Addenda:
From the reader's perspective, it doesn't appear that that's what we are supposed to believe (though I'm still wondering...), so I'm tentatively guessing that the mechanism of magic is some kind of technology, and that the in-story universe has the same laws as this one. It does seem implausible that an ancient civilization could have invented technology advanced enough to be indistinguishable from this kind of magic, but that could be different in an alternate history, and it still seems less implausible than any set of physical laws that would actually make this kind of magic a normal, natural thing that a non-industrial civilization could invent/discover.
We are supposed to be wondering why magic works at all, right? It doesn't seem like Eliezer to expect us to be satisfied with an Inherently Mysterious phenomenon at the center of the story, even if it's a story based on someone else's fictional world that already had that feature... but I don't know, maybe it's a demonstration that, no matter how ridiculous the rules are, rationality will still allow you to win.
But I'm still hoping that magic will be explained at some point, and I'm still looking for clues about it.
I think magic will be explained as an addition onto physics: a new "force" is involved, but still behaves in an intelligible way. I can't imagine how the MoR series would explain the magic exhibited thus far as coming from current physical understanding.
Unless the magicians control quantum wavefunctions directly, or something like that. Or Harry is a brain in a vat.
Update: Please post new comments in the latest HPMOR discussion thread, now in the discussion section, since this thread and its first few successors have grown unwieldy (direct links: two, three, four, five, six, seven).
As many of you already know, Eliezer Yudkowsky is writing a Harry Potter fanfic, Harry Potter and the Methods of Rationality, starring a rationalist Harry Potter with ambitions to transform the world by bringing the rationalist/scientific method to magic. But of course a more powerful Potter requires a more challenging wizarding world, and ... well, you can see for yourself how that plays out.
This thread is for discussion of anything related to the story, including insights, confusions, questions, speculation, jokes, discussion of rationality issues raised in the story, attempts at fanfic spinoffs, comments about related fanfictions, and meta-discussion about the fact that Eliezer Yudkowsky is writing Harry Potter fan-fiction (presumably as a means of raising the sanity waterline).
I'm making this a top-level post to create a centralized location for that discussion, since I'm guessing people have things to say (I know I do) and there isn't a great place to put them. fanfiction.net has a different set of users (plus no threading or karma), the main discussion here has been in an old open thread which has petered out and is already near the unwieldy size that would call for a top-level post, and we've had discussions come up in a few other places. So let's have that discussion here.
Comments here will obviously be full of spoilers, and I don't think it makes sense to rot13 the whole thread, so consider this a spoiler warning: this thread contains unrot13'd spoilers for Harry Potter and the Methods of Rationality up to the current chapter and for the original Harry Potter series. Please continue to use rot13 for spoilers to other works of fiction, or if you have insider knowledge of future chapters of Harry Potter and the Methods of Rationality.
A suggestion: mention at the top of your comment which chapter you're commenting on, or what chapter you're up to, so that people can understand the context of your comment even after more chapters have been posted. This can also help people avoid reading spoilers for a new chapter before they realize that there is a new chapter.