Rust Belt Philosophy

As a prelude to another post about this Steven Landsburg fellow, let's take a look at what he says about math and physics. We've seen this particular combination before, with the main point being that math works suspiciously well as a predictor of natural physical events. (Artificial physical events, especially the ones that take place in computers, should almost certainly be exempted from this suspicion: we set them up specifically to work that way, after all, so there's no real coincidence.) The motivation behind this observation is that it makes math look like a really-existing framework upon which the universe has, in some sense, been built. I personally am not sure that this would imply anything interesting even if it were true (or if it were false, for that matter), but it still seems rather intriguing.

For his part, Landsburg wants to look at the reverse: for him, the odd thing is "that sometimes the miracle runs in the opposite direction, and offers a curious use of physical reasoning to reveal a purely mathematical truth!" He says, as an example, that in order to see that "the arithmetic mean is always at least as big as the geometric mean," you could just take "several buckets of water, all at different temperatures [and then b]ring them together and let them sit until they all reach a single new temperature," at which point that "new temperature must exceed the geometric mean of the original temperatures." If we put aside the Rube-Goldberg-esque complexity of what's going on here, though, I'm not sure why this is supposed to be so miraculous.

Think of this much simpler example and see if it moves you any: take two pennies and then add one penny. Now you have three pennies, thus demonstrating the mathematical truth that two plus one equals three. Is that really a miracle? Is it, moreover, "unreasonable" for us to expect that sort of learning to take place? It's certainly not surprising that the universe is governed by laws, at least not at a face level, so that can't be the source of the supposed unreasonableness. I'd also be pretty skeptical if he said he was surprised that people could learn abstract truths from particular examples thereof: that's pretty much the only option. But if it's not surprising to discover that some physical laws are mathematical, and if it's also not surprising to discover that people learn by generalizing from specific examples, then how is any part of this surprising or interesting?

Probably the best Landsburg could do with this would be to say that it's surprising because it means that mathematical laws are at work in reality - but that's the original surprise, the one he says he's not talking about. I dunno, maybe there's something I'm missing here, but it really looks like Landsburg oversold this one. Maybe one of my readers can clear this up?

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