Stathis Papaioannou wrote:
> Peter Jones writes:
>>There is a very impoertant difference between "computations do
>>not require a physical basis" and "computations do not
>>require any *particular* physical basis" (ie computations can be
>>implemented by a wide variety of systems)
> Yes, but any physical system can be seen as implementing any computation with 
> the appropriate
> rule mapping physical states to computational states. 

I think this is doubtful.  For one thing there must be enough distinct states.  
It's all very well 
to imagine a mapping between a rock and my computer idealized as isolated 
closed systems - but in 
fact they are not isolated close systems.  When you're talking about simulating 
the universe in 
computation it has a lot more states than a rock and it isn't close either.

>Attempts are made to put constraints on what
> counts as implementation of a computation in order to avoid this 
> uncomfortable idea, but it 
> doesn't work unless you say that certain implementations are specially 
> blessed by God or something. 
> So at least you have to say that every computation is implemented if any 
> physical universe at all
> exists, even if it is comprised of a single atom which endures for a 
> femtosecond. That's an absurd 
> amount of responsibility for a little atom, and it makes more sense to me 
> (although I can't at the 
> moment think of a proof) to say that the atom is irrelevant, and the 
> computations are implemented 
> anyway by virtue of their status as mathematical objects.

Or by virtue of there being universes.

Brent Meeker

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