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.

There is substantial evidence to suggest that the theory of “space” as a continuous object is incorrect. There is now much work being done in loop quantum gravity to show that space does have irreducible pieces and that objects move through space discretely and not continuously. So in that sense, objects would not have continuous curves.

Furthermore, from a statistical physics perspective, while the curves may even be continuous they are certainly not smooth. The motion of particles, though appearing smooth on time scales we are accustomed to observing, are actually very rough and jagged, sort of like Brownian motion, as a result of millions of discrete bombardments from smaller particles.

Now, I don’t pretend to be an expert on Economics, so I won’t try to assess whether or not Physics Envy is common problem in the field. From what I do know about the subject, though, I don’t think that there is any question that there are many useful - even essential - uses for mathematics. There’s also some definitely some potential for Physics Envy abuses, but my impressions are that Economists generally do a decent job of policing themselves - most of them seem to understand the mathematics they are using.