3 ms·

Rational numbers can produce "continuous" values to a precision way beyond what any equipment you could get your hands on could differentiate without physically

• eigenket 3y ago
  That is certainly true. In fact you don't even need rational numbers, it is entirely possible that there are a finite number of positions on the universe, for example. Nevertheless physics seems to work very nicely when expressed in the language of calculus. Everything from Schrödinger's equation to the Einstein field equations, and from classical mechanics to the standard model of particle physics are expressed in the language of calculus. This all looks like a wild and strange coincidence if fundamentally we are living in a relm like the rationals, where calculus doesn't really make sense.
  • meindnoch 3y ago
    Unless the resolution of the rational model is fine enough to be indistinguishable from the continuous solution.
    • astrange 3y ago
      That would be very fine indeed since the CMB doesn't eg seem to be pixelated and we don't observe numeric instability anywhere.
      • naasking 3y ago
        I wouldn't even assume that discrete theories must have a resolution that can be detected.
        • astrange 3y ago
          Any amount of quantization should have very noticeable indirect effects somewhere. Try implementing game physics and you'll see it.