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

91–100 of 231 posts

Re: Physics is unreasonably good at creating new math

#91

Post by imchillyb »

Discoveries are made and measurements are taken with the tools available.

The measurements, theories, and currently understood or applicable math may not match up with observations.

People ponder and discover, then attempt to explain the observations and measurements with a new theory. If the theory pans out, a deeper explanation of that theory is necessary and that's where the new math's at.

It's not that physics is good at creating math. Physics is good at describing our observations /with/ math. That's kind of its whole job.

Next time you look at raindrops in a puddle, try to imagine how you would describe those movements scientifically. One needs math for that.

Sometimes the available tools and math are sufficient for a thorough explanation, and sometimes one needs to invent a universe of math to describe a tiny fluctuation.

Re: Physics is unreasonably good at creating new math

#92

Post by dxbydt »

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.

> pontificate about things that are too small or too dark and far away to see

I was bitten by this last week. I am enrolled in an aops physics course, titled Mechanics. So the last time I took any Mechanics was 40 years ago as a high school student in India. Most of the curriculum then was about stuff banging into each other aka collisions, & asking what happens to the result. Like some golf ball rolls down an inclined plane at some angle theta & hits a identical stationary ball & the objects stick together & we're supposed to compute where they end up. I was curious what American students learn, so I enrolled in this aops course.

Last week's assignment asks me - under which scenario will conservation of momentum make an accurate prediction. The 3 scenarios are - truck collides with car, eagle comes to rest at perch after flying from far away, and two galaxies colliding into each other to form a third megagalaxy.

I naturally picked truck & car - so aops knocks off 2 points for the wrong answer! Apparently if a truck collides with a car there will be so much thermal energy produced by the friction of the road, any prediction you make about the final velocity of the car assuming conservation of momentum will be bogus.

So then I pick eagle coming to rest - aops knocks off 2 more points for the wrong answer! Apparently when eagle comes to land, it will open its giant wings to create air resistance, so momentum won't be conserved.

Ok so that leaves the 2 galaxies. I pick that & get my correct answer, a pathetic score of 3/7. I'm left wondering how do we even know this is correct. Galaxies are too far away to observe. How is one supposed to compute the mass of 2 separate galaxies, & then find their moving velocities accurately, & then find the final velocity of the combined galaxy, & thus confirm momentum was conserved ? Seems very far fetched. I would rather go with the car & truck.

Re: Physics is unreasonably good at creating new math

#93

Post by zachf »

77pt77 wrote: post #71
glenstein wrote: post #58

Earlier quoted context omitted.

Witten has revolutionized mathematical physics, and his development of topological quantum field theory was nothing short of monumental. Much of Witten's own point above is that advancements in string theory have cashed out in revolutionary new mathematical approaches that would be of lasting value even string theory itself never receives any experimental confirmation. I think article highlights something very beauti…

The only cheap thing here is the amount of actual physics that came out of all of this ptolemaic endeavor. And writing ptolemaic is probably too charitable because the Almagest at least predicted movements quite well at the time (apparently it now deviates too much).

Is your preferred remedy that quantum gravity be entirely defunded, or instead that more funding be redirected to any of the other programs to study quantum gravity? If the latter, which ones in your opinion are more likely to be productive than string theory?

Re: Physics is unreasonably good at creating new math

#94

Post by FuriouslyAdrift »

alickz wrote: post #67
janalsncm wrote: post #61

Earlier quoted context omitted.

I don’t agree with this. I think there are definitely people like Michio Kaku who have books to sell who spend their time pontificating. People just think that physics looks like pontificating because that’s what it looks like on TV. But there are also active researchers doing real research. Physics postdocs aren’t just sitting around in a circle making up stories about what the universe is like.

please forgive my ignorance, has there been notable progress in the field of physics in the last decade? noteworthy breakthroughs i mean i ask out of layman curiosity

The confirmation of the Higgs boson is pretty huge...

Re: Physics is unreasonably good at creating new math

#95

Post by tomrod »

jfactorial wrote: post #43
tomrod wrote: post #41

Earlier quoted context omitted.

But Platonists, ironically on many levels, are also real. Sometimes complex. But never fully imaginary.

There are no Platonists, only imitations of the one true heavenly Platonist.

Genuinely chuckling.

Re: Physics is unreasonably good at creating new math

#96

Post by glitchc »

l33t7332273 wrote: post #55
glitchc wrote: post #34

Earlier quoted context omitted.

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

I’m struggling to see your point. My interpretation is that in each of those times, we used some math to talk about things we couldn’t observe until we were able to make experiments to observe them. Are you saying that one day we will be able to devise experiments to observe these things?

Short answer: Yes, and new instruments to make those measurements possible. That's how physics has always progressed. Why would this point in time be suddenly different from the past 400 years? Because we can't see a clear path forward? That's always been the case. Insight and ingenuity of individuals is what gets us through it every time.

Re: Physics is unreasonably good at creating new math

#97

Post by janalsncm »

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…

One that many people may be familiar with is Stable Diffusion, which is used in many AI image generators today. There is an analogy between random noise -> image and a random distribution of gas particles -> concentrated volume of particles.

https://arxiv.org/abs/1503.03585

Re: Physics is unreasonably good at creating new math

#98

Post by janalsncm »

crazydoggers wrote: post #17

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’…

If this was true then every bit of math must have a real-world application. But math doesn’t need to have real-world applications in order to be valid.

Re: Physics is unreasonably good at creating new math

#99

Post by marcosdumay »

slashdave wrote: post #63
marcosdumay wrote: post #27

Try to make some innovative software product without talking to any user. You'll see why physics is good at crating new math.

Do you value the quality of a mathematical theory by the number of applications, or the intrinsic beauty of the theory itself?

It doesn't matter. Constraints enable art, not the other way around.

Re: Physics is unreasonably good at creating new math

#100

Post by whimsicalism »

hangsi wrote: post #66
whimsicalism wrote: post #19

Earlier quoted context omitted.

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

The common method for choosing the next output token for an LLM is sampling from a Boltzmann distribution. If you have seen the term "temperature" in the context of language models, that is a direct link to the statistical gas mechanics.

i don't find the connection between softmax and boltzmann really all that deep tbh (compared to say, the connection between field theory/ising models and EBM)
Post reply on HN