Locklin on science

Conservation laws in the Ising universe: Econophysics breakthroughs

Posted in econophysics by Scott Locklin on May 11, 2011

Toffoli is one of my favorite physicists. His research has been consistently excellent, and he has been a pioneer in a number of fields. Unlike most physicists, who are content to mine their little niche, Toffoli is a risk taker: a would-be conquerer of new worlds. As Borel said of Poincare; he is a conquerer, not a colonist. His latest paper has tremendous implications in all kinds of interesting areas in Finance, econophysics, sociology and machine learning.

Remember way back when I blathered about the random field Ising model as a model for collective human behavior about a year ago? Well, Toffoli has forged ahead and derived conservation laws for this model. What does this mean for the science of social groups? Well, it means you can derive global behavior from first principles, aka microstructure. Sometimes you’ll be able to derive microstructure from observed global behavior. All this has rather large implications in fields which map well onto the Ising model.

One of the fields, of course, is econophysics: a developing branch of science which studies group behavior in an economic setting. Another is sociology, of which econophysics is a subset. Finally, there is machine learning: the Hopfield net a sort of ur-version of the Neural net, is an Ising model. It’s also a special case of Bayesian networks.

What does this sort of thing mean? Conservation laws are more or less how physicists think about the world. Should we develop a more detailed mathematical framework for the Ising model, it may be possible to analyze all kinds of orderly behavior which takes place naturally in systems which are well modeled by the Ising model. It’s entirely possible there are all manner of conservation laws derivable about Ising models, based on their geometry and other detailed aspects of their structures.

This could mean humans may some day understand some of the spooky behaviors of crowds. We can already understand lots of these spooky behaviors via numeric simulation and thermodynamic arguments. Imagine knowing how to spook a crowd into doing what you want? OK, this is kind of science fiction stuff (though looking around … maybe not so much; the RFIM reduces to something real simple when the driver field, aka mass media, is really strong). Consider a more pedestrian application: how do you pick the right kind of machine learning algorithm for a given task? How does one architect a neural net in order to solve a problem? Conservation laws *will* help people to do this, based on the symmetries of the problems at hand. If this doesn’t result in some breakthroughs in machine learning, it’s because people aren’t paying attention.

On a more pragmatic level, trending systems can be understood in the RFIM framework, and energy/time invariance conservation makes these sorts of models much easier to think about. Gentlemen: start your automated theorem provers.

2 Responses

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  1. Phaedon said, on May 17, 2011 at 6:57 pm

    I’ve wondered if there is a similar use of Ising-type models for home prices. Houses exist roughly on a lattice, interact in price most strongly with nearest neighbors, etc. This seems to lend itself immediately to an econophysics line of investigation. In fact, I’ve noticed in my town, which is sort of benefiting from the increased hiring by the nearby university, its increased number of students who bring mommy and daddy’s money, etc. that the system is being driven through a critical point. And we get the expected scale invariance of domains and subdomains: overall a poor town, with a few good neighborhoods, which contain some bad blocks, which still have good streets except for a few rundown houses, etc.

    But much like the applause of an audience in a symphony hall, this problem is almost hand picked to have an Ising-type description. More complicated social phenomena don’t lend themselves to obvious physics analogies.

    • Scott Locklin said, on May 17, 2011 at 8:24 pm

      Well, they did pick it for that reason. Kind of neat it works so well. The same paper also applied the model to cell phone use diffusion in the general population, though I think they used a Barabasi-Albert (scale free/power law distributed nodes) lattice for that.

      I’m sure you could find price domains in housing prices. Almost worked for a group where this sort of data would have been available, and mentioned it to them. Probably scared them away with such mad scientist talk. I was particularly interested in the phase transitions. Will a neighborhood gentrify, or won’t it?

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