..I'm also interested in the implicit use of time, or sequence, in many of the ideas discussed here.
For instance you might say that some of your Somethings are 'bitstrings' that could make up one of Bruno's or Jürgen's worlds/observers. Part of our idea of a string is the convention that one element comes first, then the second, then the third, et cetera. However, the information that accounts for that convention is not contained in the string itself. 'Taking' a Something as a bitstring involves some degree of external convention.
So my question is, what do you mean when you say "a universe that has a sequence of successive states that follow a set of fixed rules?" What could make one state "give rise" to the "next" state? Citing "causality" just gives a name the problem; it doesn't explain it. And I don't think introducing a Turing machine helps with this basic problem, since in any automaton you have rules that say e.g. state X at time T begets state Y at time T+1, again placing a convention of sequence (time, here) external to the system itself.
This question doesn't engage with your schema head-on; it's more of a side detour I've thought of asking about many times on the list; I thought it might get explained at some point. Well, now I'm asking.
Best regards Pete
On Dec 17, 2004, at 6:48 PM, Hal Ruhl wrote:
My interest was to have a dynamic which did not impose any residual information on the All. My current view is that each state of that dynamic has to be completely independent of the current state. The way I describe this is to say that the dynamic is inconsistent. It helps this idea if there are kernels that are pairwise inconsistent. I think that is straight forward enough. If there are kernels that are self inconsistent then all the better. Why should they be selected out?
Can any of this exclude a universe that has a sequence of successive states that follow a set of fixed rules? I think that one must insist that the inconsistency permeate every corner of the dynamic i.e. some level of external noise impressed on all state sequences.
As to does mathematics contain information, mathematics has the potential to erect boundaries so by my definition it is information. It also seems possible that there is room for what might be called bifurcated boundaries - inconsistencies.