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.
First, complex systems theory has very little vocabulary/ideas of their own. What few they do have (e.g. “emergence”) are not especially useful yet, because there’s not much substantive theory backing them up yet. They’re basically just pattern matching, but we don’t yet know whether the patterns correspond to any common underlying structure.
Second, because complex systems theory draws from so many other areas, it is useful as a gateway into a bunch of other fields. In studying the vocabulary/ideas of “complex systems theory”, you’ll mostly be studying tools from other fields which aren’t really specific to complex systems, but those tools are really general and interesting. It’s especially useful in that complex systems theory tends to draw on the most general tools from other fields, so you’ll end up learning tools with quite wide applicability.
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.
How useful is their vocabulary and their set of ideas to understand the real world, not as a professional researcher, but just as a rationalist?
Two answers to this.
First, complex systems theory has very little vocabulary/ideas of their own. What few they do have (e.g. “emergence”) are not especially useful yet, because there’s not much substantive theory backing them up yet. They’re basically just pattern matching, but we don’t yet know whether the patterns correspond to any common underlying structure.
Second, because complex systems theory draws from so many other areas, it is useful as a gateway into a bunch of other fields. In studying the vocabulary/ideas of “complex systems theory”, you’ll mostly be studying tools from other fields which aren’t really specific to complex systems, but those tools are really general and interesting. It’s especially useful in that complex systems theory tends to draw on the most general tools from other fields, so you’ll end up learning tools with quite wide applicability.