From: Mark Waser (mwaser@cox.net)
Date: Fri Aug 13 2004 - 06:33:21 MDT
>> I'm an infinite set atheist, because no one has ever reliably reported
the observation of an infinite set
I'm curious why you're not willing to accept the set of all integers as an
infinite set. Or how about the set of all decimal numbers between 0 and 1?
Also, inductive logic clearly proves the existence of infinite sets.
>> But I'm not a continuous space atheist
On the other hand . . . . I'd like to see you prove that space in continuous
(particularly in light of quantum mechanics). Your perception (and
modeling) is that space is continuous but space could just as easily be a
set of non-contiguous teleporter points.
- - - - -
I also find all of these "everything is math" arguments extremely
disingenuous since they all seem to rely on the fact that what any one being
(or set of beings) is finite and therefore can be described with a finite
set of data points.
Mark
----- Original Message -----
From: "Eliezer Yudkowsky" <sentience@pobox.com>
To: <sl4@sl4.org>
Sent: Friday, August 13, 2004 12:26 AM
Subject: Re: All is number
> 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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