Quote:
|
Originally Posted by flstf
Isn't this more like a discovery than a logical construct at least until we try to assign an exact number to it?
|
Yes, it certainly has a physical meaning. What I meant is that when you start talking about pi being irrational, then you're not really referring to physical measurements anymore. It is an abstraction, although one which is motivated by experiments like the one you mention with a wagon wheel.
To be a little more precise in what I'm talking about, we know that geometry is not quite Euclidean. Different circles would have different effective values of pi (although they can be related to the usual pi given some extra parameters). More seriously, it seems that distances cannot take on continuous values. Space itself probably becomes discretized in a sense below a certain scale. In all of this, it is still useful to keep the mathematical definition of pi, but it loses some of its simple physical interpretation.