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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

#211

Post by skissane »

bgnn wrote: post #209
seanhunter wrote: post #178

Earlier quoted context omitted.

This is actually a variant on a very old joke from Persia originally told about Mullah Nasreddin rather than mathematicians[1] [1] https://en.wikipedia.org/wiki/Nasreddin#cite_ref-32

True, but Nasreddin was not from Persia but from Asia Minor during Seljuk rule.

I think the person you were replying to was saying that the joke about Nasreddin was from Persia, not that Nasreddin was from Persia. And, they cite that joke to a Wikipedia article, which in turn cites it to a blog post, which quotes it from a book which claims to be translated from Persia. So the attribution of (at least that specific instance of) the joke to Persia is correct.

Also, it is unclear if Nasreddin ever actually existed, or if he is purely legendary. Turkish folklore claims he lived in Asia Minor during the Seljuks, but Uzbek folklore claims he was an Uzbek who lived in Uzbekistan. Some Azerbaijani scholars have identified him with the 13th century Persian polymath Nasir al-Din al-Tusi.

Re: Physics is unreasonably good at creating new math

#212

Post by tech_ken »

namaria wrote: post #170
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…

That doesn't hold up to a reading of the history of maths. So much of it was invented by someone just noodling around with numbers and would find some use in physical science hundreds of years later.

Is this different from when I said:

> It's not just physics that drives interesting math, and it's not just recently that this relationship holds

When you say

> So much of it was invented by someone just noodling around with numbers

I think you're ignoring where the numbers being played with came from. Very rarely does someone just invent a fresh problem de novo and start messing with it AFAIK; the 'playful mathematics' approach is still reusing tools which were developed in application, just (typically) a long period of time after that original application. Euclid's geometry doesn't exist without the invention of a compass and rule for drafting. Yes he's playing with the concepts freely, but it's not just some arbitrary toy ideas, they're rooted in a practical reality (albeit deeply).

Re: Physics is unreasonably good at creating new math

#213

Post by speedchess »

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.

> One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea:

It's actually a 19th century idea. The discovery or acceptance of non-euclidean geometry in the 19th century untethered math from physics or physics from math.

> and it seems to be disappearing in the twenty-first.

It can't disappear because math is no longer tied to the physical world. Math is simply theorem generation regardless of whether the axioms and theorems apply to the physical world.

The math used in physics is only a tiny subset of possible math.

Re: Physics is unreasonably good at creating new math

#214

Post by glenstein »

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).

Building out the toolkit of physics is vital to the advance of physics itself, and last I checked Ptolemy hasn't produced tools that have advanced our understanding of Bekenstein-Hawking entropy in black holes.

Re: Physics is unreasonably good at creating new math

#215

Post by glenstein »

naasking wrote: post #128
zachf wrote: post #122

Earlier quoted context omitted.

There are in fact exceptionally strong incentives to discover alternatives to quantum gravity which could be tested in experiments. These are the same incentives that always drive the scientific process, and new theories cost next to zero to produce. The reason string theory is popular is not because string theorists somehow prevent funding of other directions. It is because string theory has given us tools like AdS/…

Oh Ads, you mean that space that emphatically does NOT describe our universe? Ads/CFT is overblown. It's just an interesting mathematical result that hasn't borne much meaningful fruit for actual physics. I'm sorry, but string theorists absolutely do prevent funding other research because funding is finite, grad students have to research something their advisors think is worthy, and their advisors have their heads fu…

>Ads/CFT is overblown

This is a preposterously uncharitable characterization of something that again, was I think a triumph of string theory, the likes of which cannot be claimed by any competing theory. It is a framework for understanding black hole information loss, and it even has specific applications in condensed matter physics for modeling high temperature superconductors.

Re: Physics is unreasonably good at creating new math

#216

Post by hirvi74 »

FromTheSteppe wrote: post #171
SkiFire13 wrote: post #169

Earlier quoted context omitted.

I would argue that in the twenty-first century the distinction is even greater thanks to computer science.

Haha in my country half the computer science degrees are titled "Applied Mathematics".

Such a title makes me feel like I might come off smarter than I actually am -- I like it. Especially when considering my mathematically understanding and abilities.

Re: Physics is unreasonably good at creating new math

#217

Post by glenstein »

analog31 wrote: post #142
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.

Something I've speculated about is that we just don't know if and when the next answer will arrive. The past few centuries have certainly stoked our expectations for rapid progress, but it's not guaranteed. There's no success-or-failure metric for the search, until an answer is found. It took humanity something like 1000 years between when the ancient Greeks could formulate general quadratic equations, and someone ca…

I completely agree. As you say it could be that we don't get an answer for a century, a millenium, or ever. Even if string theory is on the right track, it might be that we never, ever, apprehend anything more than tantalizing clues.

To quote Ed Witten from the same interview I was referencing previous [0], he likes to say that string theory is a 21st century theory that fell, by chance, into the 20th century.

[0] https://www.youtube.com/watch?v=77wN6C-NWD8

Re: Physics is unreasonably good at creating new math

#218

Post by saagarjha »

dxbydt wrote: post #181
saagarjha wrote: post #152

Earlier quoted context omitted.

TIL AoPS has physics classes now

i am essentially a rayiner on steroids, in that i believe america has absolutely nothing meaningful to offer to the world at large other than aops and rsm. its such an extraordinary institution. large number of international signups - so tons of indian and chinese kids burning the midnight oil solving woot alongside their american compatriots. just an amazing, spectacular creation all around. if the nobel committee h…

"I am essentially a rayiner on steroids" has to be the most unhinged thing I have read on this site today lmao

Re: Physics is unreasonably good at creating new math

#219

Post by naasking »

glenstein wrote: post #215
naasking wrote: post #128

Earlier quoted context omitted.

Oh Ads, you mean that space that emphatically does NOT describe our universe? Ads/CFT is overblown. It's just an interesting mathematical result that hasn't borne much meaningful fruit for actual physics. I'm sorry, but string theorists absolutely do prevent funding other research because funding is finite, grad students have to research something their advisors think is worthy, and their advisors have their heads fu…

>Ads/CFT is overblown This is a preposterously uncharitable characterization of something that again, was I think a triumph of string theory, the likes of which cannot be claimed by any competing theory. It is a framework for understanding black hole information loss, and it even has specific applications in condensed matter physics for modeling high temperature superconductors.

Sorry, but I'll have to side with Nobel laureate Anderson who disagrees about the utility of Ads/CFT for condensed matter physics:

https://pubs.aip.org/physicstoday/article/66/4/9/414412/Stra...

Like I said, Ads/CFT's alleged "successes" are overblown.

As for it being a framework for understanding black hole information loss, it's merely one idea that has questionable application to our universe. We'll see if anything actually useful comes from it.

Re: Physics is unreasonably good at creating new math

#220

Post by naasking »

zachf wrote: post #131
naasking wrote: post #128

Earlier quoted context omitted.

Oh Ads, you mean that space that emphatically does NOT describe our universe? Ads/CFT is overblown. It's just an interesting mathematical result that hasn't borne much meaningful fruit for actual physics. I'm sorry, but string theorists absolutely do prevent funding other research because funding is finite, grad students have to research something their advisors think is worthy, and their advisors have their heads fu…

No, this is a shallow understanding of AdS/CFT. If you want to study quantum gravity when it is weakly coupled to matter, you can use AdS/CFT regardless of whether the background space is asymptotically AdS by embedding a brane near the boundary and working in a perturbative expansion. If you want to study the physics of quantum de Sitter space with a field theory dual, you can study any of the recent work on TTbar d…

> Because that would obviously be an untenable position, and the whole point is that quantum gravity AdS (basically) is CFT (it’s an equality! It goes both ways), just in different variables. You can actually study non-gravitational physics with it, using a gravitational language. That’s awesome stuff!

Which makes it an interesting mathematical construct, but in what way does that actually help physics? I included a link to one critique of Ads/CFT in another post, and others have critiqued its applications to QCD and other alleged "successes" because the important properties to do meaningful work in those domains just aren't there.

The versions of this correspondence that are easy to work with also depend on supersymmetry, for which every experiment has failed to find any evidence in the expected regimes. In the old days we'd call this "refuted", but these days it just means reworking it (adding a new epicycle?) to get "new bounds".

Ads/CFT is a mildly interesting mathematical derivation, but its actual utility for physics is questionable.

> He gets funding from string grants. Nobody is angry about that. Anybody can do this.

Maybe anybody can do this now, and I think that's because, as I said, string theory's stranglehold has weakened because of well-motivated criticisms over the past 15 years or so. The evidence of string theory's former dominance is right in what you said: string theory grants.

> but the entire community has always supported and listened.

I think some physicists are open minded, and some are not. You need only look at how physicists who work MOND are treated to see how not open minded some physicists are. MOND is not a final theory, but it and the people who work on it are scorned despite it's unreasonably good predictive success over the last 40 years.

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