4 ms·
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
by 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 agoYou 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 agoMy 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 agoThere 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 agoAs 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 agoSpace itself doesn't exist. As soon as you put something that exists in it, that part of it is no longer space.