Philosophia Naturalis 13 is up at the Cocktail Party, which makes me think about economists again...
A lot has been said about the dismal science, both its applications, and the inapplicability of its grander theorizing.
Which is actually rather unfair, economics is, in parts, well founded quantitative and based on well defined assumptions that are tested both by observational data and microeconomic experiments.
I conjecture that much of the problems of economics may come from the fact that most of the people who "do" economics - whether by trying to apply academic economic theory, or by being participants in the economy - only comprehend the economics at the level of first order perturbation theory.
This seems particularly true of "econ 101 libertarians" and applied business studies types, who seem have turned off their brain input somewhere after "rational economic actor" and before "externalities", but the short version of their strength, and limitation, seems to boil down to seeing economic acts as linear perturbations on a fixed background - they don't tend to experience or understand backreaction, global optima or non-perturbative effects.
Problem is, that a lot of the important stuff in the long term is non-perturbative.
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Although I've only coauthored a few refereed Mathematical Economics papers, and a couple on the arXiv, I don't think it's fair to damn Economnists as a class just because some of the stupid ones are stupid.
I mean, that would by like dismissing Science Fiction writers as a class because some Saturday Morning animation writers don't do good world building.
There are Economists who actually understand aspects of the Real World, culturally, Financially, managerially, and with good mathematical models.
Of course they are in the minority.
Sturgeon's rule applies in this discipline too.
Some of my very best and closest friends are economists...
They understand. Or maybe they'll disown me, I'll find out soon I guess!
But I think my comments also holds - in "physics speak", most economics is done at the first order perturbation level - the backreaction problem is hard, doubly so when the subject of the matter can read your paper predicting their behaviour and change their mind out of pure spite...
I like your analogy to the backreaction problem. That's why John Forbes Nash, Jr., made such a tremendous contribution. The calculation of Nash equilibrium in economic games where indeed the players know what you think they are doing in response to what you think they think, and so forth to infinity.
Such systems exhibit chaotic dynamics in games as simple as Rock Paper Scissors (multiple rounds, with learning), as the folks at the Santa Fe Institute proved.
The problems of which series converge, which diverge, and which lead to scale-free behavior, i.e. true phase changes and criticality, are interesting.
My primary Economics coauthor HATES the term Econophysics, but the very fact that this term has appeared in Physics Today suggests that your analogy is not too far from the truth.
The Black-Scholes equation won a Nobel prize deservedly, because it allowed financial derivatives to be evaluated. But what happens to the derivatives market when every firm uses that in their modeling? We arrived some years ago at that position. Financial instruments grew more complicated, and hedge funds absorbed a trillion dollars, and did not fit the market when every hedge fund understood the same equations in the same "quants."
So now the USA and the world economies are poised on a precipice.
Black-Scholes just assumes that a variable "volatility" can be measured and plugged in. But where does volatility come from? And what if it shows long term autocorrelations? And what if it exhibits heteroskedacity, with the parameters of a stochastic model unexpectedly changing?
Hello, here we are.
Exactly, Renaissance and Goldman Sachs et al are large enough to be non-perturbative, but far worse than that, the "large N" of other traders are using correlated strategies, so the volatility has strong inbuilt autocorrelations that make the market non-perturbative.
They've programmed "panic" into the trading algorithms.
Although I see on Hsu's blog that some clever clogs have already set up new hedge funds that hedge failure of classical hedge funds! Which may provide negative feedback, or wild oscillations if there is phase lag ;-)
Interesting times.