Biologists
often emphasize the part that computers will play, and it's true that
computers will be indispensable, but there's a third leg, which is good
theoretical ideas. It won't be enough to have big computers and great
data. You need ideas and I think that those ideas will be expressed
in the language of complex systems mathematics. Although that phrase,
complex systems, has been talked about a lot, I hope people out there
appreciate what a feeble state it's in, theoretically speaking. We really
don't understand much about it. We have a lot of computer simulations
that show stunning phenomena, but where's the understanding? Where's
the insight? There are very few cases that we understand, and so that
brings me back to synchrony. I like that example of synchrony as a case
of spontaneous order because that's one of the few cases that we can
understand mathematically. If we want to solve these problems, we've
got to do the math problems we can do, and we need the simplest phenomena
first, and synchrony is among them. It's going to be a long slog to
really understand these problems. In broad strokes, there were hundreds of years after Aristotle when we didn't really understand a whole lot. Once Kepler, Copernicus, and Newton began explaining what they saw through math, there was a great era of understanding, through certain classes of math problems that could be solved. All the mathematics that let us understand laws of physics—Maxwell's equations, thermodynamics, on through quantum theory—all involve a certain class of math problems that we know how to solve completely and thoroughly: that is, linear problems. It's only in the past few decades that we've been banging our heads on the non-linear ones. Of those, we understand just the smallest ones using only three or four variables—that's chaos theory. As soon as you have hundreds, or millions, or billions of variables—like in the brain—we don't understand those problems at all. That's what complex systems is supposed to be about, but we're not even close to understanding them. We can simulate them in a computer, but that's not really that different from just watching. We still don't understand. |