Hi jason,
Le 05-févr.-07, à 17:05, Jason a écrit :
>
> On Feb 2, 10:03 am, Bruno Marchal <marc....domain.name.hidden> wrote:
>>
>> This is a bit ambiguous. The UD dovetails on all computations. Let us
>> write (comp i k j) for k-th step of computation i on input j.
>> One computation can then be identified (in a first approximation at
>> least) with a sequence like:
>> (comp 777 1 24) (comp 777 2 24) (comp 777 3 24) (comp 777 4 24) (comp
>> 777 5 24) (comp 777 6 24) (comp 777 7 24) (comp 777 8 24) (comp 777 9
>> 24) (comp 777 10 24) ....
>> This represents the computation of F_777(24), that is the 777th
>> partial
>> recursive function on input 24.
>> Now we know that F_777(24) could be undefined, and that is why the UD
>> has to dovetetail. So the order of the "states" generated by the UD is
>> not, strictly speaking the order of states defining a computation.
>> Also, the UD is infinitely redundant: in particular the function F_777
>> has other code, for example 8888, i.e. F_777 = F_8888. It could be
>> that
>> the computation (comp 777 i 24) and (comp 8888 i 24) are equivalent
>> (same algorithm) or completely different (different algorithm), but
>> actually it is not easy at all to define such equivalence relation
>> between computation an states.
>> I mean, even from a pure third person point of view, it is not obvious
>> to define computations and order on them.
>> Then, from a first person point of view, the difficulty is made
>> bigger.
>> It could be, that although F_a and F_b computes different function
>> (and
>> thus follows completely different algorithm), it could be that (comp a
>> 234 24) and some sub-state of (comp b 34 1000), say, are equivalent
>> from a first person point of view, which needs to take into account
>> all
>> the infinity of computations going through my "current state".
>> So I'm afraid that at some point we have to take a more abstract route
>> (like with the combinators, which better represent possible
>> computations, or like with the lobian interview).
>> What is correct, and has been singled out by Stathis, is that comp
>> eludes the "material implementation" problem, given that we take all
>> abstract possible relationship between those objects, and they are all
>> well defined as purely number theoretical relations. Note that this is
>> something I have tried to explain to Jacques Mallah sometimes ago, but
>> without much success. This does not make much sense in ASSA
>> approaches,
>> but, like George Levy I think, I don't believe in absolute probability
>> of being me, or of living my current "observer moment". Such a
>> probability can be given the value one (said George) but it is close
>> of
>> saying that the universe is here, which tells us nothing, really. It
>> is
>> like answering "who are you?" by I am me".
>>
>
> Bruno,
>
> Let me begin with saying that I believe in a form of computationalism
> in that ultimate ensemble, or plato's heaven contains a turing machine
> running every possible program. I also beleive this universe is, on a
> small enough scale, purely digital. My question to you is, without
> accepting some form of fundamental probability, how can the Universal
> Dovetailer be preferred over Jürgen Schmidhuber's program? Both the
> UD and JS's iterative counting program will produce all possible
> output states. The difference to me is that every state is equally
> likely under JS's program, while the UD will prefer some states and
> evolutions of states.
JS "great programmer", well I take it as an informal version of the UD.
I think Wei Dai proposed the counting algorithm as a sort of UD.
Whatever. As you describe the UD, it should be clear it renders justice
to the "relative computational state", and is coherent with RSSA
(relative self-sampling assumption).
But the main difference between the UD, as it has to be used with comp,
and JS approach is that the UD Argument relies on the distinction
between first person and third person points of view (which is not done
by JS: see my conversation with him in the archive).
And then a result is that "there is no primary physical universe", and
the appearance of a physical universe has to be an appearance of
something not entirely computable: If I am a machine then the UNIVERSE,
or GOD or <WHAT'S-ITS-NAME> is not a computable object.
Somehow, Schmidhuber develops a constructive physics. This can be
interesting, and can have application, but is useless for a theory of
evreything including the mind and persons.
> The multiplicity of some states, to me, creates
> a probability question.
For all of us, I think. Indeed, it was my purpose to show that if comp
is correct, the mind body problem, actually its body problem part, is
reduced partially into a relative probability question on first person
computational states/history.
> Therefore it becomes meaningful to consider
> what programs will contain the largest number of observer moments, and
> how common will those programs be within the UD.
I think this is only partially correct due to the fact that you are
vague about the 1 or 3 - person distinction in the "observation
process", but you are certainly "roughly" right, if I may say.
Best regards,
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Mon Feb 05 2007 - 11:29:02 PST