[time 212] Re: [time 207] Re: [time 206] Observation and infinity

Ben Goertzel (ben@goertzel.org)
Sat, 10 Apr 1999 21:34:35 -0400

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

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,
which some people would call God ...

This was the philosophical position of Georg Cantor who first developed the
mathematics of infinity,

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


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