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...
Physics is unreasonably good at creating new math
21–30 of 231 posts
Re: Physics is unreasonably good at creating new math
#22One 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.
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.
Re: Physics is unreasonably good at creating new math
#23One 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.
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.
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Re: Physics is unreasonably good at creating new math
#24Earlier 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
"In this house we side with Aristotle."
Re: Physics is unreasonably good at creating new math
#25See 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...
`"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.
Re: Physics is unreasonably good at creating new math
#26I 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.
Re: Physics is unreasonably good at creating new math
#27Try to make some innovative software product without talking to any user. You'll see why physics is good at crating new math.
Re: Physics is unreasonably good at creating new math
#28“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.
Re: Physics is unreasonably good at creating new math
#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 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.
Re: Physics is unreasonably good at creating new math
#30I 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.