Re: on formally describable universes and measures

From: Marchal <marchal.domain.name.hidden>
Date: Fri Jan 12 03:27:30 2001

Hi Juergen,

> Bruno, here are 3 comments (my stuff is indented):
>
> Let me rewrite this:
> 1. there is a computable universe to which we belong =>
> my mind can be simulated on a TM.
> 2. my mind can be simulated on a TM =>
> there is no computable universe to which we belong
> I understand 1. I do not understand 2. What do you mean?
>
>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) Why does the above imply there is no computable universe to which we
> belong?
> (2) At any given time certain universes will be much more
> likely than others, because it is much easier to compute them.
> (3) Most universes in the continuum do not exist from a computational
> perspective, because you cannot compute the continuum. With TMs
> you are limited to the countable realm.


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).

2: I agree that there is some interesting truth in (2). But this will
   work only if you show how computational easiness entails the highness
   of the measure of personal computational consistent extensions.
   (My feeling is that easiness is important but not enough).

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.

Bruno
  
Received on Fri Jan 12 2001 - 03:27:30 PST

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