Wednesday, February 28, 2007

This Years Model III

The massive (and historically cheap) increase in computing power that began in the 1950s and 60s changed the way that many previously difficult problems could be solved. In some cases, the analytical techniques had been around for a long time; cheap computing simply meant that they could be extended to larger problems, or applied to things that hadn’t been worth such analysis in times past. But there were also a number of methods of analysis that were invented during (or just immediately before) that fortuitous period: Shannon’s information theory, Danzig’s linear programming, von Neumann and Morgenstern’s game theory, and Kalman filtering, just off the top of my head.

One big chunk of real estate in this New World was labeled Operations Research. It came out of the post-war Department of Defense and more or less took the corporate world by storm, since it offered the hope (and often delivered) of untangling complicated production and logistics operations into an at least somewhat optimized operation. I learned my OR material from the RPI School of Management, along with a good stiff dose of advanced statistics.

But Systems Engineering, and its not-quite-a-cult sibling, General Systems Theory was where the really big game lived. Here was a tool kit of almost mind bogglingly powerful techniques, things like linear systems analysis, discrete time systems, transform theory, including frequency domain analysis, Laplace transforms, and on and on.

There was already a lot of history in linear systems theory, because linear systems could often be solved analytically. Moreover, any RCL circuit is a linear system, so circuit theory and electrical engineering had all these cool techniques already in the can. Mechanical engineering also had linear systems as a backbone, with every mass-spring system (and in ME, almost everything is a mass-spring system), getting the same treatment. So the science of simulations already had plenty of analog models being used, with tuned circuits often used to simulate mechanical devices, or chemical processes, or, well, other electrical devices.

All well and good, but I had my eye on non-linear systems.

Non-linear systems are where “Everything You Know is Wrong.” The phrase most often used is “counterintuitive.” What are now called chaotic systems are non-linear. In fluid mechanics, this was called “the turbulence problem,” and it had been known to be a bitch for a long, long time. What the computer revolution did was to give people a handle on just how bitchy it was.

Now linear systems can be very complicated, too complicated for a human mind to understand it, even. And linear systems can surprise you when they get very complicated as well. But in non-linear systems, even simple systems can be surprising. And it gets even worse when you connect them together.

The result is that there aren’t very many ways of analyzing non-linear systems. Most of them, in fact, consisted of making the system somehow appear to be linear, then using the linear techniques. It that didn’t work, you were stuck with the only other general method, which was modeling. Prior to electronic computers, the model was usually a real, physical model, like an aerodynamic model in a wind tunnel, or a small propeller in a tub of water.

With computers, however, you could make large scale numerical models, computer models as they were called, then just models, as the computer oracle took over the world.

I’ll talk a little about some of the math in my next essay, but I’ll end this one on a note about the sociology of it all. The thing is, computers became a magic wand. The Next Big Thing is often a magic wand in the popular imagination. That’s why Clarke got so much mileage out of his “Any sufficiently advanced technology…” aphorism. When people see something doing cool stuff, they expect it to do other cool stuff, without understanding any of it. So “computer model” became a powerful buzz phrase. It also fed into the tendency of people to project their own fantasies onto technology. The computer model became an oracle, its pronouncements inherently partaking of the mojo of science.

For myself, arrogant individual(ist) that I am, I never bought into the idea that “the model says…” “Models don’t say anything,” I would assert, “Modelers do.”

I was right, of course. As if that has ever done me any good.

No comments: