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Thursday, May 07, 2009

Economics, ant farmers and free will theorems

Wow, it's been almost a week since my last post. I was pretty busy at the Perimeter Institute -- my brain is occupied trying to digest all the new things I've learned :-)

The conference had its origins in an essay Can science help solve the economic crisis? written by several of the organizers. The essay received responses from several prominent thinkers, and led to an exchange between Stanford economist Paul Romer and mathematician turned quant Eric Weinstein (see further down the page at the link above). Romer agreed to debate Weinstein, but then failed to show up! [Note added: in a private communication to me, Paul Romer writes that there was a misunderstanding and he never agreed to participate in a debate.]

The meeting went full speed from 9 AM until late at night for four days. The attendees were a mix of theoretical physicists (with particle physics and complexity theory, especially the Santa Fe Institute, well represented), practitioners from Wall St. (often from a math or physics background), academic economists (Barkley Rosser, Richard Freeman, etc.) and evolutionary biologists. See here for video recordings of talks. There were many good talks but I especially recommend Doyne Farmer's for the physicist's complex systems view of economics.

Too much ground was covered for a short summary, but one area of interest for almost all attendees was the possibility of going beyond the neoclassical paradigm via simulations of interacting agents. Examples of such simulations were discussed in several of the talks, including by Santa Fe "ant farmers" Bruce Sawhill and Jim Herriot, who used agents to model air traffic for the ambitious DayJet startup (see here and here).

The technology is certainly there to do some massive, quasi-realistic simulations of an actual economy (as opposed to an isolated financial market or sub-economy). The main problem, which wasn't given as much attention as I might have liked, is that the results are limited by the quality of the individual agents, who must have at least rudimentary learning capabilities to be realistic. Hence one is led full circle back to problems related to AI, machine learning and even psychology or cognitive science.

When I wasn't at the conference I managed to have several interesting physics discussions. Below are links to some recent work by John Conway and Simon Kochen that came up in two separate conversations I had at Perimeter -- one with Rob Spekkens (he and I were discussing related issues, although he didn't mention these papers specifically) and with Nima Arkani-Hamed, who was visiting from IAS.

The Free Will Theorem

On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications.

See also the Strong Free Will theorem.

I feel the name of the theorem is a bit misleading, but inevitably so as it is quite difficult to define free will. The main feature of the papers is the great clarity of thought and presentation. In content, they are not so different from the older GHZ result which was formulated in terms of what the authors called local realism. To be honest I don't quite agree with Conway and Kochen's interpretation of their own results -- it's obvious that the results are easily consistent with many worlds quantum mechanics, which does not (at least from my spacetime perspective) allow for free will.

Here are 6 lectures on the theorem and related topics, given by Conway recently at Princeton. See also 'tHooft's response to their result.

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