“’Physics envy’ – physics abysmally misconstrued!” – http://www.repiev.ru/articles/Physics-Envy.htm

You seem oblivious to what the critics are actually saying. Which particular critics have you read deeply?

[quote]Our problems, when they occur, do not lie in our tools but in the quality of our ideas[/quote]

Exactly. But the emphasis on maths has allowed generations of PhD students to get their doctorates without ever having to even understand the arguments against economic orthodoxy (the Monetarist-Neo-Classical, psuedo-Keynesian orthodoxy). The emphasis on maths allows economics the pretence of science. One can teach economics without really having to get to grips with ones own critics (the heretic economists). When Paul Krugman gave a lecture at the LSE recently guess how many LSE professors turned up to listen to him, refute him, etc? Precisely zero. They live in a bubble universe.

[quote]Critics of mathematics in economics, however, rarely come to grips with these specific issues of problem solving and understanding[/quote]

Having studied maths and science I can tell you that, based on false or incoherent axioms you can do ‘anything’ with maths (or science). Nothing you do will be of any use but you could, easily spend your life doing it. That’s why foundations are so important in science. Even today, we spend so much time and energy trying to get the foundations of science right. The critics of economics are saying that economic orthodoxy (such as the 64 professors who ignored Krugman when he journeyed to visit them, at their own manor) have fraudulently presented their subject to the rest of us.

I advise you to spend time studying the philosophy of science. Einstein’s critique of Newton, especially the history leading up to it is particularly useful and the reformulated axioms the lead to his Special and General relativity is illuminating. No need to actually understand relativity for this. All you need to know is why Newton was ‘wrong’.

Economics is at a pre-scientific stage. If it actually admitted as much I would give it far more respect. Outside of a scientific discipline I find it impossible to see any use in mathematical models. That’s the critique being levelled led at economics. ‘Physics envy’ is just a metaphor.

In fact, if a theory is strong enough on that dimension, is also tractable, and produces intersting results, we can bet heavily on its success even before empirical testing. Think about Shannon’s communication theory. The mapping is so clear between the theory and the systems it aims to describe that mathematical derivations are almost conclusive. An empirical “test” of the theory is silly. Close, but not quite as locked in, would be something like the arbitrage theory of options pricing cited in this thread many times already. The mapping isn’t as clear as in communications theory, e.g. because there are questions about whether you can at every moment execute the trades you need to make the arbitrage work, but the basic structure is pretty compelling and maps pretty clearly to actual financial markets.

So a good filter in doing any kind of theory is to economize on the number of variables whose defintion and conceptual measurement are equivocal or ambiguous. (I’m not inveighing against hidden variables, just ones whose nature isn’t clear in your own mind.) You often can’t eschew these messy variables completely, at least at first, but it’s a good idea to treat them as having a high shadow price.

Goddard’s rockets occasionally exploded on the launch pad; that hardly negates his contributions to science.

I am a biologist who makes theories about gene regulation. I spend a lot of time telling biologists NOT to have physics envy: The set of things that can be calculated in physics is smaller than one might think, and often involves very specialized situations. For example, the Lamb Shift caluculation, accurate to about one part in 100 million, applies to a single hydrogen atom, but hydrogen atoms come in pairs, not one at a time. In biology, on the other hand, the genetic code is accuarate to about the level of the lamb shift calculation, is used everywhere, and is expressable
by a simple table without equations.

I think that the problem with math in ecomomics is not in the equations, but rather the state variables used in the equations. The varibles in a theory need to have a fairly fixed mapping to the real world. As a poster noted above, this works well in celestial mechanics,
where the absurd approximation of representing an
entire planet by a point with mass but zero size works well because the distances between planets are large compared with their diameters. This breaks down if two planets collide, obviously. In biology it’s trickier—
sometimes you can use chemical concentrations but sometimes you have to do statistics on individual atoms.

In economics the state variables represent human beings. If they are “well-informed” and “rational” then average behaviors follow certain laws. Sometimes, however, an individual knows something no one else knows or does something crazy or unpredicable that has major consequences. For example, it seems to me that a complete theory of economic dynamics must predict the future evolution of economies, but such efforts (Malthus and Marx?) have failed because ultimately economics couples to the whole of human activity.

I think the problem is that the achievements of physics (or their technological byproducts) are to some extent accessible to the man in the street, whereas to appreciate the achievements of economics you have to more or less become at least an amateur economist, at which point the sunk costs effect kicks in and your inclination to take potshots at the foundations of the discipline is probably going to decline.

My own difficulty is that in the hands of some, economics seems to be used largely to provide “scientific” justification for various ideological positions, though of course it’s more palatable when I happen to like the ideology concerned.

Cordially,

d-squared… Thank you. I didn’t realize that Merton was the one who helped Black; I had also long since forgotten that Ito’s lemma was involved.