Hi Bruno:

I have attempted to answer some of your questions below. I have removed some terms and replaced others to improve clarity [I think]. This effort also improved the statement of the model. As I have tried to point out in other posts I believe the model has many features in common with Russell's book such as an entity [the All] containing all descriptions, an evolution, conscious observers, local time, an accessability between observer events, "selection" via the existence of SAS, a randomness that can support "creation" or at least its illusion. The model is not the same as Russell's as I derive mine from a primitive of a simple list of fragmentary descriptions and the ability to divide that list into two lists in many [uncountably infinite ? see below] ways. The timeless dynamic [random - absent order] I derive for the system may produce another difference between the two approaches because what I see within mine is that all sequences of all states of all universes experience a flow of instantations of physical reality [over and over] some of which instantations bridge between states [due to the randomness] thus giving any Self Aware Structures described in these states a flow of awareness [consciousness].


I believe that your approach may be in my All to some degree but in my view physics and mathematics are derived from the list and the inherent ability to sub divide it.

The one to ones with the natural numbers and the reals I mentioned earlier have been removed as being confusing at this stage. I only reference the properties of countable, uncountable, and power set.

As to measure, if one assumes that the list is countably infinite then its divisions are uncountably infinite in number which results in an uncountably infinite number of descriptions of states of universes. All of these would be given instantations of physical reality over and over and in random sequence. Long well behaved sequences that support SAS would be uncountably infinite in number.

Definitions:

Object: That which has a degree of physical reality such as a ball. The degrees of physical reality are distinguished by imperativeness and duration.

Idea: That which is expressed by an arrangement of sub components of an object. Mathematics is an idea in our universe expressed by the pattern of ink on paper or neurons in our brain.

The list of all properties: The list of all the possible properties of objects and ideas. The list consists of fragments of descriptions such as red, large, spherical, addition, prime, etc. This list can not be empty since there is unlikely to be less than a nothing and a nothing has at least one property - emptiness. The list is most likely to be at least countably infinite and can be assumed to be countably infinite. The list is the primitive of the model. It has existence but not physical reality.

Information: Information is the potential to establish a division between two parts of the list of all properties that is to divide the list into two sub lists. Each sub list is then a full description of [definition of] an object [such as a state of a universe] and any ideas expressed within it. A full description is not the object itself and has no degree of physical reality. At most information need only consist of one of the two sub lists [one of the two full descriptions established by a division]. The cardinality of all sub lists [the power set of the list] is c if the list is assumed to be countably infinite.

Kernel of information: The information relevant to a specific division of the list - it is at most a single full description, the remaining portion of the list is not required as information in order to establish the division.

The All: An object structured to express the idea "The complete ensemble of kernels" [all information [equivalent to no net information]].

The Nothing: An object structured to express the idea "That which is empty of all kernels" [no information [equivalent to no net information]].

A Something: A division of the All into two subparts. Somethings need not be static divisions of the All.

True Noise: The inconsistency of any evolution of a Something reflected in the pattern and duration of physical reality given to states of universes it encompasses or absorbs in the course of its evolution.

Model

Proposal: The existence of our and other universes and their dynamics are the result of unavoidable definition, incompleteness, and inconsistency.

Justification:

1) Notice that "Defining" is the same as establishing a division of the list of all properties - a boundary between what an object is and what it is not. This thus simultaneously defines a second object: the "is not". An object can not be defined in isolation and definition establishes an [is,is not] pair.

2) Given the definitions of the All, and the Nothing:

3) These definitions are really a single definition forming an [is,is not] pair and arise from the same division of the list. This division places "empty of kernels" in one of the sub lists [the "is" or the "is not"] and the remainder of the list in the other sub list [the "is not" or the "is"].

4) These definitions are unavoidable because at least one of the [All, Nothing] pair must be an object and have high degrees of physical reality if "no net information" is a key to an explanation of our universe [as mulitverse or any other form]. Since they form an [is, is not] pair and any selection of one over the other for physical reality would be net information they bootstrap each other to the highest degree of physical reality.

5) The Nothing has a logical problem: since it is empty of kernels it can not answer any meaningful question about itself [as an object it expresses no ideas] including the unavoidable one of its own stability [the duration of its physical reality].

6) To answer this unavoidable question the Nothing must at some point gain access to the interior of the All [the only place information resides] in an attempt to complete itself. The appropriate information is not likely to be the first information passing into the Nothing so its incompleteness will persist and likely get worse re the added information. Further it can no longer be a Nothing but rather becomes an evolving Something within the All absorbing kernel after kernel. This "destruction" of the Nothing could be viewed as a spontaneous symmetry breaking establishing a dynamic within the All.

7) However, the [All,Nothing] pair is unavoidable and a Nothing must be restored.

8) Thus the process repeats in an always was and always will be manner and the cycle is random.

9) The process divides the All into two evolving Somethings - i.e. evolving multiverses - each with many kernels. Evolving Somethings are unlikely to reach completeness short of encompassing the entire All. Notice that half the multiverses are "contracting" - i.e. losing kernels [but the cardinality of the number of kernels is c].

10) Notice that the All also has a logical problem. Looking at the same meaningful question of its own stability it contains all possible answers because just one answer would constitute an exclusion of specific kernels which is contradictory to the definition of the All as the complete kernel ensemble. Thus the All is internally inconsistent.

11) Therefore the evolution of a Something in the All must echo this inconsistency. That is each step in the evolution of a Something can not be completely dependent on the history of that evolution. The Dynamic in the All is random [An ongoing change absent any order is not time like in my opinion].

12) Some kernels are states of universes and when the boundary of an evolving Something passes about a kernel, the kernel can have a moment of a degree of physical reality. [The kernel is actually transferred from one Something to another. This moment can extend [to all degrees due to the randomness] so that successor states can have a degree of overlapping physical reality resulting in a flow of awareness or "consciousness" for some sequences of states for universes that contain Self Aware Structures.

13) From within any Something the future pattern of reality moments due to (11) would be non deterministic i.e. suffer True Noise.

14) The All of course contains a kernel re the founding definition [a kernel need only be one side of a definition] and thus there is an ongoing potential to have [All,Nothing] pairs. This completes the system in that the origin of the dynamic basically destroys [All, Nothing] pairs but there is a lasting potential to form new ones.

Hal Ruhl





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