On 07 Mar 2011, at 15:26, Digital Physics wrote:
You write "white rabbits (flying crocodiles) are not random
structures. They are aberrant
consistent extensions, a bit like in our nocturnal dreams." I agree
that white rabbits have programs much shorter than those of random
structures.
It depends. Very short programs can generate all random structures.
White rabbits have intrinsically very deep (in Bennett's sense)
programs. They are relatively costly. But technically this is not
enough for eliminating them from the first person appearance, unless
we use the self-referential logics.
But you also claim that "most will consider their histories ...
Chaitin-incompressible".
In the case of you being duplicated in W and M iteratively. Not in
case of you in the UD's work.
This means long programs and no predictability at all, contradicting
daily experience.
Not at all. If you agree with Everett, and send a beam of particles
prepared in the state (up + down) on a "{up, down}-mirror", you see
the splitting of the beam. If you label the left and right electrons
by W and M, you can bet the strings will be incompressible, and this
is a quantum analog of iterated self-duplication. This gives an hint
for the vanishing of the WR: computable histories about the
substitution level, and randomness below. That justifies in part the
quantum appearance from the digitalness of the mind (not of matter).
Then you say "but computer science and mathematical logic shows that
it is not easy either to prove that comp and first person
indeterminacy implies [flying rabbits]". I don't understand - it has
been shown it's not easy to prove that? How has it been shown it's
not easy to prove that?
That is actually rather obvious, if you know just a bit of computer
science. To get all the computational histories, you need Church
thesis and the enumeration of all partial computable function. By the
padding theorem, this is a highly redundant and fractal (and complex)
structure, and by the theorem of Rice, the set of codes corresponding
to any non trivial functions is not recursive (making our substitution
level) unknowable. So it is rather highly complex to derive the
possibility of white rabbits from that. In this list we discuss
alternate manner to approach that measure problem.
And you say: "There is no reason for making all relative histories
equally likely." But then what's the alternative?
To study the math of the universal dovetailing, and of what machine
can say about themselves and about they consistent extension
relatively to it.
Accepting the comp theory, together with the classical theory of
knowledge, although we don't have the measure, we can extract the
logic obeyed by the particular case of the "measure one". I have
succeeded in showing that it obeys already a quantum-like logic. This
needs a bit of advanced computer science/mathematical logic. See my
paper for details and references.
I have to say that I am a bit astonished that some people seems to
have difficulties to grasp that once we assume comp, theoretical
computer science becomes *the* key tool to progress on the fundamental
question. The beam example above suggests empirically that we are
physically duplicated in the iterative way. But obviously we are not
just duplicated iteratively, we are also obeying computational laws,
and arithmetical laws, etc. If that was not the case, comp would imply
white noise and would fall immediately in Russell's Occam catastrophe.
But, thanks to God, universal numbers does not put only mess in
Platonia, they generate also a lot of order.
-- Bruno Marchal
From: marc...@ulb.ac.be
To: everything-list@googlegroups.com
Subject: Re: first person indeterminacy vs predictability
Date: Mon, 7 Mar 2011 14:58:15 +0100
On 07 Mar 2011, at 10:47, Digital Physics wrote:But if most
histories are equally likely, and most of them are random and
unpredictable and weird in the sense that suddenly crocodiles fly
by, then why can we predict rather reliably that none of those weird
histories will happen?
From: marc...@ulb.ac.be
To: everything-list@googlegroups.com
Subject: Re: first person indeterminacy
Date: Sun, 6 Mar 2011 19:47:20 +0100
You can also consider the iteration of self-duplication. If you
iterate 64 times, there will be 2^64 versions of you. First person
indeterminacy is the fact that most of the 2^64 versions of you will
agree that they were unable to predict in advance what was the next
outcome at each iteration. Most will consider that their histories
(like:
"WMMMWWMWMMMMWWWMMWMMWWWWWM ..." (length 64)
are random, even Chaitin-incompressible.
Nobody said that the histories are generated by the iterated self-
duplication. The iterated self-duplication is used here only to
understand what is the first person indeterminacy in a very simple
context (the context of pure iterated self-duplication).
Assuming comp, the 3-histories(*) are generated by the UD, which is
a non trivial mathematical object, and 1-histories(*) appears in the
relative 1-person way by a highly complex mixing of computable
histories and oracles (which can be handled mathematically with the
logics of self-reference). There is no reason for making all
relative histories equally likely. It is not easy to prevent white
rabbits and flying crocodile, but computer science and mathematical
logic shows that it is not easy either to prove that comp and first
person indeterminacy implies them. And if we prove comp implies
them, then observation and induction makes comp false or very non
plausible.
"Note also that, as Russell Standish recalled recently, white
rabbits (flying crocodiles) are not random structures. They are
aberrant consistent extensions, a bit like in our nocturnal dreams."
Bruno
(*) the suffix 1 and 3, in 1-x and 3-x, means x as seen by the first
person or the third person respectively, as defined for example in
the sane04 paper:http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
http://iridia.ulb.ac.be/~marchal/
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