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

Date: Mon, 22 Apr 2002 22:07:54 -0700

Explorations of the definitional basis of a universe and its effect on the

idea of decisions:

First examine a deterministic universe j such that [using notation from a

post by Matthieu Walraet]:

Tj Tj Tj

Sj(0) ----------------> Sj(1) ----------------> Sj(2) ....

----------------> Sj(i)

An interpretation is that all the information needed to get from Sj(0) to

Sj(i) is contained in Sj(0) and the rules of state evolution for that

universe that is Tj.

I see a problem with this interpretation.

Suppose we write an expression for the shortest self delimiting program

able to compute Sj(i) as:

(1) Pj(i) = {Tj[Sj(i - 1)] + DLj(i)} computes Sj(i)

where DLj(i) is the self delimiter.

Compressing Sj(i - 1) it can be written as Pj(i - 1) and this short hand

substituted into (1) to yield:

(2) Pj(i) = {Tj[Pj(i - 1)] + DLj(i)} computes Sj(i)

Note that Pj(i) is always longer than Pj(i - 1) because it contains Pj(i -

1) plus the Tj plus the delimiter so Sj(i) contains more information [using

the program length definition of information] than Sj(i - 1) and thus more

information than Sj(0).

What kind of information is it? I see it as location record keeping

information. The universe is at state i of the recursion and this extra

information is the tag providing that location. The effect has several results:

1) This new information can never be removed from such a universe so its

local "time" has an arrow.

2) New information can manifest as either a decorrelation of the bit

pattern of and/or an increased length of the string representing Sj(i). The

length of the string is interpretable as "space" [a fixed number of bits

say x bits describe the configuration of a small region of that "space" and

there are y regions requiring description so an increase in length of the

string causes y to increase.]. Note that the effect increases as the

recursion progresses since DLj(i) increases monotonically with i. Thus such

a universe should see a long term acceleration in the rate of expansion of

its "space".

3) So how do we define a universe? Suppose many universes are following

the same recursion some at earlier states and some at later states than

universe j. It seems best to define such universes by the state they are

in [which includes Tj and DLj(i)]. Where did the additional information

come from? The additional information is not that a universe can follow

the recursion but rather as stated above the location of a particular

universe in the recursion. Since this information is not in Sj(0) or Tj it

must have come from outside universe j.

Universes that are not deterministic but have rules that allow external

true to enter are easier to analyze in this regard since the current state

seems the only reasonable definition.

4) For a deterministic universe is the additional information true

noise? In at least one sense it is because a particular universe j is

defined by its current state it can not tell which state including the

current state was or is Sj(0) so there is no clue as to what the

information means or if it is somehow even additional or new or which

information is involved. This is the same as the situation for a universe

whose rules allow external origin true noise.

5) This would seem to enhance the case against the idea of "decision" since

noise [chance] of some sort seems to be everywhere.

6) Behavior similar to (2) is found in universes that are sufficiently well

behaved so that it is possible to propose a prior state such that the

universe's rules when stripped of their allowance for external true noise

can deterministicly arrive at the universe's current state. This proposed

prior state need not have been the actual prior state.

Hal

Received on Mon Apr 22 2002 - 19:17:18 PDT

Date: Mon, 22 Apr 2002 22:07:54 -0700

Explorations of the definitional basis of a universe and its effect on the

idea of decisions:

First examine a deterministic universe j such that [using notation from a

post by Matthieu Walraet]:

Tj Tj Tj

Sj(0) ----------------> Sj(1) ----------------> Sj(2) ....

----------------> Sj(i)

An interpretation is that all the information needed to get from Sj(0) to

Sj(i) is contained in Sj(0) and the rules of state evolution for that

universe that is Tj.

I see a problem with this interpretation.

Suppose we write an expression for the shortest self delimiting program

able to compute Sj(i) as:

(1) Pj(i) = {Tj[Sj(i - 1)] + DLj(i)} computes Sj(i)

where DLj(i) is the self delimiter.

Compressing Sj(i - 1) it can be written as Pj(i - 1) and this short hand

substituted into (1) to yield:

(2) Pj(i) = {Tj[Pj(i - 1)] + DLj(i)} computes Sj(i)

Note that Pj(i) is always longer than Pj(i - 1) because it contains Pj(i -

1) plus the Tj plus the delimiter so Sj(i) contains more information [using

the program length definition of information] than Sj(i - 1) and thus more

information than Sj(0).

What kind of information is it? I see it as location record keeping

information. The universe is at state i of the recursion and this extra

information is the tag providing that location. The effect has several results:

1) This new information can never be removed from such a universe so its

local "time" has an arrow.

2) New information can manifest as either a decorrelation of the bit

pattern of and/or an increased length of the string representing Sj(i). The

length of the string is interpretable as "space" [a fixed number of bits

say x bits describe the configuration of a small region of that "space" and

there are y regions requiring description so an increase in length of the

string causes y to increase.]. Note that the effect increases as the

recursion progresses since DLj(i) increases monotonically with i. Thus such

a universe should see a long term acceleration in the rate of expansion of

its "space".

3) So how do we define a universe? Suppose many universes are following

the same recursion some at earlier states and some at later states than

universe j. It seems best to define such universes by the state they are

in [which includes Tj and DLj(i)]. Where did the additional information

come from? The additional information is not that a universe can follow

the recursion but rather as stated above the location of a particular

universe in the recursion. Since this information is not in Sj(0) or Tj it

must have come from outside universe j.

Universes that are not deterministic but have rules that allow external

true to enter are easier to analyze in this regard since the current state

seems the only reasonable definition.

4) For a deterministic universe is the additional information true

noise? In at least one sense it is because a particular universe j is

defined by its current state it can not tell which state including the

current state was or is Sj(0) so there is no clue as to what the

information means or if it is somehow even additional or new or which

information is involved. This is the same as the situation for a universe

whose rules allow external origin true noise.

5) This would seem to enhance the case against the idea of "decision" since

noise [chance] of some sort seems to be everywhere.

6) Behavior similar to (2) is found in universes that are sufficiently well

behaved so that it is possible to propose a prior state such that the

universe's rules when stripped of their allowance for external true noise

can deterministicly arrive at the universe's current state. This proposed

prior state need not have been the actual prior state.

Hal

Received on Mon Apr 22 2002 - 19:17:18 PDT

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