Ok, sorry for being a smart-ass. Instead of baiting the discussion to make my point, I'll try to simply state the position clearly.
We humans cannot deal with infinite structures, like pi. Numbers like pi and e and Omega and all the others are the devil! :) And we all know the devil is in the details... We carry them along in our mathematics all the way to the "end" so that they can be "evaluated" in the final step. But I ask you: When does the universe evaluate its expressions? Is there an "end" to the universe when all the values for pi and e are fully computed and all their magic is brought to life? If we simply carry these finite expressions along so that they can be evaluated later, "if we choose to, but they don't really make a big difference anyway", then what use did we make of the continuum? Maybe we were just fooling ourselves and delaying the inevitable. F = G * m1 * m2 / r^2 That's a finite expression. We always assume that we can calculate F and to any degree of precision we like. But then does this capture the whole picture? If we are guaranteed to have rounding errors because our computers only have so much RAM, then have we really explained all there is to explain? No. Something more (or less!) is necessary... When searching for a Theory of Everything, we need an expression, a formula, a program that doesn't have any rounding errors. I still claim... it must be finite and discrete. Does this make any more sense now? Chasing the real devil / details of pi is a hopeless task. It would be better to just acknowledge that we can never *implement* pi and resolve to work with finite expressions and finite mathematics. I feel that this "bottom up" approach is our only chance fr success. Joel
