At 19:05 -0400 29/09/2002, Wei Dai wrote: >On Thu, Sep 26, 2002 at 02:58:57PM +0200, Bruno Marchal wrote: >> Originally the passage from the first person to the first person plural was >> done in reaction to my ex-boss wanting an explanation of the comp >> indeterminacy in term of betting games. > >What do you mean by this? Explanation or reference please?
Explanation. Take the duplication W M. Suppose you will be duplicated from here to two different places W and M. In computer jargon you are cut here and paste in W and in M. Comp indeterminacy comes from the fact that you cannot be sure in advance where you will feel yourself being, from a 1-person point of view,. At first, probabilities, perhaps in the frequency type approaches, could be justified by iterating the procedure. If you repeat the procedure 64 times, the majority of the 2^64 resulting person would recognize their inability to predict their path (WWMWMMM....). Not all "probabilist" accept such sort of justification and some objects that the 1-person uncertainty has no operational meaning. Indeed, you cannot apparently use the duplication to win or lose a bet in a fair game with a third person. Two cases can be considered: the Candidate C (the one who will undergo the duplication W M) put one dollar in a bank. The third person bets one dollar that C will find himself in W, against C who bets one dollar that he will find himself in M. Of course C is transformed into C_M and C_W in the duplication process. CW must gives one dollar to the third person who must gives one dollar to the C_M. The third person neither can win nor lose. The money is just exchanged between the "doppelgangers". A similar exchange occurs if the candidate have his money with him so that his account is duplicated (except the bill loose his value ...). Now, the point I make is that betting strategies for handling uncertainty can be re-established by ... duplicating the third person too, sharing the W-M trips with the candidate. In some sense, it is a way for the third person to entangle its story with the candidate's story. In that case the multiplied third person will recognize in each of his stories that he has win or lose the bet. This gives rise to a notion of first person plural discourse, which is just sharable first person discourse, and which can make some of the typical first person notions (like the 1-indeterminacy) into locally third person notions (like the apparant quantum indeterminacy). This is what I happen in the description of multi-observer measurements has explained by Everett. Looking to the up or down state of 64 photon beam each in the superposition state (up + down), you will find yourself multiplied in the 2^64 "UP UP DOWN ..."-like stories, but if you did decide to phone me for telling in which story you are you will multiplied me in a coherent way. The strict coherence giving the right entanglement has not yet been derived from comp. Nor has been proved comp give incorrect coherence conditions. The many world, or any modal realism, multiplies collection of observers. If the multiplication is enough coherent, this entails first person plural notions which appears to the observers inside each population as third person. Technically, it is here that a "nice" tensorial product should rise. Bruno
