Sean Carroll: Difference Between Math and Physics | AI Podcast Clips
00:00:00.000 | >> What's the difference between math and physics to you?
00:00:07.240 | >> To me, very, very roughly, math is about the logical structure of all possible worlds
00:00:12.280 | and physics is about our actual world.
00:00:16.600 | >> And it just feels like our actual world is a gray area when you start talking about
00:00:21.520 | interpretations of quantum mechanics or no.
00:00:24.600 | >> I'm certainly using the word world in the broadest sense, all of reality.
00:00:30.520 | I think that reality is specific.
00:00:32.320 | I don't think that there's every possible thing going on in reality.
00:00:36.000 | I think that there are rules, whether it's the Schrodinger equation or whatever.
00:00:40.080 | So I think that there's a sensible notion of the set of all possible worlds and we live
00:00:44.740 | in one of them.
00:00:46.000 | The world that we're talking about might be a multiverse, might be many worlds of quantum
00:00:49.240 | mechanics, might be much bigger than the world of our everyday experience, but it's still
00:00:52.520 | one physically contiguous world in some sense.
00:00:58.640 | >> So if you look at the overlap of math and physics, it feels like when physics tries
00:01:05.800 | to reach for understanding of our world, it uses the tools of math to sort of reach beyond
00:01:12.160 | the limit of our current understanding.
00:01:15.880 | What do you make of that process of sort of using math to, so you start maybe with intuition
00:01:22.920 | or you might start with the math and then build up an intuition or, but this kind of
00:01:27.200 | reaching into the darkness, into the mystery of the world with math?
00:01:31.760 | >> Well I think I would put it a little bit differently.
00:01:33.280 | I think we have theories, theories of the physical world, which we then extrapolate
00:01:39.480 | and ask, you know, what do we conclude if we take these seriously well beyond where
00:01:43.960 | we've actually tested them?
00:01:45.680 | It is separately true that math is really, really useful when we construct physical theories.
00:01:50.960 | And famously Eugene Wigner asked about the unreasonable success of mathematics and physics.
00:01:55.560 | I think that's a little bit wrong because anything that could happen, any other theory
00:02:01.680 | of physics that wasn't the real world, but some other world, you could always describe
00:02:06.240 | it mathematically.
00:02:07.240 | It's just that it might be a mess.
00:02:09.720 | The surprising thing is not that math works, but that the math is so simple and easy that
00:02:15.200 | you can write it down on a t-shirt, right?
00:02:17.080 | I mean, that's what is amazing.
00:02:19.200 | That's an enormous compression of information that seems to be valid in the real world.
00:02:25.560 | So that's an interesting fact about our world, which maybe we could hope to explain or just
00:02:29.880 | take as a brute fact, I don't know.
00:02:32.400 | But once you have that, you know, there's this indelible relationship between math and
00:02:37.600 | physics.
00:02:38.600 | But philosophically, I do want to separate them.
00:02:41.240 | We don't extrapolate math because there's a whole bunch of wrong math that doesn't apply
00:02:46.160 | to our world, right?
00:02:47.600 | We extrapolate the physical theory that we best think explains our world.
00:02:51.080 | [ Silence ]
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