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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 ab

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.
    - Koshkin 3y ago
      A language is invented; mathematics is discovered.
      - godelski 3y ago
- auggierose 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. And those people would be right, as the mathematical universe is part of our shared universe/reality. It's not just language and games. A Turing Machine either halts, or it doesn't. But if you want to solve a concrete problem (in physics, for example), it is best to develop/find/learn the mathematics you need to solve your problem, and not the other way around.
  - godelski 3y ago
    I'm not sure what your argument proves. No one said it is just games either. I think you're turning what I said into something else. Languages are incredibly impressive and powerful things. I feel like you're making languages appear simple and of low utility. But language has been one of the, if not the most, powerful tool humans have ever created, especially when you consider written language. The latter allowing us to pass along information asynchronously through time and space. Do not miss the power of this tool just because it is something we use so frequently. There's a reason we use it so frequently. The reason we use the language of math is because it is so precise. But you just described a turing machine without using math. Keep in mind that physics is also a language. Physics is an ever evolving model, a description of our reality. But it is not more than that, a model. But all models being wrong does not equate to models being useless. Physicses (yes, there are multiple ones), are clearly quite powerful and useful models that have enabled us to do quite amazing things as well. But I'm also not going to start programming in Brainfuck or with Magic cards. But I do have a deep passion for mathematics and it is something I use every day and spend quite a lot of time learning even outside my work. Your argument demonstrates the usefulness of mathematics, but does not demonstrate that it isn't a language. I also would like to remind you that you can create pretty useless algebras. Maybe also checkout Wolfram's section on recreational mathematics. Maybe also dig into my name sake's multiple theorems. Most people misunderstand the results, but I don't think it diminishes their worth, they are quite important and amazing. And the incompleteness theorem is deeply related to turing completeness as well as superposition and a famous logic paradox.
mjan22640 3y ago
Mathematics is overdone nitpicks.

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.
  - Koshkin 3y ago
    A language is invented; mathematics is discovered.
    - godelski 3y ago
auggierose 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. And those people would be right, as the mathematical universe is part of our shared universe/reality. It's not just language and games. A Turing Machine either halts, or it doesn't. But if you want to solve a concrete problem (in physics, for example), it is best to develop/find/learn the mathematics you need to solve your problem, and not the other way around.
- godelski 3y ago
  I'm not sure what your argument proves. No one said it is just games either. I think you're turning what I said into something else. Languages are incredibly impressive and powerful things. I feel like you're making languages appear simple and of low utility. But language has been one of the, if not the most, powerful tool humans have ever created, especially when you consider written language. The latter allowing us to pass along information asynchronously through time and space. Do not miss the power of this tool just because it is something we use so frequently. There's a reason we use it so frequently. The reason we use the language of math is because it is so precise. But you just described a turing machine without using math. Keep in mind that physics is also a language. Physics is an ever evolving model, a description of our reality. But it is not more than that, a model. But all models being wrong does not equate to models being useless. Physicses (yes, there are multiple ones), are clearly quite powerful and useful models that have enabled us to do quite amazing things as well. But I'm also not going to start programming in Brainfuck or with Magic cards. But I do have a deep passion for mathematics and it is something I use every day and spend quite a lot of time learning even outside my work. Your argument demonstrates the usefulness of mathematics, but does not demonstrate that it isn't a language. I also would like to remind you that you can create pretty useless algebras. Maybe also checkout Wolfram's section on recreational mathematics. Maybe also dig into my name sake's multiple theorems. Most people misunderstand the results, but I don't think it diminishes their worth, they are quite important and amazing. And the incompleteness theorem is deeply related to turing completeness as well as superposition and a famous logic paradox.

mjan22640 3y ago

Mathematics is overdone nitpicks.