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From: H J Ruhl <HalRuhl.domain.name.hidden>

Date: Thu, 24 Oct 2002 22:39:38 -0700

Refinements to the next stages of my model.

Proposal

A type #2 universe can look and evolve like our universe.

Justification: Stage 1

Designate the succession of states for universe "j" as Sj(i) and its

representative binary bit string as Uj(i) where "i" runs over some range of

integers from 1 to n.

If we restrict the discussion to universes of type #2 as proposed and make

the additional cut of restricting discussion to type #2 universes in which

the true noise monotonically accumulates [i.e. make the Second Law of

Thermodynamics an axiom for the universe globally, but not necessarily

always so locally] then the "complexity" of Sj(i) and Uj(i) must

monotonically increase as i counts up.

If we measure the complexity of Uj(i) in the manner of Algorithmic

Information Theory i.e by the length of the shortest self delimited program

able to compute Uj(i) which generally increases in length as the degree of

internal de-correlation and the length of string Uj(i) increase then:

1) To maintain a degree of internal correlation as its complexity increases

Uj(i) must locally increase correlation while it is also locally

de-correlating.

2) Finite strings can easily increase local correlation by appending or

inserting finite correlated strings and they can also progressively

internally de-correlate as information is added so they can satisfy the

requirements for Uj(i) given in (1).

Thus it may be simplest to represent states of some type #2 universes with

finite strings Uj(i). Finite strings have limited resolution potential,

but nevertheless can describe the location of discrete points within a 3D

space on a grid with finite non zero pitch.

An additional cut is now made to restrict examination to type #2 universes

that can be modeled as finite face centered cubic 3D grid multi state

cellular automata subject to true noise.

Notice that an increase in length of Uj(i) can be identified as the

addition of a new cell i.e. the expansion of the universe's space.

Further if the rules of state succession for a universe have an

appropriately constructed "Do not care" component then their repeated

application to the data of each successive state will lead to an

accelerating increase in the complexity of the finite Uj(i) [i.e. despite

the true noise the rules are such that each successive shortest program

Pj(i) that computes Uj(i) effectively contains the previous state's

shortest program Pj(i -1) plus the noise as data plus the rules acting on

the data plus its own delimiter] and so the length of Uj(i) must increase

in an accelerating manner to contain this complexity increase i.e. the

universe's space expands at an accelerating pace.

Hal

Received on Thu Oct 24 2002 - 22:42:52 PDT

Date: Thu, 24 Oct 2002 22:39:38 -0700

Refinements to the next stages of my model.

Proposal

A type #2 universe can look and evolve like our universe.

Justification: Stage 1

Designate the succession of states for universe "j" as Sj(i) and its

representative binary bit string as Uj(i) where "i" runs over some range of

integers from 1 to n.

If we restrict the discussion to universes of type #2 as proposed and make

the additional cut of restricting discussion to type #2 universes in which

the true noise monotonically accumulates [i.e. make the Second Law of

Thermodynamics an axiom for the universe globally, but not necessarily

always so locally] then the "complexity" of Sj(i) and Uj(i) must

monotonically increase as i counts up.

If we measure the complexity of Uj(i) in the manner of Algorithmic

Information Theory i.e by the length of the shortest self delimited program

able to compute Uj(i) which generally increases in length as the degree of

internal de-correlation and the length of string Uj(i) increase then:

1) To maintain a degree of internal correlation as its complexity increases

Uj(i) must locally increase correlation while it is also locally

de-correlating.

2) Finite strings can easily increase local correlation by appending or

inserting finite correlated strings and they can also progressively

internally de-correlate as information is added so they can satisfy the

requirements for Uj(i) given in (1).

Thus it may be simplest to represent states of some type #2 universes with

finite strings Uj(i). Finite strings have limited resolution potential,

but nevertheless can describe the location of discrete points within a 3D

space on a grid with finite non zero pitch.

An additional cut is now made to restrict examination to type #2 universes

that can be modeled as finite face centered cubic 3D grid multi state

cellular automata subject to true noise.

Notice that an increase in length of Uj(i) can be identified as the

addition of a new cell i.e. the expansion of the universe's space.

Further if the rules of state succession for a universe have an

appropriately constructed "Do not care" component then their repeated

application to the data of each successive state will lead to an

accelerating increase in the complexity of the finite Uj(i) [i.e. despite

the true noise the rules are such that each successive shortest program

Pj(i) that computes Uj(i) effectively contains the previous state's

shortest program Pj(i -1) plus the noise as data plus the rules acting on

the data plus its own delimiter] and so the length of Uj(i) must increase

in an accelerating manner to contain this complexity increase i.e. the

universe's space expands at an accelerating pace.

Hal

Received on Thu Oct 24 2002 - 22:42:52 PDT

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