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What is complexity science? (Not computational complexity theory) How useful is it? What areas is it related to?

by crabman2 min read26th Sep 202010 comments


World Modeling

I've been reading "Playing with movement - Hargrove 2019". This book told me about "complexity science", which is a field which supposedly studies complex systems and it does it not by reductionism, but by looking at the system as a whole. It seems that some key concepts used in complexity science are: complex system, emergence, adaptivity, nonlinearity, self-organization, constraints, attractors, feedback loops. This book pitched an idea that with many complex adaptive systems, if you want the system to achieve a certain goal, it's bad to specify a specific plan for it and instead it's better to specify or build constraints under which the system, being adaptive and all, will achieve the goal on its own, supposedly in a more optimal way. Examples:

  • System: my body. Goal: get healthy by physical exercise. Specific plan: do strength training by doing specified sets of reps, using specific instructions on how to position my body. Alternative (constraints): live in such an environment that a lot of physical activity will happen naturally.
  • System: economics of a country. Goal: make it productive. Specific plan: central planning of what to produce, in what quantities and how. Alternative: free market economy, the organizations will behave however they want, and hopefully the whole system will act in an optimal way.
  • System: my body. Goal: eat healthily. Specific plan: write down a schedule of specific meals for the next year and eat them. A potential problem is I might miss something and that might lead to a lack of some nutrients. If instead I eat whatever I want, I will probably crave those other nutrients and hence I'll go and eat them. Obviously, this has downsides.

This idea seems plausible and very important. However, I've never heard of complexity science before. I've been following all kinds of links about complexity science trying to figure out what it is, what fields it's related to and what subareas it has. Also, I want to know how much of it is correct and how to apply it in the real world. Please help me figure out these questions. So, I guess I want a primer. Except I know that if I find a primer written by a complexity scientist, it'll claim that complexity science is the greatest invention ever. Instead, I want a sceptical primer which specifies the domain of applicability of complexity science and the domain of applicability of theory of complex adaptive systems. Below, I list some more specific questions.

  • It seems complexity science is also sometimes called complexity theory (different from computational complexity theory) and is somehow related to systems theory and complex systems science. Systems theory is supposedly a synonym for cybernetics. And maybe systems theory is related to systems thinking. How are all these areas related and to which does the study of complex adaptive systems belong?
  • Complexity science is somehow related to a bunch of math areas: chaos theory, differential equations, fractals, and cellular automata. But at the same time, it seems related to sociology, the study of human organizations, and has some applications to medicine and biology.
  • I want to read or study something to better understand the idea described earlier. I want to understand when that idea is true and when it's false. Any recommendations or thoughts? Is this idea also studied in other scientific fields?
  • In general, how awesome is complexity science? Is it almost entirely correct like math or physics? Or is it full of incorrect information like psychology and other social sciences? It is at least not 100% crackpottery, since some books are published by Princeton university press and Oxford university press.
  • Complexity science seems useful for rationality. Why isn't it popular on Lesswrong?

And here are some links and sources I found about complexity science:


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3 Answers

I can only give a very partial answer, focusing on the negative side. I hope someone more informed on the positive side can add their perspective.

"Complex systems" has always seemed to me to be a non-apple, and many of the words used around it, like "emergence", are synonyms for "magic". Real things are done under the umbrella of the term, but I see no coherence in the area that the umbrella covers. It is, however, a fertile field for generating popsci books.

BTW, "complexity theory" is also the name of a branch of mathematics that studies what resources (usually time and space) are required to solve computational problems, like sorting a list, or finding a 4-colouring of a given map. This complexity theory has nothing to do with the "complexity science" you are asking about. I mention it only to avoid a possible confusion.

I've studied the subject a bit - one book, a set of lectures, and generally keeping an eye on things from SFI for a few years (they're a reasonably-well-known institute specifically devoted to complex systems).

General summary:

  • Complex systems theory is mostly applied math, and the people doing it are mostly physicists and applied mathematicians. The results are almost always technically correct, although not necessarily interesting - it's rarely obvious how well the models generalize.
  • As of today, "complex systems theory" is really just a bunch of mostly-unrelated math topics (especially chaos, dynamical systems, networks, and the like) which seem to involve some qualitatively-similar behavior. The central question of the field is characterizing that behavior, and figuring out why it pops up in so many systems.
  • The "qualitatively-similar behavior" in question is basically: when systems are large (i.e. many interacting parts) and have no special structure (nonlinear, random network structure, etc), they tend to be chaotic but have some "simple" large-scale statistical behavior. What complex systems theorists would really like is a fully general theory of what large-scale behavior results from what systems.
  • That theory doesn't exist yet. It may not exist at all. So for now, the field looks like a bunch of people studying mostly-unrelated models, without much in the way of unifying results. They do at least share some common tools, though - statistical mechanics, scaling laws, and phase changes are major themes.
  • (Also, there's a bunch of popsci books/articles which are largely unrelated to the actual math, as one usually expects from such things. Just ignore those.)

In short: it's a field where a lot of people think there's something interesting to be found, but it hasn't been found yet.

Hey, I've become interested in this field too recently. I've been listening to the Jim Rutt show which is pretty interesting, but I haven't dived into it in any real depth. I agree that it is something that we should be looking more into.

I won't pretend to be an expert on this topic, but my understanding of the differences is as follow:

  • Systems theory tends to involve attempts to understand the overall system, while complex systems are much more likely to have emergent novel behaviour, so any models used need to be held more lightly/it's more likely that we have macro level trends that are there and we just don't know why
  • Cybernetics is mostly about control systems (classic example is the thermostat). Feedback loops are an important part of systems theory, but they are just one particular tool.
  • Regarding the breadth of applications, we can model dynamics in formal mathematical situations, then try to claim that similar dynamics occur in actual physical systems