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From: Christopher Maloney <dude.domain.name.hidden>

Date: Thu, 03 Jun 1999 21:59:29 -0400

As a recent member of this list, I'm slowly getting up to

speed with all the reading material. I've been reading the

archives of this list, and am up to about article 150 (out

of about 650!). I'll refrain from posting on old discussions

until I've finished that, as perhaps the old issues I feel

the urge to post about have already been resolved.

Meanwhile, here are a few thoughts on Tegmark's paper. This

is about 1/2 of the review that I'm writing on it (I always

review these sorts of things for my own purposes anyway).

---------------

This was an excellent paper, which effectively explicated many of the

ideas I've been formulating over the last fourteen years. The

fundamental principle put forth is the Principle of Plenitude, that

all mathematically consistent structures exist. Basically, he makes

the statement that mathematical existence is the same as physical

existence.

He introduces the acronym SAS (self-aware substructures) for

conscious entities within a mathematical structure. This is fine by

me, but Sarah (my wife) didn't know what to say when I called her my

favorite self-aware substructure.

The initial defense of this basic principle is well presented. He

presents four possibilities, the first three of which are lumped

together:

1. The physical world is completely mathematical

(a) Everything that exists mathematically exists physically

(b) Some things that exist mathematically exist physically,

others do not.

(c) Nothing that exists mathematically exists physically

2. The physical world is not completely mathematical

There is not much that can be said about choice number 2, that the

physical world is not mathematical. So this paper does not even

attempt to argue that point. I, on the other hand, am going to have

to address it head on if I'm going to direct my book towards

non-scientists. I think most non-scientists would not agree that the

world is mathematical. I think that belief reduces to materialism,

versus mysticism.

1c. can be dispensed with instantly, if you agree with Descartes that

"I think, therefore I am". I don't know if any philosophers have

seriously attempted to refute the existence of something. I wouldn't

buy it, anyway.

So that leaves the choice between 1a and 1b. He asks the poignant

question which I've read elsewhere: why would some possible

structures exist but not others? The best defense along these lines

comes in his footnote number 16, where he describes that the entire

universe could be shown to be isomorphic to a small set of data that

describes its initial conditions and its mathematical laws. This

data could probably fit on a CDROM. Now, do you really need the

CDROM in order for that universe to exist? I think he got this

argument from Physics of Immortality, by Tipler.

Section II of the paper categorizes mathematical structures, thus

putting the phrase "all logically possible universes" on a firmer

footing. This presentation was concise and fun. Interestingly, he

doesn't even need to keep the idea that the mathematical structure be

free from contradiction. Actually, and mathematical structure that

allows a contradiction immediately reduces to a trivial thing in

which all statements are provable theorems.

He made one statement, that "mathematical structures are 'emergent

concepts'", that I'm not sure I agree with. I think that I probably

don't understand what he means by this statement, but it seems to me

that mathematical structures are fundamental.

Date: Thu, 03 Jun 1999 21:59:29 -0400

As a recent member of this list, I'm slowly getting up to

speed with all the reading material. I've been reading the

archives of this list, and am up to about article 150 (out

of about 650!). I'll refrain from posting on old discussions

until I've finished that, as perhaps the old issues I feel

the urge to post about have already been resolved.

Meanwhile, here are a few thoughts on Tegmark's paper. This

is about 1/2 of the review that I'm writing on it (I always

review these sorts of things for my own purposes anyway).

---------------

This was an excellent paper, which effectively explicated many of the

ideas I've been formulating over the last fourteen years. The

fundamental principle put forth is the Principle of Plenitude, that

all mathematically consistent structures exist. Basically, he makes

the statement that mathematical existence is the same as physical

existence.

He introduces the acronym SAS (self-aware substructures) for

conscious entities within a mathematical structure. This is fine by

me, but Sarah (my wife) didn't know what to say when I called her my

favorite self-aware substructure.

The initial defense of this basic principle is well presented. He

presents four possibilities, the first three of which are lumped

together:

1. The physical world is completely mathematical

(a) Everything that exists mathematically exists physically

(b) Some things that exist mathematically exist physically,

others do not.

(c) Nothing that exists mathematically exists physically

2. The physical world is not completely mathematical

There is not much that can be said about choice number 2, that the

physical world is not mathematical. So this paper does not even

attempt to argue that point. I, on the other hand, am going to have

to address it head on if I'm going to direct my book towards

non-scientists. I think most non-scientists would not agree that the

world is mathematical. I think that belief reduces to materialism,

versus mysticism.

1c. can be dispensed with instantly, if you agree with Descartes that

"I think, therefore I am". I don't know if any philosophers have

seriously attempted to refute the existence of something. I wouldn't

buy it, anyway.

So that leaves the choice between 1a and 1b. He asks the poignant

question which I've read elsewhere: why would some possible

structures exist but not others? The best defense along these lines

comes in his footnote number 16, where he describes that the entire

universe could be shown to be isomorphic to a small set of data that

describes its initial conditions and its mathematical laws. This

data could probably fit on a CDROM. Now, do you really need the

CDROM in order for that universe to exist? I think he got this

argument from Physics of Immortality, by Tipler.

Section II of the paper categorizes mathematical structures, thus

putting the phrase "all logically possible universes" on a firmer

footing. This presentation was concise and fun. Interestingly, he

doesn't even need to keep the idea that the mathematical structure be

free from contradiction. Actually, and mathematical structure that

allows a contradiction immediately reduces to a trivial thing in

which all statements are provable theorems.

He made one statement, that "mathematical structures are 'emergent

concepts'", that I'm not sure I agree with. I think that I probably

don't understand what he means by this statement, but it seems to me

that mathematical structures are fundamental.

-- Chris Maloney http://www.chrismaloney.com "Knowledge is good" -- Emil FaberReceived on Thu Jun 03 1999 - 19:42:51 PDT

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