Re: Turing vs math

From: Marchal <>
Date: Thu Oct 21 03:45:36 1999

I agree a lot with the last post by Juergen Schmidhuber.

I take the opportunity to describe briefly the difference between
Schmidhuber and me. It is relevant for the current Alistair-Russell
debate (IMHO).

i-POV means from the ith person point of view (i = 1 or 3).

I don't take the notion of observer for granted. I modelise it
with the notion of self-referentially correct universal machines.
This put very high constraints on the concept of communicable
proposition (3-POV), knowable truth (1-POV), observable facts
(3-communicable and 1-non-communicable like qualia).
This entails also different logic for the 3-POV and 1-POV.

The PE-omega experience (see below) shows that the computationalist
 hypothesis entails that the physical
laws emerge on the possible 1 and 3 discourses of the
self-referentially correct universal machines.

In my thesis I show that indeed
a precise quantum logic comes from the logic of 3-observation.

This entails that at some point I think Juergen is a little to rapid.
For exemple when Schmidhuber write

>The prior U suggests: you are in the simplest universe compatible with
>your existence. The conditional probability of some universe, given
>yourself, is high if that universe is computable by a short algorithm. To
>use the example in [1], a universe in which lambs start attacking lions
>seems less probable than the present one, because apparently it requires
>more information than conveyed by the few physical laws causing "normal"
>animal evolution. Similarly for "flying rabbits".

The problem is that "to be in a universe" has no clear meaning with
comp. (Independently that the argument of the short algorithm is
probably correct and fundamental). The hunting of the flying rabbit is
basically correct, but even with my precise notion of observer
it is not so easy to solve it completely).

Here is a copy of my concise formulation of the Universal Dovetailing
argument from a older post (the PE-omega experience as I call it in
this list). It gives the explanation that the whole UD* must be taken into
account to define the measure on computational histories.
I recopy it because it is not easily readable in the archive (the lines
are too long).

Begin copy

UD, the Universal Dovetailer, is equivalent to Schmidhuber
Great Programmer.
UD is a finite program.
UD* is the infinite extension of the UD.

James Higgo wrote:

>Bruno, you say "you can only associate mind with the
>whole UD*." - I'm not sure why.

Here is a short answer. Take your time to read it, and please tell
me if you disagree at some point.
It is necessary to concentrate ourself on the following thought
experiments (PE, PE1, PE2, PE3, PE4, PE-omega).

The "practitionners" of computationnalism can use classical
teletransport as a mean to move from one place A to another
place B. This mean he is "read" at A, send (by wave radio,
for exemple) at B, annihilated at A, and reconstituted at B.
Let us call that experience : the primitive experience or
simply the PE.

Let us look first at two independent changes of the PE.

PE1 : if, knowing it or without knowing it, the reconstitution
is time-delayed at B, this doesn't change anything from his
first-person point of view. In particular if he is certain to
get B with PE, he must be certain to get B, in PE1.
(The delay is supposed to be finite).

PE2 : if he is told he will be reconstituted at B and B',
his first-person futur is undetermined. The domain of
undeterminism is {B, B'}.
Of course, from a third person point of view, everything
is determined.

Do you agree until here ?

Now, consider the following experience PE3 which mixed PE1
and PE2.
He is told that he will be reconstituted at B and at B'
(like PE2), but a time-delay of reconstitution is introduced
at B (like PE1).
Now, if you agree with what I say about PE1 and PE2,
 you should agree with :

IF he quantifies the indeterminism on {B, B'} in some way
for PE2, THEN he must give the same quantification for
the indeterminism on {B, B'} with PE3.
For exemple, if he quantifies {B, B'} with a uniform
probability distribution with PE2, he must quantify {B, B'}
with a uniform probability distribution with PE3. To sum up,
the delay doesn't change his expectation.

This follows from comp (think on the first-person communication
by the average robot instead of you, for exemple). The average
robot = the normal (gaussian) robot when these duplication
experiences are iterated.

OK ?

I guess you will also accept that nothing will change, in
neither PE nor PE1 nor PE2, nor PE3, if at B (for exemple)
he is reconstituted in a perfect virtual environment
(which could exist by COMP). This is PE4.

If you agree, you are ready for "PE-omega", which is just
the infinite running of the UD.

Suppose that you are in some state of mind s, captured at
some digital level by a computationnal state S (which exist
by COMP, and there is no restriction on the level other than
permitting digitalisable capture).

Now suppose the UD is running, and that it never ends
(accidentally). Then you will be virtually reconstituted,
in the state S, an infinite number of times in the all UD*.

End copy.

Because your 1-feeling doesn't depend on the time when the
UD access your state of mind, the whole (infinite) UD* is needed
in the definition of the measure on the computational histories.

Now, either with the movie argument (the marchal-maudlin
crackpot proof as Jacques M Mallah once put it) or with some strong
Occam razor, the UD doesn't need to be physically implemented.

Note also that the UD dovetails on the oracle computations, so that
the "non computable stuff" could still have an important role
with comp. (I say that before).

Received on Thu Oct 21 1999 - 03:45:36 PDT

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