Physics is unreasonably good at creating new math
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Re: Physics is unreasonably good at creating new math
#2Could this be a case of physics being more "tangible", thus leading to more obvious paths? Like, if you only study pure maths and you stay in your field, can you really point to a concrete direction for where to look for new stuff? In physics, your job is literally to study how the universe already behaves, so you have a frame of reference to take inspiration from and the efforts are a bit more concentrated. In fact, since models don't describe reality perfectly, you can always observe where it fails to know in which direction to attack. In maths, on the other hand, everything that is proven is correct forever. The model is reality. So it seems to be more difficult to find criticalities to look for. It's more of a "I wonder if this property does or doesn't hold" ordeal, which seems much more vague. Just a question.
Re: Physics is unreasonably good at creating new math
#3One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea: it wasn't made during the nineteenth century or before, and it seems to be disappearing in the twenty-first.
Re: Physics is unreasonably good at creating new math
#4Physics is also great for machine learning, though the approaches can be rather unintuitive. For example message passing and belief propagation in trees/graphs (Bayesian networks, Markov random fields etc.) for modeling latent variables are usually taught using the window/rainy weather marginal probability analogy and involves splitting out a bayesian/statistical equation into subcomponents via the marginalization chain rule. For physicists however, they tend to teach it using Ising models and magnetic spin, which is a totally different analogy.
A lot of the newer generative ML models are also using differential equations/Boltzmann distribution based approaches (state space models, "energy based" models) where the statistical formulations are cribbed wholesale from statistical physics/mechanics and then plugged into a neural network and autodiff system.
The best example is probably the Metropolis-Hastings algorithm which was invented by nuke people.
https://web.archive.org/web/20150603234436/http://flynnmicha...
Re: Physics is unreasonably good at creating new math
#5One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea : it wasn't made during the nineteenth century or before, and it seems to be disappearing in the twenty-first.
What does that mean? Physics is still empirical at the end of the day. Experiments decide what theories best explain the world. Math doesn't have such a requirement. It doesn't need to model natural phenomenon. Your physics lecturer sounds like a Platonist.
Re: Physics is unreasonably good at creating new math
#6One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea : it wasn't made during the nineteenth century or before, and it seems to be disappearing in the twenty-first.
What does that mean? Physics is still empirical at the end of the day. Experiments decide what theories best explain the world. Math doesn't have such a requirement. It doesn't need to model natural phenomenon. Your physics lecturer sounds like a Platonist.
I don't think OP is really wrong here. Wasn't there a debate in the late 19th century that basically asked if math had to have some mapping to the natural world, or should it work independently? I though there was some argument about this with Hilbert and Poincaré about this, and Hilbert more or less won.
Re: Physics is unreasonably good at creating new math
#7One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea : it wasn't made during the nineteenth century or before, and it seems to be disappearing in the twenty-first.
> it wasn't made during the nineteenth century
That's because people were totally focused on physics, and math was just a useful tool sometimes. Doing physics was the true goal and observation the final arbiter of truth.
Nowadays, that distinction is blurred but for the opposite reason; people think that anything conceived by sound math must be true, and observation has taken a back seat.
Re: Physics is unreasonably good at creating new math
#8One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea : it wasn't made during the nineteenth century or before, and it seems to be disappearing in the twenty-first.
What does that mean? Physics is still empirical at the end of the day. Experiments decide what theories best explain the world. Math doesn't have such a requirement. It doesn't need to model natural phenomenon. Your physics lecturer sounds like a Platonist.
See Our mathematical universe : my quest for the ultimate nature of reality by Max Tegmark
Re: Physics is unreasonably good at creating new math
#9One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea : it wasn't made during the nineteenth century or before, and it seems to be disappearing in the twenty-first.
What does that mean? Physics is still empirical at the end of the day. Experiments decide what theories best explain the world. Math doesn't have such a requirement. It doesn't need to model natural phenomenon. Your physics lecturer sounds like a Platonist.
> "Your physics lecturer sounds like a Platonist."
I don't understand what this means, but it made me envision a McCarthy-esque witch hunt for "Platonist and Platonist sympathizers" lurking amongst the faculty
Re: Physics is unreasonably good at creating new math
#10Could this be a case of physics being more "tangible", thus leading to more obvious paths? Like, if you only study pure maths and you stay in your field, can you really point to a concrete direction for where to look for new stuff? In physics, your job is literally to study how the universe already behaves, so you have a frame of reference to take inspiration from and the efforts are a bit more concentrated. In fact,…
Almost like the case of constrained environments being a fertile ground for new creative solutions!