Russell Standish wrote:
> 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!
Or if the length of the code has nothing to do with it's probability.
Brent Meeker
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Received on Tue Dec 12 2006 - 17:07:54 PST