I think my model has a rationale for the necessary existence and functioning of Bruno's substitution mechanism.
I claim in my current model that the Everything and the Nothing if they are absent information must alternate with each other. I model the Everything as a pattern of all patterns, each embedded pattern being repeated an infinite number of times. At each manifestation of the Everything - since there is no history - the pattern of patterns realized is a random selection from all possible patterns of patterns. Each embedded pattern seems computable. They are at most representable by a countably infinite string of bits. SAS are embedded in some isomorphisms to some embedded patterns. So if we equate the level of substitution as the entire Everything [the only reasonable approach IMO] the alternation between Everything and Nothing looks like Bruno's substitution mechanism. Further since each cycle creates a new pattern of patterns it is in effect a transporter of an isomorphism into a new universe. See more on this below. Now from here what I focus on is the mechanism of transfer of particular isomorphisms from imbedded pattern to imbedded pattern. In my model I call the process a compare. The isomorphism compares nearby embedded patterns with its set of rules and transfers to an acceptable one. Any SAS can sense the compare process as alternate possible courses of action. The rules can have a non deterministic content. Some alternate course of action choices are then a selection of one undecidable out of several that were pre assembled by the SAS through the necessary agent of the "do not care" part of the rules. This allows the accumulation of a sense of self in the SAS and looks, I think, like the fuzzy conscious state being discussed. Each manifestation of the Everything is a new pattern of patterns - a new universe - and stirs the pot so to speak. I argue for a non deterministic content by attempting to show that Chaitin's incompleteness forces the issue onto the transfer process. This can be aided by Godelian incompleteness if the rule set is complex enough. The transporter also injects a non deterministic aspect to SAS supporting universes since while the SAS can show that the transporter exists and functions it is not possible to tell when it has functioned. Hal
