5 ms·

Terrible headline for an interesting article. “Echoes” suggest a causal relationship, which would be a fascinating to see occur emanating from physical propert

Terrible headline for an interesting article. “Echoes” suggest a causal relationship, which would be a fascinating to see occur emanating from physical properties and reflecting in mathematical abstractions. What this actually sounds like is “Reflecting on work by physicists helps mathematicians find analogous relationships in their own field” — which is cool and makes for a good story, but is very much not the same thing.

deleted 3y ago
[deleted]
resters 3y ago
While this is a valid nitpick, I think people sometimes overdo it. Mathematical objects can be both abstractions and systems in and of themselves. They are abstract "enough" to be useful as models, but anyone who infers causality has a fundamental misunderstanding of what mathematics is. I think this comes from our priority in the educational system of teaching mathematical techniques applicable to specific subjects rather than focusing on mathematics as the art of using and manipulating mathematical objects. On the other hand, I had an interesting chat with sommeone who had earned a pH.D in mathematics and physics (and one other discipline which I forget) and he regretted wasting his time learning about mathematical systems that were not applicable to physics research. I didn't retort, but if I had I would have said simply that one never knows how useful links might be found and that there have been a lot of surprises.
- godelski 3y ago
  Well I think part of the problem is that our education system results in many people thinking mathematics is anything other than a language. Most often people think that math is something we are uncovering about the universe. The OP's critique makes perfect sense from the perspective that physicists (and other sciences) utilize mathematical language. The "causal" relationship is as interesting as "English linguists discover new insights about colors by learning Russian." Similarly I would say physics is a language, though much more grounded in the observable world (since this is explicitly what physicists are trying to do: model our world/universe/reality). > and he regretted wasting his time learning about mathematical systems that were not applicable to physics research. Which shows the above claim about language. Though I'm a bit surprised since these ideas often connect due to the abstractions. 3 PhDs is a bit insane. 2 is even odd. Why go back to school when you already know how to research?
  - jebarker 3y ago
    > Why go back to school when you already know how to research? There's a couple of reasons I can think of. One is that if you want to do fundamental research in a particular field then you probably need other people to work with and that's mostly going to be in academia and PhD is the pathway. The other is that if you take a break from academia after a PhD it's really hard to come back. Three PhDs does seem extreme though! I'm sort of in the latter position. I did a PhD in math, have spent 15 years in govt and industry but a part of me wishes I could go back to pure math research. I think the only path to do that would probably be to do a PhD in a related field such as theoretical physics.
    - godelski 3y ago
      Interesting. I totally get the desire to have collaborators but at the same time I'm particularly burnt out on academia. And most of my PhD has been teaching myself things so tbh I'm not sure what I need the institution for. Not that there aren't useful things that they can provide, but there's also problems that come with it too.
  - fn-mote 3y ago
    > many people thinking mathematics is anything other than a language. I disagree with the claim that mathematics is only language, if by language you mean terms and definitions. The EASY part of mathematics is the language. There are deep truths, too, and they are not just language. For a (kind of) popular example, the question of "Where do the zeros of the Riemann zeta function lie?" is way way more than just vocabulary. There is a 20 minute video by 3Blue1Brown on the subject. [1] [1]: https://www.youtube.com/watch?v=sD0NjbwqlYw https://www.youtube.com/watch?v=sD0NjbwqlYw
    - godelski 3y ago
      > The EASY part of mathematics is the language. This is where I highly disagree. Doing the math is doing the language. I'm not sure which part is "easy". Even setting up problems is often incredibly difficult. This is where many physics students often struggle, despite having strong math skills there's a challenge to describe the problem to be solved. Even strong mathematicians often struggle to translate between mathematics and their native spoken language. Though 3B1B is quite good at doing this, though there is quite a lot of simplification to goes on due to the target audience. Like I said to the sibling comment, do not mistake how powerful and impressive language is. It created our modern world and there's a reason it is more important to us than even our phones. But all languages, including math, are never complete. They cannot describe everything, unfortunately. But I thought my name would have indicated that I was well aware of this notion. > "Where do the zeros of the Riemann zeta function lie?" is way way more than just vocabulary And a language isn't just vocabulary. That's like saying a programming language (which remember has a direct correspondence. They're equivalent) is just tokens. Idk if you want to look into CH Correspondence, Lambda Calculus, Abstract Algebra, Category Theory, or if I should just quote Poincare about mathematics being the study of relationships.
- mjan22640 3y ago
  Mathematics is overdone nitpicks.
Ar-Curunir 3y ago
Have you ever heard of poetic license? Mathematics doesn’t have to be boring and pedantic all the time.

deleted 3y ago

[deleted]

resters 3y ago

While this is a valid nitpick, I think people sometimes overdo it. Mathematical objects can be both abstractions and systems in and of themselves. They are abstract "enough" to be useful as models, but anyone who infers causality has a fundamental misunderstanding of what mathematics is. I think this comes from our priority in the educational system of teaching mathematical techniques applicable to specific subjects rather than focusing on mathematics as the art of using and manipulating mathematical objects. On the other hand, I had an interesting chat with sommeone who had earned a pH.D in mathematics and physics (and one other discipline which I forget) and he regretted wasting his time learning about mathematical systems that were not applicable to physics research. I didn't retort, but if I had I would have said simply that one never knows how useful links might be found and that there have been a lot of surprises.

godelski 3y ago
Well I think part of the problem is that our education system results in many people thinking mathematics is anything other than a language. Most often people think that math is something we are uncovering about the universe. The OP's critique makes perfect sense from the perspective that physicists (and other sciences) utilize mathematical language. The "causal" relationship is as interesting as "English linguists discover new insights about colors by learning Russian." Similarly I would say physics is a language, though much more grounded in the observable world (since this is explicitly what physicists are trying to do: model our world/universe/reality). > and he regretted wasting his time learning about mathematical systems that were not applicable to physics research. Which shows the above claim about language. Though I'm a bit surprised since these ideas often connect due to the abstractions. 3 PhDs is a bit insane. 2 is even odd. Why go back to school when you already know how to research?
- jebarker 3y ago
  > Why go back to school when you already know how to research? There's a couple of reasons I can think of. One is that if you want to do fundamental research in a particular field then you probably need other people to work with and that's mostly going to be in academia and PhD is the pathway. The other is that if you take a break from academia after a PhD it's really hard to come back. Three PhDs does seem extreme though! I'm sort of in the latter position. I did a PhD in math, have spent 15 years in govt and industry but a part of me wishes I could go back to pure math research. I think the only path to do that would probably be to do a PhD in a related field such as theoretical physics.
  - godelski 3y ago
    Interesting. I totally get the desire to have collaborators but at the same time I'm particularly burnt out on academia. And most of my PhD has been teaching myself things so tbh I'm not sure what I need the institution for. Not that there aren't useful things that they can provide, but there's also problems that come with it too.
- fn-mote 3y ago
  > many people thinking mathematics is anything other than a language. I disagree with the claim that mathematics is only language, if by language you mean terms and definitions. The EASY part of mathematics is the language. There are deep truths, too, and they are not just language. For a (kind of) popular example, the question of "Where do the zeros of the Riemann zeta function lie?" is way way more than just vocabulary. There is a 20 minute video by 3Blue1Brown on the subject. [1] [1]: https://www.youtube.com/watch?v=sD0NjbwqlYw https://www.youtube.com/watch?v=sD0NjbwqlYw
  - godelski 3y ago
    > The EASY part of mathematics is the language. This is where I highly disagree. Doing the math is doing the language. I'm not sure which part is "easy". Even setting up problems is often incredibly difficult. This is where many physics students often struggle, despite having strong math skills there's a challenge to describe the problem to be solved. Even strong mathematicians often struggle to translate between mathematics and their native spoken language. Though 3B1B is quite good at doing this, though there is quite a lot of simplification to goes on due to the target audience. Like I said to the sibling comment, do not mistake how powerful and impressive language is. It created our modern world and there's a reason it is more important to us than even our phones. But all languages, including math, are never complete. They cannot describe everything, unfortunately. But I thought my name would have indicated that I was well aware of this notion. > "Where do the zeros of the Riemann zeta function lie?" is way way more than just vocabulary And a language isn't just vocabulary. That's like saying a programming language (which remember has a direct correspondence. They're equivalent) is just tokens. Idk if you want to look into CH Correspondence, Lambda Calculus, Abstract Algebra, Category Theory, or if I should just quote Poincare about mathematics being the study of relationships.
mjan22640 3y ago
Mathematics is overdone nitpicks.

Ar-Curunir 3y ago

Have you ever heard of poetic license? Mathematics doesn’t have to be boring and pedantic all the time.