> The fact that an Algorithm is "independent of any particular
> implementation" is not reducible to the idea that Algorithms (or Numbers,
> White Rabbits, etc.) can exist without some "REAL" resources being used in
> their implementation (and maybe some kind of "thermodynamics").
To paraphrase Bill, that depends on what the meaning of the word "real" is.
My point being that, if one accepts, even if only hypothetically (humor me),
that a (toy) universe can be modeled by a CA, then would not the
self-consistent "physics" of the universe emerge from "following" the rule?
Given this, then, would not the "resources" be mapped directly only to those
physics and not directly to ours, even though the CA is "implemented"
according to and via our physics. What I'm getting at here is that "weight"
as a function of mass and gravitation may well have no direct correspondence
in the CA's physics. If not, then it could be argued that the computation
within the context of it's own universe has no "weight" (i.e: consumes no
EXTRA-universal resources) even though the implemention of same does.
Then question then becomes, I suppose, if in fact our universe is a digital
one (if not strictly a CA) havng self-consistent emergent physics, then
might it not follow that it is "implemented" (run?) via some extra-universal
physical processes that only indirectly correspond to ours?
(if the above is too painfully obvious (or goofy?) and/or old news then,
again, do humor me..)