JM: Agreed that the use of the model "says nothing" about cause. (Did I ever say it did?)
I don't agree that use of the model is an attempt to find "the invisible hand of one facet of human history." Some people who use such mathematical models may make such claims, but I don't know we should accept those claims, without further facts and arguments. The ideological claims made by some people who use mathematical models should be judged with high-level of skepticism. But that does not mean that the use of a mathematical model is not interesting or that the correlation of the Gibbs distribution with wealth distribution in various societies would not be significant. If the correlation holds it is non-trivial on its face.
A mathematical model is not a theory, in and of itself, but can only be an aid to theory making. Sometimes mathematical models may point to a phenomena in the world that may not be theoretically understood. There is no clear theoretical understanding of why the Fibonacci numbers show up time and time again in nature. One assumes it has something to do with good "packing" and "efficient" arrangement. But I can predict that the spirals of a sunflower will display some successive values of the Fibonacci sequence without ever seeing the sunflower. The Fibonacci numbers applied to natural circumstances is an elementary example of a mathematical model. I don't necessarily have to have a theory of why the Fibonacci numbers appear over and over again in nature in order to show that the model allows me to observe a phenomena that may be significant. The problem is that we don't know _how_ significant such a model might be unless the use of the model is theoretically informed. (See _Topics in Mathematical Modeling_ K. K. Tung)
_If_ and only _if_ it can be shown that wealth distribution can be modeled by the Gibbs distribution in many diverse societies, then, I think a good conclusion would be, that this would be an interesting observation that probably deserves an explanation. (In my original question about this study I was proposing that we take the above "If and only if" as a counterfactual and then try to understand the implications. But most people seem to assume that I was going ga-ga over the study.)
As far as Smith's "invisible hand" is concerned (along with many similar Hegelian notions) it is a pre-thermodynamic notion for self-regulatory and homeostatic concepts, such as negative and positive feedback, etc. But when using a mathematical model such as the Gibbs distribution, such concepts as defined by thermodynamics _are precisely what are at issue_. It is this and only this that would make the findings interesting and possibly unexpected. It is precisely to such notions of feedback, etc. that is implied by the Gibbs distribution. For you to tell me that somewhere here there is an "invisible hand" operating in a model that applies to the Gibbs distribution to empirical evidence is only telling me that a thermodynamic mathematical model leads backward to a inchoate notion that was a precursor to thermodynamic thinking.
But let me emphasize, there is no implied theory, cause or explanation in the result that finds that in societies wealth distribution matches the Gibbs distribution. What would make the finding interesting or unexpected, is if it is both consistent and true among many diverse societies, _and_ not true among some number of other kinds of society. Then one might be able to conclude that there must be some kind of "regulatory" mechanism at work "somewhere". The regulatory mechanism, whatever it might be, does not necessarily have to be "invisible".
Jerry Monaco
> http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
> The Unreasonable Effectiveness of Mathematics in the Natural Sciences by
Eugene
> Wigner
>
> So why should we be surprised about the mathematizability of social
phenomena
> with all the attendant failures over the centuries?
>
> Cue to Ted Winslow on the virtues of anti-formalism in political economy.
>
> Ian
>
>
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