Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
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:
You do not need to rot13 anything about HP:MoR or the original Harry Potter series unless you are posting insider information from Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).
If there is evidence for X in MOR and/or canon then it's fine to post about X without rot13, even if you also have heard privately from Eliezer that X is true. But you should not post that "Eliezer said X is true" unless you use rot13.
The difference is that the factoring trick involved several thousand other timelines that had to be resolved while adding any information he lacked to the message involved one. Spontaneously generating timeline stabilizing random data that only requires resolving a low number of timelines to calculate being preferred over having to calculate thousands makes sense, being preferred over a stabilization that requires calculating at most one other timeline does not.
It's not really any different from any other trick that involves him observing the results of his time travel before he carries it out. The difference between a) resolving to use time travel to get himself out of the empty class room and b) just having thought of it and being willing to get himself out of the empty classroom if he observes it actually having happened is that in a) he would do it even if he had not observed the results, there is no other potential behavioral difference between a) and b) for the difference in outcome to correspond to.