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/
