Thanks very much for your clarifications. I clearly misunderstood the intent of your point 8. I thought you were arguing that, if we analyze the structure of all possible 1st-person histories of all possible self-aware-subsystems in Platonia, we would find that histories that exhibit the basic elements of what we commonly think of as our "laws of physics" - say, light, gravity, etc. - have a greater measure than those histories that contain (say) "srats and gilixas", and that therefore our "local laws" are the most common ones in Platonia. I find this position highly dubious, but I no longer think that's what you were saying.
My new interpretation of what you're saying (and correct me if I'm wrong again) is that if you were to examine the entire ensemble of "next-possible-states" of *me* (Kory Heath) at this moment, you would find that (as a mathematical fact, part of the basic structure of Platonia) most of them contain galaxies and stars, etc. Therefore, the regularities I see around me are simply the emergent effect of my "first person indeterminacy domain". If we imagine some other computational state that represents a SAS with a personality, memories of growing up in a world that contains "srats and gilixas", etc., most of that SAS's next-possible-states would contain srats and gilixas, so a very different set of stable "local laws" would emerge from that SAS's "first person indeterminacy domain". (We can imagine that the resulting regularities resemble a 4+1D cellular automata, which contains nothing like our gravity, light, etc.).
I'm still confused by some parts of your post. I don't see why the assumption that most of my "next-possible-states" do in fact contain stars and galaxies necessarily follows from points 1-7. Here's a very rough sketch of what I think points 1-7 *do* imply:
Platonia contains every possible computational state that represents a self-aware structure, and for each such state there are X number of next-possible-states, which also exist in Platonia. The chances of one self-aware state "jumping" (I know my terminology is dangerously loose here) to any particular next state is 1 / X, where X is the total number of next-possible-states for the state in question. Any regularities which emerge out of this indeterminate traversal from state to state will be perceived as local "laws of physics".
Now, you say: "Let us (re)define the laws of physics as the laws we can always predict and verify consistently (if any!). Now, having accepted the 1-7 points, the occurrence of such laws must have a measure 1, so the laws of physics must be derivable from what has measure 1 relatively to the measure on the computational histories." I agree with this, but to me it seems like a simple tautology - another statement of my above paragraph. It sounds to me like you're saying that the (local) laws of physics are whatever regularities emerge when we examine the entire ensemble of next-possible-states from my current state (and the ensemble of all the next-possible-states from each of those possible-states, and so on). This is tautologically true - "whatever emerges, emerges". The real question is, what reason do we have to believe that any regularities actually emerge? In other words, how do we *know* that most of my "next-possible-states" do in fact contain stars and galaxies? This idea doesn't necessarily follow from anything in points 1-7.
Perhaps you're arguing the following: we do in fact perceive a world filled with regularities, which we have codified into our local "laws of physics". Therefore, *if* points 1-7 are true - that is, if "comp" is true - then it must be the case that most of my "next-possible-states" do in fact contain stars and galaxies and gravity and light. If I were (somehow) able to completely mathematically analyze one of my computational states and all of its next-possible-states, and if I then determined that the probabilities in this ensemble of next-possible-states *didn't* match the regularities I actually perceive, then I should conclude that comp is false. If this is your argument, then it might be helpful to add another point - lets call it Point 7.5 - which states that "we do in fact perceive regularities that we codify into (local) laws of physics". Then your argument can run: if points 1-7.5 are all true, then it must be true that most of my next-possible-states contain stars and galaxies.
This argument implies a constraint on comp - which is good, because it means that comp is falsifiable - but it doesn't give me any clue how to show mathematically that most of Kory Heath's next-possible-states actually do contain stars and galaxies - i.e. that most of Kory Heath's next-possible-states match the laws of physics, or at least exhibit some kind of probabilistic bias that would result in perceived regularities. I suppose that this is what you mean when you say that we need to ""modelize" or better "identify" a platonistic observer by a sound modest
(lobian) universal church-turing-post-markov-fortran-lisp-java-whatever machine (including quantum one)", and to "interview it about those relative consistent extensions and its inferable platonistic geometries and what is stable in their discourses." I have to confess that I don't have a very clear picture of what results you've derived from all of that.
I'm also somewhat confused by the following statement:
But "platonistically" it remains that if comp is true the actual physical invariant must emerge as an average on ALL the maximal consistent extensions relative to our actual states (worlds, observer-moments, whatever ...). Although that can be proved useless for actually predicting the behavior of the chalk, it is enough for deriving physics.
If this is enough for "deriving physics", why isn't it enough to predict the behavior of falling chalk, since gravity is one of the most basic elements of our physics? Or are you referring to something different than the "local geographical laws" that we call physics?
-- Kory
