Dear Alastair: The infinite tape was just a way to show how your example actually has a most interesting behavior under an extension to more dimensions and to infinity. I believe you still miss what I am trying to say.
The nested Everythings are not and can not be exact copies of each other. This would constitute an information generating selection. Rather they are each differently and dynamically parsed. The parsing is the venue for interpretations - universes. The idea that the Everything is dynamic is not new. After all many allow that there are all those UTMs - which I incorporate as a type #1 universe generating sub component of my model - running in there somewhere. To have an infinite number of copies of just one of these dynamics just begs the question: why that one? The picture in my approach is as follows: The Everything - the ensemble of all counterfactuals, and the Nothing - the absence of facts of any sort, are themselves mutual counterfactual. They must both be in the ensemble. Each Everything contains an infinite regression of Everything/Nothing counterfactual pairs and is itself a member of such a regression. There is an infinite and necessarily dynamic - again to avoid selection - boundary between the Everything and Nothing counterfactuals. The location of this boundary is different and dynamic at each level of the nesting [repeats are possible but this is not relevant]. Each different level is a different venue - different logical structures expressed. Thus within the Everything taken in total a universe based on any number of logical elements is accompanied by an infinite number of equally logically rich but logically different universes. So there is no numerical bias towards logically anemic universes. My only assumption is: There is no information. Even limiting the system to one level of Everything is an information generating selection. Yours Hal At 2/25/02, you wrote: >You now appear to be talking about the indeterminate case (where effectively >you can't fire individual random arrows), which is excluded on empirical >grounds (see sect. 2 again). I repeat, the selective use of copies as given >in the paper - *within* the context of states, and where relative >frequencies match those of other states - will differ (as far as I can tell) >from your 'nested everythings', which, if applicable, will be treated as a >distinguishable state, and so amenable to an ordering process (under all >possibilities). > >Thank you anyway for your comments which have definitely been helpful to >me - I think we are bound to come up with different solutions if we have >different starting assumptions.