From: Eliezer Yudkowsky (sentience@pobox.com)
Date: Fri May 28 2004 - 01:51:09 MDT
J. Andrew Rogers wrote:
>
> The basic problem that I see is that no distinction is made in the math
> between non-deterministic systems and systems which are not measurably
> deterministic in some finite context. And that an assumption of
> non-determinism is used for some of the physics appears incorrect prima
> facie from an information theoretic standpoint. One could throw in a
> bunch of stuff about Fisher information etc, but i think the real
> problem lies in the assumption I already mentioned. So from this
> standpoint, the standard deterministic model would still seem to apply.
>
> I've noticed that very few papers actually deal with the measurability
> of determinism in their models, which is closely related to predictive
> limits (how I became acquainted with the concept a number of years
> ago). It is nonetheless a very important concept to keep straight when
> talking about computation on finite state machinery because the
> consequences are broad and subtle.
E.T. Jaynes wrote about this very clearly when he pointed out that there is
no such thing as a "random variable". There are simply variables such that
our predictions of them can do no better than maximum entropy. This
inability is a property of our mind, not reality. Pretending that the
randomness is a property of the variable itself is a case of what Jaynes
calls the Mind Projection Fallacy.
The way physics *really* works, of course, certain quantum experiments
appear to be "random" because versions of you exist entangled with both
outcomes. If you say "heads", one version of you shall see heads, and one
version tails; if you say "tails" the same is true. All quite
deterministic. Since I comprehended many-worlds theory and Jaynes, I find
that I have absolutely no idea what a "random variable" or
"non-deterministic" process might be. I am not sure that the concept is
logically consistent, and it doesn't matter, since in this real world there
is nothing non-deterministic. I have dispensed with the concept of
physical randomness, and can no longer imagine what I once thought it
meant. It is like trying to imagine "time" after reading Barbour.
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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