From: Eliezer Yudkowsky (sentience@pobox.com)
Date: Thu Aug 12 2004 - 22:26:21 MDT
J. Andrew Rogers wrote:
>
> You can no more imagine a world where mathematics doesn't apply than you
> can imagine the number pi.
Why can I not imagine pi? Pi is a finite Turing machine, even if the
decimal expansion is infinite. I'm an infinite set atheist, because no one
has ever reliably reported the observation of an infinite set, despite
occasional rumors. But I'm not a continuous space atheist or an irrational
number atheist. I inhabit a continuous space, and irrational numbers such
as pi play a role in physics. My infinite set atheism just implies that
any physically real continuous distribution is finitely parameterizable,
and the role of irrational numbers in physics doesn't change this.
Now if you said that no one could imagine the sequence of digits in the
decimal expansion of pi, I would agree.
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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