From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Sun Jan 03 1999 - 17:50:42 MST
Nick Bostrom wrote:
>
> Eliezer S. Yudkowsky wrote:
>
> > I got the impression
> > that during the very early Big Bang, everything was within everything
> > else's light cone.
>
> Not in standard Big Bang cosmology, and hence the "horizon problem"
> -- how to explain why distant regions of the universe are in thermal
> equilibrium despite them never having been in causal contact.
> Inflation theory tries to solve this problem by postulating an epoch
> of very rapid expansion in the early universe, so that all that we
> see when we look around in cosmos today originated from such a small
> volume that within that volume things had had time to interact before
> the inflation set in.
My impression was that the problem was how to explain the
mass-distribution discontinuities (that caused the coalescence of
galaxies) when the whole Universe was in causal contact; that inflation
was postulated to provide a period when rapid expansion inflated small
variances into large discontinuities without permitting the system to
equalize. I yield, however, to superior knowledge.
Doesn't make a difference; the point is that in the standard cosmology
the early Big Bang was in causal contact.
> > Of course, that doesn't mean an infinite number of
> > actions could be performed. What's the function for the radius of the
> > Big Bang as a function of time? Anyone know?
>
> It depends on the global topology of the universe. If the universe is
> closed then when it is radiation dominated (as it was in its early
> stages) it expands as
>
> R = sqrt[A^2 + t^2], where t is a time parameter -A<t<+A.
>
> If open, then
>
> R = sqrt[t^2 - A^2], where +A<t<positive infinity
>
> (Note that in the latter case, R is not a radius -- the universe is
> spatially infinite at all times -- but a scale factor.)
>
> Finally, if the universe is flat, then
>
> R = sqrt[2At], 0<t< positive infinity
>
> where again R is a scale factor.
I get the impression that in all cases, the sum of computing power is
infinite. At time 1/t (t=10^45, for example), distance is proportional
to either 1/t or 1/t^2, so the farther back you go towards the
beginning, the closer things are and the less time it takes to communicate.
If between time t and u light can bounce back and forth once between two
particles, it can also bounce once between t/2 and u/2, or t/1000 and u/1000.
That's in a flat universe; in an open or closed universe, it can bounce
back and forth a thousand times between t/1000 and u/1000.
In either case, it looks to me like you get an infinite number of
interactions in linear sequence.
--
sentience@pobox.com Eliezer S. Yudkowsky
http://pobox.com/~sentience/AI_design.temp.html
http://pobox.com/~sentience/sing_analysis.html
Disclaimer: Unless otherwise specified, I'm not telling you
everything I think I know.
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