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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

#191

Post by naasking »

hughesjj wrote: post #162
naasking wrote: post #119

Earlier quoted context omitted.

The Higgs boson was predicted in 1964. Gravitational waves were predicted in 1916. Bell's theorem was published in 1964. Basically every recent discovery in physics has been observations confirming old predictions and refuting the endless zoo of poorly motivated, imaginary particles that seems to be standard practice these days. There have been almost no truly significant, novel predictions that have a hope in hell o…

You don't consider ER=EPR as novel? Or CA-duality? Agreed that Post-quantum gravity is really cool and "fresh" Higgs/Bell/GW were experimental results, I was indeed trying to show that there's a huge lag between prediction and observation. Imo the paradigm shift that we're slowly undergoing is thinking about physics from a information theoretic perspective instead of a kinematics one. I'd argue that's even more funda…

They might be novel mathematical constructs but seemingly have no bearing on our universe. ER=EPR doesn't really solve anything because GR remains fundamentally incompatible with QM's linearity. That's the problem that needs to be solved. The core idea of ER=EPR wasn't even particularly novel, as Hadley effectively did something very similar back in 1997 [1].

CA-duality is again mathematically interesting, but physically dubious because it's based on anti-de Sitter space, which does not describe our universe.

Information theoretical formulations of QM are mildly interesting, but I don't think they will be revolutionary, and I don't think they are tackling the core problem, which is QM's linearity where we classically observe a non-linear universe.

[1] https://arxiv.org/abs/quant-ph/9706018

Re: Physics is unreasonably good at creating new math

#192

Post by trashtester »

dxbydt wrote: post #92
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.

> pontificate about things that are too small or too dark and far away to see I was bitten by this last week. I am enrolled in an aops physics course, titled Mechanics. So the last time I took any Mechanics was 40 years ago as a high school student in India. Most of the curriculum then was about stuff banging into each other aka collisions, & asking what happens to the result. Like some golf ball rolls down an inclin…

> conservation of momentum make an accurate prediction.

Accurate prediction of what?

If it's the velocity and location in the end state, the best answer is the eagle (once it comes to rest). The momentum of Earth is so huge that the eagle will end up precisely on the perch (if we disregard the inability of a living bird to be completely still)

For the cars, the exact end state depends on many other factors, as you say.

Finally, for the colliding galaxies, there may be some uncertainty about how dark matter and dark energy (or their absence) affect galaxy collisions. This may be beyond the understanding of whoever wrote the test, though.

Re: Physics is unreasonably good at creating new math

#193

Post by trashtester »

saagarjha wrote: post #151
lilyball wrote: post #121

Earlier quoted context omitted.

I have no idea if we've observed it. Galaxy collisions take a very long time, I'm not sure how we'd ever be in a position to observe both the starting state and result. That said, the point of the law of conservation of momentum is we don't need to observe it to know that it happens. Momentum is conserved, that's a fact. So the question becomes, what is it that makes this law not produce a good prediction about a sce…

That is, until gravitation waves carry away the energy :)

It doesn't matter much if they carry away energy, though the waves also carry away some momentum, I suppose, unless they're symmetric on both sides.

Re: Physics is unreasonably good at creating new math

#194

Post by entropicdrifter »

8n4vidtmkvmk wrote: post #158
thruway516 wrote: post #153

Earlier quoted context omitted.

Software developer: It is more important to find out how the keys were dropped in the first place. And after I do that it will be more efficient to just generate new keys. Disclosure, I'm a software developer

Write a unit test to prevent future key droppings.

(The actual unit test merely confirms that dropping the keys in one highly specific way is now impossible. The keys cannot fall from between your fingers because the code now mandates that you wear mittens)

Re: Physics is unreasonably good at creating new math

#196

Post by verisimi »

TheOtherHobbes wrote: post #185
verisimi wrote: post #38

Earlier quoted context omitted.

I agree, I think. I would say it like so, that maths is a sort of highly technical, rigorous language, but like any language it will describe what you want it to. It is easy to think that it is describing the underlying terrain, but it is actually working on three (shared) and model which have of the terrain. So, as we consider different things, maths will follow.

Its grammar is limited in ways we don't understand, because the grammar is based on abstractions of our experiences of the world and the relationships between them. If we can't imagine entire classes of relationship - likely because we do not have limitless intelligence - then the model will always be a partial analogy, not a full and complete abstraction.

I think we agree.

Re: Physics is unreasonably good at creating new math

#197

Post by vehemenz »

gitaarik wrote: post #173
vehemenz wrote: post #44

Earlier quoted context omitted.

> 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, mat…

Well if the fundamental constants were different, math would still work the same way. But if a universe acts in a completely different way, say like a dream world, where they is no logical physical causaulity, our universe's math would be irrelevant. You could still think about it but it would be irrelevant to that universe, and not applicable. And so you would also not be able to derive that math from within this un…

The properties of the universe affects mathematics insofar as matter is organized and living agents have a use for it, but its abstractions and logical relations still do not require the universe. I think a metaphysical position like physicalism would have to be invoked for that.

Re: Physics is unreasonably good at creating new math

#198

Post by trashtester »

tines wrote: post #89
hughesjj wrote: post #84

Earlier quoted context omitted.

> I say the math can’t be invalidated by observations I meant, isn't a counter-example or proof by contradiction an invalidation by a type of observation?

No, proof by contradiction is a logical construction, has nothing to do with the real world. Proof by counter-example could or could not be observation, depending on whether your example comes from observation or from pure logic.

I suppose even in pure math, if you postulate a set of axioms, then proceed to to prove some theorems, you're still at risk of someone providing something like a counter-example showing that your axioms are not consistent, and that not all of them can be true at the same time.

Meaning that even if the inductive logic is 100% correct, the theory can be incorrect due to using mutually exclusive (in some non-obvious way) axioms.

Re: Physics is unreasonably good at creating new math

#199

Post by trashtester »

nobodyandproud wrote: post #49
bee_rider wrote: post #31

Earlier quoted context omitted.

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 facto…

In Physics, you just remove all possible theories that are inconsistent with observations.

For instance, you can prove that Newton's laws are not 100% accurate.

Re: Physics is unreasonably good at creating new math

#200

Post by vagrantJin »

leptons wrote: post #155
Hasu wrote: post #140

Earlier quoted context omitted.

It is a common (but not universal[0]) practice in English writing to use either "he" or "she" as a pronoun for a person of unspecified gender to avoid the awkwardness of "they" or "one" or constructions like "he or she". No gender has been specified here, this is a neutral use of "she". [0] Very few practices in English writing are universal.

I think your entire reasoning is in reverse. Using "she" where no gender needs to be specified is the awkward thing to do, and it's not neutral, it's explicitly designating a female gender . Using "they/them" is far less awkward, the reader doesn't have to have any kind of opinion about the text based on gender associations, making it less awkward .

I must have missed the bit where gender was relevant to the joke being made.
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