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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

#41

Post by tomrod »

aeneasmackenzie wrote: post #32
teqsun wrote: post #9

Earlier quoted context omitted.

> "Your physics lecturer sounds like a Platonist." I don't understand what this means, but it made me envision a McCarthy-esque witch hunt for "Platonist and Platonist sympathizers" lurking amongst the faculty

Just say witch hunt. McCarthy was entirely correct that there were a lot of communists and communist sympathizers, so many that many of the people he thought were helping him were themselves communists or communist sympathizers. Witches on the other hand are not real.

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

Re: Physics is unreasonably good at creating new math

#42

Post by dizzant »

LeifCarrotson wrote: post #15
selectodude wrote: post #11

Earlier quoted context omitted.

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.

This is an interesting take, the article touches on it too.

> “Physicists are much less concerned than mathematicians about rigorous proofs,” says Timothy Gowers, a mathematician at the Collège de France and a Fields Medal winner. Sometimes, he says, that “allows physicists to explore mathematical terrain more quickly than mathematicians.”

GP is right that the currently observed physical laws go far beyond our ability to observe them in reality because of the cost of observations. International effort over decades is required to create facilities capable of making helpful new observations: think of LHC, LIGO, James Webb, etc.

On the other hand, once the facilities are built and ground-breaking observations appear, we suddenly have a debt of theoretical and simulated exploration to understand all their implications. The low cost of computation greatly extends the value we can take from every truly new observation of reality.

In order to observe something new, we must be able differentiate it from something already understood. It seems like the physics and math communities are currently in a season of increasing our understanding of the existing models well enough to motivate trying to break them.

Re: Physics is unreasonably good at creating new math

#43

Post by jfactorial »

tomrod wrote: post #41
aeneasmackenzie wrote: post #32

Earlier quoted context omitted.

Just say witch hunt. McCarthy was entirely correct that there were a lot of communists and communist sympathizers, so many that many of the people he thought were helping him were themselves communists or communist sympathizers. Witches on the other hand are not real.

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.

Re: Physics is unreasonably good at creating new math

#44

Post by vehemenz »

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’…

> On some level mathematics is a description of reality that we can use to compute things in reality.

This is contested by nominalists. They'd say you have it backwards. Mathematics is just an abstraction/language that can be used as a tool. The reason we're able to understand the world through mathematics says more about the power of mathematics than it does about the world. If the physical world were different, math would still work.

Re: Physics is unreasonably good at creating new math

#46

Post by nobodyandproud »

tech_ken wrote: post #22
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.

Well also the idea of physics as the field we currently have didn't exist much before the 17th century. Movement of bodies, astronomy, fluid dynamics, electromagnetics, optics, etc. all kind of were their own thing (if they existed at all). Fundamental developments in calculus in the late 1600s enabled these subjects to be collected under one method of study/analysis which we now call physics. As much of modern math…

It—that is, science at the time—all fell under the umbrella term of natural philosophy.

Re: Physics is unreasonably good at creating new math

#47

Post by zeroonetwothree »

Do we know if it’s better at creating new math than other fields? For example, computers sure created a lot of new math. Statistics was entirely driven by external pressure from medicine, social sciences, and business. Finance and economics created a lot of math around modeling and probability. And so on.

Re: Physics is unreasonably good at creating new math

#49

Post by nobodyandproud »

bee_rider wrote: post #31
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.

This was the result of Philosophers ultimately winning, despite the fact that they are so annoyingly pedantic that we pretend not to care about their work, and also, by ignoring them we can invent iPhones which are really neat. You can’t prove anything by observation. You can gather evidence through repeat experiment and become reasonably confident as your theory continues to not be incompatible with the observed uni…

“Prove” could mean many things. For physics, prove what?

That a given model is the one and only model that accurately explains the known universe? Then I agree. Observation won’t get you there. Asymptotic at best.

But by “prove”, that it accurately or usefully makes predictions with respect to certain constraints (which may not be known)?

That’s a more modest use of “prove”, where observation is certainly a key factor.

Re: Physics is unreasonably good at creating new math

#50

Post by jjk166 »

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.

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