Hi Brent:

> I find myself agreeing with you on your general point that any
> computational theory of everything must be strictly finite - not just
> countable.

Thank goodness!  I was beginning to think I was all alone!!

> On the other hand I think you are missing the point about pi. Pi can
> be represented by a short program that will compute pi to however
> many decimal places are required in any given calculation.

Yes, I do understand this.  I've just done a lousy job explaining it.

> That program, not the decimal representation, can be inserted in
> place of pi in any calculation where we would write "pi". So in that
> sense it has a finite, even small, representation.

Ahhh... but does that little program ever return a value?  Does it ever
finish?

No.

So if this tiny pi program is required as a step in a larger program (like
my little example that uses the function pi() ), then main program will
never get beyond the first call to the function pi().  The universe would
enter this function and never return.

Sure, we can use the tiny pi program to symbolically represent the idea of
pi.  And there may even be some things we can learn from that little
program.  We can even manipulate it by concatinating it with other programs
or some piece of prose text, etc.  But we must never be allowed to RUN that
program (as a step in a larger program), or else we won't be able to do any
other calculations.  We can never use the RESULT in a larger program, since
the result is infinite.

>> If we cannot program it... it's not a Theory of EVERYTHING. It's
>> just a description.
>
> I'm not so sure about this.  A program is also just a description.

But it's not only a description... it's a perfect description.  It's an
implementation.  And it is identical to the workings of the universe it
instantiates.  Whereas formulas based on continuous or non-local ideas (e.g.
Newtonian Mechanics) only give a rough picture - and leave out the
all-important details.

Joel



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