Complexity
10 Apr 2009 17:40
A definition would be nice. So would an ordinal if not a cardinal measure. Is it clear that humans are more complex than whales? Than chimpanzees? Than termites? Than termite mounds?
Is there any trend towards greater complexity over time among living things? On the Earth as a whole? The universe as a whole? Is there any deep explanation (élan vital anyone?) or can it be accounted for by the usual suspects --- natural selection, "plenty of room at the top," chance? --- Even if we do come up with a measure of complexity, it will be very difficult to apply to the fossil record, since the soft parts are pretty well gone, and so we can't know (much) about the innards of the brain, or the immune system. (In fact, could you infer the existence of immune systems from the fossil record? This is important, since it's complex if anything is, and if we can't infer it, how do we know there weren't other things, also confined to the soft tissues, which weren't comprably complex?)
The "sciences of complexity" are very much a potpourri, and while the name has some justification --- chaotic motion seems more complicated than harmonic oscillation, for instance --- I think the fact that it is more dignified than "neat nonlinear nonsense" has not been the least reason for its success. --- That opinion wasn't exactly changed by working at the Santa Fe Institute for five years.
See also: Adaptation; Agent-based Modeling; Artificial Intelligence; Artificial Life; W. Ross Ashby; Biological Order and Levels of Organization; Cellular Automata; Chaos and Non-linear Dynamics; Cognitive Science; Collective Cognition; Complexity Measures; Cybernetics; Darwin Machines; Developmental Biology; Dissipative Structures; Edge of Chaos; Emergent Properties; Ergodic Theory; Evolution; Evolution of Complexity; Evolutionary Computation; Evolutionary Economics; Information Theory; Institutions and Organizations; Learning in Games; Machine Learning, Statistical inference and Induction; Multi-Agent Systems; Neural Nets, Connectionism, Perceptrons; Neuroscience; Nonequilibrium Statistical Mechanics and Thermodynamics; Pattern Formation; Physics of Computation and Information; Physical Principles in Biology; Physics; Power Law Distributions and Long-Range Correlations; Ilya Prigogine; QWERTY; Random Boolean Networks, Nk Networks; Self-organization; Simulations; Statistical Mechanics; Tsallis Statistics
- Recommended, less technical:
- Robert Axelrod and Michael D. Cohen, Harnessing Complexity: Organizational Implications of a Scientific Frontier
- John Tyler Bonner, The Evolution of Complexity, by Means of Natural Selection [Review]
- Jack Cohen and Ian Stewart, The Collapse of Chaos [A great book, except that, as they themselves say of Dawkins, the philosophy is completely backwards, especially on reductionism and emergent properties.]
- John Holland not only helped found evolutionary computation, but has written a good book on Emergence [Review: Game Rules, or, Emergence according to Holland, or, Confessions of a Creative Reductionist]
- Steven Johnson, Emergence: The Connected Lives of Ants, Brains, Cities and Software [What I buy my relatives when they ask me what all the fuss is about.]
- Heinz Pagels, The Dreams of Reason: The Computer and the Rise of the Sciences of Complexity [What I used to buy my relatives. Deserves to be brought back into print.]
- Herbert Simon, The Sciences of the Artificial [Especially the last chapter, "The Architecture of Complexity". A large fraction of complexity research --- and an even larger fraction of the good stuff --- is variations on themes by Simon.]
- Recommended textbooks:
- Remo Badii and Antonio Politi, Complexity: Hierarchical Structures and Scaling in Physics [Review]
- Nino Boccara, Modeling Complex Systems [Review]
- Gary William Flake, The Computational Beauty of Nature [Review: A Garden of Bright Images]
- Josef Honerkamp, Stochastic Dynamical Systems: Concepts, Numerical Methods, Data Analysis
- Recommended, more technical:
- John Bickle, "Understanding Neural Complexity: A Role for Reduction", Minds and Machines 11 (2001): 467--481
- Terry Bossomaier and David Green (eds.), Complex Systems
- The work of the computational mechanics group at Santa Fe is, IMHO, the closest anyone has got yet to a general, rigorous way of tackling complexity, and it is scandalously little-known. [That sentence was there years before I became part of the group --- and is still there years after I left.]
- Joshua Epstein, "Agent-based Computational Models and Generative Social Science", Complexity vol. 4, no. 5 (1999): 41--60
- Joshua Epstein and Robert Axtell, Growing Artificial Societies: Social Science from the Bottom Up
- J. Doyne Farmer, Alan Lapedes, Norman Packard and Burton Wendroff (eds.), Evolution, Games, and Learning: Models for Adaptation in Machines and Nature (a.k.a. Physica D 22.)
- Stephanie Forrest (ed.), Emergent Computation: Self-Organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks (a.k.a. Physica D 42)
- Stuart Kauffman, The Origins of Order [Interesting, but the writing is confused. Favors intrinsic trends towards complexity, self-organization and "the edge of chaos."]
- D. L. Stein, "Spin Glasses: Still Complex After All These Years?" cond-mat/0301104
- Modesty forbids me to recommend:
- CRS, "Methods and Techniques of Complex Systems Science: An Overview", chapter 1 (pp. 33--114) in Deisboeck and Kresh (eds.), Complex Systems Science in Biomedicine = nlin.AO/0307015
- Dis-recommended:
- I have a long list, available upon request. I may add it here sometime when I'm feeling more full of venom than the present.
- To read:
- {1989--1993} Lectures in Complex Systems [Proceedings of the SFI summer schools; lots of valuable stuff, not listed under "recommended" because I'm not finished with all of them!]
- K. J. Aström, Control of Complex Systems
- Fatihcan Atay, Sarika Jalan and Jürgen Jost, "Randomness, chaos, and structure", arxiv:0711.4293
- Sunny Auyang, Foundations of Complex Systems Theories: In Economics, Evolutionary Biology, and Statistical Physics
- Bechtel and Richardson, Discovering Complexity
- Bossomaier and Green, Patterns in the Sand
- W. W. Burggren and M. G. Monticino, "Assessing Physiological Complexity", Journal of Experimental Biology 208 (2005): 3221--3232 [Reprint]
- Eric J. Chaisson
- Cosmic Evolution : The Rise of Complexity in Nature [Review by Dan McShea in American Scientist; proposes defining complexity operationally as power dissipated per unit mass, according to McShea. Why this should be complexity, I don't get....]
- "Complexity: An Energetics Agenda", Complexity 9 (2004): 14--21 [PDF reprint from Chaisson's website]
- S. V. Emelyanov and S. K. Korovin, Control of Complex and Uncertain Systems: New Types of Feedback
- Nick Gessler, Artificial Culture: Experiments in Synthetic Anthropology
- Giorgio Israel, "The Science of Complexity: Epistemological
Problems and
Perspectives", Science in
Context 18 (2005): 479--509 [From the abstract: "The
aim of the present article is to analyze the epistemological status attributed
in the science of complexity to several fundamental ideas, such as those of
scientific law, objectivity, and prediction. The aim is to show that the hope
of superseding reductionism by means of concepts such as that of ¡Èemergence¡É
is fallacious and that the science of complexity proposes forms of reductionism
that are even more restrictive than the classical ones, particularly when it
claims to unify in a single treatment problems that vary widely in nature such
as physical, biological, and social problems." Thanks to Prof. Israel for
a reprint.]
- J. Stephen Lansing
- "Complex Adaptive Systems", Annual Review of Anthropology 32 (2003): 183--204
- Perfect Order: Recognizing Complexity in Bali [Blurb, ch. 1]
- Tom Leinster
- "General self-similarity: an overview", math.DS/0411343
- "A general theory of self-similarity I", math.DS/0411344
- "A general theory of self-similarity II: recognition", math.DS/0411345
- Simon Levin
- "Complex Adaptive Systems: Exploring the known, the unknown, and the unknowable", Bulletin of the American Mathematical Society 40 (2002): 3--19 [PDF. Survey, emphasis on evolutionary ecology]
- Fragile Dominion: Complexity and the Commons
- Christian Lindgren, "Information Theory for Complex Systems" (Online lecture notes, dated Jan. 2003)
- Melanie Mitchell, Complexity: A Guided Tour
- Harold Morowitz, The Emergence of Everything
- Harold Morowitz and Jerome L. Singer (eds.), The Mind, the Brain, and Complex Adaptive Systems
- Giorgio Parisi, "Complex Systems: a Physicist's Viewpoint," cond-mat/0205297
- Max Pettersson, Complexity and Evolution [mostly of interest to me because of the introduction by Joseph Needham]
- J. Barkley Rosser, Jr., "On the Complexities of Complex Economic Dynamics", Journal of Economic Perspectives 13 (4) (1999): 169--192 [JSTOR link]
- L. S. Schulman and B. Gaveau, "Complex systems under stochastic dynamics", cond-mat/0312711
- Didier Sornette, Critical Phenomena in Natural Sciences: Chaos, Fractals, Self-Organization and Disorder: Concepts and Tools
- Stein (ed.), Spin Glasses and Biology
- Michael Strevens, Bigger than Chaos: Understanding Complexity through Probability
- Tainter, Collapse of Complex Societies
- Ulam, Analogies between Analogies [online]
- Elias Zafiris
- "Complex Systems from the Perspective of Category Theory: I. Functioning of the Adjunction Concept," PITT-PHIL-SCI 1236
- "Complex Systems from the Perspective of Category Theory: II. Covering Systems and Sheaves," PITT-PHIL-SCI 1237
- J. Stephen Lansing
