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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Mon, 26 Apr 2004 12:46:03 +0200

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

Date: Mon, 26 Apr 2004 12:46:03 +0200

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:

Nice.

Yes.

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.

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.

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.

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....

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!

That's the whole point indeed.

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 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?

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

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