Notebooks

## The Genealogy of Complexity

13 May 2021 01:05

The construction of the universe is certainly very much easier to explain than is that of a plant. --- Lichtenberg
Pinky: What are we going to do tonight, Brain?
Brain: The same thing we do every night, Pinky --- try to take over the world!

This is an outline for a book which I drafted in 2003. (The notes say they began 7 March but I kept working on it for a while that year and perhaps even the next.) This was, naturally, when I was a post-doc at the University of Michigan's Center for the Study of Complex Systems (after being a grad student and post-doc at SFI), and writing "Methods and Techniques of Complex Systems Science". Since then, while I've mined ideas in it for some weblog posts (some of them linked to below), I've basically left it alone for 18 years, only to be reminded of it recently. Because an outline that's old enough to vote is not one I am likely to get around to any time soon, I thought I might as well toss it out, in case someone else can make any use of it. Beyond adding those links, and correcting some obvious typos, I have made absolutely no attempt to bring my old outline up to date. Looking back, the biggest deficiency is that it doesn't give enough attention to the genuinely interdisciplinary aspects of the movement, and how that came about. Also, yes, the networks stuff proved to be a success story!

I might take up this project at some future point --- stranger things have happened --- but no promises.

#### The preamble

In this book, I try to answer some questions about a curious phenomenon. At the end of the 20th century and the beginning of the 21st, a fairly large number of theoretical physicists, primarily trained in statistical mechanics, began to work on subjects which had traditionally been regarded as outside the domain of physics, generally under the rubric of "complex systems". The most prominent targets of this disciplinary imperialism were evolutionary biology, financial markets and other areas of economics, and social networks, but there were also expeditions into social psychology, linguistics, information theory, neuroscience, immunology and organismal biology. In all these areas, the physicists proposed mathematical models, as one might expect of people exhaustively trained in mathematical modeling, but they systematically ignored the existing theories and models, in favor of new, simple models of the sort which had been familiar in statistical mechanics since the 1920s. Why did the physicists think this was a good idea? Why did they want to study complex systems, instead of the traditional topics of statistical physics? How were they able to make the switch? And, finally, did it do any good?

Self-exemplification: this is a study in the history and sociology of science by somebody with absolutely no credentials in the field, but who is (if I say so myself) a highly trained statistical physicist, specializing in complex systems, who spent five years as a graduate student and post-doc at the Santa Fe Institute, the organizational center of the movement described. Clearly, any pretense of disinterested neutrality would be laughable. But I try to be fair.

#### The outline

1. The Road to Santa Fe
1. "The Basic Notions of Condensed Matter Physics"
What people studying statistical physics learned in graduate school, circa 1970 to the present.
• The explicit curriculum: statistical mechanics, many-body calculations, fluctuations, perturbation theory, phase transitions, spontaneous symmetry breaking, order parameters, fluctuations again.
• The implicit curriculum: "generative atomism" (in the phrase of Paul Humphreys), generative approach to macro-phenomena; crucial role of toy models in pedagogy; intellectual arrogance as a part of physics culture; inferiority complex of condensed matter with respect to elementary particle theory.
• What these physicists did not learn: statistics; and often, modern theory of random processes. (They didn't have to learn statistics because of the division of labor within physics: data analysis is done by experimentalists or phenomenologists.)
2. The Renormalization Revolution, circa 1960 to 1980
• Renormalization group; history from Kadanoff on, in potted form.
• Universality. Ability to extract quantitative predictions from qualitative toy models.
• Moral: "details don't matter" (as I heard Per Bak put it more than once verbatim)
3. Nonlinear dynamics
1. Chaos Theory: Role of this in recruiting younger cohorts to the enterprise. Qualitative dynamics as an end in itself (plus possible methodological justification in reconstruction-up-to-a-diffeomorphism results). Universality again. Physicists reinvent time series analysis. (Statistical time series analysis develops before nonlinear dynamical systems theory, hence couldn't incorporate it.) The break-out to non-physical fields. Real contribution of Santa Cruz: bringing dynamical systems results into contact with experimental data.
2. Fractals and Power Laws: Turbulence and chaos lead to $1/f$ noise and power-laws. Self-similarity. Additional interest in power-law fluctuations from phase transitions. Affirming the consequent: thinking that power laws signal critical phenomena. The encounter with Zipf.
3. Pattern Formation: The actual theory, as opposed to Prigogine, etc. Swinney and Golub: chaos stuff actually works in the lab on pattern formation! The Turing theory of morphogenesis gets taken up.
4. Computer Power and Human Reason
• Simulation becomes cheap.
• Code-sharing as a way of encouraging others to take up new methods.
• The parallel to developments in statistics (bootstrap, cross-validation, frequentist nonparametrics, practical Bayesianism with Markov chain Monte Carlo)
5. Like-Minded Independent Thinkers: Opportunities, Ambitions, and Self-Organizing Interests
• Capsule history of Santa Fe, CNLS, other centers. But why then, and that way?
• The Malthusian dynamics of academic disciplines: Professors are self-reproducing. Someone who's a faculty member for 30 years, with one student at a time for 5 years each, has supervised few dissertations by the standards of many departments. But that professor has also reproduced themselves 6 times over in 30 years, for a growth rate of just over 5% per year. Since faculty jobs do not grow at 5% per year (not for long anyway), academic disciplines perpetually face the need to (a) export their surplus population to industry (where they are neutered and do not themselves reproduce), or (b) expand the territory of subject-matter which patrons and/or students will pay members of that discipline to work on.
• The exhaustion of readily solvable and interesting problems in conventional statistical mechanics. The apparent profusion of opportunities in other domains. (Alternate outlet: soft condensed matter; numerically more important. But complex systems are sexier.) Formation of institutions and professional communities of physicists around these themes. Public cachet. (The development of "cultural studies" out of literary criticism as a parallel, and nearly simultaneous, example of a discipline confident in its methods and running out of traditional topics claiming a radically wider scope.)
• Development of confidence in toy models, and that details don't matter. Feeling that one (a) knows what features are important to get right in the model, and which can be tweaked to taste, and (b) which results generalize. In large part craft skill here is tradition, and learning how to analogize to examples in the tradition. Backed up, in some cases, by universality or genericity results, which however tend to fade into the background for working scientists, as opposed to mathematicians.
6. The Curious Incidents of the Dogs That Did Not Bark in the 1970
• Movements which failed to take off among statistical physicists: general systems theory, catastrophe theory, Prigogine, Haken and synergetics.
2. Boltzmanns of Animate Matter: Portraits of Physicists in the Other Sciences
In chronological order of departure from physics.
Query: should Prigogine be included here?
1. A. J. Lotka Is Devoured and Transformed by Population Dynamics
2. Bob May Goes Native in Ecology
3. Gene Stanley Invests Himself in the Stock Market Really Being a Polymer
4. Per Bak and the Career of Self-Organized Criticality
5. Constantino Tsallis and the Career of Non-Extensive Entropy
• Notice that Tsallis, even more than Stanley or Bak, is able to pitch his work directly to the community of physicists interested in complex systems.
There's a progression over time, whereby what these scientists do comes more and more to be seen as part of physics, and their writings can be aimed at, and read by, other physicists. Tsallis can more or less ignore what people from other sciences think!
3. Simple Models of Complex Systems, 1985--2000
1. The Evolution of Simple Models of Evolution
2. Econophysics
• The Hunt for Fat Tails
• Modeling Markets
• Drinking Games
3. Physicists on Language and Information
4. Scaling in the Blood, or, Galileo Was Wrong
5. Networks
6. Neurons, Real and Fake
7. Miscellanea
• Models of war, social influence, ...
4. Results and Prospects
1. The State of Complex Systems
2. The Moral of the Story
• Success stories: either (a) methods for data analysis, without models (e.g., attractor reconstruction), or (b) applied to things which are toy models, like artificial neural networks. Exceptions (possible): biological scaling and networks. (Is the network stuff really just math which mathematicians didn't happen to do?)
• Physicists are acting as applied mathematicians. Partly a natural upward drift --- applied mathematicians, themselves, drift into pure math, and pure mathematicians into logic and category theory (while category theorists, of course, map into themselves).
• There is a legitimate role for scientists specializing in the construction and analysis of mathematical models. People who want to do that are probably not best served by first getting a degree in physics, though there doesn't seem to be a better discipline yet. Physics needs to shrink, and modeling needs to emerge.