From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Sun May 16 1999 - 11:30:54 MDT
It seems to me that all CAs (cellular automata) are inherently
incompatible with the spirit of Special Relativity, at least in the
current formalism. CAs have what we might call a One True Space of
Simultaneity, the prohibition of which was the entire point of having
Special Relativity in the first place. The whole problem with CAs, that
the speed of light will appear different to different observers, derives
from the fact that there are absolute positions (the cells) and thus
absolute velocities. Maybe you could alter the formalism so that the
cells didn't have absolute positions, but you'd still have the problem
that the number of cells between cell A and cell B, and thus the time
for light to go between them at one tick per cell, is absolute; and thus
the speed of light (relative to your own speed) is NOT. In Special
Relativity, a fast-moving observer would have to see fewer cells and
slower ticks.
Maybe you could alter the formalism to fix that. Frankly, I don't think
so. CAs separate space and time into neat little independent Newtonian
coordinates. I don't see how you can have one objectively correct
universal separation into discrete cells and not have neat little
Newtonian coordinates. In Special Relativity spacetime is continuous,
and the transformation of some axis from space into time is also continuous.
One might say that Special Relativity says that "real" things occupy a
continuum between rules and data, while in Turing machines things are
separated into rules and data. Another of the many reasons to
best-guess that the physical Universe is noncomputable. And also a
rationale for Power-class technologies like Greg Bear's "descriptor
theory", or being able to change the laws of physics: I think we'll
find that there's no rigid distinction between substance, law, and
metalaw, and that all three can be changed. Well, now I'm getting
Eganic, so I better sign off.
--
sentience@pobox.com Eliezer S. Yudkowsky
http://pobox.com/~sentience/AI_design.temp.html
http://pobox.com/~sentience/singul_arity.html
Disclaimer: Unless otherwise specified, I'm not telling you
everything I think I know.
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