Joel Dobrzelewski wrote: > > But I don't dispute this, as I wasn't talking about the finite > representation. I was talking about the infinite process / function that pi > represents. > > Maybe this is obvious, but my whole point is that we are fooling ourselves > if we think we can compute physics using expressions that consume infinite > resources (memory, or computing time). Yes, I understand that the universe > as a whole may grow without bound (infinite history), but at any given > moment, it must be a finite size. Otherwise we can't compute it! >
Yes - I understand that is your point of view, as it is also that of Hal Ruhl's. It is not shared by the majority - eg myself, Juergen or Bruno. To be quite frank, whether something can be computed using 32 bit "integers", or IEEE floating point numbers or not is rather irrelevant to fundamental theories of reality. This is why Juergen's "all possible descriptions" approach has more legs. As an instance of the sort of problems you face, the number 0.1 can be represented as a finite string in base 10, but cannot be represented as a finite binary string (floating point number). Is 0.1 a valid number then? Unless you completely do the Kronecker thing, or course.... ---------------------------------------------------------------------------- Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia [EMAIL PROTECTED] Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks ----------------------------------------------------------------------------
