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What does that mean? Physics is still empirical at the end of the day. Experiments decide what theories best explain the world. Math doesn't have such a require

What does that mean? Physics is still empirical at the end of the day. Experiments decide what theories best explain the world. Math doesn't have such a requirement. It doesn't need to model natural phenomenon. Your physics lecturer sounds like a Platonist.

tombert 2y ago
I don't think OP is really wrong here. Wasn't there a debate in the late 19th century that basically asked if math had to have some mapping to the natural world, or should it work independently? I though there was some argument about this with Hilbert and Poincaré about this, and Hilbert more or less won.
mrtesthah 2y ago
See Our mathematical universe : my quest for the ultimate nature of reality by Max Tegmark https://archive.org/details/ourmathematicalu0000tegm https://archive.org/details/ourmathematicalu0000tegm
- goatlover 2y ago
  That's metaphysics not science. I'm not against metaphysics, but philosophy is distinct from physics. And it's Tegmark's particular metaphysics. Interesting but hardly a consensus among physicists or philosophers.
  - deleted 2y ago
    [deleted]
lupire 2y ago
It's a very weak loose statement, but I think the idea is that leading scientific and mathematical thinkers (think Newton as a quintessential example) were "natural philosophers" who studied whatever caught their interest and took it wherever it went. Astronomers invented lenses and ground them and studied the starts and developed algebra and calculus to model the observations. Some people were more narrowly focused, like Gauss who did mostly math (but an amazing breadth of math!) There was a lot of hesitancy about math that couldn't be empirically illustrated by building out of atoms, like irrational numbers and then transcendental numbers and imaginary numbers and then infinite structures.
- failbuffer 2y ago
  Add negative numbers to your list as well. Mathematicians used to rearrange terms specifically to avoid them (e.g. before the concept existed).
teqsun 2y ago
> "Your physics lecturer sounds like a Platonist." I don't understand what this means, but it made me envision a McCarthy-esque witch hunt for "Platonist and Platonist sympathizers" lurking amongst the faculty
- HPsquared 2y ago
  "In this house we side with Aristotle."
- aeneasmackenzie 2y ago
  Just say witch hunt. McCarthy was entirely correct that there were a lot of communists and communist sympathizers, so many that many of the people he thought were helping him were themselves communists or communist sympathizers. Witches on the other hand are not real.
  - tomrod 2y ago
    But Platonists, ironically on many levels, are also real. Sometimes complex. But never fully imaginary.
    - jfactorial 2y ago
      There are no Platonists, only imitations of the one true heavenly Platonist.
      - tomrod 2y ago
        Genuinely chuckling.
  - bee_rider 2y ago
    He missed most of the actual Soviet agents, though, right? Both seem to have mostly focused building up a lie to suppress some outside-the-norm element that the guy in charge wanted to hunt. That McCarthy also managed to have some real agents to miss is not a big difference.
Joker_vD 2y ago
> Math doesn't have such a requirement Geometry? Lobachevsky actually proposed a test on measuring sum of angles of a celestial triangle to decide which geometry actually applied to the real world.
- verzali 2y ago
  There are multiple geometries though, they don't have to describe the real world. In mathematics you are free to base your geometry on whatever axioms you want, whether they are realistic or not. I'd say the question of which geometry applies in the real world is more a question for physicists (or cosmologists, today).
  - Joker_vD 2y ago
    This is a very late-XIX century development. Geometry used to be an integral part of physics, vide Newton's Principia.
    - meroes 2y ago
      Wondering if Euclid’s parallel postulate was independent goes back millennia though. And that’s like the key ingredient for multiple geometries.
      - Joker_vD 2y ago
        No, it's trying to prove that Euclid's parallel postulate can be derived from other axioms is what goes back millennia. People were certain it's a) true, b) necessary consequence of other axioms. Gauss was probably the first to consider the possibility that it may be false; others at best tried reductio ad absurdum, arrived to some wildly unusual theorems, decided those were absurd enough to demonstrate the truth of the fifth postulate, and went back to trying to derive it.
        meroes 2y ago
        It's either true as an axiom or true as derived from other axioms and/or theorems. In neither case does latching onto Euclid's other common notions/postulates/theorems as the selection it must be proved true from make sense as a 1.5kya long task. I think there must have been a sense that it was true only as an axiom. Proving it from other axioms/theorems was then a goal to secure it's truth "further". But you'd only attempt that if you thought there was something questionable in the first place.
deleted 2y ago
[deleted]

tombert 2y ago

I don't think OP is really wrong here. Wasn't there a debate in the late 19th century that basically asked if math had to have some mapping to the natural world, or should it work independently? I though there was some argument about this with Hilbert and Poincaré about this, and Hilbert more or less won.

mrtesthah 2y ago

See Our mathematical universe : my quest for the ultimate nature of reality by Max Tegmark https://archive.org/details/ourmathematicalu0000tegm https://archive.org/details/ourmathematicalu0000tegm

goatlover 2y ago
That's metaphysics not science. I'm not against metaphysics, but philosophy is distinct from physics. And it's Tegmark's particular metaphysics. Interesting but hardly a consensus among physicists or philosophers.
- deleted 2y ago
  [deleted]

lupire 2y ago

It's a very weak loose statement, but I think the idea is that leading scientific and mathematical thinkers (think Newton as a quintessential example) were "natural philosophers" who studied whatever caught their interest and took it wherever it went. Astronomers invented lenses and ground them and studied the starts and developed algebra and calculus to model the observations. Some people were more narrowly focused, like Gauss who did mostly math (but an amazing breadth of math!) There was a lot of hesitancy about math that couldn't be empirically illustrated by building out of atoms, like irrational numbers and then transcendental numbers and imaginary numbers and then infinite structures.

failbuffer 2y ago
Add negative numbers to your list as well. Mathematicians used to rearrange terms specifically to avoid them (e.g. before the concept existed).

teqsun 2y ago

> "Your physics lecturer sounds like a Platonist." I don't understand what this means, but it made me envision a McCarthy-esque witch hunt for "Platonist and Platonist sympathizers" lurking amongst the faculty

HPsquared 2y ago
"In this house we side with Aristotle."
aeneasmackenzie 2y ago
Just say witch hunt. McCarthy was entirely correct that there were a lot of communists and communist sympathizers, so many that many of the people he thought were helping him were themselves communists or communist sympathizers. Witches on the other hand are not real.
- tomrod 2y ago
  But Platonists, ironically on many levels, are also real. Sometimes complex. But never fully imaginary.
  - jfactorial 2y ago
    There are no Platonists, only imitations of the one true heavenly Platonist.
    - tomrod 2y ago
      Genuinely chuckling.
- bee_rider 2y ago
  He missed most of the actual Soviet agents, though, right? Both seem to have mostly focused building up a lie to suppress some outside-the-norm element that the guy in charge wanted to hunt. That McCarthy also managed to have some real agents to miss is not a big difference.

Joker_vD 2y ago

> Math doesn't have such a requirement Geometry? Lobachevsky actually proposed a test on measuring sum of angles of a celestial triangle to decide which geometry actually applied to the real world.

verzali 2y ago
There are multiple geometries though, they don't have to describe the real world. In mathematics you are free to base your geometry on whatever axioms you want, whether they are realistic or not. I'd say the question of which geometry applies in the real world is more a question for physicists (or cosmologists, today).
- Joker_vD 2y ago
  This is a very late-XIX century development. Geometry used to be an integral part of physics, vide Newton's Principia.
  - meroes 2y ago
    Wondering if Euclid’s parallel postulate was independent goes back millennia though. And that’s like the key ingredient for multiple geometries.
    - Joker_vD 2y ago
      No, it's trying to prove that Euclid's parallel postulate can be derived from other axioms is what goes back millennia. People were certain it's a) true, b) necessary consequence of other axioms. Gauss was probably the first to consider the possibility that it may be false; others at best tried reductio ad absurdum, arrived to some wildly unusual theorems, decided those were absurd enough to demonstrate the truth of the fifth postulate, and went back to trying to derive it.
      - meroes 2y ago
        It's either true as an axiom or true as derived from other axioms and/or theorems. In neither case does latching onto Euclid's other common notions/postulates/theorems as the selection it must be proved true from make sense as a 1.5kya long task. I think there must have been a sense that it was true only as an axiom. Proving it from other axioms/theorems was then a goal to secure it's truth "further". But you'd only attempt that if you thought there was something questionable in the first place.

deleted 2y ago

[deleted]