Dear Stephen,
At 13:25 14/06/04 -0400, You (Stephen Paul King) wrote:
>Dear Bruno,
>
> Does your thesis survive without the notion of duplicatability or
> copying? As I have pointed out, QM does not allow duplication and I am
> hard pressed to understand how duplication can be carried out in
> classical physics.
Remember the Universal Dovetailer Argument (UDA, see link in my url). It
shows that the stability of any piece of matter is due to a continuum of
(infinite) computational histories. A priori this is not Turing-emulable.
So, for the same reason there is a notion of comp-immortality, there is a
quasi obvious "non cloning" theorem for the comp-observable piece of
information.
It remains to be seen if this can be explained by the machine-itself (cf
the logic G) or its guardian angel (cf G*). But that, only the future will
say. Big first evidences have appeared, though, in the sense that the
general shape of quantum logic appears for the comp-observable.
> If we merely consider the Platonia of mathematics we find only a
> single example of each and every number. If we assume digital
> substitutability there would be one and only one number for each and
> every physical object. Where does duplication obtain in Platonia? If
> duplicatability is an impossible notion, does your thesis survive?
It is known that "classical information" is duplicable. This is actually
illustrated by the fact that this current mail will be multiplied without
loss of information (same number of bits) to the readers of the everything
and FOR list. I mean: at some right level with respect to the content of
this post.
(Assuming no bugs, no moderation, etc.)
OK. I could give you another answer. I could say that duplication is not
only allowed in QM, but is very easy to do. Just look at a cat in the
superposition state dead (d) and alive (a). If you (y) look at it: this
happens: y(a+d) = y_a a + y_d d, where y_i = y (you) with the 1-memory of
a dead (resp alive) cat. Of course you can object that if you don't look at
the cat the situation is really described by y a + y b, and if you look at
the cat this becomes y_a a + y_d d, so that no duplication has occurred:
just a differentiation. Right, but recall that this *is* the way I have
explained why, just with classical comp, we are obliged to consider in fine
that with comp too we have only differentiation. Do you remember the "Y = |
|" drawing? That is: if you duplicate yourself into an exemplary at Sidney,
and one at Pekin, from an original at Amsterdam, your "probability weight"
at Amsterdam is bigger. A future duplication add weight in the present.
That's why I agree with David that in QM it is preferable to consider the
Schroedinger (or Heisenberg) Equation as describing differentiation instead
of duplication. But the same is true for classical comp, by the way the UDA
forces the probability weights.
Last answer (I agree the matter is subtle, and it is better to have more
than one explanation). Remember simply I do not assume QM at the start. If
comp would entails the duplicabilty of matter, then, as far as we can
correctly believe in QM, comp would be refuted. But as I said, comp
predicts the non-duplicability of matter. The thought experiment used in
the UDA does NOT presuppose the duplicability of matter, only the
duplicability, at some level, of the 3- *person*. (Not of the 1-person
which is never duplicated: as Everett puts it: the observer cannot feel the
split, and the 1-person is the observer/feeler, etc.).
You can sum up things with the following slogan:
Duplicability of the soul (the 1-person, say) => the non-duplicability of
whatever remains stable in its observations. (3-person or 1-person plural).
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Tue Jun 15 2004 - 07:19:04 PDT