"A theorem doesn't weigh anything, and neither does a computation."
Nice try but that is a very smelly Red Herring. Even Conway's Life can
not exist, even in the abstract sense, without some association with the
possibility of "being implemented" and it is this "Implementation" that I am
Let us consider Bruno's beloved "Arithmetic Realism". Are we to believe
that Arithmetic can be considered to "exist" without, even tacitly, assuming
the possibility that numbers must be "symbolic representable"? If they can
be, I strongly argue that we have merely found a very clever definition for
the term "meaninglessness".
I beg you to go directly to Turing's original paper discussing what has
become now know as a "Turing Machine". You will find discussions of things
like "tape" and "read/write head". Even if these, obviously physical,
entities are, as you say, "by definition within a universe" and that such
"universes" can be rigorously proven to be "mathematical entities", this
only strengthens my case: An abstract entity must have a possibility of
being physically represented, even if in a "Harry Potter Universe", to be a
meaningful entity. Otherwise what restrains us from endless Scholastic
polemics about "how many Angels can dance on the head of a Pin" and other
The fact that an Algorithm is "independent of any particular
implementation" is not reducible to the idea that Algorithms (or Numbers, or
White Rabbits, etc.) can exist without some "REAL" resources being used in
their implementation (and maybe some kind of "thermodynamics").
BTW, have you read Julian Barbour's The End of Time? It is my opinion
that Julian's argument falls flat on its face because he is making the very
same mistake: Assuming that his "best-matching" scheme can exists without
addressing the obvious status that it is an NP-Complete problem of
uncountable infinite size. It is simply logically impossible to say that the
mere postulation of a Platonia allows for the a priori existence of the
solution to such a computationally intractable problem.
----- Original Message -----
From: "Hal Finney" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, January 20, 2004 1:39 PM
Subject: Re: Is the universe computable
> 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 http://rendell.server.org.uk/gol/tm.htm, 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