On 07 Mar 2011, at 17:26, Digital Physics wrote:
I agree that white rabbits have programs much shorter than those
of random structures.
It depends. Very short programs can generate all random structures.
You mean the short program that computes the entire set! But this is
irrelevant here: to predict a concrete individual history, we must
consider the probability of the program that computes this concrete
individual history, and nothing else. The description of the entire
set is much shorter than the description of most of its individual
elements. But it is useless as it has no predictive power.
Schmidhuber has a lots of papers on this:
http://www.idsia.ch/~juergen/computeruniverse.html
The entire set of random string is useful to illustrate the first
person indeterminacy, and that was its role in my reply to Andrew and
1Z. So your remark is unfounded.
We have discussed this a lot with Juergen on this list. To keep its
position he was obliged to assume that finite strings can never be
said random, even form a first person point of view. You might take a
look in the archive. To sum up, Schmidhuber missed the first person
indeterminacy.
You have to understand that the point here consists not in solving the
mind-body problem, but in formulating it in the computationalist
theory of the mind.
White rabbits have intrinsically very deep (in Bennett's sense)
programs.
No, because many programs making white rabbits for video games are
both short and fast, that is, those rabbits are not deep in
Bennett's sense.
But a sustaining white rabbit human hallucination is another matter.
And this is what we have to take into account in the "measure problem"
when we are confronted with the universal dovetailing.
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 seems very unclear. What's the difference?
It is the difference between a counting algorithm, and a universal
algorithm. You might identify numbers and programs, and in that case
the difference is the difference between a list of programs, and a
list of the executions of the programs. If you have read enough in the
archive or in my paper to understand the first person indeterminacy
notion, you might understand that, from the first person points of
view, such a distinction does matter.
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,
sure, this still makes sense
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).
Well, to me this sounds a bit like jargon used to hide the lack of
substance.
I meant "computable histories *above* the substitution level", and
"randomness below". More precisely the randomness pertains on the set
of all computations going through my current relative states. This is
a consequence of the UD Argument. I refer you to my sane04 paper:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
Or can you explain this clearly? Excuse me for skipping the
remainder of this message.
I suggest you read the paper sane04(*). If you have a (real precise,
not philosophical) problem, just ask a precise question. We were
discussing the seventh step of the UD Argument. It would already be
easier if you can acknowledge the understanding of the first six
steps. Note that the skipped message was alluding to the more
technical part of the work, where the measure one is given by a
variant of Gödel-Löb self-reference logics, which I name "arithmetical
hypostases", because I have used them to provide an arithmetical
interpretation of Plotinus theology, including his notion of matter.
The whole result is that comp, with the classical theory of knowledge,
is an empirically testable theory.
Bruno Marchal
(*)
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
http://iridia.ulb.ac.be/~marchal/
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