4 ms·

PI is a concenpt. Of course it doesn't exist physically* in the universe. * Well, various "physical" representations/encodings of this concept must exist in di

by hasenj 12y ago

PI is a concenpt. Of course it doesn't exist physically* in the universe. * Well, various "physical" representations/encodings of this concept must exist in different people's brains.

kazinator 12y ago
Whether the existence of pi is different from the existence of a given stone is a philosophical question! Maybe you and I exist exactly in the same sense that pi exists: no more, no less. Concepts can be reshaped. If pi is merely a concept, why can't we conceive it to be something else, like 4.0?
- TheOtherHobbes 12y ago
  In a curved spacetime Pi could easily be 4.0. Pi is an idealised approximation of a certain kind of curvature in a certain kind of spacetime. Pi appears to have infinite precision only if you assume the curvature and the spacetime are perfectly smooth and have infinite resolution. Given there's a Planck limit, it's unlikely the universe really is perfectly smooth. So Pi in the real universe is not very likely to have infinite precision. That's where the concept of Pi as a Platonic example of mathematical perfection trips over the reality of physics as a messy thing where traditional math structures can only ever provide approximate descriptions. Beyond a certain level of detail Other Stuff is happening, and you can't assume smoothness or infinite precision. We don't know a whole lot about the Other Stuff yet. One reason is that math was built to work with smooth functions with infinite precision, and there's no equivalent math that describes the lumps of whatever spacetime is made of, or the relationships between the lumps.
  - kazinator 12y ago
    Pi isn't an approximation but a real number which is uncomputable, but otherwise precisely identified. On the other hand, a rational number like 3.14159 serves as an approximation of pi. pi doesn't help you find the distance around a circle in some curved space-time, but pi is what it is.

by hasenj 12y ago

PI is a concenpt. Of course it doesn't exist physically* in the universe. * Well, various "physical" representations/encodings of this concept must exist in different people's brains.

kazinator 12y ago

Whether the existence of pi is different from the existence of a given stone is a philosophical question! Maybe you and I exist exactly in the same sense that pi exists: no more, no less. Concepts can be reshaped. If pi is merely a concept, why can't we conceive it to be something else, like 4.0?

TheOtherHobbes 12y ago
In a curved spacetime Pi could easily be 4.0. Pi is an idealised approximation of a certain kind of curvature in a certain kind of spacetime. Pi appears to have infinite precision only if you assume the curvature and the spacetime are perfectly smooth and have infinite resolution. Given there's a Planck limit, it's unlikely the universe really is perfectly smooth. So Pi in the real universe is not very likely to have infinite precision. That's where the concept of Pi as a Platonic example of mathematical perfection trips over the reality of physics as a messy thing where traditional math structures can only ever provide approximate descriptions. Beyond a certain level of detail Other Stuff is happening, and you can't assume smoothness or infinite precision. We don't know a whole lot about the Other Stuff yet. One reason is that math was built to work with smooth functions with infinite precision, and there's no equivalent math that describes the lumps of whatever spacetime is made of, or the relationships between the lumps.
- kazinator 12y ago
  Pi isn't an approximation but a real number which is uncomputable, but otherwise precisely identified. On the other hand, a rational number like 3.14159 serves as an approximation of pi. pi doesn't help you find the distance around a circle in some curved space-time, but pi is what it is.