Update: Discussion has moved on to a new thread.
The hiatus is over with today's publication of chapter 73, and the previous thread is approaching the 500-comment threshold, so let's start a new Harry Potter and the Methods of Rationality discussion thread. This is the place to discuss Eliezer Yudkowsky's Harry Potter fanfic and anything related to it.
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. The fanfiction.net author page is the central location for information about updates and links to HPMOR-related goodies, and AdeleneDawner has kept an archive of Author's Notes.
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:
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Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).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.
It's also an invalid conclusion for other reasons. Harry hasn't actually done anything uncomputable with a time turner, and the one occasion that he came close (trying something computable but slow), all that he got for his pains was ‘DO NOT MESS WITH TIME’. It's very easy to compute this.
Even if Harry does something that seems uncomputable, that proves nothing [ETA: although of course it is evidence and Harry's estimate of simulation should go down in accordance with Bayes's Rule], since he only observes finitely many experiments, and any finite result is (trivially) computable. It's always possible that the system could break down when you push it further. (Presumably it has an error catcher that outputs ‘DO NOT MESS WITH TIME’ when this happens.)
As far as we know, the real world is computable, and it's computed this story. Therefore nothing in it is definitely uncomputable.
That message came from Harry, not from physics. Roughly speaking it indicates that a stable loop where Harry gets hysterical is easier to arrive at than a stable loop where the problem is solved. ie. In one of the instances something surprising and dangerous but non-fatal (would have) happened so that (potential) Harry would have set up a stable time loop that prevented that branch from ever happening. (Or maybe Harry just went paranoid for no reason - hard to tell with him.)