Thread

The Relation Between Mathematics and Physics by Paul Dirac (1939)

172 points · 84 comments · rramadass

GoblinSlayer · 1789637250 · focus · HN ↗
>but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen
This is quantifiable, right? Should be possible to measure how many mathematicians favor ideas like turbulence, macroscopic quantum physics, anthropic principle, analog geometry, finitism. I think, mathematics doesn't really try to match physics yet.
1. huurtehoog · 1789648350 · focus · HN ↗
  I think this passage is more about the fact that mathematics is a form of symbolic computation people create and it is weirdly congruent to the physical measurements and models of reality. Not that mathematicians see certain models and objects used in physical models in a favorable way. What favor even means here?
  It is quantifiable: several mathematical objects and categories people invented to do symbolic computation in letters and published papers are somehow very useful to model and understand data from physical measurements of reality.
  I highly recommend reading the "Unreasonable effectiveness of mathematics" essay by Wigner:
  <a href="https://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableEffectiveness.pdf" rel="nofollow">https://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableE...
  1. GoblinSlayer · 1789677405 · focus · HN ↗
    I don't see unreasonable effectiveness of mathematics. On one hand, it's a self fulfilling prophecy: if your math doesn't work, just make different math, and so on until it works (gravity was invented 6 times or so), so it's as effective as logic. On the other hand, it's fundamentally approximation limited by precision, so for any model we know when it breaks. And it's basically unworkable for chaotic or exponentially complex phenomena.
    podocarp · 1789690076 · focus · HN ↗
    You're just claiming it's effective. We know it's effective. But there's no reason it should be effective. It's primarily because philosophy has not caught up and we still can't explain the foundations of mathematics and causality. These things seem to be baked into our very nature. It is possible to image an alien race with different conceptions of logic and causality that are just unable however hard they try to formulate either proper mathematics or proper physical laws from mathematics. (Take for example the Pythagoreans who could not believe irrational numbers existed, so the famous cube root of 2 was fake news to them. They could never build their little cubic altar to whomever.)
    GoblinSlayer · 1789723253 · focus · HN ↗
    Mathematics can model simple parts of physics, because mathematics is simple and can do simple things, like a puddle fits in the hole. It doesn't model complicated parts of physics, because it can't to complicated things, because mathematics is invented by humies and thus limited by humie cognitive abilities.
    huurtehoog · 1789730107 · focus · HN ↗
    > Mathematics can model simple parts of physics, because mathematics is simple and can do simple things, like a puddle fits in the hole. It doesn't model complicated parts of physics, because it can't to complicated things,
    You ought to learn some advanced mathematics to avoid making such absurd claims as "mathematics is too simple to model complex physics"
    Pray tell what parts of physics are too complicated for mathematics
    [deleted] · 1789752259 · focus · HN ↗
    [deleted]
    GoblinSlayer · 1789803522 · focus · HN ↗
    Chaos, biology and exponential complexity.

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