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.
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.
Proposal: The existence of our and other universes and their dynamics are
the result of unavoidable definition, incompleteness, and inconsistency.
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
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
7) However, the [All,Nothing] pair is unavoidable and a Nothing must be
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
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.