(Recall: the 1-9 points we mention can be find by clicking on http://www.escribe.com/science/theory/m5384.html )
At 00:04 24/04/04 -0400, Kory Heath wrote:
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".
K: 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".
Well, we should expect that what makes stable those different geographical data (galaxies and gilixas) are semblable. The physical laws should be what makes both galaxies and gilixas stable. The laws of physics will be the same, but they can be "implemented" in highly different "geographical" manners.
(We can imagine that the resulting regularities resemble a 4+1D cellular automata, which contains nothing like our gravity, light, etc.).
Actually (but this is a premature technical point) 4+1D classical cellular automata will not work. Let us come back to this point later. (You can remember me). It *is* a probable non trivial consequence of 9.
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.
Well, it follows from comp and the data "stars and galaxies", and the belief that stars and galaxies are not complete illusion. It is clear that at some point it will be necessary to be a little more specific about the distinction geography/physics. Grosso modo laws should be necessary, unlike geographical data which are contingent but should be consistent with the physical laws. Up to this point (the whole 1-8) it is natural to expect that physical laws could be trivial (equivalent to the classical tautologies for example): in that case, comp would entails that there is no physical laws (at least in the strong sense I use implicitly until now). Everything would be geographical! But I will give below reason to believe that comp does not make physics so trivial. The basic reason comes from Godel's theorem.
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".
I mainly agree. The differences are those I usually make. Indeed a machine can have only a finite number of possible states, but the DU (comp platonia) will go through those states infinitely often and the probability will be defined on the set of complete histories (those distinguishable in principle). A priori there are 2^aleph_0 histories. Your last sentence is a little bit ambiguous (probably because we have not yet decide a criteria for the geography/physics distinction). It is really the invariant we observe "out of this indeterminate traversal from state to state" which will play the role of laws of physics, and those will be global. Now those laws will be among those things which make galaxies stable, but I would not put the existence of galaxies in the "local" physical laws, only what makes those galaxies stable. So that "laws" will be global (by mere definition). I have mention that up to this point the laws could be trivial, but of course they could also be non trivial; so much that the existence of galaxies would be a law. I doubt it but the whole point of 1-8 is to show that with comp the laws of physics are derivable by the 1-view of consistent machines, and we will see....
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.
I am sorry. I didn't express myself in a very perspicuous way. It certainly looks like a tautology. I think I should have just say: from 1-8 the laws of physics should be redefined as what is consistent and verifiable in all "next states" (all closer consistent extensions). This looks still tautological, but actually is not. But here we are at the pivotal moment between the point 8 and 9. It is really Godel's theorem which will make the notion of verifiable and consistent not trivial at all. Remember simply that the second Godel incompleteness theorem entails that a consistent machine cannot even prove the existence of just one consistent extension!
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 -
That's the whole point indeed.
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.
OK, but that will follow from the point 9, which is the one you originally ask me about. We will come back on this. The important point is that once we keep up comp through the eight points, we see that the laws of physics, whatever they are, must be given by the invariant in the comp-accessible worlds.
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 have derived the logic of the yes-no possible physical experiments, or, put in another way, I have derived the mathematical constraints bearing on the measure one verifiable propositions. Normally I have derived enough to say if there is a quantum computer present (or not) in the neighborhood (collection of the closer consistent extension) of any observer-sound lobian machine. That would make a great part of quantum physics into physical laws in the sense of comp. It would be a pleasure to explain this with more details. Are you willing to hear a little bit about Godel's theorem and some of its generalisation by Lob and Solovay?
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?
OK here I have been *very* unclear. I should have said that with comp we can indeed derive the behavior of the chalk, but only by deriving the laws of physics first. This is true for quantum mechanics also. The "real" fundamental laws are so complex that they are useless for mondane prediction. Nobody will ever use Feynman path integral technic for predicting the chalk behavior, and this is truer once we use comp where it can be shown that an exact derivation of the exact behavior is uncomputable (but that is the case also, in an lesser way, with QM).
To sum up: with the comp hyp 1-8 shows that the laws of physics are given by the proposition UD-accessible, verifiable and consistent. The point 9, that is an actual beginning of a derivation of the physical laws gives quickly something non tautological and actually not trivial at all thanks to the bearing of Godel's incompleteness phenomena about what sound machines can actually prove and infer about their consistent extensions. Thanks for giving me the opportunity of being (hopefully) clearer. Have you still some question on the 1-8 points? If not, we can tackle the point nine which is obviously more technical (but full of marvellous quasi-magical happenings!) OK?