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But if at some point further decimals cannot be experimentally proven to be right, at best you can say "pi is such and such for such precision" and any definiti
by abrezas 10y ago
But if at some point further decimals cannot be experimentally proven to be right, at best you can say "pi is such and such for such precision" and any definition that gives the same number up to that precision must be accordingly accepted. Otherwise you need to demonstrate an experiment that uses further precision.
But we don't do that, and that's why mathematics don't have to do with experience, they are an entirely different tool that also happens to be useful in experimental science.
- hyperpape 10y ago"why mathematics don't have to do with experience" is too strong. Nothing you just said implies that math isn't intimately connected to empirical predictions in some way. What it shows is that contrary to Jules' earlier statements, there's no statement by statement correspondence--for any given mathematical statement, you can't find an interesting empirical prediction you associate with it.
- abrezas 10y agoI don't believe they are entirely independent, but there's nothing you can look outside your window that will change any mathematical theorem.
- jules 10y agoI agree with this statement (depending on how you interpret "change": if the world was different we may have been lead to prove different theorems), and nothing I've said previously contradicts it.
- jules 10y agoI never claimed that, in fact I said precisely the opposite: > Of course this isn't always the most interesting test
- hyperpape 10y agoSubstitute non-trivial for interesting. For instance, a calculation of pi to 50 digits will map to the same test as a calculation of pi to 51 digits. But the claims have different content so they should map to different tests!
- jules 10y agoIf mathematics doesn't have to do with experience, how do you explain the fact that when we measure pi it's 3.14? Pi is just pi defined in a mathematical way. It's true that there are other numbers or objects which can make a prediction about the measured ratio of the perimeter to the diameter, but those are not pi. Whether those other objects may be equally valid as pi for making that prediction depends on the details. There may be reasons to prefer one to the other even if they make the same predictions up to measurement precision. We usually prefer the simpler explanation for example. This is equally true in physics and other subjects. Note that as a device for predicting the ratio of the perimeter to the diameter, pi is not perfect. Our space is curved, so for large circles the ratio will deviate from pi, and you have to use a more complicated method based on Riemannian manifolds.