On Feb 2, 10:03 am, Bruno Marchal <[EMAIL PROTECTED]> 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".
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. The multiplicity of some states, to me, creates
a probability question. 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.
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