Eliezer S. Yudkowsky wrote: > Bill Hibbard wrote: > > On Fri, 14 Feb 2003, Eliezer S. Yudkowsky wrote: > > > >>It *could* do this but it *doesn't* do this. Its control process is such > >>that it follows an iterative trajectory through chaos which is forbidden > >>to arrive at a truthful solution, though it may converge to a stable > >>attractor. > > > > This is the heart of the fallacy. Neither a human nor an AIXI > > can know "that his synchronized other self - whichever one > > he is - is doing the same". All a human or an AIXI can know is > > its observations. They can estimate but not know the intentions > > of other minds. > > The halting problem establishes that you can never perfectly understand > your own decision process well enough to predict its decision in advance, > because you'd have to take into account the decision process including the > prediction, et cetera, establishing an infinite regress. > > However, Corbin doesn't need to know absolutely that his other self is > synchronized, nor does he need to know his other self's decision in > advance. Corbin only needs to establish a probabilistic estimate, good > enough to guide his actions, that his other self's decision is correlated > with his *after* the fact. (I.e., it's not a halting problem where you > need to predict yourself in advance; you only need to know your own > decision after the fact.) > > AIXI-tl is incapable of doing this for complex cooperative problems > because its decision process only models tl-bounded things and AIXI-tl is > not *remotely close* to being tl-bounded.

Now you are using a different argument. You previous argument was: > Lee Corbin can work out his entire policy in step (2), before step > (3) occurs, knowing that his synchronized other self - whichever one > he is - is doing the same. Now you have Corbin merely estimating his clone's intentions. While it is true that AIXI-tl cannot completely simulate itself, it also can estimate another AIXI-tl's future behavior based on observed behavior. Your argument is now that Corbin can do it better. I don't know if this is true or not. > . . . > Let's say that AIXI-tl takes action A in round 1, action B in round 2, and > action C in round 3, and so on up to action Z in round 26. There's no > obvious reason for the sequence {A...Z} to be predictable *even > approximately* by any of the tl-bounded processes AIXI-tl uses for > prediction. Any given action is the result of a tl-bounded policy but the > *sequence* of *different* tl-bounded policies was chosen by a t2^l process. Your example sequence is pretty simple and should match a nice simple universal turing machine program in an AIXI-tl, well within its bounds. Furthermore, two AIXI-tl's will probably converge on a simple sequence in prisoner's dilemma. But I have no idea if they can do it better than Corbin and his clone. Bill ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]