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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

#121

Post by lilyball »

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…

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.

Re: Physics is unreasonably good at creating new math

#122

Post by zachf »

naasking wrote: post #120
zachf wrote: post #93

Earlier quoted context omitted.

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?

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…

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.

Re: Physics is unreasonably good at creating new math

#123

Post by groos »

tech_ken wrote: post #29

> 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 rela…

G.H. Hardy would like to disagree.

https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology

Re: Physics is unreasonably good at creating new math

#124

Post by Jerrrrrrry »

slashdave wrote: post #63
marcosdumay wrote: post #27

Try to make some innovative software product without talking to any user. You'll see why physics is good at crating new math.

Do you value the quality of a mathematical theory by the number of applications, or the intrinsic beauty of the theory itself?

  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

Re: Physics is unreasonably good at creating new math

#125

Post by waveBidder »

glitchc wrote: post #96
l33t7332273 wrote: post #55

Earlier quoted context omitted.

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?

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.

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.

Re: Physics is unreasonably good at creating new math

#127

Post by jjgreen »

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.

Re: Physics is unreasonably good at creating new math

#128

Post by naasking »

zachf wrote: post #122
naasking wrote: post #120

Earlier quoted context omitted.

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…

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/…

Oh Ads, you mean that space that emphatically does NOT describe our universe? Ads/CFT is overblown. It's just an interesting mathematical result that hasn't borne much meaningful fruit for actual physics.

I'm sorry, but string theorists absolutely do prevent funding other research because funding is finite, grad students have to research something their advisors think is worthy, and their advisors have their heads full of "beautiful math" so that's what they tell their students to work on if they want their PhDs, and that's what they hire their post grads to work on if they want a job.

Only now as the strong theory haze has started dissipating are we starting to see novel approaches, like Oppenheim's post quantum gravity theory.

Re: Physics is unreasonably good at creating new math

#129

Post by gerdesj »

groos wrote: post #123
tech_ken wrote: post #29

> 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 rela…

G.H. Hardy would like to disagree. https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology

Unfortunately, he is unable to join the discussion. Deploying a ghost as an argument in and of itself is hardly useful.

Personally I tend to disagree with "I hope it isn't useful" or whatever the GHH quote is about maths being practicably applicable to the world/universe n that.

Why not tell us what you think? Mr Hardy's well documented positions on many things are well known but yours are not.

Re: Physics is unreasonably good at creating new math

#130

Post by tech_ken »

groos wrote: post #123
tech_ken wrote: post #29

> 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 rela…

G.H. Hardy would like to disagree. https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology

I don’t think his point and mine are incompatible, the language can have beauty in its own right and still be a model. Legos can be built into something which resemble a house, or something which resembles nothing real; their usage is a separate thing from the joy that comes from playing with them. Math is driven by utility and elaborated by enthusiasts.
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