Physics is unreasonably good at creating new math • Hacker News Board

Re: Physics is unreasonably good at creating new math

#31

Post by bee_rider » Wed, Sep 04, 2024, 4:19 PM UTC

tines wrote: post #7

cjs_ac wrote: post #3

One 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.

This was the result of Philosophers ultimately winning, despite the fact that they are so annoyingly pedantic that we pretend not to care about their work, and also, by ignoring them we can invent iPhones which are really neat.

You can’t prove anything by observation. You can gather evidence through repeat experiment and become reasonably confident as your theory continues to not be incompatible with the observed universe. Then the problem of induction says, “well, it isn’t incompatible with the part of the universe… that you’ve observed, yet!” And then you say, “ok, but I want to use my theory to invent an iPhone, and I think there are enough people in the part of the universe that I’ve already observed. I looked very hard to find evidence against my theory, and I don’t think anyone will find evidence against it before I’ve sold enough iPhones to retire.”

Math, of course, is that stuff which can’t be invalidated by observations. But it is very hard to do enough math to retire off it.

Re: Physics is unreasonably good at creating new math

#32

Post by aeneasmackenzie » Wed, Sep 04, 2024, 4:21 PM UTC

teqsun wrote: post #9

goatlover wrote: post #5

Earlier quoted context omitted.

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

Just say witch hunt. McCarthy was entirely correct that there were a lot of communists and communist sympathizers, so many that many of the people he thought were helping him were themselves communists or communist sympathizers. Witches on the other hand are not real.

Re: Physics is unreasonably good at creating new math

#33

Post by TheRealPomax » Wed, Sep 04, 2024, 4:22 PM UTC

LeifCarrotson wrote: post #15

selectodude wrote: post #11

Earlier quoted context omitted.

To some extent, observation has taken a back seat because we're at the point in our physics journey where we pontificate about things that are too small or too dark and far away to see. We simply can't observe this stuff anymore.

Furthermore, we might not be able to observe it but we can observe simulations of it. If it was not possible to simulate, I think we'd be less invested in the math and physics of it.

Furthermore, even if you can write down the math, it might not even be solvable (sometimes provably so) and simulations (or more accurately, numerical analysis and the finite element method) are our only option.

Re: Physics is unreasonably good at creating new math

#34

Post by glitchc » Wed, Sep 04, 2024, 4:26 PM UTC

selectodude wrote: post #11

tines wrote: post #7

Earlier quoted context omitted.

> 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.

To some extent, observation has taken a back seat because we're at the point in our physics journey where we pontificate about things that are too small or too dark and far away to see. We simply can't observe this stuff anymore.

Like the atom was in the 18th century? Electrons and protons in the 19th? Quarks in the 20th?

Re: Physics is unreasonably good at creating new math

#35

Post by Joker_vD » Wed, Sep 04, 2024, 4:29 PM UTC

verzali wrote: post #14

Joker_vD wrote: post #13

Earlier quoted context omitted.

> Math doesn't have such a requirement Geometry? Lobachevsky actually proposed a test on measuring sum of angles of a celestial triangle to decide which geometry actually applied to the real world.

There are multiple geometries though, they don't have to describe the real world. In mathematics you are free to base your geometry on whatever axioms you want, whether they are realistic or not. I'd say the question of which geometry applies in the real world is more a question for physicists (or cosmologists, today).

This is a very late-XIX century development. Geometry used to be an integral part of physics, vide Newton's Principia.

Re: Physics is unreasonably good at creating new math

#36

Post by graycat » Wed, Sep 04, 2024, 4:30 PM UTC

Physics research gets funded because of applications, existing or promising, for curiosity, fundamental science, the economy, medicine, and national security, etc. Since math can help physics research, that research is funded and motivated to make applications of math, old or new. Math alone is less involved with applications.

Re: Physics is unreasonably good at creating new math

#37

Post by torrefatto » Wed, Sep 04, 2024, 4:33 PM UTC

This is the well known litany from string theorists to try and justify the inordinate amount of money threw at them to get back nothing of physical value: no falsifiable prediction.

Instead of reasoning on the worth of the effort spent in this direction to investigate nature (a very tangible companion) they try to steer the discourse toward this nonsense. We spent >50 years listening to these tales and the time has long passed since we are required to stop playing with these smoke and mirrors.

Re: Physics is unreasonably good at creating new math

#38

Post by verisimi » Wed, Sep 04, 2024, 4:33 PM UTC

tech_ken wrote: post #29

> Hitchin agrees. “Mathematical research doesn’t operate in a vacuum,” he says. “You don’t sit down and invent a new theory for its own sake. You need to believe that there is something there to be investigated. New ideas have to condense around some notion of reality, or someone’s notion, maybe.” This is kind of it I think. It's not just physics that drives interesting math, and it's not just recently that this rela…

I agree, I think. I would say it like so, that maths is a sort of highly technical, rigorous language, but like any language it will describe what you want it to. It is easy to think that it is describing the underlying terrain, but it is actually working on three (shared) and model which have of the terrain. So, as we consider different things, maths will follow.

Re: Physics is unreasonably good at creating new math

#39

Post by Onavo » Wed, Sep 04, 2024, 4:34 PM UTC

whimsicalism wrote: post #19

Onavo wrote: post #4

Physics 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 ch…

What modern ML uses those techniques? my understanding is ebm is quite rare

Research mostly, lots of these techniques are used for speech synthesis and occasionally image models (not LLMs)

Re: Physics is unreasonably good at creating new math

#40

Post by jmyeet » Wed, Sep 04, 2024, 4:35 PM UTC

I'm not a physics or math whiz but isn't the relationship more of a virtuous cycle?

I think I read that the 20th century was a revolution because of the marriage between physics and math. Quarternions are key to relativity. Discrete math is littered all over quantum mechanics and the Standard Model. Like U(1) describes electromagnetism, SU(2) describes the weak force and SU(3) describes the strong nuclear force. In particular the mass of the 3 bosons that mediate the weak force is what led directly to the Higgs mechanism being theorized (and ultimately shown experimentally).

One of the great advances of the 20th century was that we (provably) found every finite group. And those groups keep showing up in physics.

The article mentions how string theory has led to new mathematics. This is really interesting. I'm skeptical of string theory just because there's no experimental evidence for "compact dimensions". It seems like a fudge. But interestingly there have been useful results in both physics and maths based on if string theory was correct.