I see. So I guess there is some benefit gained from this, but it is very minor. It seems to me that the simplest rule that explains why Harry's integer factorization is not okay, but, for example, the "silver on the tree" password from the end of TSPE is okay, is the following: if you would gain information at time T, and send information from time T to any time S < T, then it must be the case that you would have gained that same information even if you hadn't learned it at time S.
Now consider your "keying" scenario. We have clones 0-5, and at time 1 clone x goes back to time 0 and becomes clone x+1. When clones give a "time key," it will be a number between 0 and 6, identifying a clone/wall-clock pair. Now suppose at wall-clock time T clone 1 says: "the thought I had at time P doesn't work." Assume for simplicity that time P refers to clone 0 at a wall-clock time S > T (though it would work out the same anyway). Now at time S, when clone 0 has the thought, he has two choices. On the one hand, he can continue working out why it doesn't work, but in this case he gains only the minor benefit of knowing in advance that it will not work out. On the other hand, he can move on and not consider the thought, but at time T as clone 1 just repeat (without knowing why), the fact that it doesn't work. In that case, he gained information that he would not have learned had he not told himself. Or, in your terminology, recursion was required in order to reach a stable state.
then it must be the case that you would have gained that same information even if you hadn't learned it at time S.
that doesn't follow. Where would Harry have gotten the pies if not from Harry+1?
In that case, he gained information that he would not have learned had he not told himself. Or, in your terminology, recursion was required in order to reach a stable state.
The recursion is non-iterative beyond the number of loops actually manifested, however. Each individual only adjusts the one previous, and only in immediately non-iterative manners. "...
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: