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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

Date: Wed, 21 Jan 2004 02:50:13 -0500

At 1/19/04, Stephen Paul King wrote:

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

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