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From: Joel Dobrzelewski <dobrzele.domain.name.hidden>

Date: Tue, 26 Jun 2001 11:57:32 -0400

Hi Brent:

*> I find myself agreeing with you on your general point that any
*

*> computational theory of everything must be strictly finite - not just
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*> 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
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*> be represented by a short program that will compute pi to however
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*> 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
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*> place of pi in any calculation where we would write "pi". So in that
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*> 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

Received on Tue Jun 26 2001 - 08:54:41 PDT

Date: Tue, 26 Jun 2001 11:57:32 -0400

Hi Brent:

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

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

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.

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

Received on Tue Jun 26 2001 - 08:54:41 PDT

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