Best read by those who are already relatively familiar with Harry Potter.
Those of you who read my previous post know that I mentioned Harry Potter and the Methods of Rationality in passing, and that I described it as "one of the greatest pieces of literature I have ever read." Harry Potter and the Methods of Rationality (abbreviated from here on out as HPMoR or just MoR) is a piece of fanfiction (cue protests from those of you who haven't taken my previous post to heart that no, it can't possibly be good), written by one Eliezer Yudkowsky, rationalist and AI researcher. Among other changes, the central premise is that Harry's aunt Petunia married a scientist and Oxford teacher, and Harry, a child prodigy in MoR canon, was raised in a loving household and was taught rationality from a young age. This is far from the only departure from canon, and I doubt it is even the most dramatic - among other things, Quirrell is more competent than most of the other teachers at Hogwarts. But I digress.
In the story's beginning, Harry of course receives his Hogwarts letter, and when his father is understandably unconvinced, Harry manages to get a letter to Hogwarts asking someone to come to his home for a demonstration. McGonagall arrives and, as a quick proof, levitates Harry's father for a few moments before letting him down. You are all thinking that what happens next is that both Harry and his father, Scientifically-Minded as they are, immediately construct flimsy rationalizations as to why it was a trick, which McGonagall dispels with a more compelling demonstration, and then they rationalize that one, and so on ad nauseam. That is not at all what happens. Harry establishes beforehand that there is no way McGonagall could be faking it, and when McGonagall successfully levitates Harry's father, he promptly accepts the existence of magic, which under the circumstances is about the right thing to do.
Then McGonagall shows Harry her Animagus transformation, and Harry says this:
"You turned into a cat! A SMALL cat! You violated Conservation of Energy! That's not just an arbitrary rule, it's implied by the form of the quantum Hamiltonian! Rejecting it destroys unitarity and then you get FTL signaling! And cats are COMPLICATED! A human mind can't just visualize a whole cat's anatomy and, and all the cat biochemistry, and what about the neurology? How can you go on thinking using a cat-sized brain?"
I can't personally verify any of what he says about quantum mechanics, but it's not exactly an area of expertise, and Yudkowsky assures the reader in the beginning that all mentioned science is accurate. Everything from "cats are complicated" onward strikes me as common sense, though. Particularly striking is Harry's reaction upon fully realizing that most of physics is basically gone now; he doesn't abandon his rationality altogether, but instead realizes that "the March of Reason would just have to start over, that was all; they still had the experimental method and that was the important thing."
This, ladies and gentlemen, is fantasy done right.
It's quickly revealed that MoR-Harry has a disorder in which his sleep cycle is 26 hours long instead of 24, which sounds like a convenient plot device that the author just made up(Harry has not been attending public school for some time because of it), but it turns out that that's a real thing that can actually happen, which quite frankly amazed me when I found out.
One of my favorite of MoR's changes was the considerable fleshing-out of the Houses. Rather than putting all of the protagonists in Gryffindor, Yudkowsky puts them where they belong; Hermione goes to Ravenclaw with the more-rational Harry, and Neville goes to Hufflepuff. Ron, who isn't seen much, still goes to Gryffindor. In addition to this change, the qualities of each house (except Gryffindor) are fleshed out. Ravenclaws are not defined just by intelligence, but by curiosity; Hufflepuffs are known for being a supportive and tightly-knit group of loyal friends; and Slytherins aren't just evil, but cunning and ambitious, which Yudkowsky actually goes to the trouble of distinguishing from evil. Gryffindor basically remains the house of the brave, and MoR-Harry expresses disdain for it early on, though not without reason. His first impression of Gryffindor is that of Gryffindor prefects refusing to help Neville find his toad on the Hogwarts Express. It is, of course, something of a generalization, but Harry calling Gryffindor house the house of "wannabe heroes" is essentially accurate in MoR canon, and probably not to far off the mark in official canon either.
Lastly, Yudkowsky describes MoR as a story for adults, not because it's particularly violent or raunchy (most main characters are around eleven), but because it is intellectual. I didn't really have problems, but I have historically been a horrible judge of how my intellect compares to that of normal teenagers, so teenage readers, I have no idea whether you should expect it to go over your head or not. (And don't worry if you drew a complete blank at Harry's intellectual freakout above; so did I when I read it.) That said, it's a piece of fiction that's well worth reading for more than its entertainment value, and as I said, I'd recommend it as required reading if I didn't fear that that would cause those who read it to perceive it as worse.
And if you really enjoy it, to the extent that you want to start emulating Harry, and it doesn't go over your head, then I recommend checking out the author's profile.