From: Lee Corbin (lcorbin@tsoft.com)
Date: Mon Jun 10 2002 - 17:46:59 MDT
Hal writes
> Lee Corbin writes, regarding Wei Dai's proposal to corral as much matter
> and energy as possible locally before it disappears over the event
> horizon:
> > We have to go lasso that matter only if by "our civilization"
> > you mean something that does not apply to our colonies. Why
> > are you not content with our merely sending our programs
> > (equals our selves) out to the distant matter to colonize it?
> > It still seems to me that you are wasting absolutely huge
> > resources.
>
> If you have twenty bits' worth of matter, and it gets separated into
> two ten-bit heaps, then each one can only go through 2^10 or 1024
> different states. So there are a total of 2048 states being explored.
> Whereas if you bring the 20 bits together, you can go through 2^20 states
> or over 1 million. Generally collecting matter together will allow for
> exponentially more states to be explored than allowing it to be separated.
Yes, you are correct: in fact, the addition of one single atom
or one neuron (or one state of a TM) increases the possibilities
astronomically. This is the Busy Beaver problem, fundamentally.
However, if one already has a reasonable amount of material,
say a billion tons or so, then one has from the approximately
10^9 * 1000 kg a huge number of possibilities---something on
the order of 10^10^10 possible states. I'm not really concerned
about what happens ten to the nine billion seconds from now.
Lee
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