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!
>

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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....
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