I have been having a valuable discussion on this type of modeling and this has resulted in some improvements in my approach.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxx I currently define information as fact(s) that are absent counter facts. Example: [sort of] In our universe the rules dictate that any sufficiently large mass wants to assume a shape that is essentially a sphere. There are numerous other possibilities that could be the rule in some other universe. The ensemble of all these various rules is a complete set of counter facts that contains no information re this shape issue. Call such facts factuals. Call counter facts counterfactuals A fact that has counterfactuals is itself a counterfactual. The objective is to model our universe using no information that is by using just complete sets of counterfactuals. First examine the following: "The Everything which is defined as the ensemble of all counterfactuals exists." This existence by itself would be a factual and violate the objective. Now let us examine two counterfactuals. 1) The Everything which is the ensemble of all counterfactuals exists. 2) The Nothing which is the absence of all facts both counterfactual and factual exists. The Everything and the Nothing are antipodal representations of no information. The existence of either is the counterfactual to the existence of the other and so the dual existence is allowed under the objective since it represents no information. While the Nothing can not contain the Everything nor itself by definition and the Everything can not contain one or the other, can the Everything contain both? At the moment I think it can and this just produces an infinite nesting. That is the initial "mathematical" foundation. Next is the exploration of the manifestation of this foundation while defining physical universes as isomorphisms to this manifestation. At any nesting level if the manifestation was unchanging or structurally sequenced that would be a factual. If the manifestation at any given level is a random sequence of piece after piece of the Everything of that level each of which would be automatically accompanied by the counterfactual residual portion of the associated Nothing there would be no factual. Evolving universes must be isomorphic to a portion of each successive manifest counterfactual. The nesting would allow an infinite number of such universes. The rules of isomorphic shift [the laws of physics] for each such universe must have some random [true noise] content in order to sustain the succession of isomorphisms to the random sequence of counterfactuals. Hal