Music, molecules and misanthropy (econophysics part 1)
I make no secret of my disdain for “social scientists.” Most social science is just some guy telling you a story, and pretending to be a big shot. It isn’t much different to me than some ancient bearded fellow at the campfire explaining lightning as sparks from Thor’s hammer. Economists shouldn’t be so bad. They have actual numeric data, data on the economy itself, financial data and individual data. They have grand theories about how the world works. They should be able to do something. But their ideas usually have the substance of political ideology. If they’re feeling particularly ambitious, they’ll wire their idiot ideology up to some weaksauce math like Granger causality.
Physicists are people interested in modeling things from first principles. They occasionally try to come up with some more interesting models than professional economists have come up with thus far. For example, consider a bunch of people in an auditorium listening to some bad opera music. According to something like standard utility theory, each person in the audience will clap based on how much they individually enjoyed the opera. The collective clapping function is the linear sum of the individual clapping functions. If you believe standard utility theory, every individual in the crowd has N claps worth of utility in them, and will give those N claps according to when they precious well intend to clap and stop. Same thing with standing ovations.
Ever been in one of these audiences? If you have, and you paid attention, you’d notice that people mostly clap and stop clapping in total synchrony with people around them. Same thing with standing. Occasionally some brave person will stand prematurely, and the social forces in the theater will force him back down again. Then the damn fool will stand up again when the rest of the crowd tells him it is OK. Same thing with clapping, or stopping clapping. Some people will stop clapping before those around them do. They sit uncomfortably for a while, then they start clapping again, until everyone else around them decides to stop. You can also observe patterns and defects in the behavior of people in this social lattice: there may be a group on the right, or towards the front who are more enthusiastic or subject to peer pressure.
“people, or spin-1/2 particles? hard to say from far enough away; everything looks small”
As it turns out, this behavior can be modeled pretty well using the ferromagnetic random field Ising model; a model which derives magnetic properties based on how microscopic spins in a substance work and interact with each other. In a ferromagnet, such spins have what amounts to peer pressure from exchange forces arising from the Pauli exclusion principle. A random field is added to each spin location to give a “tendency” to an individual clapper (or a spin). An overall driver field is added to provide a stimulus (this field can be 0, like when there is no external magnetic field, or they turn out the lights). And you can vary the strength of the “peer pressure” forces between spins or clappers. You can observe all the phenomena of ferromagnetism: domain walls, echos and hysteresis in the social lattice of the clapping opera fans. One of the interesting results of all this is that, in systems with a lot of peer pressure, you can get very abrupt drop off of clapping without a sharp change in the driver field (aka, how much the lights come on after the Opera). In fact, this is sometimes observed, generally in societies with strong peer pressures. Even when it is not abrupt, the drop off follows a pretty distinct scaling law. The details of such models are mostly in the network type, which, in the case of concert halls, is a square lattice, like the one shown below.
“+/- denotes opinion, color is tendency, and the big arrow an external driver field”
I’m not the only person to think of using Ising models to model crowd behavior; there is a small industry of econo-physicists who use such models. I originally read about it years ago in a book called Synergetics by Hermann Haken (a book which has been formative in my way of looking at the world). Not only are these kinds of models pretty good at reproducing phenomenology, as J.P. Bouchaud and friends proved, they’re even pretty good at reproducing actual numbers in more or less controlled experiments. They’re good at other things too; for example, such networks can reduce to Hopfield nets in some approximations. Which rather indicates they’re also useful for modeling how individuals make certain kinds of decisions as well. In other words; not only do you act like you are one of these spin-1/2 particles, in many situations, you act like your brain is made up of a scale free network of them. The same models can be used to model advertising or political campaigns, rumors, mass hysterias and fashion trends. And the numbers match up pretty well. I’ve seen the model applied to all kinds of things. I even know about a way of mapping it onto the Bass diffusion model.
“The end of a clapping session. Note rapid fall off; the black curve dies off faster than the echo time of the room it happened in, meaning social pressure to stop clapping travels faster than the speed of sound -I stole the graph from a paper by Q. Michard and J.P. Bouchaud” which is well worth your attention if you like this brief treatment
Consider all this the next time you are in a concert hall clapping for some trained baboon who thinks he is Ludwig von Beethoven, and the dimwits next to you are going into transports over what a wonderful performance it was (of course it was wonderful; they paid $300 for the seats!). Do you find yourself clapping because you think the monkey deserves it? Or do you find yourself clapping because you’re a molecule in a lattice of humanity? What does that say about you in the rest of your day to day life? How much of what you do and think you are is just because of social pressure? How many celebrated trends and movements, no more enduring and dignified than a spin-1/2 particle helplessly flopping around in response to other mindless spin-1/2 particles? Let’s face it; if you know someone else who has similar opinions to yours, if you run in a crowd, if there are others who are like you: this is probably why. You have to be pretty misanthropic to grasp this on an emotional level, but it’s something philosophers have been saying for centuries, and now a days you can actually write code which models it.
The implications for trading trends are obvious. Since people in “peer pressure” situations can change their minds abruptly, one needs to be ready for the flip over, or at least aware of the nonlinear conditions which can lead to an abrupt change in people’s positions. Are their hints as to when people are going to stop clapping? Well, let’s talk about that in part two. Professor Didier Sornette seems to think so. Sornette worked with the Random Field Ising model, but his fame has come from a sort of scaling law he has come up with dealing with trend followers and opinion bubbles.