Re: Misc-Chris

From: Marchal <marchal.domain.name.hidden>
Date: Thu Jul 15 08:02:38 1999

Chris wrote:

>Using a simple von Neumann description, a perfect fidelity
>self-simulation would involve emulating its own program, _and
>duplicating all of its internal data_. The latter is obviously
>impossible.

In fact, altough it is hard to believe, it is possible !
It is a consequence of the second recursion theorem. Look at Cutland's
chapter 11.

Here is the basic idea:

Let D be a special duplicating machine which outputs a description
of his input applied to it (the input) self. For exemple:

  D(A) => description of A(A)
  D(B) => description of B(B) "=>" means "outputs"
  D(C) => description of C(C)

There is nothing magic or circular in D. It just build a description
of his input applied to the input :
D(x) => description of x(x), whatever x is.

Now it suffices to apply D to itself:

  D(D) => description of D(D)

i.e. the expression "D(D)" will ouput an exact description of itself.
Is it not magic !

Now, you can easily make the following generalisation. Suppose you
want a program who simulate itself, or more generaly which apply T to
itself. (The simulation is the case T = a universal program,
the self-reproduction is the case T = a identity program, etc.).

Build a new D such that


  D(A) => T(A(A))
  D(B) => T(B(B)) "=>" means "outputs"
  D(C) => T(C(C))

i.e. D(x) => T(x(x))

Here too it's enough to apply D on itself: D(D) => T(D(D)). So the
 expression D(D) applies T to itself.

OK ?

Now, what is impossible, is that, for a consistent prover machine,
to build a copy of itself AND to prove that the copy of itself is
a copy of itself. This is not a direct consequence of Godel's theorems,
but is a consequence of the correct part of Lucas-Penrose argument.
(perhaps more on this latter).

>So let me see if I'm understanding this correctly. Penrose says that
>consciousness cannot be the result of computational processes because
>there will always be true statements which a computational process
>would find undecidable (Goedel statements for that process). But
>humans,
>on the other hand, would be able to "see" the truth of Goedel-esque
>propositions because of our amazing, non-computational intuition. But
>the counter to this argument is that:
> 1. if a particular human's consciousness is the result of a
> computable process,
> 2. there will be Goedel statements for that particular human, but
> 3. they will be of such a complexity that the human would not
> possibly be able to decide the truth or falsity without the aid
> of a computer, which,
> 4. changes the computable process into a human+computer system,
> 5. rendering the original statement decidable in the new system.

Not too bad :-)
But in 3. the impossibility is not linked to the complexity. It works
even with high level description of yourself. For exemple the expression
"Chris" is a high level description of yourself. And here is a simple
true self-referential sentence that you will never believe:

  "Chris will never believe this very sentence"

... unless you are inconsistent (you believe false propositions).

>When you say that this is related to the topic above, I think you
>must be talking about the inability of any machine to fully model
>itself. Is this right?

No, because a machine can fully model itself. But the consistent
machine cannot prove that such model is indeed a correct model of itself.
Now, like the computationalist in front of his teleportation machine,
the machine can build itself, and BET the product is indeed itself. And
if the machine adds that as a new axiom, indeed the machine becomes
a new machine, etc.

>> [BM] In fact those "De Broglie-Bohm" zombies are even incorporeal !
>> They are not made with particules !
>
>
> [CM] Okay, let me again try to see if I understand where you're coming
>from. This is related to your crackpot proof that "not comp" or
>"not phys-sup", correct?

Not really. It comes from the fact that the Bohm interpretation of
QM is really a many-world interpretation of QM such that:

1) The position observable is priviledged
2) Particules haves initial conditions such that they will remain
in one branche.

The result is a multiverse where only one "real" branche is full of
particules and the others are just empty. They are nevertheless
influencing the position of the particules in the "real" branche through
the action of Bohm's quantum potential.
It is a remarkable and non trivial fact that this theory is consistent
with QM.
The other branches can be seen as empty waves, but SHOULD the initial
conditions be different, they would have been full or partially full.
So the other branches describe kind of counterfactual worlds which, from
inside are not distinguishable from the real world. That is why I see it
as a kind of cosmic solipsisme: all Universes exists, but only our own
universe own consciousness and particules !

Bruno.
Received on Thu Jul 15 1999 - 08:02:38 PDT