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
> physical
> 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. 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.

Stathis Papaioannou
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