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Physics is unreasonably good at creating new math

nautil.us

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Re: Physics is unreasonably good at creating new math

#71

Post by 77pt77 »

glenstein wrote: post #58
77pt77 wrote: post #30

Earlier quoted context omitted.

And that amounted to 60 years (and counting) of absolutely nothing in terms of how the physical world works. Even Witten's achievements objectively reduce to an alternate proof of the positivity energy theorem in GR. This is an abject failure by all metrics.

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).

Re: Physics is unreasonably good at creating new math

#73

Post by aithrowaway1987 »

> Might there be certain laws of physics that are also “necessary” in the same way? In his paper, Molinini argues that the principle of conservation may be one such law. In physics, some properties of a system, such as energy or momentum, can’t change. A bicyclist freewheeling down a hill, for example, is converting her gravitational potential energy into movement energy, but the total amount of energy she and her bike have stays the same.

Arithmetic itself is a consequence of physical conservation: if you have a collection of four acorns, another collection of three acorns, then combine them without dropping an acorn, then you must have a collection of seven acorns. It is our deep physical understanding of space and causality which leads to simple arithmetic being intuitively true to most (if not all) vertebrates. (If the squirrel only got six acorns after combining then there must be a causal explanation for the quantitative discrepancy; another squirrel stole an acorn from the older stash, or maybe it fell in a hole.)

Re: Physics is unreasonably good at creating new math

#74

Post by Retric »

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?

To be beautiful it must first exist.

It’s far more difficult to come up with novel mathematics without some external inspiration.

Re: Physics is unreasonably good at creating new math

#75

Post by meroes »

Joker_vD wrote: post #35
verzali wrote: post #14

Earlier quoted context omitted.

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 .

Wondering if Euclid’s parallel postulate was independent goes back millennia though. And that’s like the key ingredient for multiple geometries.

Re: Physics is unreasonably good at creating new math

#76

Post by paulpauper »

jjk166 wrote: post #50
torrefatto wrote: post #37

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 l…

> justify the inordinate amount of money threw at them They're theorists, you're paying for pencils and paper. String theory may not have produced a theory of quantum gravity yet, but neither has any other line of inquiry.

sorta. the construction of particle accelerators has been justified to test the hypotheses of string theory

Re: Physics is unreasonably good at creating new math

#77

Post by paulpauper »

77pt77 wrote: post #30
glenstein wrote: post #26

I understand that one huge reason for Ed Witten's optimism about strong theory is this very fact. That, in his terms, the process of building out string theory has led to the uncovering of so much "buried treasure" in the form of novel developments of maths. Of course it's not anything like a proof but something that bolsters an intuition.

And that amounted to 60 years (and counting) of absolutely nothing in terms of how the physical world works. Even Witten's achievements objectively reduce to an alternate proof of the positivity energy theorem in GR. This is an abject failure by all metrics.

And that amounted to 60 years (and counting) of absolutely nothing in terms of how the physical world works.

this is in part because it's outside the scope of existing technology

Re: Physics is unreasonably good at creating new math

#78

Post by nyc111 »

The subject of study of physics is "physical quantity" which is defined as a number with a unit. Physical quantity doesn't have to be a "physical" quantity. So physics does not study exclusively physical objects. I think this is how mathematics and physics are related, mathematics does not deal with units (except unity).

Re: Physics is unreasonably good at creating new math

#79

Post by hughesjj »

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

Absolutely, they're still handing out nobels after all.

Personally I think the ER=EPR conjecture and the complexity/action duality hypothesis are incredibly interesting. Technically ER=EPR was formulated in 2000s (maybe 90s?) and CA-duality is approaching if not just past 10 years old, but the thing about asking for breakthroughs is that they take a while to percolate. Ex Hawking radiation wasn't formulated until, like, 50-70 years after the "basis" (schwarzshild, Schrodinger) was formed.

There's also been a ton of productive research integrsting computer science and physics lately ( on hn last week: https://arxiv.org/abs/2403.16850 and 2022 novel prize; https://www.scientificamerican.com/article/the-universe-is-n...)

Also JWST just keeps on giving, and gravitational waves were only confirmed in 2017. If you extend a bit further higgs was in the 2010s

So, in summary, in the late 10 years - we've shown a break in our intuition of physics (nonloca-realness, that 2022 paper) - proposed some novel yet elegant theories (CA-duality, and I'd hope you'd begrudge me er=EPR) - confirmed some insane provings to the underlying reality (gravitational waves)

If those aren't noteworthy, I'd ask what you consider noteworthy any why you consider it noteworthy

Re: Physics is unreasonably good at creating new math

#80

Post by Misdicorl »

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 past decade is a difficult framing to ask the question in. Notable breakthrough results are usually understood in hindsight and a decade just isn't a lot of time for that context and understanding to develop. Science also doesn't necessarily develop in this way with consistent progress every X timespan. Usually you get lots and lots of breakthroughs all at once as an important paradigm is shattered and a new one is installed. Then observations with tiny differences slowly pile up and a very blurry/messy picture of the problems with the new paradigm takes shape. But none of those things feels like a breakthrough, especially to a layman.

That said: I'll submit the first detection of gravitational waves as two black holes merged together in 2020 as meeting the bar of "notable breakthrough in the last decade".

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