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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

#221

Post by zachf »

naasking wrote: post #220
zachf wrote: post #131

Earlier quoted context omitted.

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…

Okay, I’ll tell you about my own research. From studying the way that geometric surfaces work in AdS, we conjectured a relationship between the stress tensor of QFT and entanglement entropy. This is because those quantities translate into geometrical analogs in the quantum gravity theory. We then proved this same relationship holds in some simple field theories and then other physicists proved it in the general case. So we learned something about non gravitational physics from gravitational physics. We study a specific, tractable case (AdS, mapping onto CFT) and then use it to learn about the general case (every QFT). That’s how physics works! You study the spherical cows. Eventually you learn something universal. All this is because I started with an open mind, and pursued the full consequences of AdS/CFT.

Your complaint about supersymmetry is like saying that Newtonian physics can’t work because objects are not rigid, continuous solid bodies. And yeah, that’s true, there are none of those in nature. Does that mean Newtonian physics is not useful? NO! It’s a model that’s useful. Is it wrong? Kinda. And the models that have unbroken SUSY are “wrong” too, in the same way. But the point is—-it’s obviously useful!

Please try to be open minded about string theory, especially if you wish to lecture about small-mindedness around MOND. Diminishing the real accomplishments of physicists doesn’t make other fields more likely to get funded—it makes it more likely that bureaucrats defund everyone. That’s the lesson of the SSC.

Re: Physics is unreasonably good at creating new math

#222

Post by 77pt77 »

glenstein wrote: post #214
77pt77 wrote: post #71

Earlier quoted context omitted.

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.

Those guys basically developed Fourier analysis with very clunky notation.

We'll be very lucky if these guys are doing anything even remotely as useful.

Re: Physics is unreasonably good at creating new math

#223

Post by 8n4vidtmkvmk »

yetihehe wrote: post #174
moi2388 wrote: post #164

Earlier quoted context omitted.

Now I didn’t drop them but forgot to even bring them..

Just execute `make building` again and you should get new keys generated.

Right. Just regenerate the keys and the house, then just delete the unneeded house. Storage is cheap.

Re: Physics is unreasonably good at creating new math

#224

Post by xanderlewis »

yread wrote: post #208
jjgreen wrote: post #127

A physicist, walking home at night, spots a mathematician colleague under a street lamp staring at the ground, "something wrong?" he asks; "I've dropped my keys" he replies, "whereabouts?" asks the physicist, keen to help. "Over there" says the mathematician pointing; "So why don't you look over there?" retorts the physicist, "the light is better here" says the mathematician. Disclosure, I'm a mathematician.

Physics faculty wants to buy a new expensive research machine. University rector is furious at all this spending and tries to talk some sense into them: "Why aren't you more like the mathematicians, they just need a paper a pencil and an eraser. Or like the philosophers, they just need a paper and pencil" Or one more related to this article: Mathematicians waste time designing the topology of coats for people with 3…

I had a lecturer (for a fairly advanced set theory course) who said he told his young son, when teaching him to count, that he, as a set the theorist, ‘doesn’t do finite’. I guess when his son got to school 1+2 might have been ‘the successor of 2’, but anything else would have been ‘less than omega’.

Re: Physics is unreasonably good at creating new math

#225

Post by xanderlewis »

ndsipa_pomu wrote: post #137
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’…

Not sure that I agree as does a mathematical circle actually exist? We can produce things that approach the concept of a circle and similarly, we can measure circumference and diameter to a level of precision to approach the value of pi, but we never have a perfect circle or the exact value of pi. I tend towards maths being distinct from physics as some areas of maths deal with concepts that can only have a passing r…

> Not sure that I agree as does a mathematical circle actually exist?

The set of unit norm complex numbers surely exists just as much as the real numbers exist, doesn’t it? A circle is an idea, and it certainly exists.

Re: Physics is unreasonably good at creating new math

#226

Post by ndsipa_pomu »

xanderlewis wrote: post #225
ndsipa_pomu wrote: post #137

Earlier quoted context omitted.

Not sure that I agree as does a mathematical circle actually exist? We can produce things that approach the concept of a circle and similarly, we can measure circumference and diameter to a level of precision to approach the value of pi, but we never have a perfect circle or the exact value of pi. I tend towards maths being distinct from physics as some areas of maths deal with concepts that can only have a passing r…

> Not sure that I agree as does a mathematical circle actually exist? The set of unit norm complex numbers surely exists just as much as the real numbers exist, doesn’t it? A circle is an idea, and it certainly exists.

I think you're using a different meaning of "exists" than I am.

Ideas don't exist as you can't point at them, steal them, destroy them etc. I can point at something that approaches the concept of a circle and I can point at a set of objects that can be counted, but I can never see a mathematical circle (zero thickness would make it impossible to see) and I can't see a "four" without representing it by a symbol or collection of objects.

Re: Physics is unreasonably good at creating new math

#227

Post by glenstein »

77pt77 wrote: post #222
glenstein wrote: post #214

Earlier quoted context omitted.

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.

Those guys basically developed Fourier analysis with very clunky notation. We'll be very lucky if these guys are doing anything even remotely as useful.

They produced conceptual breakthroughs that have advanced our understanding of black hole physics in ways not previously possible. If that was just lying around as a simple repurposing of a Fourier analysis, it wouldn't have sat around as an unresolved problem for decades.

But I understand that words meaning things is not part of the operative definition of success in the goalpost relocation industry.

Re: Physics is unreasonably good at creating new math

#228

Post by xanderlewis »

ndsipa_pomu wrote: post #226
xanderlewis wrote: post #225

Earlier quoted context omitted.

> Not sure that I agree as does a mathematical circle actually exist? The set of unit norm complex numbers surely exists just as much as the real numbers exist, doesn’t it? A circle is an idea, and it certainly exists.

I think you're using a different meaning of "exists" than I am. Ideas don't exist as you can't point at them, steal them, destroy them etc. I can point at something that approaches the concept of a circle and I can point at a set of objects that can be counted, but I can never see a mathematical circle (zero thickness would make it impossible to see) and I can't see a "four" without representing it by a symbol or col…

I guess one way to decide on a definition of ‘exists’ — since a given thing probably either exists or doesn’t — is to instead decide when it doesn’t exist.

Does a five-sided triangle exist? Well, the very concept seems to be self-contradictory, but surely the idea exists (since I just mentioned it, and you probably understood what it meant and could see why it was contradictory), and even if you don’t believe the idea exists you must eventually concede that the sentence that describes it exists!

If you think things can only exist if you can point at them, steal them and destroy them, then would you say the natural numbers (= 0, 1, 2, 3, …) don’t exist? That would seem to be a strange notion of existence.

Other than that it isn’t a physical object you can hold in your hand, I don’t see why there’s anything problematic about regarding the circle as an object that exists, even if it’s just (in some sense) a theoretical object.

If you take your position to its extreme (but, I would argue, logical) conclusion, almost nothing in your everyday life exists. It’s all atoms, and the fact that you regard, say, a guitar as being a guitar is rather weird because any given guitar is almost certain to be atomically distinct from every other guitar that has ever existed. Are guitars just ideas? Would you say there’s ‘no such thing as a guitar’ because they’re all just approximations to the ideal guitar?

Put simply: what does rejecting the existence of ideas buy you? I don’t see how it’s a productive (or very insightful) position to hold.

Re: Physics is unreasonably good at creating new math

#229

Post by ninetyninenine »

dxbydt wrote: post #110
lilyball wrote: post #102

Earlier quoted context omitted.

With the car & truck, and with the eagle, a lot of energy is lost into the environment. With two galaxies colliding, there is no environment to speak of. They're in space, and space is as close to a perfect vacuum as one might reasonably imagine. So the only real escape for energy is light, but I don't think there's any reason to believe colliding galaxies will produce absurd amounts of excess light (if it did we'd h…

I have zero issues with your logical reasoning - its the same reasoning aops gives. I'm simply asking - how do you know for sure that this actually happens in practice ? Like, have we observed such a thing ? I'm genuinely curious, no snark. If all we have is reasoning, with zero observation, then its equivalent to what JFK says in Oliver Stone's picture - "Theoretical physics can prove that an elephant can hang from…

The question is testing if your reasoning is in line with what you were taught. It is not questioning your ability to validate your reasoning experimentally.

I came to the same conclusion as the replier almost immediately as I was reading the question. It was obvious to me. But I do agree it’s a bad question as it relies on a lot of assumptions. Maybe the question is just testing if your ability to make reasonable estimates assumptions.

Re: Physics is unreasonably good at creating new math

#230

Post by ndsipa_pomu »

xanderlewis wrote: post #228
ndsipa_pomu wrote: post #226

Earlier quoted context omitted.

I think you're using a different meaning of "exists" than I am. Ideas don't exist as you can't point at them, steal them, destroy them etc. I can point at something that approaches the concept of a circle and I can point at a set of objects that can be counted, but I can never see a mathematical circle (zero thickness would make it impossible to see) and I can't see a "four" without representing it by a symbol or col…

I guess one way to decide on a definition of ‘exists’ — since a given thing probably either exists or doesn’t — is to instead decide when it doesn’t exist . Does a five-sided triangle exist? Well, the very concept seems to be self-contradictory, but surely the idea exists (since I just mentioned it, and you probably understood what it meant and could see why it was contradictory), and even if you don’t believe the id…

I'm simply drawing a distinction between something that physically exists versus something that doesn't physically exist.

Ideas don't (physically) exist although a representation of an idea can exist e.g. a mathematical circle doesn't physically exist, but representations of circles do exist and they vary with how close they get to the idea.

With your guitar example, you demonstrate how we classify things in a messy way. Because the idea of a guitar doesn't exist, but lots of representations of guitars exist, we just refer to those objects as "guitars" as we can recognise the "guitar idea" that they are made to represent.

Distinguishing between physical existence and non-physical existence is very useful - it allows you to separate the map from the territory. It's very useful to abstract the concept of "five" and recognise that it's different to five objects, despite them being so closely related. The abstraction of numbers becomes more useful when considering ideas such as negative or imaginary numbers - it would be difficult to reason about and use them if we continually think of numbers as only "counting objects".

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