Bruno Marchal claimed:
> my mind can be simulated on a TM =>
> there is no computable universe to which we belong
I did not understand. Bruno tried to clarify:
>This is linked to the distinction between first and third person points
>of view. Remember that if the "great programmer" generates to identical
>version of you (one now, the other in 10^100 years), your personal
>experience will depend on the existence of the two versions. So if my
>mind is emulable by a TM, and if what exists is what the DU generates,
>then to predict my futur I must take into account all the identical or
>sufficiently version of me the DU will generates now or in any finite time
>from now), and there exists a continuum of such computational extensions.
>(cf the UDA thought experiment).
>1: The above implies there is an infinity of semicomputable processes
>dovetailing on the reals (or recursively equivalent things) going through
>my state of mind. (Remember my invariance lemma, see my ``Computation,
>Consciousness and the Quantum at http://iridia.ulb.ac.be/~marchal).
I have to repeat my question: Why does this imply there is no computable
universe to which we belong??? On the contrary, the dovetailer computes
many computable universes to which you belong. On the other hand,
no dovetailer can compute noncomputable universes, or a continuum.
>3: Suppose I am "read" and annihilate at Brussels. Then my coded
>description is duplicate and send to Washington and Moscow. "I" am
>reconstitute in both W and M. I pretend that in Brussels, where people
>describes me the whole experience, I must prepare myself to appear
>either in W or in M, and I cannot know which one. That is the uncertainty
>domain is {W, M}. Now, I pretend the measure of uncertainty is unchanged
>if at Moscow we wait one year (or 10^100 year, or any finite time)
>because from my first person point of view I cannot be aware of those
>delays. This is the "time" part of the invariance delay. Now, let the
>great programmer (UD) make his work. He will generate the computational
>state corresponding to that coded description + the dummy data O. And
>he will generate the computational state corresponding to that coded
>description + the dummy data 1. And he will generate the computational
>state corresponding to that coded description + the dummy data 00, etc.
>That is, he will generate infinitely often that code plus the (dummy or
>not) data 0, 1, 00, 01, 10, 11, 000, 001, ..., 01110010010111100, ....
>This means that here and now, although the work of the UD is always localy
>computational, my *uncertainty* is defined on all infinite computation
>going through my state. If you agree that a program generate PI when he
>generates all the successive approximation of PI (3, 3.1, 3.14, 3.141,
>3.1415, 3.14159, ...), then you should agree that the DU generates in
>that sense ALL real numbers (although he does not put them in a list,
>and so there is no contradiction with Cantor non enumerability theorem!).
>That is why the poor little machine cannot not face the continuum.
Pi is enumerable. Most reals are not. Most of the dummy data is much
less likely than extraordinary data (such as Pi), if the dummy data
probability is approximable by a computer. Compare "Algorithmic Theories of
Everything":
http://www.idsia.ch/~juergen/toesv2/node23.html
Instead of giving examples, could you just provide a short proof of your
claim that there is no computable universe to which we belong?
-----------
>> Futures that are hard to compute are less likely.
George Levy replied:
>True from the third person perspective.
>True from the first person perspective if nothing in those futures
>threatens the continued existence of the observer
>Partially false from the first person perspective if there are
>contingencies in those futures threatening the continued existence of the
>observer. Then these contigencies must also be factored in the
>probabilities of these futures happening, more precisely, being observed
>by the (first person) observer.
Of course, the weak anthropic principle already filters out those
histories incompatible with your existence. See Example 1 and Equation (1)
of "Algorithmic Theories of Everything":
http://www.idsia.ch/~juergen/toesv2/
http://www.idsia.ch/~juergen/toesv2/node2.html
Juergen
Received on Wed Jan 17 2001 - 00:47:08 PST