Wednesday, February 28, 2007

This Year’s Model I

I’ve been asked to write a few things about models and modeling, as that is (in theory at least) my core area of expertise. Before I get to the cool stuff, the computer simulation models that I’ve spent at least 25 of the last 35 years working with, I’m going to “go meta” for a bit.

The word “model” in the most general sense in science is very, very broad, and can be applied to almost anything. In fact, any abstraction is a “model” of something else, as is any analogy, simile, theory, or description. This almost, but not quite, makes the general sense of model so general as to be useless.

At this high level of abstraction, even the idea of “fact” becomes a theory. Indeed, it’s pretty hard to find an instrument or even a sensory experience, that doesn’t depend upon some theoretical construct for its meaning and interpretation. So “meaning” becomes a model, as does “language,” and “thought.” That’s what Plato was getting at when he was babbling about shadows on the cave wall. Reality itself is a theoretical construct.

In the recent past, Steve Gillette and I have had a few back and forths that touch on this area when we were discussing “brute facts” vs “institutional facts.” That division is similar to the “analytic” vs “synthetic” distinction suggested by the Positivists (who rewrote a page out of Kant). It’s also possible to map “analytic” to “deductive” and “synthetic” to “inductive.” The basic idea is that there are certain sorts of propositions (or facts) that are derived from a priori definitions, using logic to derive propositions of greater and greater complexity. These are analytic/deductive/institutional propositions/facts. Then there are other sorts of propositions/facts that must take the sensory world into account in their formulation. These are synthetic/inductive/brute facts.

One of the big arguments that this sort of talk produces is that it suggests that mathematics is an invention, similar to, for example, the law, or musical theater. Some mathematicians claim instead that mathematics has objective reality. I’ll only note that the best mathematician I know personally is of the strong opinion that mathematics is a human invention.

Grind this grist fine enough and you get back to basic epistemology and questions about the nature of reality. Fine. I consider my position on the matter to be entirely defensible, but recognize that it seems to be hard to get across to some people. I once had a fairly lengthy online exchange with someone where I was trying to get across to him the difference between an abstract concept that the concrete reality that the concept might cloak. Consider a three-sided load bearing structure that we call a truss. One might very well locate a fossil, or a geological formation that can be said to be a three-sided load bearing structure. Was it a truss a million years ago? He insisted that it was, completely oblivious to my suggesting that “truss” is a human invention, and without humans, no truss exists.

I know, I know, a pointless argument, except maybe not, because it is a trap to believe that concepts exist apart from the conceiver. The sentence “If a tree falls in the forest, does it make a sound?” is a Zen koan, actually, and, contrary to common belief, koans often have answers. In this case, the answer is, “The one I’m thinking of did.”

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