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as per the article, in this universe, and potentially others as long as they have some notion of smooth space, we infer an abstract ideal of flatness and from t

as per the article, in this universe, and potentially others as long as they have some notion of smooth space, we infer an abstract ideal of flatness and from there derive Pi.

blamestross 5y ago
The notion of smooth space is an approximation, it doesn't exist. So yes, you could find a space with an "apparent pi" within a given delta of the ideal, but it won't be "ideal pi"
- AnimalMuppet 5y ago
  You either missed or ignored keithnz's point. There are plenty of spaces that are close enough to smooth that we can deduce the properties of a perfectly smooth space, and from that, the value of a perfect pi. So we can't find a space that has that same perfect pi. So what?
  - blamestross 5y ago
    My point is that the argument is wrong. "ideal flat space" isn't a property of our universe. That "perfect pi" is a property of the mathematical abstraction of "smooth space". Our universe might asymptotically flirt with such a state but "flat space" isn't real not in the sense that the speed of light and force constants are descriptions of things that actually happen and actually exist.
    - keithnz 5y ago
      There is no real argument, essentially the article says well, "it depends" and basically we have no idea, but, given a few assumptions, is it reasonable that other universes would have denizens that conceive of circles and calculate the same value of Pi? and they postulate that if that also had a notion of flat space (not that the universe comports to that) then they too probably would come up with the same value of Pi
    - kaba0 5y ago
      As others have already mentioned, no geometry is required for the definition of pi. Real numbers are enough, where of course the problematic infinity does come up - but there do exist quite simple approximations that will calculate pi to any degree of precision regardless of physical space.
- DonHopkins 5y ago
  Space itself doesn't exist. As soon as you put something that exists in it, that part of it is no longer space.

as per the article, in this universe, and potentially others as long as they have some notion of smooth space, we infer an abstract ideal of flatness and from there derive Pi.

blamestross 5y ago

The notion of smooth space is an approximation, it doesn't exist. So yes, you could find a space with an "apparent pi" within a given delta of the ideal, but it won't be "ideal pi"

AnimalMuppet 5y ago
You either missed or ignored keithnz's point. There are plenty of spaces that are close enough to smooth that we can deduce the properties of a perfectly smooth space, and from that, the value of a perfect pi. So we can't find a space that has that same perfect pi. So what?
- blamestross 5y ago
  My point is that the argument is wrong. "ideal flat space" isn't a property of our universe. That "perfect pi" is a property of the mathematical abstraction of "smooth space". Our universe might asymptotically flirt with such a state but "flat space" isn't real not in the sense that the speed of light and force constants are descriptions of things that actually happen and actually exist.
  - keithnz 5y ago
    There is no real argument, essentially the article says well, "it depends" and basically we have no idea, but, given a few assumptions, is it reasonable that other universes would have denizens that conceive of circles and calculate the same value of Pi? and they postulate that if that also had a notion of flat space (not that the universe comports to that) then they too probably would come up with the same value of Pi
  - kaba0 5y ago
    As others have already mentioned, no geometry is required for the definition of pi. Real numbers are enough, where of course the problematic infinity does come up - but there do exist quite simple approximations that will calculate pi to any degree of precision regardless of physical space.
DonHopkins 5y ago
Space itself doesn't exist. As soon as you put something that exists in it, that part of it is no longer space.