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

Date: Sun, 11 Jul 1999 23:11:50 -0400

Devin Harris wrote:

*> Again, the question of how infinite is the Universe that
*

*> contains MWs. Or said otherwise, how vast or how ruled is
*

*> the possible world, assuming all possibilities exist?
*

I posted about this before, in

http://www.escribe.com/science/theory/index.html?mID=674.

I think that what Devin describes in his last post is

correct: that the cardinality of the structure in which

we find ourselves must be, in some sense, be infinitely

infinite. It must be Aleph-infinity, if this makes any

sense. A trivial application of the SSA indicates this.

I've thought about this some, but I am not a mathemetician,

so I'd appreciate any feedback.

For any arbitrary (finite or infinite) set S, the Power

Set of S is denoted *S, and is the set of all subsets of

S. For example, if S contains {1, 2, 3}, then *S would

be { {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} }.

*S is called the "Power Set" because, for finite sets:

|*S| = 2 ^ |S|,

where |S| is the cardinality of S.

For infinite sets, I believe that this power equation is

defined in terms of |*S|.

Cantor's theorem states that, for any set (finite or

infinite), |*S| > |S|. This provides a mechanism for

generating infinite sets with ever increasing cardinality.

defined in terms of |*S|. Now, the cardinality of the

power set of integers is c, the cardinality of the real

numbers. I think of this intuitively by imagining that

every real number can be expressed as an infinite number

of binary digits, for example,

...1101001000101110110101.11101010001010101001...

Each digit can have one of two values, and there are

|Z| digits, so c = 2^|Z|.

Does anyone know what the cardinality of the branches in

the traditional MWI is? By traditional, I mean that from

the Schrodinger's Equation. It seems plausible to me

that it's 2^c, by an intuitive reasoning similar to the

above. I think it depends on whether the universe is

finite or infinite in the number of particles it holds.

Now, if the original line of reasoning is correct, then

I predict that further breakthroughs in physics will

exhibit, by some mechanism (this is obviously highly

speculative) that the cardinality of the "branches" is

of a new order. By the SSA, we must find ourselves in

universes with physical laws that admit the greatest

number of SASs. Perhaps this feature has already been

exhibited by some of the more advanced quantum theories

out there - I admit ignorance of QFT in general.

The only mechanism that I can imagine is some sort of

infinite regress with regards to the structure of the

universe. That is, I would guess that no matter how

far we dig into the underlying structure of matter, we

will always uncover deeper layers.

Date: Sun, 11 Jul 1999 23:11:50 -0400

Devin Harris wrote:

I posted about this before, in

http://www.escribe.com/science/theory/index.html?mID=674.

I think that what Devin describes in his last post is

correct: that the cardinality of the structure in which

we find ourselves must be, in some sense, be infinitely

infinite. It must be Aleph-infinity, if this makes any

sense. A trivial application of the SSA indicates this.

I've thought about this some, but I am not a mathemetician,

so I'd appreciate any feedback.

For any arbitrary (finite or infinite) set S, the Power

Set of S is denoted *S, and is the set of all subsets of

S. For example, if S contains {1, 2, 3}, then *S would

be { {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} }.

*S is called the "Power Set" because, for finite sets:

|*S| = 2 ^ |S|,

where |S| is the cardinality of S.

For infinite sets, I believe that this power equation is

defined in terms of |*S|.

Cantor's theorem states that, for any set (finite or

infinite), |*S| > |S|. This provides a mechanism for

generating infinite sets with ever increasing cardinality.

defined in terms of |*S|. Now, the cardinality of the

power set of integers is c, the cardinality of the real

numbers. I think of this intuitively by imagining that

every real number can be expressed as an infinite number

of binary digits, for example,

...1101001000101110110101.11101010001010101001...

Each digit can have one of two values, and there are

|Z| digits, so c = 2^|Z|.

Does anyone know what the cardinality of the branches in

the traditional MWI is? By traditional, I mean that from

the Schrodinger's Equation. It seems plausible to me

that it's 2^c, by an intuitive reasoning similar to the

above. I think it depends on whether the universe is

finite or infinite in the number of particles it holds.

Now, if the original line of reasoning is correct, then

I predict that further breakthroughs in physics will

exhibit, by some mechanism (this is obviously highly

speculative) that the cardinality of the "branches" is

of a new order. By the SSA, we must find ourselves in

universes with physical laws that admit the greatest

number of SASs. Perhaps this feature has already been

exhibited by some of the more advanced quantum theories

out there - I admit ignorance of QFT in general.

The only mechanism that I can imagine is some sort of

infinite regress with regards to the structure of the

universe. That is, I would guess that no matter how

far we dig into the underlying structure of matter, we

will always uncover deeper layers.

-- Chris Maloney http://www.chrismaloney.com "Knowledge is good" -- Emil FaberReceived on Sun Jul 11 1999 - 20:17:55 PDT

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