysis of wholes instead of the combination of parts. Even where some sense of "the whole is the sum of its parts" is valid, the parts are not the constituents familiar in small systems. They are customized entities obtained by analyzing the system for the understanding of prerecognized macrobehaviors, and they have internalized most inter-constituent relations. The general idea of optimization, which is extensively applied in all three sciences, is also introduced.
Both the system and its constituents are individuals, the former is explicitly composite and the latter situated. Thus the general concept of individual must incorporate the idea of integrity in view of an individual's parts and the idea of distinctiveness in view of the myriad relations binding an individual to the multitude. These general ideas are examined in chapter 3, which introduces the state space and its utility in representing various individuals. Like most chapters in the book, this one contains four sections, one of which discusses the general philosophical ideas, the other three examine how the general ideas are separately instantiated in biology, economics, and physics.
Scientists seldom try to find exhaustive substantive theories covering all aspects of a kind of many-body system. Instead, they raise specific questions targeting some salient features and make simplifications to disentangle the targeted phenomena from other factors. The result is a host of models and regional theories explaining various aspects. Chapters 4 to 6 examine three broad classes of model and approximation with an ascending degree system integrity. Going through the three classes of model, our attention shifts from individual constituents to the system as a whole. The shift in focus reflects the varying nature of the system properties under investigation; individual constituents are more prominent for the explanation of resultant properties than emergent properties. We will find that not only the characters and interpretations of the constituents change, new individuals such as collective excitations and social institutions appear. The varying image of the constituents and the shifting balance between the constituents and the system easily fuel ideological controversy when the nature and assumptions of various models are not made explicit.
The independent-individual approximation discussed in chapter 4 is the simplest and most widely used approximation. In it, the characters of the constituents are transformed to absorb most of their mutual relations, and the residual relations are fused into a common situation determined by all but impervious to each. Consequently the system becomes a "lonely crowd" of solipsistic individuals responding only to the common situation.
The idea of emergence is explored in the two subsequent chapters. In the models examined in chapter 5, the many-body system is more integrated because its constituents are no longer uncorrelated. Some constituents behave in unison, others cohere preferentially, leading to the appearance of novel entities that constitute an intermediate layer of structure. In the models examined in chapter 6, the constituents are so tightly correlated the system defies modularization and must be treated as a whole and represented by concepts of its own. The models show explicitly how the details about the constituents drop out as we systematically retreat to coarse views for the conceptualization of macroscopic regularities. The insignificance of microscopic peculiarities in many macrophenomena is encapsulated in the universality of many macroconcepts.
Part II considers the notions of time in dynamic, stochastic, and historical processes. Chapter 7 analyzes the relation of the general concept of time to that of thing, event, and causality. It sets the sciences we are investigating in a broader context by relating their temporal concepts to the temporal concepts in relativistic physics that encompasses all changes and the temporal concepts in our everyday thinking that makes use of the tenses.
Deterministic dynamics, familiar since Newtonian mechanics, has recaptured headlines with notions such as nonlinearity, chaos, bifurcation, and strange attractor. Chapter 8 explores the modern formulation of deterministic dynamics in terms of state spaces, its connection to stochastic processes via the ergodic theory, and its role in the foundation of statistical mechanics. It shows how simple dynamic rules, when iterated many times, can generate highly complex and chaotic results. Yet among all the unpredictable complications, sometimes simple new structures emerge at a coarser level that are susceptible to sweeping generalization, as apparent in the universality of some features.
In Chapter 9, I examine the structure of the calculus for probability and stochastic processes and argue that their wide application in the sciences does not suggest the dominion of chance as some inexplicable cause or propensity. The meaning of accident and randomness is explored by comparing deterministic and stochastic formulations of the same process. It again illustrates that important conceptual differences arise from the changes in scale, focus, and perspective, not from the intervention of mysterious forces.
Chapter 10 investigates the difference in the temporal notions of the sciences: evolution is natural history; economics looks forward; physics has no idea of past and future. Yet the time in thermodynamics is already more complicated than the time in mechanics, which lacks even the notion of irreversibility. The emergence of temporal irreversibility is a major problem in the foundation of statistical mechanics. Time is no less a problem for biology and economics. Finding no law that covers the history of organic evolution, biologists join historians in using narratives to explain specific incidences. Economists are still wrestling with the representation of uncertainty regarding the future, which is crucial in decision and planing.
This book considers only those categories that are embodied in the theories of economics, evolutionary biology, and statistical physics. The topics of these sciences belong to the mid-range phenomena of the world, being neither elementary nor too complicated. Their theories need not worry about problems that arise in the study of more extreme topics. Constrained by the data of philosophizing, I will take for granted many general concepts, notably that of object, experience, and space-time. These concepts, explicitly embodied in quantum field theory, I have analyzed in a previous work. Also neglected are consciousness, intentionality, ethics, aesthetics, and other personal categories. The Homo sapiens in biology is an animal. Since the free-market economy is the unintended consequence of human action, economic theories can abstract from intention and work with behavior instead of action. Homo economicus, whose whole being is the maximization of the utility of marketable commodities, lacks vital dimensions of a full person. Uncovering the general nature that Homo economicus shares with things accentuates our awareness of what is peculiarly human.
Most helpful customer reviews
15 of 16 people found the following review helpful.
A Professional work
By Will McWhinney
This is an amazing work. Sunny Auyang has written an easily comprehenedible book on applications of complexity theories to economics, biology and physics. It is a professional writing to professionals in different fields.One needs college level maths and some physics to fully grasp it but she has made minimum use of mathematical symbols. Her writing flows, the examples are clear, some illuminate important issues in the applied fields, some are just homey bits that convey an idea insightfully. A lot of depth in her philosophical explorations of the complexity ideas. I consider this to be a must for any person studying or instructing in system thinking.
12 of 14 people found the following review helpful.
4.5 Stars-The whole is not the sum of the parts;Excellent and scholarly
By Michael Emmett Brady
This is a very interesting book.The author demonstrates that she has command over a number of different fields.She exhibits a wide ranging scholarship in this book.In a nutshell,one can categorize the major conclusions she arrives at as the whole is not the sum of the parts alone.Neither a strictly micro or macro approach to the different fields she investigates,using a complex systems framework, yields the idealized types of scientific discovery and knowledge one finds postulated in some philosophy of science discourses that emphasize deductive closure laws.I have one slight criticism of the book,which is why I have subtracted one half a star.The author has a deep general understanding of the Keynes-Knight distinction between risk and uncertainty in economics(and in social sciences).However,she lacks an understanding of the specifics of Keynes's approach in the A Treatise on Probability(1921;TP).She is unaware of Keynes's interval estimate approach to probability,his index,w,used to measure the completeness of the evidence ,ranging from ignorance through partial knowledge to a complete information set,and Keynes's conventional coefficient of weight and risk,which treats risk, based on the purely deductive laws of probability, as a special case.This would be a very minor criticism if she had integrated the work of D.Ellsberg(Ellsberg's 2001 book,Risk,Ambiguity,and Decision gives a modern,improved and updated version of the TP) and B.Mandelbrot into her discussions involving economics,risk,and uncertainty(Ellsberg's Ambiguity with his rho and alpha indexes and the wild versus mild risk of the cauchy distribution versus normal distribution as discussed by Mandelbrot).Unfortunately,Ellsberg's contributions are not discussed at all while Mandelbrot receives a single footnote that completely ignores his contributions to economics.She can certainly obtain a 5-star rating by bringing out a revised edition in which the original,technical, pioneering work of Keynes is covered followed by the modern and updated contributions of Ellsberg and Mandelbrot.
0 of 0 people found the following review helpful.
Truly a beautiful mind.
By michael willy
A clear, perceptive exposition that provides the reader with an ability to recognize patterns at work in biology economics and physics. Truly a beautiful mind.
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