Why Does Mathematics Work?

Susskind's answer

Discuss the language of the universe.

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Re: Why Does Mathematics Work?

#61  Postby newolder » Jun 01, 2019 8:14 am

Are you asking that I should strike them from the record here?
I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops. - Stephen J. Gould
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Re: Why Does Mathematics Work?

#62  Postby Cito di Pense » Jun 01, 2019 8:24 am

newolder wrote:Are you asking that I should strike them from the record here?


No, I think it's a good example of a video in which somebody who knows what he's talking about is talking about that. I accept that there are many good reasons that trying to explain cutting edge physical theory in a non-technical way always fails. This makes no attempt to explain anything to anyone, so no harm is done.
Хлопнут без некролога. -- Серге́й Па́влович Королёв

Translation by Elbert Hubbard: Do not take life too seriously. You're not going to get out of it alive.
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Re: Why Does Mathematics Work?

#63  Postby surreptitious57 » Jun 02, 2019 5:35 am

This is the problem with simplifying something for a lay audience - do it too much and it renders the whole thing invalid
So the responsibility should be on the lay audience educating itself rather than on the professionals spoon feeding them
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
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Re: Why Does Mathematics Work?

#64  Postby zoon » Jun 02, 2019 9:56 am

surreptitious57 wrote:This is the problem with simplifying something for a lay audience - do it too much and it renders the whole thing invalid
So the responsibility should be on the lay audience educating itself rather than on the professionals spoon feeding them

In the video which newolder linked in post #49, Witten emphasises that professional mathematicians often find quantum theory beyond them, and that most physicists don't understand the details of mathematical proofs. If those professionals don't generally understand each other, I don't think there's too much hope of the rest of us understanding both? We tend to take their word for it, so long as the latest gizmos work. I find some attempt to follow the spoon feeding is fun, in the same spirit in which I like to have a vague idea of what's going on underneath the bonnet of my car.

At one point in the video, Witten jokes that the reason mathematics works in physics, is that the universe was designed by a mathematician. As far as I know, this was in fact Newton's view of the matter, he saw his mathematical discoveries as further evidence for God as masterful creator (his religious views were heretical, he wasn't sucking up to the authorities). Perhaps this is the only positive answer to that "why" question which our minds would accept (the negative, and presumably correct, answer being that we can't answer it, we don't know)? Is there any possible equivalent of the theory of evolution by natural selection, which turned out to be the non-supernatural answer to "why do living things appear to be designed to be functional, to have goals?"

(It's true that most of us don't find the idea of god as mathematician appealing, because most of us aren't capable of an intuitive grasp of the mathematics which physicists use. God as functional designer makes intuitive sense to everybody.)

Edited to add:
I don't agree with Susskind's view at the beginning of the OP interview, that it's not possible to imagine a universe which doesn't follow mathematical laws. Before the rise of modern science, especially Newton's laws, people from hunter-gatherers onwards tended to assume spirits were in charge, and that if there were any ultimate answers to "why" questions, they would be in similar terms to explanations of human activities: things happened because the spirits wanted them to happen. I don't think anyone was seriously putting forward the idea that human brains might be mechanisms that could be described mathematically before the sixteenth century?
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Re: Why Does Mathematics Work?

#65  Postby BWE » Jun 09, 2022 9:27 pm

Thommo wrote:
TopCat wrote:
Calilasseia wrote:Because at bottom, mathematics is the study of reliably repeatable interactions and well-defined entities taking part therein.

Isn't that true only of a subset of mathematics?


You are correct. There are all sorts of obvious examples of mathematics that resemble that definition in few meaningful ways. Set theory, the study of proper classes, geometric objects like the Klein bottle or a well known result like the Banach–Tarski paradox to name but a few.

None of those govern interactions at all, or indeed real world objects, or anything you might term repeatable in any sensible way.

To be fair I don't think there's any recognised good definition of mathematics at all. In general it's not the sort of thing mathematicians worry about.

I see oddities from set theory (there are quite a few involving the AoC especially) and my feeling is that they probably do actually show up in our universe in ways our metaphors don't give us access to yet. But I do think there are some oddities that are specifically artifacts of our modeling processes, notably time and infinity.
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