September 25, 2003

Spontaneous Order

Posted by shonk at 11:08 PM in Geek Talk | TrackBack

That being said, I take some objection to Doss's comments and some of those made by Tim in response to the post. Quoth Doss:

So if those researching Sync want to have success when it comes to thinking, subjective creatures, they'd be best advised to, as Alfred Marshall suggested, "burn the mathematics."

And Tim rather sarcastically adds:

Also, I'd like to see the equation that represents humans evaluating a widget based on their subjective preferences. Please email me that when you get a chance.

In both cases, I find myself more in agreement with another commenter on Doss's post, Paul Philip, who contends:

I disagree with your automatic dismal of mathematics. Mathematics is just a tool, the problem is with the application. Alfred Marshall once said that biology was a better method than physics for the study of economics, the problem was that biological toolkit was too incomplete. Economists imposes the metaphor of a machine on economic activity because the toolkit was more complete at the time. The real problem is that the machine metaphor is very limited. There are problems in the science of self-organizing systems which require some complex mathematics. The results will be useful to the degree that the model encoded in the math fits with reality.


However, there are problems where math is the right tool. (Again, the problem in neoclassic economics ISNT the use of math, it is the limited metaphor imposed by the math - it is the inappropriate use of tools).

In fact, I might go even further than he does. First of all, I'd like to point out that, according to Strogatz, the study of spontaneous order is a subset of complexity theory, an offshoot of chaos theory. Now, I'm by no means an expert on chaos theory, but it is, without doubt, a field with heavy-duty mathematical content. Absent the tools of statistics and, oddly enough, topology, chaos theory could hardly have gotten off the ground (an excellent introduction to the ideas of chaos is Ian Stewart's Does God Play Dice?; note that even though it is introductory and intended for the non-specialist, Stewart's book has heavy mathematical content and an even stronger, invisible mathematical foundation -- and, of course, Stewart himself is a mathematician). So, to me, the notion that a study of spontaneous order can divorce itself from mathematics is absurd. Furthermore, I just want to point out that what is being called "mathematics" in these objections to mathematics is, primarily, statistics and calculus. Mathematics is a much broader field than these two particular areas and many would argue that statistics, while it uses mathematical tools, is actually a separate field. The fact that Statistics and Mathematics are different departments in most major universities is an exemplum of this idea.

Incidentally, I'd also like to point out that the Austrians' claim to be divorced from mathematics is totally absurd. Now, I am by no means an expert on Austrian economics, but, although the Austrians may dispense with the rather tedious and twisted equilibrium calculations that are the trademark of neoclassical economics and econometrics, I would contend that the Austrian approach is actually very mathematical. In fact, as noted by Philip above, neoclassical economics is actually more similar to physics, in my view, than it is to mathematics. After all, mathematics is decidedly not empirical. Mathematicians and Austrian economists, as I understand the field, argue a priori, starting with certain axioms and hoping to deduce certain theorems from those axioms. In fact, this deduction takes place under the auspices of logic which, though not always recognized as a part of mathematics, was certainly demonstrated to be equivalent by Russell and Whitehead. In any case, I think both Austrian economics (despite its flaws) and mathematics can be seen as a kind of meta-system, a way of thinking rather than a particular approach.

And, as I read it, evolutionary psychologists like Dawkins (ev. psych. is closely related to spontaneous order) do something similar. For example, in The Selfish Gene, Dawkins is largely examining certain phenomena (like charity) and and then trying to postulate simple principles which, if adhered to, would eventually evolve into the complex observed phenomena. These principles, though not axioms in the mathematical sense, have certain similarities.

My point is not to demonstrate that the study of spontaneous order is a mathematical discipline, nor that it should be. Rather, I just want to make the point that it has certain similarities to mathematics and, of course, will necessarily need to use mathematical tools in many instances. In fact, though I admit to not knowing nearly enough to be able to have any insights, it seems like mathematics, especially areas of study like graph theory and networks, might be able to shed some light on some of the applications of spontaneous order mentioned by Strogatz:

"In addition to the shear wonder of knowing why crickets chirp in sync or how the cells in your heart keep in step for three billion beats in a lifetime, there are applications in medicine and communications. For example, maybe you want to understand cardiac arrhythmias or how the brain works. There are also applications in super conducting and wireless communications,"

Is it clear yet that I'm procrastinating?