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. "Nope. Nope. Nope. Maybe. Nope. Nope. Maybe."
That lets you prune out failed items but doesn't recurse back to an instantaneous success.
that doesn't follow. Where would Harry have gotten the pies if not from Harry+1?
He got them from the breakfast table. Where did he get the idea to get them? Well, he would have seen the pies later on anyway. Just like he would have learned about time turners later on in the day anyway, but a more stable scenario was obtained by learning about them earlier.
The recursion is non-iterative beyond the number of loops actually manifested, however.
I'm not quite sure how to parse this. If you would think about an idea at time T, but don't because future you...
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: