Bruno Marchal writes (quoting SP):
> > It seems to me trivially obvious that any sufficiently complex > > physical system implements any finite computation, just as any > > sufficiently large block of marble contains every marble statue of a > > given size. The difference between random noise (or a block of > > marble) on the one hand and a well-behaved computer (or the product of > > a sculptor's work) on the other is that the information is in the > > latter case presented in a way that can interact with the world > > containing the substrate of its implementation. But I think that this > > idea leads to almost the same conclusion that you reach: it really > > seems that if any computation can be mapped to any physical substrate, > > then that substrate is superfluous except in that tiny subset of cases > > involving well-behaved computers that can handle counterfactuals and > > thus interact with their environment, and we may as well say that > > every computation exists by virtue of its status as a platonic object.> > > > I mainly agree with you, except perhaps that I would not go so quickly > from> "any sufficiently complex physical system implements any finite > computation" to> "any computation can be mapped to any physical substrate",> I doubt long and deep (in Bennett technical sense) computation can be > mapped to *any* physical substrate.
I admit that the latter statement does not necessarily follow from the former. But suppose all that exists is a single hydrogen atom in an otherwise empty universe, no MW, just the atom with some version of CI of QM. Over eternity, how many distinct physical states will this atom go through? We could map one distinct computational state to one distinct physical state. Well, why should a transistor or valve switching on and off implement a certain computation but not a hydrogen atom changing states? Furthermore, given that the mapping of physical state to computation is arbitrary (a switch going on/off/on could be saying 1/0/1 or 0/1/0 or even 1/1/0, the mapping changing halfway through the computation in the last example), we could "reuse" physical states multiple times to implement whatever computation we want. This is a lot of responsibility for one little hydrogen atom, and it seems to make more sense to say that in fact computation does *not* supervene on the physical.
> This is important because consciousness should relie on infinite > computations.
This may actually be the case, but why does it necessarily have to be the case?
> But then I agree with, even if my mind (by chance) supervene on some > local piece of stuff, and even if this adds some weight to my > computational states, it will do so insofar as I will not see the > difference when surviving on some continuation of that computation > somewhere else. Eventually all notions of "somewhere else" should > themselves be explained from the UD, so...> > > > I say "almost" because I can't quite see how to prove it, even though > > I suspect that it is so.> > > We will come back on this. I must explain better what is a computation > in Platonia, sure.
Stathis Papaioannou
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Received on Wed Jul 19 2006 - 23:32:35 PDT