Le 15-nov.-05, à 10:56, Brian Scurfield a écrit :
> --- In Fabric-of-Reality.domain.name.hidden, Bruno Marchal <marchal.domain.name.hidden...>
> wrote:
>
>>> It has often been pointed out on this list that universes are those
>>> parts of the multiverse down which information flows. So Harry
>>> Potter "universes" are not in fact universes.
>>
>> What do you mean by "parts of the multiverse down which information
>> flows"?
>
> OK, let's start with information. I have in mind David's qualitative
> definition here:
>
> http://xxx.lanl.gov/abs/quant-ph/0104033
>
> To quote:
>
> 1. A physical system S *contains information* about a parameter b if …
> the probability of some outcome of some measurement on S depends on b.
>
> 2. A physical system S *contains no information* about b if … there
> exists a complete description of S that is independent on b.
>
> What is meant by information flow is explained here:
>
> http://groups.yahoo.com/group/Fabric-of-Reality/message/9247
>
> Basically, information flows when the output depends in some way on
> the input.
>
> As David has shown, the structure of the multiverse is determined by
> information flow. A universe is a part of the multiverse where
> information flows freely.
OK. I guess you know that this is not a standard use of the term
"information", like the one of Shannon, where the bits measure some
degree of surprise and unpredictibility (and this can been make precise
with notion of Kolmogorov/Chaitin/Solovay notion of information).
David Deutsch's notion of information can be related to some logician's
attempt to define a sort of qualitative information, and as such it is
quite interesting, but also natural, to find it in an attempt to
retrieve classical computational histories from the quantum theory.
Now you should keep in mind that David does postulate the existence of
some continuum causal structure, and, as you know, I am doubtful this
can make sense once we accept the computationalist hypothesis (cf
Maudlin's Olympia, my work, etc.). Actually I think David Hume makes
already important steps in that direction.
Just to illustrate: imagine the case of iterated self-duplication with
reconstitutions in Sidney and Beijing: S and B. From the point of view
of the "average candidate" normal histories, in the form of sequences
of P and S, will be highly unpredictable, but in all case there will
be no causal relations between the events "I feel myself to be in S" or
"I feel myself to be in P".
Exceptional histories, like the one in which the sequence gives the
binary digits of the number PI, play the role, curiously enough, of the
Harry Potter histories, in that case.
So the two notion of information are quite complementary. It is almost
like one grows up when the other diminishes.
>
>> Harry Potter universes are just improbable, and information grows to
>> much there.
>
> Things spontaneously organise themselves in an HPU, but the output
> does not depend on the input; there is no information flow in the
> sense described above.
So I agree. And of course I was considering a Shannon form of
information.
> When Harry Potter does a trick, in almost all
> universes the trick does not work. But one cannot say the trick
> succeeded in those universes that do become HPU's because one can't
> single out beforehand those exceptionally rare universes that will
> become HPU's.
I agree.
>
>> It is almost like they got singularities in the amount of
>> information. But death, well, really it is an open problem, because
>> you must take into account the normal (statistical, based on the
>> measure on the "observer/moment/states/worlds...") possible
>> histories just going locally through exceptional states,
>
> Meaningful histories must have a flow of information right?
I don't think so. I would say that meaningful histories are the
relatively consistent (non contradictory) one---which will get some
right measure assuming comp, and the correctness of my derivation, to
be sure. Those meaningful histories will appear, from the observer
first person point of view be related to some local flux of information
in David's sense. But I don't know how to take for granted those
meaningful histories at the start (unless, like David, you already
postulate some "prior programs" as an explanation of the appearance of
the universe. But then again you will be confronted with the comp
version of the Mind/Body, or 1-person/3-person relations again.
> In some
> histories, the Universal Dovetailer has outputted a series of random
> numbers that just happen to be indistinguishable from your life
> history up to today. In these histories, your past state does not
> determine your present state (although they are in every way
> indistinguishable from histories where your past state really does
> determine your present state).
I would say you belong to all histories. But with comp you are so
constituted that only the consistent one will make sense and will be
stable enough.
> Almost all of these histories will turn
> to junk at the very next moment. But some won't.
Yes but here you touch the real difficulty which could one day kill the
comp hyp. The difficulty is that "junk" can be consistent. Harry Potter
universe are consistent. White Rabbits are consistent. We can only
thrown them away once we have shown they have low relative measure.
Deutsch's justification is correct but incomplete, I think. It is
complete only by postulating the existence of a causal realm, or of a
special prior universal program a-la-Schmidhuber. I have already
criticize such move once we assume comp keeping in mind the distinction
between the points of view.
> Let's suppose that a
> huge meteorite is about to crash into your house.
Let us suppose .... (thanks!!!)
> In most histories
> you will be dead and vapourised.
Just to be clear, you and all other people (other than me) will seen me
dead (and vaporized if you insist ;).
I will most probably not feel myself dead or vaporized (obvious with
comp).
> But in some of the random histories
> that give the illusion of order and information flow you survive
> because the next state just happens to correspond to you sitting alive
> - looking very black and charred - in a giant crater.
>
> Can you really be said to be alive post-impact if these random
> histories are all that is left?
>
> I guess you will answer that there will still be histories post-impact
> where your next state really does depend on your previous state even
> if those histories were random (in just the right way) during impact.
> Correctomundo?
Quite correct. Why do you ask if you know the answer? You see, a
machine cannot distinguish random stories (Shannon information high,
Deutsch information low) from complex stories (Shannon information low
or much less high, and Deutsch information high). In the normal
situations, we can indeed survive only in those where Deutsch
information is high, but "near death" we will survive in the "most"
normal relatively to the normal histories which gave rise to us, and
immediately "after" we will proceed in those new relatively normal
extensions.
Deutsch paper is very interesting and I agree with many things there,
but I would not take notion like continuum and causality as granted. I
would say those things, like the "collapse of the wave", emerges from
the relatively consistent observations available to us.
In "the structure of the multiverse" deutsch write:
<<This does not imply that such a subsystem constitutes half the region
of the multiverse in which R exists. Proportions in the latter sense –
which formally play the role of probabilities under some circumstances,
as shown in Deutsch (1999) – are determined by the Heisenberg state as
well as the observables, and do not concern us here because the present
discussion is not quantitative.>>
My general problem here would be to find a way to relate more clearly
the quantitative shannon form of information and its probability link,
with the Deutsch information notion.
Some logician like Abramsky (is he in Oxford?) seems to have make
attempts in similar direction. Keith Devlin wrote also a book on
"non-shannon" like information.
Another direction would consist in deepening the interview with the
universal (lobian) machine. Each theaetical knowledge notion should
lead to an information structure. I cannot explain this without digging
more on the modal logic of self-reference, and the theaetical
transformations. So ask me on the everything list if you want me to
make clearer that last paragraph. It could interest also the FOR
people, because I do think that the difference between "p &
provable(p)" with "consistent(p) & provable(p)" is akin to the
"correction", proposed by Popper/Deutsch and Rafe Champion here, of
the platonist "true opinion" notion of knowledge (= first theatetical
trick) which leads to a more conjectural from of knowledge. By
incompleteness "consistent(p)" is necessarily conjectural.
...must go now. Hope I'm clear enough.
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Wed Nov 16 2005 - 10:35:30 PST