On Tue, Dec 12, 2006 at 08:54:51AM -0800, Brent Meeker wrote:
> > 
> > You're still missing the point. If you sum over all SASes and other
> > computing devices capable of simulating universe A, the probability of
> > being in a simulation of A is identical to simply being in universe A.
> > 
> > This is actually a theorem of information theory, believe it or not!
> 
> I wasn't aware that there was any accepted way of assigning a probability to 
> "being in a universe A".  Can you point to a source for the proof of this 
> theorem?
> 
> Brent Meeker
> 

See theorem 4.3.3 aka "Coding Theorem" in Li and Vitanyi.

Being in a simulation corresponds to adding a fixed length prefix
corresponding to the interpreter to the original string, although
there will also be other programs that will be shorter in the new
interpreter.

After summing over all possible machines, and all possible programs
simulating our universe on those machines, you will end with a
quantity identical to the Q_U(x) in that theorem, aka "universal a
priori probability".

Note that in performing this sum, I am not changing the reference
machine U (potential source of confusion).


Of course this point is moot if the universe is not simulable!

Cheers

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A/Prof Russell Standish                  Phone 0425 253119 (mobile)
Mathematics                              
UNSW SYDNEY 2052                         [EMAIL PROTECTED]
Australia                                http://www.hpcoders.com.au
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