From: Matt Mahoney (matmahoney@yahoo.com)
Date: Thu May 08 2008 - 15:38:16 MDT
--- Stuart Armstrong <dragondreaming@googlemail.com> wrote:
> > Your failure to see the relevance is a sign of high genetic fitness.
> > Don't take it as a criticism.
>
> I don't take it as a criticism! I take it with a degree of
> bewilderment bordering on complete incomprehension. I started the
> thread talking about post-singularity signaling and its effect on
> competition and culture - you responded talking about genetic fitness,
> beliefs versus reality, and whether we are just simulations.
>
> I feel there is a very interesting point there somewhere, but could
> you tell me what it is? In detail?
My question is whether "after the singularity" makes any more sense than
"before the big bang". I alluded to two types of time, making "after"
poorly defined. Physical time is symmetric with regard to past and
future. Perceptual or computational time is not. It is directed toward
increasing thermodynamic entropy and irreversible computational operations
such as writing into memory. We may quantify perceptual time by
considering two states S1 and S2 of an intelligent agent and algorithmic
complexity K() such that if
K(S2|S1) = t
K(S1|S2) = 0
then S2 occurs at time t after S1 on a perceptual time scale. When you
were a child and 5 minutes seemed like an hour, it was because you were
learning faster. Likewise, for a computation it makes more sense to count
instructions than seconds.
This model assumes no forgetting. In reality, K(S1|S2) > 0, so "after" is
a partially ordered relation with a beginning but no end. (This is true
in cosmology and general relativity too, so it should not seem so
strange).
In physical time, knowledge is assumed to accumulate at a hyperbolic rate.
A singularity occurs when knowledge becomes infinite, say, after 40 more
Earth orbits around the Sun. In perceptual time a singularity seems to be
infinitely far into the future. Thus, "after the singularity" does not
make sense.
With regard to simulation, I was talking about a time "just before" the
singularity in physical time, when it is possible to simulate universes
containing intelligent agents programmed to believe their environment is
real. I agree that it makes no difference from your viewpoint whether the
universe is real or not, because there is no way to distinguish the
possibilities. I actually believe that the universe we observe is one of
an enumeration of all possible universes, possibly at the bottom of a
chain of simulations within simulations. I believe the top of the chain
is isomorphic to N, the set of natural numbers, which is the most likely
possibility given a Solomonoff prior. Our observable universe seems to be
generated by a program with a complexity of a few hundred bits.
-- Matt Mahoney, matmahoney@yahoo.com
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