## Complexity

*06 Aug 2021 09:53*

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.]
- Melanie Mitchell, Complexity: A Guided Tour [Disclaimer: I used to work for Melanie.]
- 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."]
- M. E. J. Newman, "Complex Systems: A Survey", American
Journal of Physics
**79**(2011): 800--810, arxiv:1112.1440 [literature survey] - D. L. Stein, "Spin Glasses: Still Complex After All These Years?" cond-mat/0301104
- Michael Strevens, "How Are the Sciences of Complex Systems Possible?", Philosophy of Science
**72**(2005): 531--556

- 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!]
- 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
- 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]

- Nick Gessler, Artificial Culture: Experiments in Synthetic Anthropology
- Sebastian Grauwin, Guillaume Beslon, Eric Fleury, Sara Franceschelli, Céline Robardet, Jean-Baptiste Rouquier, Pablo Jensen, "Complex Systems Science: Dreams of Universality, Reality of Interdisciplinarity", arxiv:1206.2216
- Cliff Hooker (ed.), Philosophy of Complex Systems
- 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 'emergence' 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.] - Meinard Kuhlmann, "Mechanisms in Dynamically Complex Systems", phil-sci/8442
- James Ladyman and Karoline Wiesner, What Is a Complex System?
- J. Stephen Lansing
- "Complex Adaptive Systems", Annual
Review of Anthropology
**32**(2003): 183--204 - Perfect Order: Recognizing Complexity in Bali

- "Complex Adaptive Systems", Annual
Review of Anthropology
- J. Stephen Lansing and Murray P. Cox, Islands of Order: A Guide to Complexity Modeling for the Social Sciences
- 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

- "Complex Adaptive Systems: Exploring the known, the
unknown, and the unknowable", Bulletin of the American Mathematical
Society
- Christian Lindgren, "Information Theory for Complex Systems" (Online lecture notes, dated Jan. 2003)
- Daniel W. McShea and Robert N. Brandon, Biology's First Law: The Tendency for Diversity and Complexity to Increase in Evolutionary Systems
- Sandra Mitchell
- 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
- M. Norton Wise (ed.), Growing Explanations: Historical Perspectives on Recent Science
- Ulam, Analogies between Analogies
- Wiesner and Ladyman, "What Is a Complex System?" [PDF preprint]

- To write, someday:
- The Genealogy of Complexity
- The Statistical Analysis of Complex Systems