Mathematics is a Telescope

As I mentioned in the previous post, I don't agree with E.O. Wilson's position, excerpted from his new book, that great scientists shouldn't learn math. And that, strangely enough, seems to be his position. Not that great scientists don't need math, but rather that they should go out of their way not to learn it. After reading a few rebuttals to Wilson's op-ed, I think I can agree with the folks who claim that Wilson probably has greater mathematical exposure than he lets on, and certainly greater exposure than your average undergraduate. And it even sounds like he had to fight hard, at times, for that background.

Instead of retreading the ground that has been well-covered by others, I'll take this in a different direction. At one point last semester, I wanted to write a post something like "Learn Science So You Can Ask Better Questions." I had this urge after attending a talk by Ole Peters at Maryland's Applied Dynamics Seminar. The talk was titled 'Non-ergodic dynamics of economic models,' and while that may not sound interesting to the uninitiated1, you'll have to trust me that his presentation was excellent. He gave a TEDx talk on similar topics which you can find here. Unfortunately, the TEDx version is more in the vein of popular science; at the Applied Dynamics seminar, he got into the nitty details (i.e. the interesting parts). For those details, see this paper.

For the purposes of this post, the contents of the talk doesn't matter. Suffice it to say that Peters was asking extremely interesting questions about market dynamics, income inequality, and the stock market bubbles of the past ten years. He asked these questions with relatively straightforward tools from probability theory and dynamical systems (mainly, stochastic ordinary differential equations). But calling these tools 'straightforward' is a bit of a dodge. These tools hadn't been developed until the start of the 20th century, and weren't formally shown to work until its middle. And now they allows us to ask more interesting questions2, and do so with the confidence that we're not making stuff up.

And that's the point: these mathematical tools, in the hands of the right scientist, are just that — useful new ways of looking at the universe. You can do science without microscopes or telescopes or Large Hadron Colliders. But only a very limited science.

This couldn't be further from Ernest Rutherford's claim that, "[a]ll science is either physics or stamp collecting." All of the branches of science could benefit from the asking of more interesting questions. That's not to say that the methodology should come first. We need both tool makers and tool wielders3. It's a strange modern phenomena to see these two types of scientists as diametrically opposed.

Giving up on that divide is something E.O. Wilson and I can agree on.

  1. And as someone who claims that putting dollar signs in front of any number immediately makes it uninteresting, I originally didn't expect much from the talk, either.

  2. Or ruin large parts of the economy, if misunderstood.

  3. Unfortunately for me, I'm not bright enough to be tool maker and not clever enough to be a tool wielder, so I have to settle for some sort of hodge podge middle ground.