At 13:19 19/01/04 -0500, Stephen Paul King wrote:

>Where and when is the consideration of the "physical resources" required
>for the computation going to obtain? Is my question equivalent to the old
>"first cause" question?

Anything "physical" is by definition within a universe (by my definition,
anyway!).  What are the physical properties of a system in our universe?
Mass, size, energy, electrical charge, partical composition, etc.  If we
at least hypothetically allow for the existence of other universes,
wouldn't you agree that they might have completely different physical
properties?  That they might not have mass, or charge, or size; or that
these properties would vary in some bizarre way much different from how
stable they are in our universe.

Consider Conway's 2-dimensional Cellular Automota universe called Life.
Take a look at, an amazing
implementation of a computer, a Turing Machine, in this universe.
I spent a couple of hours yesterday looking at this thing, seeing how
the parts work.  He did an incredible job in putting all the details
together to make this contraption work.

So we can have computers in the Life universe.  Now consider this: what
is the mass of this computer?  There is no such thing as mass in Life.
There are cells, so you could count the number of "on" cells in the system
(although that varies quite a bit as it runs).  There is a universal
clock, so you could count the time it takes to run.  Some of our familiar
properties exist, and others are absent.

So in general, I don't think it makes sense to assume literally that
computers require physical resources.  Considered as an abstraction,
computation is no more physical than is mathematics or logic.  A theorem
doesn't weigh anything, and neither does a computation.

Hal Finney

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