**Ben Goertzel** (*ben@goertzel.org*)

*Sat, 10 Apr 1999 21:34:35 -0400*

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At 06:39 PM 4/10/99 -0400, Stephen P. King wrote:

*>Dear Ben,
*

*>
*

*> Not to be quaint, but why does an atheist need to assume a finite
*

*>universe?
*

Sorry, that was just an overly recondite joke ;)

But there was a serious point lurking inside it!

I do believe the universe should be considered finite, from the point of

view of science

Infinity I identify with the algorithmically random, i.e. the ineffable,

incomprehensible,

which some people would call God ...

This was the philosophical position of Georg Cantor who first developed the

mathematics of infinity,

incidentally

The set of uncomputable numbers, which is almost all real numbers, is a set

S with the peculiar

property that:

We can prove that no example of a member of S can ever be given

This is because if a number is "given" as an example, it is being finitely

expressed, and S

is exactly the set of numbers that cannot be finitely expressed

This is very Zen-like to me. The Void is indescribable; whatever

description you give is not the Void

because it is a description. S, the set of uncomputable numbers, is the

Void ;)

Discrete entities, numbers of finite algorithmic information, are the

observable world

I incline toward discrete models, but find it fascinating when continuous

models enhance our

understanding of discrete data and discrete math. Essentially, what is

happening here is that

the incomprehensible is comprehended ~indirectly~ as a pattern in the

observable.

ben

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