Reddit mentions of COMPLEXITY: THE EMERGING SCIENCE AT THE EDGE OF ORDER AND CHAOS

Well this thread title drew me like a hunk of iron to the world's biggest magnet.

The short answer to the title question is "no, except maybe in some very trivial sense." The longer answer is, well, complicated. Before I ramble a little bit, let me say that we should distinguish between the rhetorical and (for lack of a better word) "metaphysical" interpretations of this question. In many cases, the language used to describe some theory, problem, proposal, or whatever is indeed unnecessarily complicated in a way that makes it difficult to communicate (some parts of the humanities and social sciences are particularly bad offenders here). That is indeed a problem, and we should strive to communicate our ideas in the simplest language that's appropriate for the audience we're talking to. I take your friend's thesis to be a bit more substantive than that, though: he's claiming something like "all big messy systems are really just lots of small simple systems, and we can learn everything we need to know about the world by looking at the small simple systems." That's the viewpoint that I think is mistaken.

I think it's really important to distinguish between complicated and complex, both in the context of this discussion and in general. Lots of things are complicated in the sense of being big, having lots of moving parts, difficult to understand, or exhibiting nuanced behavior. A box of air at thermodynamic equilibrium is complicated: it has lots of parts, and they're all moving around with respect to one another. Not all complicated systems are also complex systems, though, and understanding what "complex" means turns out to be really tricky.

Here are some comparisons that seem intuitively true: a dog’s brain is more complex than an ant’s brain, and a human’s brain is more complex still. The Earth’s ecosystem is complex, and rapidly became significantly more complex during and after the Cambrian explosion 550 million years ago. The Internet as it exists today is more complex than ARPANET—the Internet’s progenitor—was when it was first constructed. A Mozart violin concerto is more complex than a folk tune like “Twinkle, Twinkle, Little Star.” The shape of Ireland’s coastline is more complex than the shape described by the equation x2 + y2 = 1. The economy of the United States in 2016 is more complex than the economy of pre-Industrial Europe. All these cases are relatively uncontroversial. What quantity is actually being tracked here, though? Is it the same quantity in all these cases? That is, is the sense in which a human brain is more complex than an ant brain the same sense in which a Mozart concerto is more complex than a folk tune?

These questions are extremely non-trivial to answer, and a very large number of whole books have been written on the subject already; so far, there's no universally accepted consensus of what makes complex systems special, or how to measure complexity in the natural world. There is, however, a growing consensus that P.W. Anderson was correct when he wrote in 1972 that "more is different": in many cases, systems consisting of a large number of relatively simple components interacting in relatively simple ways can display surprising, novel behavior. That's characteristic of complex systems: they behave in ways that we wouldn't expect them to (or even be able to deduce) based on an examination of their constituent parts in isolation from one another.

Complex systems often show interesting patterns of behavior that cut across scales of analysis, with their dynamics at one scale constraining the dynamics at other scales (and vice-versa). This sort of "multiscale variety" has been used to develop a mathematical theory of strong emergence, demonstrating how it can be the case that more is different. I've called this quality "dynamical complexity," and defined it as a measure of the "pattern richness" of a particular physical system: one system is more dynamically complex than another if (and only if) it occupies a point in configuration space that is at the intersection of regions of interest to more special sciences. For instance, a system for which the patterns of economics, psychology, biology, chemistry, and physics are predictively useful is more dynamically complex than one for which only the patterns of chemistry and physics are predictively useful.

The notion of dynamical complexity is supposed to correspond with (and give a physical interpretation for) the formalism of effective complexity, which is an information-theoretic concept developed by Murray Gell-Mann at the Santa Fe Institute. Effective complexity is grounded in the notion of algorithmic information content, and tracks the "amount of randomness" in a string, and how any non-randomness--information--was produced. A key feature of dynamical complexity is that the total "information content" of a physical system--the total number of interesting patterns in its behavior--may be perspectival, and thus depend on how we choose to individuate systems from their environment, and how we demarcate collections of microstates of the system into "relevantly similar" macrostates. Those choices are pragmatic, value-driven, and lack clear and uncontroversial "best answers" in many cases, contributing to the challenge of studying complex systems.

As an example, consider the task of predicting the future of the global climate. What are the criteria by which we divide the possible futures of the global climate into macrostates such that those macrostates are relevant for the kinds of decisions we need to make? That is, how might we individuate the global climate system so that we can notice the patterns that might help us predict the outcome of various climate policies? The answer to this question depends in part upon what we consider valuable; if we want to maximize long-term economic growth for human society, for instance, our set of macrostates will likely look very different than it would if we wanted to simply ensure that the average global temperature remained below a particular value. Both of those in turn may differ significantly from a set of macrostates informed by a desire to maximize available agricultural land. These different ways of carving possible future states up into distinctive macrostates do not involve changes to the underlying equations of motion describing how the system moves through its state space, nor does the microstructure of the system provide an obvious and uncontroversial answer to the question of which individuation we should choose. There is no clearly "best way" to go about answering this question.

Compare that project to modeling the box of gas I mentioned earlier and you can start to see why modeling complex systems is so difficult, and why complex systems are fundamentally different. In the case of the gas, there are a relatively small number of ways to individuate the system such that the state space we end up with is dynamically interesting (e.g. Newtonian air molecules, thermodynamic states, quantum mechanical fluctuations). In the case of the global climate, there are a tremendous number of potentially interesting individuations, each associated with its own collection of models. The difference between the two systems is not merely one of degree; they are difference in kind, and must be approached with that in mind.

In some cases, this may involve rather large changes in the way we think about the practice of science. As /u/Bonitatis notes below, many of the big unsolved problems in science are those which appear to "transcend" traditional disciplines; they involve drawing conclusions from our knowledge of economics, physics, psychology, political science, biology, and so on. This is because many of the big unsolved problems we're concerned with now involve the study of systems which are highly dynamically complex: things like the global economy, the climate, the brain, and so on. The view that we should (or even can) approach them as mere aggregates of simple systems is, I think, naive and deeply mistaken; moreover, it's likely to actually stymie scientific progress, since insisting on "tractability" or analytically closed models will often lead us to neglect important features of the natural world for the sake of defending those intuitive values.

Some good readings from the University of Cambridge Mathematical reading list and p11 from the Studying Mathematics at Oxford Booklet both aimed at undergraduate admissions.

I'd add:

Prime obsession by Derbyshire. (Excellent)

The unfinished game by Devlin.

Letters to a young mathematician by Stewart.

The code book by Singh

Imagining numbers by Mazur (so, so)

and a little off topic:

The annotated turing by Petzold (not so light reading, but excellent)

Complexity by Waldrop

The fact that you are still operating under of the assumptions that the Chicago and Austrian schools provide shows that your personal understanding of economics is at least 60 years old.

Get a book on complexity theory. If you are the practical guy you claim to be, I'm sure you will enjoy it.

Here's one for the layman: http://www.amazon.com/COMPLEXITY-EMERGING-SCIENCE-ORDER-CHAOS/dp/0671872346

Her's one if you are into math:
http://www.amazon.com/Computational-Complexity-A-Modern-Approach/dp/0521424267/ref=pd_sim_sbs_b_2

To put it simply, We could argue for years about the examples you gave simply because the complexity of those situations allows for a multitude of different, yet similarly rational, arguments (a fact which, as an admirer of the Austrian school, I'm sure you can agree with). There is a great little bit on Wikipedia's page on economic models (http://en.wikipedia.org/wiki/Economic_model) - under the heading "Are economic models falsifiable?":
The sharp distinction between falsifiable economic models and those that are not is by no means a universally accepted one. Indeed one can argue that the ceteris paribus (all else being equal) qualification that accompanies any claim in economics is nothing more than an all-purpose escape clause (See N. de Marchi and M. Blaug.) The all else being equal claim allows holding all variables constant except the few that the model is attempting to reason about. This allows the separation and clarification of the specific relationship. However, in reality all else is never equal, so economic models are guaranteed to not be perfect. The goal of the model is that the isolated and simplified relationship has some predictive power that can be tested, mainly that it is a theory capable of being applied to reality.

So the point of an economic model, indeed the point of any model is to, in the words of Wolfram, "Examine certain essential features of a system and idealize away everything else." Models are, by their very nature incomplete. There is also an infinite number of possible models, each with a varying degree of accuracy. With these two points in mind, it seems foolish for one to plant a stake in the ground at any one of them and say, with certainty, that this one is the best one. It is also similarly foolish to ask others to provide, immediately, models which will yield better results in every standard, or else you will go back to the old ones. Unfortunately, progress is made through trial and error, not sitting at a desk with head in hands.

It sounds like you might have a leg up on the "absolute beginner," but these were the books that helped me get my head around some of the basics: (using Amazon preview links for samples of the first two)

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• Melanie Mitchell's, "Complexity: A guided tour"
  
  • https://read.amazon.com/kp/embed?asin=B002SAUBWC&preview=newtab&linkCode=kpe&ref_=cm_sw_r_kb_dp_.oR1DbQ3WVQ4G
    
• Steven Johnson's "Emergence"
  
  • https://read.amazon.com/kp/embed?asin=B008TRUBLY&preview=newtab&linkCode=kpe&ref_=cm_sw_r_kb_dp_FqR1DbTYAS5TK
    
• Mitchell Waldrop's "Complexity" (for a more narrative approach.)
  
  • https://www.amazon.com/dp/0671872346/ref=cm_sw_em_r_mt_dp_U_ArR1Db8CJ1PHP
    
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    I second looking into the Santa Fe Institute and their free online courses.

You might post these singly. There is a lot of room for discussion in each one.

Your last two caught my eye. I suggest, if you have not read them, two books simply named Complexity and Emergence.

Happy Cakeday.