Why Does Mathematics Work?

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Re: Why Does Mathematics Work?

#41  Postby BWE » May 25, 2019 10:45 pm

Cito di Pense wrote:These questions are fun, and Wigner wrote a very fine essay. If we strip away all the filosofeezing, we are still only asking why something works. Maybe a better question is "why does mathematics work so well?" People try to make things work, and there are lots of innumerate people who still try to make things work (that haven't been designed for them). We might as well ask why we want stuff that works, as opposed to stuff that doesn't work. I mean, we do stuff for fun, but somehow, fun works.

At the simplest level, mathematics is a project for making knowledge systematic, where we try as hard as we can to ensure that what we come up with will work. Why does it work? Why ask why?

Wigner asked why it works so well in the physical sciences, instead of just as a project to try as hard as we can to make something work for its own sake, and that is a deep mystery. We live in this universe and want to know how it works, and we found a tool that is effective in getting the know-how together. There's always that picture that Penrose drew in the first few pages of The Road To Reality.

I confess, I didn't watch the video all the way through, after observing the limited effectiveness of the interviewer, and having first read Wigner's essay many years ago. As Ellie Arroway said, "they should have sent a poet".

I think it really boils down to the question of what it means that the universe is consistent. I also think the math question is at its root a question regarding the law of noncontradiction. But, as with most things, what I think is pretty random so ymmv.
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Re: Why Does Mathematics Work?

#42  Postby Cito di Pense » May 26, 2019 3:30 am

BWE wrote:
I think it really boils down to the question of what it means that the universe is consistent. I also think the math question is at its root a question regarding the law of noncontradiction. But, as with most things, what I think is pretty random so ymmv.


What? So we attempt to treat the consistency of the universe as having some sort of semantics? You know, as if Someone was trying to communicate with Us? Frankly, I'm not deep into the whole "blind men touching the elephant" semantics. Take a hit off the three spliffs of ultimate reality and, daddy, let your mind roll on.

To be serious for a moment, let's look at the law of non-contradiction. Of course, if we just wanted to light up the doobie and make up whatever fucking shit we wanted to, even if it entails contradictions, we'd be doing something besides mathematics

Proof by contradiction is actually a thing, as I'm sure you recall. For pure waffle, cue up the whole thing about "mathematics and science are branches of philosophy" or investigate the impossibility of the overarching system that is internally consistent. You know me: I blame God. That's what happens when we try to "boil it down". Maybe "boiling it down" is a fine antidote for not being able to remember enough details. Pending the bending of the spoons.
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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?

#43  Postby BWE » May 30, 2019 4:05 am

I wish I understood what you wrote there. I feel like I would be entertained.
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Re: Why Does Mathematics Work?

#44  Postby Cito di Pense » May 30, 2019 6:10 am

BWE wrote:I wish I understood what you wrote there. I feel like I would be entertained.


What you wrote was pondering what it means that the universe is consistent. However, you might just be on the wrong, wibbly track again. Isn't it just more correct to use consistent in reference to descriptions? These are abstractions of what we observe, and they necessarily omit details in order to give the satisfaction of consistency. Think of that as a labor-saving device. What does it mean that we want and use compact descriptions? We want so many, many things, not all of them, or even very many of them, consistent with anything you didn't just make up on the spot.

How do we get consistent descriptions? We make them that way. We find plenty of inconsistent descriptions, too, but for some reason, those are less interesting to those who ask why mathematics works.

You could go off into conniptions of ooh and aah over the fact that there are descriptions at all.

I like that idea, conniptions about descriptions. It's like a pome.
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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?

#45  Postby surreptitious57 » May 30, 2019 7:20 am

Think of it like a jigsaw puzzle that may be finite but can never actually be complete. From time to time
an odd piece that does not really fit anywhere pops up and the temptation may be to just throw it away
But it is one that belongs elsewhere so when more are found they will be connected to it in due course
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Re: Why Does Mathematics Work?

#46  Postby Cito di Pense » May 30, 2019 8:42 am

surreptitious57 wrote:Think of it like a jigsaw puzzle that may be finite but can never actually be complete.


Why? How does that help?

surreptitious57 wrote:From time to time an odd piece that does not really fit anywhere pops up and the temptation may be to just throw it away


Temptation? What the fuck is that supposed to mean?
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Re: Why Does Mathematics Work?

#47  Postby BWE » May 30, 2019 7:56 pm

Cito di Pense wrote:
BWE wrote:I wish I understood what you wrote there. I feel like I would be entertained.


What you wrote was pondering what it means that the universe is consistent. However, you might just be on the wrong, wibbly track again. Isn't it just more correct to use consistent in reference to descriptions? These are abstractions of what we observe, and they necessarily omit details in order to give the satisfaction of consistency. Think of that as a labor-saving device. What does it mean that we want and use compact descriptions? We want so many, many things, not all of them, or even very many of them, consistent with anything you didn't just make up on the spot.

How do we get consistent descriptions? We make them that way. We find plenty of inconsistent descriptions, too, but for some reason, those are less interesting to those who ask why mathematics works.

You could go off into conniptions of ooh and aah over the fact that there are descriptions at all.

I like that idea, conniptions about descriptions. It's like a pome.

Hmm. I think the thing that makes math so interesting (at least in the vein of Wigner's essay) is the fact that the law of noncontradiction appears to be absolute. I mean, there are certainly paradigm issues which will forever keep a ToE at bay, but so far there has not been a case where a directly inconsistent behavior has been discovered. It may be that you are right that we simply change our model to make inconsistencies into consistencies, but that suggests something kind of profound about models. Why do they work so well? Even granting that question may include its own answer in a circular way, it still suggests that modeling is a strange capacity that is nearly synonymous with the idea of sentience. Of course, each of those terms is a word and therefore a part of a model but strange loops involve information.
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Re: Why Does Mathematics Work?

#48  Postby Cito di Pense » May 30, 2019 8:34 pm

BWE wrote:but so far there has not been a case where a directly inconsistent behavior has been discovered.


Maybe that is because the observations we make are not of propositions. Maybe you're remarking on some other point; it's just not clear to me what your remark is about. As far as is obvious, the LNC is about propositions.

Yes, we make propositions about our observations and treat them as hypotheses or theories, but I think there are very good reasons why we don't end up with propositions of this type that directly contradict one another. I don't know. In your line of work, it may come up, but those details are for you to provide. You're waxing philosophical about "directly inconsistent behavior".

There are opinions that directly contradict each other, even coming from the same person, but we know a little about what causes that, and don't take it all that seriously. Or maybe we do and don't take it seriously. You know how that goes.

BWE wrote:that suggests something kind of profound about models. Why do they work so well?


Watch out for deepities, BWE. It's hard to show that deepity is not just something happening between your ears. Bend a spoon. It's already been touched on in this thread that there's a parallel to the anthropic principle in your question. When stuff doesn't work well, or stops working well, we throw it away or file it under "less adequate approximation". Why do models work? Yeah, we don't want tunas with good taste, we want tunas that taste good.
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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?

#49  Postby newolder » May 31, 2019 3:37 pm

Posted a couple of days ago and already one of the most viewed YouTubes yet ( :lol: ) here's 22 minute-ish discussion between Robbert Dijkgraaf & Ed Witten roughly on topic here:
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Re: Why Does Mathematics Work?

#50  Postby tuco » May 31, 2019 3:57 pm

Yeah, I wonder how many people in the world actually understand what they are talking about.
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Re: Why Does Mathematics Work?

#51  Postby newolder » May 31, 2019 4:07 pm

If it's of the order 1 in a million then that would be a few thousand and is seen as progress over the "12 people who understand relativity theory" of a hundred years or so ago. T'intertubez has its uses, y'know. :thumbup:
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Re: Why Does Mathematics Work?

#52  Postby tuco » May 31, 2019 4:15 pm

I've heard a joke going something like .. "Surely more than 12 people understood relativity theory at the time but nobody understands quantum mechanics".

Are you being defensive btw? I know what the internet is for. Just after watching 13min I concluded that to make any sense of it one needs to have such a high level of expertise, in both fields, that no matter what they say in the vid, it cant reach many people.
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Re: Why Does Mathematics Work?

#53  Postby newolder » May 31, 2019 4:25 pm

A more recent joke is that, "My quantum mechanic is so useless, she can't even align the Standard Model correctly."

and xkcd has a few too:
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Re: Why Does Mathematics Work?

#54  Postby Spearthrower » May 31, 2019 4:32 pm

newolder wrote:Posted a couple of days ago and already one of the most viewed YouTubes yet ( :lol: ) here's 22 minute-ish discussion between Robbert Dijkgraaf & Ed Witten roughly on topic here:




Found it a bit hard to understand what he was saying, and not because of the topic or the microphone, but because of his breathy delivery and habit of rushing the last words of each sentence out. Had to go keep scanning back to relisten. Still, enjoyed it eventually - cheers!
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Re: Why Does Mathematics Work?

#55  Postby newolder » May 31, 2019 4:45 pm

Spearthrower wrote:
newolder wrote:Posted a couple of days ago and already one of the most viewed YouTubes yet ( :lol: ) here's 22 minute-ish discussion between Robbert Dijkgraaf & Ed Witten roughly on topic here:

...



Found it a bit hard to understand what he was saying, and not because of the topic or the microphone, but because of his breathy delivery and habit of rushing the last words of each sentence out. Had to go keep scanning back to relisten. Still, enjoyed it eventually - cheers!

:cheers:

All those people on the poster at the back (and a few more including Nima Arkani-Hamed) got to talk at that conference too, but I haven't found the play list yet... brb.

ETA No playlist yet but the videos were all posted to the IAS youtube channel within the last day...
https://www.youtube.com/user/videosfromIAS/videos
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Re: Why Does Mathematics Work?

#56  Postby Spearthrower » May 31, 2019 4:51 pm

I fear that a lot of those talks are going to be beyond my comprehension, but I'll subscribe and dip into a few and see what I can glean, cheers!
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Re: Why Does Mathematics Work?

#57  Postby BWE » Jun 01, 2019 1:49 am

Cito di Pense wrote: it's just not clear to me what your remark is about.

lol. the irony
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Re: Why Does Mathematics Work?

#58  Postby Cito di Pense » Jun 01, 2019 3:22 am

newolder wrote:If it's of the order 1 in a million then that would be a few thousand and is seen as progress over the "12 people who understand relativity theory" of a hundred years or so ago. T'intertubez has its uses, y'know. :thumbup:


It's quite common in mathematics (and yes, physics) education, at least up through the first couple of years of university, to hear a student say, "I understood the lecture and what I read in the textbook, so I didn't bother to do the homework. I just don't understand why I failed the exam." Never mind what these fine fellows are talking about.

The folks who deliver the content of chat in youtube videos like this do not in general sample the same population as the audience that ticks the view-count of these videos.
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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?

#59  Postby newolder » Jun 01, 2019 7:39 am

Cito di Pense wrote:
newolder wrote:If it's of the order 1 in a million then that would be a few thousand and is seen as progress over the "12 people who understand relativity theory" of a hundred years or so ago. T'intertubez has its uses, y'know. :thumbup:


It's quite common in mathematics (and yes, physics) education, at least up through the first couple of years of university, to hear a student say, "I understood the lecture and what I read in the textbook, so I didn't bother to do the homework. I just don't understand why I failed the exam." Never mind what these fine fellows are talking about.

The folks who deliver the content of chat in youtube videos like this do not in general sample the same population as the audience that ticks the view-count of these videos.

Absolutely. Ed Witten is one of those who understands what he is talking about, the youtube clicks and probably most of the live audience, I guess, are not what I'm counting in the list of those who have a grasp. Authors of relevant work posted to the arXivs are more representative of those with "the knowledge" here but I don't keep a running total of them. Select Distinct from tblAuthors Order by LastName Ascending - or better Select Count(Distinct) From tblAuthors is not a query of the arXiv database I can make from here. :dunno:

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Re: Why Does Mathematics Work?

#60  Postby Cito di Pense » Jun 01, 2019 7:56 am

newolder wrote:
Cito di Pense wrote:
newolder wrote:If it's of the order 1 in a million then that would be a few thousand and is seen as progress over the "12 people who understand relativity theory" of a hundred years or so ago. T'intertubez has its uses, y'know. :thumbup:


It's quite common in mathematics (and yes, physics) education, at least up through the first couple of years of university, to hear a student say, "I understood the lecture and what I read in the textbook, so I didn't bother to do the homework. I just don't understand why I failed the exam." Never mind what these fine fellows are talking about.

The folks who deliver the content of chat in youtube videos like this do not in general sample the same population as the audience that ticks the view-count of these videos.

Absolutely. Ed Witten is one of those who understands what he is talking about, the youtube clicks and probably most of the live audience, I guess, are not what I'm counting in the list of those who have a grasp. Authors of relevant work posted to the arXivs are more representative of those with "the knowledge" here but I don't keep a running total of them. Select Distinct from tblAuthors Order by LastName Ascending - or better Select Count(Distinct) From tblAuthors is not a query of the arXiv database I can make from here. :dunno:


There's no prerequisite for watching youtube vids about the frontiers of physics. It would be a big step even to know the difference between somebody who knows what hes's talking about (and who is talking about that) and somebody who is doing neither.
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