Re: Is the universe computable

From: Kory Heath <kory.heath.domain.name.hidden>
Date: Wed, 21 Jan 2004 02:50:13 -0500

At 1/19/04, Stephen Paul King wrote:
> Were 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?

The view that Mathematical Existence == Physical Existence implies that
"physical resources" is a secondary concept, and that the ultimate ground
of any physical universe is Mathspace, which doesn't require resources of
any kind. Clearly, you don't think the idea that ME == PE makes sense.
That's understandable, but here's a brief sketch of why I think it makes
more sense than the alternative view (which I'll call "Instantiationism"):

Here's my definition of "Computational Realism", which is sort of a
restricted version of Mathematical Realism. (I'm not sure if my definition
is equivalent to what others call "Arithmetic Realism", so I'm using a
different term.) Let's say that you're about to physically implement some
computation, and lets say that there are only three possible things that
this computation can do: return 0, return 1, or never halt. Computational
Realism is simply the belief that *there is a fact of the matter* about
what this computation will do when you implement it, and that this fact is
true *right now*, before you even begin the implementation. Furthermore, CR
is the belief that there is fact of the matter about what the result of the
computation *would be*, even if it's never actually implemented. CR implies
that there is such a fact of the matter about every conceivable computation.

It's from this perspective that I can begin to explain why I feel that
implementation is not a fundamental concept. In my view, implementing a
computation is a way of "viewing" a structure that already exists in
Mathspace (or Platonia, or whatever you want to call it). Implementation is
clearly something that occurs within computational structures - for
instance, we can imagine creatures in a cellular automata implementing
computations on their computers, and they will have all the same concerns
about "physical resources" that we do - computational complexity,
NP-complete problems, etc. However, the entire infinite structure of their
CA world exists *right now*, in Mathspace. If we consider the rules to
their CA, and consider an initial state (even an infinite one - say, the
digits of pi), then there is *a fact of the matter* about what the state of
the infinite lattice would be in ten ticks of the clock - or ten thousand,
or ten million. And the key point is that the existence of these facts
doesn't require "resources" - there's really no concept of resources at all
at that level. Every single fact about every single possible computation is
simply a fact, right now. Every conceivable NP-complete problem has an
answer, and it doesn't require any "computational resources" for these
answers to exist. But of course, computational creatures like us require
computational resources to "view" these answers. Since our resources are
severely limited, we don't have access to most of the truths in Mathspace.

I don't think that this form of realism automatically leads to the
conclusion that ME == PE, but it certainly points in that direction. ME ==
PE becomes especially appealing when we consider the infinite regress
problem that the alternative position generates. You ask if your question
is equivalent to the old "first cause" question. I propose that it is
exactly equivalent, and brings with it all of the attendant paradoxes and
problems. If you believe that implementation is a fundamental concept - if
you believe that, somehow, our universe must be "instantiated", or must
have some other special quality that gives it its true reality - then
you've got an infinite regress problem. Certainly, I can imagine that our
universe is instantiated in some larger computation, but then that
computation will have to be instantiated in something else to make *it*
real... and where does it all end? Or is it turtles all the way down? Or
does our universe simply have the elusive quality of "physical existence",
while other mathematical structures lack it? In my opinion, the idea that
ME == PE points to a solution to these problems.

-- Kory
Received on Wed Jan 21 2004 - 03:24:54 PST