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I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. But nature or applications to it are the primary focus in many other f

by mkl 6y ago

I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. But nature or applications to it are the primary focus in many other fields of maths. In still others, nature would be a source of analogies, or applications of a few special cases, etc. Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example. Mathematics is the study of patterns. Any kind of pattern you can imagine, in anything, including relationships between things. What things? Any things. That covers a lot!

coldtea 6y ago
>I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. It's not about actual nature (the universe etc) being into consideration. It's about many mathematicians coming to see maths as exploration (physics-style) of a mathematical universe, so to speak, rather than a simple constructive process. So, they come to see mathematics as a kind of physics in this regard, no in the sense that they concern themselves with the outside nature. But in that math work appears to them as exploring a natural landscape (just one made of patterns and numbers).
- mkl 6y ago
  Yes, that's what my comment says (but maybe you read it before I edited it to be clearer): >> Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example.
  - coldtea 6y ago
    Yes, that. Though I wouldn't necessarily consider it "muddying the waters", but taking another criterium as important in the distinction of physics-like or not. Namely, not whether it concerns the study of the material universe, but whether it involves experimentation/discovery of in place structures, and other such physics-like processes (which they think it does).
    - nobodyandproud 6y ago
      This is muddying the waters though, though I think you’re in good company. I’m not sure if mathematics belongs in the sciences or art; it really has hallmarks of both. It a modeling language that can be used to describe the universe. You don’t have science today, without the math. Yet some of the proofs and mental exercises in pure math are almost divine; inspired in a way that resonates like a beautiful work of music.
      - coldtea 6y ago
        >This is muddying the waters though In a way, yes, as it extends the casual/conventional understanding of the term. I'm just saying it's not done to intentionally muddy the waters, but to introduce an alternative understanding. So, yeah, we agree!
- mbeex 6y ago
  The controversy between assuming a point of view of "creating" vs "discovering" things is as old as mathematics. > rather than a simple constructive process. This requires some more distinction. 'constructive' can mean very different things. Some non-intuitionists would consider their counterparts definition of 'constructive' as possibly OK, but simple - and held other cases still for construction. Anecdotally, Ramanujan received his results as an inspiration from his household deity. Thinking about it probably brings up 5 different opinions among two people.
username90 6y ago
You could say that math is the part of laws of physics which humans can't imagine being different. You can pretty easily imagine a world where newtons laws are different, but I'd argue it is impossible to imagine a world where 1 + 1 is not 2. However being impossible for us to imagine doesn't mean that such worlds can't exist, it would just have completely ridiculous consequences we can't imagine, so those rules are a part of our universe and not a fundamental logical truth.
- mkl 6y ago
  > I'd argue it is impossible to imagine a world where 1 + 1 is not 2. Actually, you've probably done that yourself, in a programming setting: integers modulo 2, where 1+1 = 0. It's useful in places and the consequences aren't too ridiculous in this case. Following through figuring out the consequences of rule changes is a key thing mathematicians do. E.g. do we need this rule? What if this was weaker? What if this was reversed? What if we had this extra restriction?
  - username90 6y ago
    That is a number system where 1 + 1 isn't 2, not a universe. At least I can't imagine a universe where the concept of 1 + 1 equals 2 doesn't exist.
    - mkl 6y ago
      Numbers don't exist in any real sense, so we're clearly not talking about the actual physical universe. The universes we're talking about are the spaces of possibilities that arise from sets of rules. Examples include number systems and physics models built on them. Newtonian physics, built on Euclidean space; Einsteinian physics, built on space distorted by mass; quantum circuits, where modular arithmetic can show up.
      - username90 6y ago
        > Numbers don't exist in any real sense I'd argue they do, numbers arise when counting and counting is definitely a part of our reality. It is pretty hard to imagine a universe where you can't count things.
kovac 6y ago
Whatever people may think what mathematicians think, this comment describes the real situation best as I've experienced it. Most pure mathematicians I've met/worked with actually look down (in a jocular way) on applied mathematics/physics. When Lagrange reformulated Newtonian physics, he was very proud of the fact that he didn't use any diagrams and arrows showing forces in his paper. In fact, of all the Physics I've seen, I found Lagrange's work to be the most beautiful and elegant. I love how the commenter put it as "Nature is of no consideration whatsoever in some fields of maths". I'd restate it as "Nature is of no consideration whatsoever in pure mathematics" and I'm quite sure that the pure mathematicians would agree.
- enriquto 6y ago
  > "Nature is of no consideration whatsoever in pure mathematics" and I'm quite sure that the pure mathematicians would agree. Only if you have the audacity to call Arnold "not a true pure mathematician"... He mockingly said that the parts of "so-called" mathematics that have no connection to nature are useless mental masturbation.
- spacedome 6y ago
  I agree this is a common sentiment among mathematicians, but this is a very modern perspective. If you look back 100 years ago to Hilbert, there was less distinction between physicists and mathematicians, much less the pure/applied rift that now exists. Arnol'd (who is referenced above) was one of the mathematicians who tried to keep this unity alive.
- guenthert 6y ago
  https://xkcd.com/435/ https://xkcd.com/435/

by mkl 6y ago

coldtea 6y ago

>I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. It's not about actual nature (the universe etc) being into consideration. It's about many mathematicians coming to see maths as exploration (physics-style) of a mathematical universe, so to speak, rather than a simple constructive process. So, they come to see mathematics as a kind of physics in this regard, no in the sense that they concern themselves with the outside nature. But in that math work appears to them as exploring a natural landscape (just one made of patterns and numbers).

mkl 6y ago
Yes, that's what my comment says (but maybe you read it before I edited it to be clearer): >> Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example.
- coldtea 6y ago
  Yes, that. Though I wouldn't necessarily consider it "muddying the waters", but taking another criterium as important in the distinction of physics-like or not. Namely, not whether it concerns the study of the material universe, but whether it involves experimentation/discovery of in place structures, and other such physics-like processes (which they think it does).
  - nobodyandproud 6y ago
    This is muddying the waters though, though I think you’re in good company. I’m not sure if mathematics belongs in the sciences or art; it really has hallmarks of both. It a modeling language that can be used to describe the universe. You don’t have science today, without the math. Yet some of the proofs and mental exercises in pure math are almost divine; inspired in a way that resonates like a beautiful work of music.
    - coldtea 6y ago
      >This is muddying the waters though In a way, yes, as it extends the casual/conventional understanding of the term. I'm just saying it's not done to intentionally muddy the waters, but to introduce an alternative understanding. So, yeah, we agree!
mbeex 6y ago
The controversy between assuming a point of view of "creating" vs "discovering" things is as old as mathematics. > rather than a simple constructive process. This requires some more distinction. 'constructive' can mean very different things. Some non-intuitionists would consider their counterparts definition of 'constructive' as possibly OK, but simple - and held other cases still for construction. Anecdotally, Ramanujan received his results as an inspiration from his household deity. Thinking about it probably brings up 5 different opinions among two people.

username90 6y ago

You could say that math is the part of laws of physics which humans can't imagine being different. You can pretty easily imagine a world where newtons laws are different, but I'd argue it is impossible to imagine a world where 1 + 1 is not 2. However being impossible for us to imagine doesn't mean that such worlds can't exist, it would just have completely ridiculous consequences we can't imagine, so those rules are a part of our universe and not a fundamental logical truth.

mkl 6y ago
> I'd argue it is impossible to imagine a world where 1 + 1 is not 2. Actually, you've probably done that yourself, in a programming setting: integers modulo 2, where 1+1 = 0. It's useful in places and the consequences aren't too ridiculous in this case. Following through figuring out the consequences of rule changes is a key thing mathematicians do. E.g. do we need this rule? What if this was weaker? What if this was reversed? What if we had this extra restriction?
- username90 6y ago
  That is a number system where 1 + 1 isn't 2, not a universe. At least I can't imagine a universe where the concept of 1 + 1 equals 2 doesn't exist.
  - mkl 6y ago
    Numbers don't exist in any real sense, so we're clearly not talking about the actual physical universe. The universes we're talking about are the spaces of possibilities that arise from sets of rules. Examples include number systems and physics models built on them. Newtonian physics, built on Euclidean space; Einsteinian physics, built on space distorted by mass; quantum circuits, where modular arithmetic can show up.
    - username90 6y ago
      > Numbers don't exist in any real sense I'd argue they do, numbers arise when counting and counting is definitely a part of our reality. It is pretty hard to imagine a universe where you can't count things.

kovac 6y ago

Whatever people may think what mathematicians think, this comment describes the real situation best as I've experienced it. Most pure mathematicians I've met/worked with actually look down (in a jocular way) on applied mathematics/physics. When Lagrange reformulated Newtonian physics, he was very proud of the fact that he didn't use any diagrams and arrows showing forces in his paper. In fact, of all the Physics I've seen, I found Lagrange's work to be the most beautiful and elegant. I love how the commenter put it as "Nature is of no consideration whatsoever in some fields of maths". I'd restate it as "Nature is of no consideration whatsoever in pure mathematics" and I'm quite sure that the pure mathematicians would agree.

enriquto 6y ago
> "Nature is of no consideration whatsoever in pure mathematics" and I'm quite sure that the pure mathematicians would agree. Only if you have the audacity to call Arnold "not a true pure mathematician"... He mockingly said that the parts of "so-called" mathematics that have no connection to nature are useless mental masturbation.
spacedome 6y ago
I agree this is a common sentiment among mathematicians, but this is a very modern perspective. If you look back 100 years ago to Hilbert, there was less distinction between physicists and mathematicians, much less the pure/applied rift that now exists. Arnol'd (who is referenced above) was one of the mathematicians who tried to keep this unity alive.
guenthert 6y ago
https://xkcd.com/435/ https://xkcd.com/435/