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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

#51

Post by bee_rider »

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.

He missed most of the actual Soviet agents, though, right? Both seem to have mostly focused building up a lie to suppress some outside-the-norm element that the guy in charge wanted to hunt. That McCarthy also managed to have some real agents to miss is not a big difference.

Re: Physics is unreasonably good at creating new math

#52

Post by goatlover »

mrtesthah wrote: post #8
goatlover wrote: post #5

Earlier quoted context omitted.

What does that mean? Physics is still empirical at the end of the day. Experiments decide what theories best explain the world. Math doesn't have such a requirement. It doesn't need to model natural phenomenon. Your physics lecturer sounds like a Platonist.

See Our mathematical universe : my quest for the ultimate nature of reality by Max Tegmark https://archive.org/details/ourmathematicalu0000tegm

That's metaphysics not science. I'm not against metaphysics, but philosophy is distinct from physics. And it's Tegmark's particular metaphysics. Interesting but hardly a consensus among physicists or philosophers.

Re: Physics is unreasonably good at creating new math

#53

Post by goatlover »

teqsun wrote: post #9
goatlover wrote: post #5

Earlier quoted context omitted.

What does that mean? Physics is still empirical at the end of the day. Experiments decide what theories best explain the world. Math doesn't have such a requirement. It doesn't need to model natural phenomenon. Your physics lecturer sounds like a Platonist.

> "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

Platonist meaning an assumption that mathematical objects have a real existence, and the universe is inherently mathematical, so we can just defer to mathematical reasoning instead of observation. I'm applying the term in a modern setting, not Plato or Aristotle debating the forms.

This debate played out in String Theory were some proponents claimed physics had progressed beyond the need for observation in favor of beautiful mathematical reasoning, that provided great explanatory power. But String Theory so far has failed to deliver a theory which describes our universe. Physics still needs to explain the actual world.

Re: Physics is unreasonably good at creating new math

#54

Post by tines »

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…

> Math, of course, is that stuff which can’t be invalidated by observations.

This is a misunderstanding of what math is, I think. You can invent a perfectly valid mathematical theory that conflicts with observations. Math is just a sequence of "if this, then this" and if the conclusions follow from the premises, it's math. But if you demonstrate that in the universe we occupy, a premise isn't true, then the mathematical theory isn't any less valid, it's just not sound in our universe.

For example, there's a ton of completely valid mathematical work on the correspondence between anti-de Sitter spaces and Conformal Field Theory. However, much of this mathematics has no application in our universe, because our universe seems to be a de Sitter space (positive cosmological constant/expanding), not an anti-de Sitter space (negative cosmological constant/contracting). That doesn't make their math invalid, it just makes it not real.

You can also do a lot of math in Minkowski spaces, which are flat. But our universe isn't flat, it's curved. Doesn't mean it's not math, just that it's not real in our universe.

Re: Physics is unreasonably good at creating new math

#55

Post by l33t7332273 »

glitchc wrote: post #34
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.

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?

Re: Physics is unreasonably good at creating new math

#56

Post by janalsncm »

tines wrote: post #7
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.

> 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.

The article discusses how Knot Theory was once conceived to explain different atoms and their properties. This physical explanation was abandoned after the electron was discovered (demonstrating the existence of sub-atomic structures). At that point, Knot Theory was correct math with no physical application.

I’m sure there are other examples but I’m not a mathematician.

Re: Physics is unreasonably good at creating new math

#57

Post by waterhouse »

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.

Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

— V.I. Arnold: "On teaching mathematics" (1997)

Re: Physics is unreasonably good at creating new math

#58

Post by glenstein »

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.

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 beautiful about how physics, including string theory, have lead to the creation of new math, and how that is suggestive of an unmet promise. To ignore that just to come in and repeat for the 1000th time the world's most repeated thing about string theory, and take a completely unnecessary cheap shot at Ed Witten is the perfect embodiment of why comment sections can too often be a depressing waste of time.

Re: Physics is unreasonably good at creating new math

#59

Post by goatlover »

Joker_vD wrote: post #13
goatlover wrote: post #5

Earlier quoted context omitted.

What does that mean? Physics is still empirical at the end of the day. Experiments decide what theories best explain the world. Math doesn't have such a requirement. It doesn't need to model natural phenomenon. Your physics lecturer sounds like a Platonist.

> Math doesn't have such a requirement Geometry? Lobachevsky actually proposed a test on measuring sum of angles of a celestial triangle to decide which geometry actually applied to the real world.

The real world determines which geometry applies. That's the crucial difference. Sometimes physicists use mathematical reasoning to figure things out that map onto the world and later observation validates their reasoning. But observation can also invalidate, and then physicists have to go back to the drawing board or devise new experiments.

Re: Physics is unreasonably good at creating new math

#60

Post by elashri »

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?

> Are you saying that one day we will be able to devise experiments to observe these things?

The problem is that we might be on an exponential scale. So instead of decades it could be centuries assuming the humanity survives and keep develop new technologies and tools.

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