Hi Kory,
(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.
Nice.
>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".
Yes.
>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?
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Mon Apr 26 2004 - 06:44:37 PDT