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From: Joel Dobrzelewski <dobrzele.domain.name.hidden>

Date: Mon, 25 Jun 2001 08:58:29 -0400

Joel:

*>> It seems to me there is a great deal more information in PI than
*

*>> just the 2 bytes it takes to convey it in an email message.
*

Russell:

*> Not much more. One could express pi by a short program - eg the
*

*> Wallis formula, that would be a few tens of bytes on most Turing
*

*> machines. Even expressing it as a pattern on your beloved CA, it
*

*> would probably not consume more that a few hundred bytes.
*

Yes, I see. Juergen pointed this out too, and I think it's a valid point to

make the distinction between different representations of the same

mathematical object. You are both correct - Pi can in fact be represented

nicely (as a program) in a finite way.

But I don't dispute this, as I wasn't talking about the finite

representation. I was talking about the infinite process / function that pi

represents.

Maybe this is obvious, but my whole point is that we are fooling ourselves

if we think we can compute physics using expressions that consume infinite

resources (memory, or computing time). Yes, I understand that the universe

as a whole may grow without bound (infinite history), but at any given

moment, it must be a finite size. Otherwise we can't compute it!

For example, if somehow the universe requires computations like the

following:

x = 0

do

x = x + pi()

print x

loop

Then we are doomed. We cannot run this kind of program. Yes, I know we can

find a finite representation like this:

x = 0

do

x = x + 1

print x; " pi"

loop

But does this REALLY make use of the details of pi? I don't think so.

I'm simply trying to get people to confront the truth that we humans are

incapable of devising Theories of Everything that are NOT run on a universal

computer. That's all.

Many will say, "Of course! We know that!".

And then they go on, as if nothing happened, talking about the probabilities

of items in infinite sets, and "independent tosses of a fair coin", and

"quantum indeterminacy", and "the continuum of the real numbers", as if

these things exist!

If we cannot program it... it's not a Theory of EVERYTHING. It's just a

description.

Let us take the realist approach and focus on the things we can actually

compute fully.

Joel

Received on Mon Jun 25 2001 - 06:00:24 PDT

Date: Mon, 25 Jun 2001 08:58:29 -0400

Joel:

Russell:

Yes, I see. Juergen pointed this out too, and I think it's a valid point to

make the distinction between different representations of the same

mathematical object. You are both correct - Pi can in fact be represented

nicely (as a program) in a finite way.

But I don't dispute this, as I wasn't talking about the finite

representation. I was talking about the infinite process / function that pi

represents.

Maybe this is obvious, but my whole point is that we are fooling ourselves

if we think we can compute physics using expressions that consume infinite

resources (memory, or computing time). Yes, I understand that the universe

as a whole may grow without bound (infinite history), but at any given

moment, it must be a finite size. Otherwise we can't compute it!

For example, if somehow the universe requires computations like the

following:

x = 0

do

x = x + pi()

print x

loop

Then we are doomed. We cannot run this kind of program. Yes, I know we can

find a finite representation like this:

x = 0

do

x = x + 1

print x; " pi"

loop

But does this REALLY make use of the details of pi? I don't think so.

I'm simply trying to get people to confront the truth that we humans are

incapable of devising Theories of Everything that are NOT run on a universal

computer. That's all.

Many will say, "Of course! We know that!".

And then they go on, as if nothing happened, talking about the probabilities

of items in infinite sets, and "independent tosses of a fair coin", and

"quantum indeterminacy", and "the continuum of the real numbers", as if

these things exist!

If we cannot program it... it's not a Theory of EVERYTHING. It's just a

description.

Let us take the realist approach and focus on the things we can actually

compute fully.

Joel

Received on Mon Jun 25 2001 - 06:00:24 PDT

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