[HN Gopher] Physics is unreasonably good at creating new math
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Physics is unreasonably good at creating new math
Author : Brajeshwar
Score : 140 points
Date : 2024-09-04 13:43 UTC (9 hours ago)
(HTM) web link (nautil.us)
(TXT) w3m dump (nautil.us)
| Almondsetat wrote:
| Could this be a case of physics being more "tangible", thus
| leading to more obvious paths? Like, if you only study pure maths
| and you stay in your field, can you really point to a concrete
| direction for where to look for new stuff? In physics, your job
| is literally to study how the universe already behaves, so you
| have a frame of reference to take inspiration from and the
| efforts are a bit more concentrated. In fact, since models don't
| describe reality perfectly, you can always observe where it fails
| to know in which direction to attack. In maths, on the other
| hand, everything that is proven is correct forever. The model
| _is_ reality. So it seems to be more difficult to find
| criticalities to look for. It 's more of a "I wonder if this
| property does or doesn't hold" ordeal, which seems much more
| vague. Just a question.
| ezst wrote:
| Almost like the case of constrained environments being a
| fertile ground for new creative solutions!
| lupire wrote:
| It's more of a hint than a constraint. It's using the
| Universe as a brainstorming partner.
| cjs_ac wrote:
| 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.
| goatlover wrote:
| 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.
| tombert wrote:
| I don't think OP is really wrong here. Wasn't there a debate
| in the late 19th century that basically asked if math _had_
| to have some mapping to the natural world, or should it work
| independently? I though there was some argument about this
| with Hilbert and Poincare about this, and Hilbert more or
| less won.
| mrtesthah wrote:
| See _Our mathematical universe : my quest for the ultimate
| nature of reality_ by Max Tegmark
|
| https://archive.org/details/ourmathematicalu0000tegm
| goatlover wrote:
| 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.
| teqsun wrote:
| > "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
| HPsquared wrote:
| "In this house we side with Aristotle."
| aeneasmackenzie wrote:
| 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.
| tomrod wrote:
| But Platonists, ironically on many levels, are also real.
| Sometimes complex. But never fully imaginary.
| jfactorial wrote:
| There are no Platonists, only imitations of the one true
| heavenly Platonist.
| tomrod wrote:
| Genuinely chuckling.
| bee_rider wrote:
| 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.
| goatlover wrote:
| 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.
| throwaway17_17 wrote:
| As fundamentally opposed to Mathematical Plantonism, I am
| fully of the opinion that I am nowhere near anything but a
| minority position among those that hold an opinion on the
| philosophy of mathematics. It would be kind of hard to have
| a witch hunt for something so common amongst working
| mathematicians:
|
| The saying that "the typical working mathematician is a
| platonist during the week and becomes a formalist on
| Sunday" is becoming increasingly familiar. During working
| days, they are convinced that they are dealing with an
| objective mathematical reality that is independent of them,
| and when on Sunday they meet a philosopher who begins to
| question this reality, they claim that mathematics is in
| fact the juggling of formal symbols (see Davis et al.,
| 2012, p. 359). The Platonist attitude of the working
| (rather than philosophizing) mathematician is so common
| that Monk (1976, p. 3) was tempted to make a subjective
| estimate to the effect that sixty-five percent of
| mathematicians are platonists, thirty percent formalists,
| and five percent intuitionists. [1]
|
| [1] - A Metaphysical Foundation for Mathematical Philosophy
| (Wojtowicz,Skowron 2022)
| lupire wrote:
| It's a very weak loose statement, but I think the idea is
| that leading scientific and mathematical thinkers (think
| Newton as a quintessential example) were "natural
| philosophers" who studied whatever caught their interest and
| took it wherever it went. Astronomers invented lenses and
| ground them and studied the starts and developed algebra and
| calculus to model the observations.
|
| Some people were more narrowly focused, like Gauss who did
| mostly math (but an amazing breadth of math!)
|
| There was a lot of hesitancy about math that couldn't be
| empirically illustrated by building out of atoms, like
| irrational numbers and then transcendental numbers and
| imaginary numbers and then infinite structures.
| failbuffer wrote:
| Add negative numbers to your list as well. Mathematicians
| used to rearrange terms specifically to avoid them (e.g.
| before the concept existed).
| Joker_vD wrote:
| > 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.
| verzali wrote:
| There are multiple geometries though, they don't have to
| describe the real world. In mathematics you are free to
| base your geometry on whatever axioms you want, whether
| they are realistic or not. I'd say the question of which
| geometry applies in the real world is more a question for
| physicists (or cosmologists, today).
| Joker_vD wrote:
| This is a very late-XIX century development. Geometry
| used to be an integral part of physics, vide Newton's
| _Principia_.
| meroes wrote:
| Wondering if Euclid's parallel postulate was independent
| goes back millennia though. And that's like the key
| ingredient for multiple geometries.
| Joker_vD wrote:
| No, it's trying to prove that Euclid's parallel postulate
| can be derived from other axioms is what goes back
| millennia. People were certain it's a) true, b) necessary
| consequence of other axioms. Gauss was probably the first
| to consider the possibility that it may be false; others
| at best tried _reductio ad absurdum_ , arrived to some
| wildly unusual theorems, decided those were absurd enough
| to demonstrate the truth of the fifth postulate, and went
| back to trying to derive it.
| meroes wrote:
| It's either true as an axiom or true as derived from
| other axioms and/or theorems. In neither case does
| latching onto Euclid's other common
| notions/postulates/theorems as _the_ selection it must be
| proved true _from_ make sense as a 1.5kya long task.
|
| I think there must have been a sense that it was true
| only as an axiom. Proving it from other axioms/theorems
| was then a goal to secure it's truth "further". But you'd
| only attempt that if you thought there was something
| questionable in the first place.
| goatlover wrote:
| 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.
| tines wrote:
| > 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.
| selectodude wrote:
| 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.
| LeifCarrotson wrote:
| 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.
| TheRealPomax wrote:
| Furthermore, even if you can write down the math, it
| might not even be solvable (sometimes provably so) and
| simulations (or more accurately, numerical analysis and
| the finite element method) are our only option.
| dizzant wrote:
| 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 College 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.
| glitchc wrote:
| Like the atom was in the 18th century? Electrons and
| protons in the 19th? Quarks in the 20th?
| l33t7332273 wrote:
| 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?
| elashri wrote:
| > 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.
| glitchc wrote:
| Short answer: Yes, and new instruments to make those
| measurements possible. That's how physics has always
| progressed. Why would this point in time be suddenly
| different from the past 400 years? Because we can't see a
| clear path forward? That's always been the case. Insight
| and ingenuity of individuals is what gets us through it
| every time.
| bluGill wrote:
| > Why would this point in time be suddenly different from
| the past 400 years?
|
| Back in the late 1800s physicists thought they were done,
| other than adding a few more decimals to the values of
| fundamental constants. There were a few "small areas"
| where things didn't make sense, but they "would figure
| them out". One of those small areas turned out to be
| relativity, and the other quantum mechanics. There are
| some known areas where we still don't know what is going
| on, but a lot of physics is adding more decimals to
| constants (finding fundamental particles were we expect
| them for example)
|
| The real question - that we cannot answer - are the
| things we don't understand small things we will figure
| out, or major things that will again turn our
| understanding of the universe upside down. Your guess is
| as good as mine.
| waveBidder wrote:
| Because the tools we need to measure differences between
| the proposed models are more than the current total
| economic output. We'll need several generations before
| its feasible.
| janalsncm wrote:
| I don't agree with this. I think there are definitely
| people like Michio Kaku who have books to sell who spend
| their time pontificating. People just think that physics
| looks like pontificating because that's what it looks like
| on TV.
|
| But there are also active researchers doing real research.
| Physics postdocs aren't just sitting around in a circle
| making up stories about what the universe is like.
| alickz wrote:
| please forgive my ignorance, has there been notable
| progress in the field of physics in the last decade?
| noteworthy breakthroughs i mean
|
| i ask out of layman curiosity
| janalsncm wrote:
| No worries. I'm (mostly) a layman too, I just happened to
| have watched this video recently:
|
| https://youtu.be/d_o4k0eLoMI
|
| Maybe a more direct answer to your question would be the
| discovery of the tetraneutron.
| hughesjj wrote:
| Absolutely, they're still handing out nobels after all.
|
| Personally I think the ER=EPR conjecture and the
| complexity/action duality hypothesis are incredibly
| interesting. Technically ER=EPR was formulated in 2000s
| (maybe 90s?) and CA-duality is approaching if not just
| past 10 years old, but the thing about asking for
| breakthroughs is that they take a while to percolate. Ex
| Hawking radiation wasn't formulated until, like, 50-70
| years after the "basis" (schwarzshild, Schrodinger) was
| formed.
|
| There's also been a ton of productive research
| integrsting computer science and physics lately ( on hn
| last week: https://arxiv.org/abs/2403.16850 and 2022
| novel prize;
| https://www.scientificamerican.com/article/the-universe-
| is-n...)
|
| Also JWST just keeps on giving, and gravitational waves
| were only confirmed in 2017. If you extend a bit further
| higgs was in the 2010s
|
| So, in summary, in the late 10 years - we've shown a
| break in our intuition of physics (nonloca-realness, that
| 2022 paper) - proposed some novel yet elegant theories
| (CA-duality, and I'd hope you'd begrudge me er=EPR) -
| confirmed some insane provings to the underlying reality
| (gravitational waves)
|
| If those aren't noteworthy, I'd ask what you consider
| noteworthy any why you consider it noteworthy
| naasking wrote:
| 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 of panning out in
| like, 40 years or more. The only mildly interesting,
| novel idea in physics has been quantum computing, and
| even that was first published in 1980.
|
| > So, in summary, in the late 10 years - we've shown a
| break in our intuition of physics (nonloca-realness, that
| 2022 paper)
|
| This paper showed no such thing, it has the same
| superdeterminism loophole as every other paper attempting
| to refute local realism.
|
| Physics is stuck in a local QM-GR minimum, and some truly
| novel ideas are needed to kickstart things again.
| Oppenheim's postquantum gravity is the first truly novel
| idea I've seen in awhile.
|
| I also agree that JWST is giving us great data, some of
| which has placed LCDM on the ropes, but astrophysicists
| are hard at work adding epicycles to keep it alive.
| Misdicorl wrote:
| The past decade is a difficult framing to ask the
| question in. Notable breakthrough results are usually
| understood in hindsight and a decade just isn't a lot of
| time for that context and understanding to develop.
| Science also doesn't necessarily develop in this way with
| consistent progress every X timespan. Usually you get
| lots and lots of breakthroughs all at once as an
| important paradigm is shattered and a new one is
| installed. Then observations with tiny differences slowly
| pile up and a very blurry/messy picture of the problems
| with the new paradigm takes shape. But none of those
| things feels like a breakthrough, especially to a layman.
|
| That said: I'll submit the first detection of
| gravitational waves as two black holes merged together in
| 2020 as meeting the bar of "notable breakthrough in the
| last decade".
| ricksunny wrote:
| >first detection of gravitational waves as two black
| holes merged together in 2020 a
|
| 2015. (Your point is otherwise taken).
|
| https://en.wikipedia.org/wiki/First_observation_of_gravit
| ati...
| FuriouslyAdrift wrote:
| The confirmation of the Higgs boson is pretty huge...
| dxbydt wrote:
| > 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 inclined
| plane at some angle theta & hits a identical stationary
| ball & the objects stick together & we're supposed to
| compute where they end up. I was curious what American
| students learn, so I enrolled in this aops course.
|
| Last week's assignment asks me - under which scenario will
| conservation of momentum make an accurate prediction. The 3
| scenarios are - truck collides with car, eagle comes to
| rest at perch after flying from far away, and two galaxies
| colliding into each other to form a third megagalaxy.
|
| I naturally picked truck & car - so aops knocks off 2
| points for the wrong answer! Apparently if a truck collides
| with a car there will be so much thermal energy produced by
| the friction of the road, any prediction you make about the
| final velocity of the car assuming conservation of momentum
| will be bogus.
|
| So then I pick eagle coming to rest - aops knocks off 2
| more points for the wrong answer! Apparently when eagle
| comes to land, it will open its giant wings to create air
| resistance, so momentum won't be conserved.
|
| Ok so that leaves the 2 galaxies. I pick that & get my
| correct answer, a pathetic score of 3/7. I'm left wondering
| how do we even know this is correct. Galaxies are too far
| away to observe. How is one supposed to compute the mass of
| 2 separate galaxies, & then find their moving velocities
| accurately, & then find the final velocity of the combined
| galaxy, & thus confirm momentum was conserved ? Seems very
| far fetched. I would rather go with the car & truck.
| lilyball wrote:
| 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 have observed it). Therefore
| the energy of the collision is preserved within the
| system, and so conservation of momentum will produce an
| accurate prediction.
| dxbydt wrote:
| 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 a cliff with its tail tied to a daisy."
| lilyball wrote:
| 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 scenario? And the
| answer is that when the scenario involves other factors
| that can take kinetic energy away from the system. In the
| car & truck scenario, we have friction with the road as a
| pretty huge factor, that removes a lot of energy. Even
| without a collision, friction is why a car needs to
| constantly burn fuel in order to keep moving at the same
| speed. So it should be no surprise that a car & truck
| collision will lose a ton of energy to friction. In the
| eagle landing scenario, that's not even a simple
| collision between the eagle and the branch, the eagle
| uses its wings to slow down, and the branch is fixed to a
| tree and absorbs the remaining energy. An eagle landing
| on a branch is an eagle that comes to rest on the branch,
| it doesn't just not conserve momentum it gets rid of all
| of it. But in the colliding galaxies scenario, there's no
| surface to have friction with, there's no wings beating
| against air, there's no tree anchoring one of the objects
| in place, nothing to absorb any energy, no environment to
| dissipate energy in. Without anything to get rid of
| kinetic energy, conservation of momentum will predict the
| results.
| bee_rider wrote:
| 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 universe. Then the problem of induction
| says, "well, it isn't incompatible with the part of the
| universe... that you've observed, yet!" And then you say,
| "ok, but I want to use my theory to invent an iPhone, and I
| think there are enough people in the part of the universe
| that I've already observed. I looked very hard to find
| evidence against my theory, and I don't think anyone will
| find evidence against it before I've sold enough iPhones to
| retire."
|
| Math, of course, is that stuff which can't be invalidated by
| observations. But it is very hard to do enough math to retire
| off it.
| nobodyandproud wrote:
| "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.
| bee_rider wrote:
| Maybe proof should be used for that more modest concept.
| In the sense of "bullet proof." Similar to a piece of
| armor with a bullet proof; the ding from where it was
| shot for testing, a physics theory could be described as
| "microscope proof," haha. We hit it with a bunch of
| microscopes and it didn't fall apart.
| hgomersall wrote:
| Interesting linguistic aside: "the exception that proves
| the rule" makes use of this more old fashioned use of
| prove, to test. So it's the exceptional case that tests
| the rule.
|
| With that in mind, "prove" is perfectly fine to use in
| the context of science.
| tines wrote:
| > 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.
| bee_rider wrote:
| I think this is a disagreement about the word invalidate,
| and maybe it was a bad pick on my part. The observations
| don't make the math wrong, maybe less useful.
|
| But, I say the math can't be invalidated by observations;
| and you describe some cases where the math is valid but
| might or might not be applicable to certain physical
| cases. So actually, I'm not clear as to what you are
| saying I'm misunderstanding.
| hughesjj wrote:
| > 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?
| tines wrote:
| 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.
| tines wrote:
| Ok, I see what you mean now.
|
| I took your word "invalidate" to mean "be proven false"
| whereas I meant "valid" as in "logically coherent, even
| if not true."
| janalsncm wrote:
| 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.
| tech_ken wrote:
| 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 follows from the lineage of calculus the border between
| the things being modeled and the tools for modeling them is
| naturally kind of blurry, however the distinction did still
| exist quite strongly throughout this entire period. Look at ex.
| probability or algebra, although often researchers were
| pursuing both physics and math, they were aware that the
| subjects were distinct.
| nobodyandproud wrote:
| It--that is, science at the time--all fell under the umbrella
| term of natural philosophy.
| waterhouse wrote:
| 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)
| janalsncm wrote:
| Physics is the subset of mathematics with physical
| application. However mathematics need not have physical
| applications in order to be valid math.
| naasking wrote:
| Math probably split off a bit because of the attempts at
| formalization. That was a useful tangent though, arguably
| giving us computer science via the lambda calculus, Turing
| machines, etc.
| Onavo wrote:
| Physics is also great for machine learning, though the approaches
| can be rather unintuitive. For example message passing and belief
| propagation in trees/graphs (Bayesian networks, Markov random
| fields etc.) for modeling latent variables are usually taught
| using the window/rainy weather marginal probability analogy and
| involves splitting out a bayesian/statistical equation into
| subcomponents via the marginalization chain rule. For physicists
| however, they tend to teach it using Ising models and magnetic
| spin, which is a totally different analogy.
|
| A lot of the newer generative ML models are also using
| differential equations/Boltzmann distribution based approaches
| (state space models, "energy based" models) where the statistical
| formulations are cribbed wholesale from statistical
| physics/mechanics and then plugged into a neural network and
| autodiff system.
|
| The best example is probably the Metropolis-Hastings algorithm
| which was invented by nuke people.
|
| https://web.archive.org/web/20150603234436/http://flynnmicha...
| scarmig wrote:
| Another is the Nakano-Amari-Hopfield model, which is based on
| Ising. Hopfield himself was a trained physicist.
| whimsicalism wrote:
| What modern ML uses those techniques? my understanding is ebm
| is quite rare
| Onavo wrote:
| Research mostly, lots of these techniques are used for speech
| synthesis and occasionally image models (not LLMs)
| hangsi wrote:
| The common method for choosing the next output token for an
| LLM is sampling from a Boltzmann distribution. If you have
| seen the term "temperature" in the context of language
| models, that is a direct link to the statistical gas
| mechanics.
| whimsicalism wrote:
| i don't find the connection between softmax and boltzmann
| really all that deep tbh (compared to say, the connection
| between field theory/ising models and EBM)
| janalsncm wrote:
| One that many people may be familiar with is Stable Diffusion,
| which is used in many AI image generators today. There is an
| analogy between random noise -> image and a random distribution
| of gas particles -> concentrated volume of particles.
|
| https://arxiv.org/abs/1503.03585
| verzali wrote:
| > "Bad" physics can sometimes lead to good math.
|
| cf. string theory
| crazydoggers wrote:
| 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'll have other ratios and values that have
| other relationships to other things in physical reality.
|
| And if reality was different, hence the physical laws were
| different then the math would be different.. and the beings in
| that world might wonder why their math and physics were so
| interconnected.
| vehemenz wrote:
| > 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.
| janalsncm wrote:
| If this was true then every bit of math must have a real-world
| application. But math doesn't need to have real-world
| applications in order to be valid.
| throw0101b wrote:
| See also perhaps the article "The Unreasonable Effectiveness of
| Mathematics in the Natural Sciences":
|
| * https://web.archive.org/web/20210212111540/http://www.dartmo...
|
| * https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
| jordanpg wrote:
| `"Well, now you are pushing your joke too far," said the
| classmate, "surely the population has nothing to do with the
| circumference of the circle."`
|
| I've always loved this line and paraphrase it often. It's an
| eminently reasonable and yet accidentally profound thing to
| say.
| glenstein wrote:
| 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.
| 77pt77 wrote:
| 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.
| glenstein wrote:
| 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.
| 77pt77 wrote:
| 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).
| zachf wrote:
| Is your preferred remedy that quantum gravity be entirely
| defunded, or instead that more funding be redirected to
| any of the other programs to study quantum gravity? If
| the latter, which ones in your opinion are more likely to
| be productive than string theory?
| 77pt77 wrote:
| I have no remedies.
|
| But I refuse to say "thank you very much" when sand has
| been thrown at my eyes for decades.
| naasking wrote:
| Your suggestion implicitly asserts that string theory was
| productive, which is exactly the claim that seems to be
| in contention.
|
| I don't think it's too wild to suggest that, without the
| constraints of string theory imposed by advisors, lots of
| novel approaches would have been tried. We have no idea
| what could have been produced.
|
| As for quantum gravity specifically, arguably not much
| progress will be made without more data, and we now have
| some proposed experiments that can be conducted here on
| Earth to test them.
| zachf wrote:
| 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/CFT that are useful in other
| contexts to understand real physics---and the
| alternatives have not (yet). There are many physicists
| who spend their lives studying alternatives to string
| theory with 100% of their time. I hope for their sake
| that there is a similar pot of gold at the end of their
| rainbows. It has not yet materialized.
| paulpauper wrote:
| _And that amounted to 60 years (and counting) of absolutely
| nothing in terms of how the physical world works._
|
| this is in part because it's outside the scope of existing
| technology
| marcosdumay wrote:
| Try to make some innovative software product without talking to
| any user. You'll see why physics is good at crating new math.
| slashdave wrote:
| Do you value the quality of a mathematical theory by the number
| of applications, or the intrinsic beauty of the theory itself?
| Retric wrote:
| To be beautiful it must first exist.
|
| It's far more difficult to come up with novel mathematics
| without some external inspiration.
| munk-a wrote:
| I judge the beauty of math and code by the how concisely and
| simply they can model the object in question - if the math
| exists abstractly and isn't trying to model any actual thing
| or concept it isn't particularly beautiful to me because it
| isn't an accomplishment of expressiveness - it's instead just
| a coincidence that if you put some symbols together you only
| need those symbols.
|
| There are, of course, times that concise expressions aren't
| possible and multiple strange and arbitrary values come into
| play (coefficients of friction or earth's gravity at sea
| level aren't particular nice numbers or expressions) and that
| just tends to highlight how beautiful things are when those
| icky real-world numbers can be canceled out and you're left
| with a clean expression.
| qubyte wrote:
| This is really interesting to me. It could imply that an ugly
| theorem is less valuable. What if a theorem is ugly but
| useful vs a beautiful but esoteric one?
| mrguyorama wrote:
| Then you should study Algorithms, where "the perfect answer
| is impossible, without simply trying all permutations, but
| this process gets you a close answer 99.9% of the time"
| marcosdumay wrote:
| It doesn't matter. Constraints enable art, not the other way
| around.
| Jerrrrrrry wrote:
| Are you as theoretical physicist interested in string theory?
|
| aint much of a Venn diagram on that one, only thing more
| circular is a non-rotating black hole, or a couple singular
| rotating points
| 77pt77 wrote:
| "Physicists are much less concerned than mathematicians about
| rigorous proofs. ... That allows physicists to explore
| mathematical terrain more quickly than mathematicians."
|
| The end.
|
| There's no magic here.
| tech_ken wrote:
| > 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
| relationship holds. Math is, IM humble O, the ultimate domain-
| specific language. It's a tool we use to model things, and then
| often it turns out that the model is interesting in its own
| right. Trying to model new things (ex. new concepts of reality)
| yields models that are interesting in new ways, or which
| recontextualize older models; and and so we need to reorganize,
| condense, generalize, etc; and so the field develops.
| verisimi wrote:
| 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.
| groos wrote:
| G.H. Hardy would like to disagree.
|
| https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology
| graycat wrote:
| Physics research gets funded because of applications, existing or
| promising, for curiosity, fundamental science, the economy,
| medicine, and national security, etc. Since math can help physics
| research, that research is funded and motivated to make
| applications of math, old or new. Math alone is less involved
| with applications.
| torrefatto wrote:
| 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 long passed since
| we are required to stop playing with these smoke and mirrors.
| jjk166 wrote:
| > 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.
| paulpauper wrote:
| sorta. the construction of particle accelerators has been
| justified to test the hypotheses of string theory
| torrefatto wrote:
| You are wrong.
|
| Particle accelerators have been built since way before any
| string theory was formulated.
|
| The biggest and most powerful existing accelerator (LHC)
| has been built to fulfill the high energy/high luminosity
| requirements to explore the Highs boson energy regime (that
| has been found) and at most the lightest supersymmetric
| particles (not found as of today).
|
| The Higgs boson is a cornerstone of the Standard Model.
| Supersymmetry is an extension to it that does not involve
| strings.
|
| https://home.web.cern.ch/science/physics/supersymmetry
| torrefatto wrote:
| You are right, the amount of money spent in string theory
| proposals has been staggering if you take into account the
| size of the field. For decades competing (or even just non-
| aligned) research lines have been starved to feed this
| behemoth.
| elashri wrote:
| > no falsifiable prediction
|
| You forgot to add "with our current technology ability to probe
| the required energy scale".
| torrefatto wrote:
| They produced a family of theories with an infinite amount of
| underlying possible geometries, and we still don't know if
| these reduce in the low energy limit to the standard model. I
| humbly suggest this reading:
|
| https://www.americanscientist.org/article/is-string-
| theory-e...
|
| If not realistically "non falsifiable" this sounds to me at
| least "not scientifically relevant" in the context of
| physics.
| tim333 wrote:
| They have probably produced some new maths, maybe as much as if
| you threw similar amounts of money at the maths department?
| bluGill wrote:
| And right now we have no reason to think either would produce
| more useful math. Math at least is honest about studying math
| for the sake of math (or truth and beauty). Nothing wrong
| with throwing money at math, but physics is supposed to be
| about understanding the universe so if we only get math we
| get a bad return on investment no matter how nice the math
| is. Even if the math turns out to be useful elsewhere we
| didn't get what we wanted out of the investment.
| torrefatto wrote:
| At the cost of starving other research lines in _theoretical
| physics_ (the thing they told are trying to work on).
| jmyeet wrote:
| I'm not a physics or math whiz but isn't the relationship more of
| a virtuous cycle?
|
| I think I read that the 20th century was a revolution because of
| the marriage between physics and math. Quarternions are key to
| relativity. Discrete math is littered all over quantum mechanics
| and the Standard Model. Like U(1) describes electromagnetism,
| SU(2) describes the weak force and SU(3) describes the strong
| nuclear force. In particular the mass of the 3 bosons that
| mediate the weak force is what led directly to the Higgs
| mechanism being theorized (and ultimately shown experimentally).
|
| One of the great advances of the 20th century was that we
| (provably) found every finite group. And those groups keep
| showing up in physics.
|
| The article mentions how string theory has led to new
| mathematics. This is really interesting. I'm skeptical of string
| theory just because there's no experimental evidence for "compact
| dimensions". It seems like a fudge. But interestingly there have
| been useful results in both physics and maths based on if string
| theory was correct.
| throwawaymaths wrote:
| We need "beermaking is unreasonably good at creating new stats"
| zeroonetwothree wrote:
| 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.
| marxisttemp wrote:
| https://archive.ph/yUiis
| slashdave wrote:
| If you want to bring physics and mathematics closer together,
| then string theory is a rather bad example to follow.
| pyb wrote:
| "Mathematics is the part of physics where experiments are cheap."
| (V.I. Arnol'd)
| 77pt77 wrote:
| Arnold was an unusual high quality thinker.
| aithrowaway1987 wrote:
| > Might there be certain laws of physics that are also
| "necessary" in the same way? In his paper, Molinini argues that
| the principle of conservation may be one such law. In physics,
| some properties of a system, such as energy or momentum, can't
| change. A bicyclist freewheeling down a hill, for example, is
| converting her gravitational potential energy into movement
| energy, but the total amount of energy she and her bike have
| stays the same.
|
| Arithmetic itself is a consequence of physical conservation: if
| you have a collection of four acorns, another collection of three
| acorns, then combine them without dropping an acorn, then you
| must have a collection of seven acorns. It is our deep physical
| understanding of space and causality which leads to simple
| arithmetic being intuitively true to most (if not all)
| vertebrates. (If the squirrel only got six acorns after combining
| then there must be a _causal_ explanation for the quantitative
| discrepancy; another squirrel stole an acorn from the older
| stash, or maybe it fell in a hole.)
| nyc111 wrote:
| The subject of study of physics is "physical quantity" which is
| defined as a number with a unit. Physical quantity doesn't have
| to be a "physical" quantity. So physics does not study
| exclusively physical objects. I think this is how mathematics and
| physics are related, mathematics does not deal with units (except
| unity).
| goldfeld wrote:
| Obviously, physics never creates any math but discovers it, there
| are no new things under the sun.
| MaxPock wrote:
| Discovered Vs invented
| imchillyb wrote:
| Discoveries are made and measurements are taken with the tools
| available.
|
| The measurements, theories, and currently understood or
| applicable math may not match up with observations.
|
| People ponder and discover, then attempt to explain the
| observations and measurements with a new theory. If the theory
| pans out, a deeper explanation of that theory is necessary and
| that's where the new math's at.
|
| It's not that physics is good at creating math. Physics is good
| at describing our observations /with/ math. That's kind of its
| whole job.
|
| Next time you look at raindrops in a puddle, try to imagine how
| you would describe those movements scientifically. One needs math
| for that.
|
| Sometimes the available tools and math are sufficient for a
| thorough explanation, and sometimes one needs to invent a
| universe of math to describe a tiny fluctuation.
| tim333 wrote:
| I've long thought physics is a subsection of maths and reality is
| a mathematical object that exists the same way that prime numbers
| or the Mandelbrot set do. Hence the unreasonable effectiveness of
| one in the other.
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