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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

#101

Post by ricksunny »

Misdicorl wrote: post #80
alickz wrote: post #67

Earlier quoted context omitted.

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

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…

>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_gravitati...

Re: Physics is unreasonably good at creating new math

#102

Post by lilyball »

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…

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.

Re: Physics is unreasonably good at creating new math

#103

Post by meroes »

Joker_vD wrote: post #86
meroes wrote: post #75

Earlier quoted context omitted.

Wondering if Euclid’s parallel postulate was independent goes back millennia though. And that’s like the key ingredient for multiple geometries.

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…

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.

Re: Physics is unreasonably good at creating new math

#104

Post by throwaway17_17 »

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

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 (Wójtowicz,Skowron 2022)

Re: Physics is unreasonably good at creating new math

#105

Post by tim333 »

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…

They have probably produced some new maths, maybe as much as if you threw similar amounts of money at the maths department?

Re: Physics is unreasonably good at creating new math

#107

Post by bluGill »

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.

> 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.

Re: Physics is unreasonably good at creating new math

#108

Post by torrefatto »

elashri wrote: post #65
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…

> no falsifiable prediction You forgot to add "with our current technology ability to probe the required energy scale".

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.

Re: Physics is unreasonably good at creating new math

#109

Post by torrefatto »

jjk166 wrote: post #50
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.

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.

Re: Physics is unreasonably good at creating new math

#110

Post by dxbydt »

lilyball wrote: post #102
dxbydt wrote: post #92

Earlier quoted context omitted.

> 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…

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 a cliff with its tail tied to a daisy."

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