Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Physics is unreasonably good at creating new math

nautil.us

Post reply on HN
Print view View original

11–20 of 231 posts

Re: Physics is unreasonably good at creating new math

#11

Post by selectodude »

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.

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.

Re: Physics is unreasonably good at creating new math

#12

Post by lupire »

goatlover wrote: post #5
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.

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.

It's a very weak loose statement, but I think the idea is that leading scientific and mathematical thinkers (think Newton as a quintessential example) were "natural philosophers" who studied whatever caught their interest and took it wherever it went. Astronomers invented lenses and ground them and studied the starts and developed algebra and calculus to model the observations.

Some people were more narrowly focused, like Gauss who did mostly math (but an amazing breadth of math!)

There was a lot of hesitancy about math that couldn't be empirically illustrated by building out of atoms, like irrational numbers and then transcendental numbers and imaginary numbers and then infinite structures.

Re: Physics is unreasonably good at creating new math

#13

Post by Joker_vD »

goatlover wrote: post #5
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.

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.

> 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.

Re: Physics is unreasonably good at creating new math

#14

Post by verzali »

Joker_vD wrote: post #13
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.

> 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).

Re: Physics is unreasonably good at creating new math

#15

Post by LeifCarrotson »

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.

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.

Re: Physics is unreasonably good at creating new math

#17

Post by crazydoggers »

I’m not sure how it could be otherwise. On some level mathematics is a description of reality that we can use to compute things in reality.

For example, pi is the ratio of a circle’s circumference to its diameter. It’s just what a circle is in two dimensions. The value of pi isn’t any more mysterious or connected to physics than the existence of this thing called a circle. If you have some other Euclidean shapes you’ll have other ratios and values that have other relationships to other things in physical reality.

And if reality was different, hence the physical laws were different then the math would be different.. and the beings in that world might wonder why their math and physics were so interconnected.

Re: Physics is unreasonably good at creating new math

#18

Post by scarmig »

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…

Another is the Nakano-Amari-Hopfield model, which is based on Ising. Hopfield himself was a trained physicist.

Re: Physics is unreasonably good at creating new math

#19

Post by whimsicalism »

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

Re: Physics is unreasonably good at creating new math

#20

Post by lupire »

ezst wrote: post #10
Almondsetat wrote: post #2

Could 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!

It's more of a hint than a constraint. It's using the Universe as a brainstorming partner.
Post reply on HN