Talk on Economics, Beauty, and Math

Those of you interested in the recent debate over math, beauty, economics, and Paul Krugman, and who are in New York on Oct 5 might be interested in a talk by Eric Weinstein at Columbia:

We will be taking a position opposite to the Claim of Nobel Laureate Paul Krugman:

“As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.”

It is our claim that in Economics as well as Physics, Mathematics and Biology, Elegance has been an essential guide to understanding how to properly construct the foundations of theory and that the true problems of the field lie elsewhere. The argument will be developed that, counter to expectation, many of the coming advances needed to repair economic theory will bring it into meaningful contact with the elegance of Field Theory, Natural Selection, Gravitation, and Soros’ Theory of Reflexivity.

Reflexivity is probably the one subject on this list that readers of the Quantum Pontiff aren’t familiar with 🙂 Actually this is not true: if you know the Kochen-Specker theorem you are well on the way of accepting the gospel according to the palindrome!
Oops 9/16/09 update: Forgot to include the link to the talk and the time/location Oct 5, 2009 6-7:30pm, 412 Schapiro CEPSR, Davis Auditorium.

13 Replies to “Talk on Economics, Beauty, and Math”

  1. Gee … I love elegant math and beautiful algorithms as much as anyone … and for sure these are the best-and-only foundations of disciplines like math, physics, and chemistry.
    But c’mon … how likely is it that math and algorithms could ever be the foundation of economics?
    The reason is simple: electrons (and integers) are all alike and have no morality. People are all different and *do* have morality. That is why pretending that people are like electrons is fundamentally wrong-headed … and worse … lends itself to abuses of political and economic power.
    For young people particularly—whose brains are still developing—abusive over-indulgence in econometric analysis can lead to compulsive behaviors and ideological fantasies.
    For mature researchers, whose use of econometric analysis is moderate, purely recreational, and solely for personal consumption — there’s no problem! 🙂

  2. Electrons may not have morals, but I’ve yet to meet one who isn’t as complex as most human beings in their interactions with the economic system. You, John, of all people should know that the real world is more messy, complex, and dirty than any theorist could ever imagine. Yet ideas straight out of field theory ARE applicable to these systems (TQFT and fractional quantum hall effect anyone?) We like to think we are “complex” and “deep” but…really? That’s some pretty extreme exceptionalism. Me I don’t think I’m daring enough to make that assumption cus, well, cus I sometimes look up at the sky (to quote van Gogh.)
    As to what you do with the resulting science, politically, I don’t see this is any different than any other such question faced by nearly every field of science. Note that I’m not saying that _past abuses_ aren’t important, I’m just saying your blaming the messenger. Isn’t it more important to strive for the ethical application and not to stop the discussion cold with anti-scientific arguments?

  3. Sorry Dave … my last two paragraphs were satirical … I should have linked to a Nancy Reagan “Just say no to econometrics” button!
    You are absolutely right that simple, elegant fundamental equations can predict hugely complex behaviors … and right also, that this is equally true in both economics and in fundamental science … and right also that we have a lot to learn about *both* the fundamental equations *and* the complex models that we can build upon them.
    David E. Shaw’s work in recent years is an outstanding example … Shaw’s team uses a lot of the same equations (perhaps even the same computer codes and hardware?) in (a) economic trading and (b) conformational biology.
    That these algorithmic tools can be misused is undoubtedly true … the dangers of misuse of economic codes are of course great … yet (IMHO) it is becoming apparent that there are even greater dangers in the potential misuse of conformational biology … and greater rewards too … and similarly great fundamental mathematical challenges, of course!
    David Shaw’s team understands this of course … and I think the appreciation is becoming widespread … that global economics and conformational biology are similarly the study of complex evolved systems … that embody wonderful mathematics … in which living person has a vital stake … and important moral issues are engaged.

  4. But c’mon … how likely is it that math and algorithms could ever be the foundation of economics?
    Quite likely, as Dave pointed out. The problem, which Krugman pointed out, is that economics has been in thrall to an elegant but wrong theory. Physics, too, has had its share of elegant but wrong theories, which are replaced once enough evidence has accumulated to disprove them, or when an even more elegant theory which better explains the evidence comes along. In economics, it’s almost impossible to do controlled experiments, and the more elegant and better theory hasn’t been developed yet (and may not for years or even decades). That doesn’t mean that no such theory can exist.
    String theory has been criticized on similar grounds. Smolin’s Not Even Wrong argues that string theorists have been working on mathematically elegant theories which have yet to predict the result of an experiment. We don’t yet know that string theory is wrong (unlike the strong form of the Efficient Markets Hypothesis, which makes the spectacularly incorrect prediction that asset bubbles cannot occur in a loosely regulated economy), but so far there is no experimental evidence supporting string theory.

  5. Isn’t it more important to strive for the ethical application and not to stop the discussion cold with anti-scientific arguments?
    First you have to make sure that the resulting science actually matches reality – which is where a lot of economics (the part of it that I see used and talked about) falls short. Seems to me economists are making pronouncements based on their models before checking to see if those models reflect reality.
    The math of a functional economic theory is likely to be beautiful (according to some, anyway), but I have my doubts that the current models of economics are any more accurate than physics by Aristotle (probably a lot less so, honestly).
    Shorter version:
    It’s the empiricism, stupid.

  6. Not to get too technical, but Princeton economist Yacine Ait-Sahalia has written an article Closed-form likelihood expansions for multivariate diffusions that directly illustrates the dovetailing of gauge-type invariances with state-space geometry (BibTeX).
    Although Ait-Sahalia’s discussion is strictly in the context of economics, his results are immediately relevant to practical QIT calculation; it is only necessary to cast Lindbladian processes (which have a gauge-type invariance) into Ito-Stratonovich form, and pullback the resulting stochastic dynamics onto a reduced dimension state-space having a Kähler structure.
    Ait-Sahalia’s geometric insights then provide key guidance in efficiently integrating the resulting dynamical equations (as summarized in this table).
    This is why I am entirely in Dave’s camp … fundamental mathematical insights *are* absolutely vital to practical progress in math, science, and engineering.
    @article{Ait-Sahalia:2008dn, Author = {A{“{i}}t-Sahalia, Yacine}, Journal = {Ann. Statist.}, Number = {2}, Pages = {906–937}, Title = {Closed-form likelihood expansions for multivariate diffusions}, Volume = {36}, Year = {2008}, note={Ait-Sahalia’s Proposition 1 (and its proof) provide key geoemtric insights into efficient integration of large-scale quantum spin dynamics}}

  7. Hi Dave—
    I suppose this isn’t too classy either, but looking at the talk announcement, my suspicions are raised by the tic of capitalizing the names of scientific fields and — especially subfields and plain ol’ nouns (Elegance). I mean, I tell people I’m a quantum physicist, not a Quantum Physicist. But I do want to find out what the clash between Obligate and Kayfabe science is about. I think Weinstein has worked on applications of gauge (shoot, I initially capitalized it!) theory in economics, which I don’t know about although it’s a topic Lee Smolin here at PI seems to think has something to it. Weinstein has spoken at PI quite a few times—the latest at a conference on “The Economic Crisis and its Implications for the Science of Economics”. The oldest video in this list might have the gauge theory / economics connections.

  8. I watched Eric Weinstein’s most recent talk at PI, “A Science Less Dismal: Welcome to the Economic Manhattan Project”. It comes across as an outline for a worthwhile project in interdisciplinary collaboration on economics, with briefest of introductions to some of the people and ideas that Weinstein envisions being involved in the project. His own work on valuing illiquid assets, and on gauge theory and prices, is given a few slides, but not enough to communicate much of its content as opposed to its subject matter, so I’ll have to go to the articles or earlier talks to see what he’s done. The principles of the collaboration seem laudable—especially confronting theories with reality. The most interesting methodological suggestion is “to use a small group of core tools (like DNA or fiber bundles) to avoid a baroque explosion of special cases.” In that case, it will obviously be of great importance that those tools be chosen well. This may well be where he parts company from Krugman’s statements about the need for “messiness”.
    I see from your earlier post on the Krugman article, Dave, that you’ve seen his earliest (of 6!) PI talks on gauge theories in economics. That’s probably next on my list to watch (or read the corresponding article).
    When I was reading about, and later doing grad school in, economics, inflation was incorporated into macro models in terms of simple phenomenological equations, like the “shifting Phillips curve”. I think these models worked pretty well at explaining the behavior of the macroeconomy, though I haven’t given that proposition careful scientific scrutiny to the level of writing an article about it. The “stagflation shows Keynes failed” business in the seventies/early eighties was preposterous and highly political, in my opinion. Seventies and early eighties macro history fits quite well with neo-Keynesian models.
    But I digress: the point I was going to make was that the phenomenological models that worked pretty well, but could perhaps use improvement, didn’t have a very clear “micro” basis. The phenomenology was that if you keep employment of economic resources above a certain “natural” level, you get inflation—possibly even increasing rates of inflation, if you attempt to keep employment too high for too long. Handwaving explanations involved “downward rigidity of prices”: for whatever reason—union contracts and pressure in the case of labor prices, other contracts written in nominal terms, perhaps, in other market, and just the fact that people “don’t like to drop prices”. Maybe Weinstein’s ideas about using gauge theory to understand inflation could help put some micro details into these handwaving explanations. If we’re lucky, maybe they could give some understanding of how these phenomenological relations between inflation and economic activity differ from time to time and place to place. It won’t be clear to me how this could be until I’ve read more articles and watched more talks, though… (re: “is anyone going to explain inflation without using gauge theory”)

  9. In seeking to better understand quantum simulation theory (which seems in essence to be pullback theory) I have been reading some of the literature of category theory, including the history of category theory.
    In this regard, Colin McLarty has written a very nice article titled The Last Mathematician from Hilbert’s Göottingen: Saunders Mac Lane as Philosopher of Mathematics
    McLarty’s article includes this passage:
    “Cohomology does not itself solve hard problems in topology or algebra. It clears away tangled multitudes of individually trivial problems. It puts the hard problems in clear relief and makes their solution possible. The same holds for category theory in general.”
    We can ask: what if we *did* have an economic theory that was possessed of the same austere elegance that mathematicians like Mac Lane and Grothendiek have infused into category theory?
    Such an elegant theory of economics would be very valuable, for sure. But on the other, perhaps it might not be all useful in grappling with the “tangled multitudes of individually trivial problems” that are the essence of real-life economic activity.
    Most often, in most disciplines of science and engineering, we seem to require *both* austere elegance (which however isn’t much use by itelf) *and* practical utility (which of course requires solid mathematical foundations.
    All of this is just an elaboration of common sense … the same common sense that Colin McLarty argues is the hallmark of category theory.
    Anyway, Colin McLarty’s article is highly recommended.

  10. One of the games that my brother-in-law would play at Goldman-Sachs was a simple cost/benefit model that is worth testing for convergence. The game is that I pay you $1 if a fair coin comes-up heads on the 1st toss. I pay you $2 if it comes-up heads on the 2nd toss, $4 if on the 3rd toss, etc. You’re going to get paid something. Now, how much will you pay me to play the game? In reverse, how much will you charge to let someone play you the game?

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