In fandom, at least the fandoms which I am on the fringes of, people talk about canon. Something is canon if it is in the official work, but not all official work is necessarily canon. For example, the events in the Star Wars Holiday Special are not canon because they’re not part of the main story1.
Fan fiction is definitively not canon. Fanfic is writing using someone else’s world, and often their characters. It’s actually a really good way to start writing, even though it’s almost never publishable2, because the characters and the setting are already established. I’ve written a little bit myself, although I originally conceived it as an idea for a script I would send in to the Star Trek producers.
The inevitable combination of these is called head canon, your personal interpretation of the story incorporating fan fiction elements.
All of which is to say that Harry Potter and the Methods of Rationality is fan fiction, an alternative version of the Harry Potter story with an adjusted premise, which enriches my head canon version of original the Harry Potter stories.
The adjusted premise3 is that Petunia Evans did not marry Vernon Dursley but instead took someone sensible as her husband: Michael Verres, a University professor and rationalist. Harry grows up as an only child, having been adopted and loved by his adoptive parents. This means that Harry is well read and already a well-developed intellect when it comes to science and logic.
The magical world is not prepared.
I would probably have read this fanfic even if it hadn’t turned into a mesmerising story because of its origins as an interesting pedagogical conceit: teach the principles of rational decision-making in a (frankly) irrational context; and investigate how someone possessed of deep critical faculties and a mysterious dark side would analyse the structure of magic and magical Britain.
But then it did turn into a good story, and many of the concepts it explores are embedded in my head canon because they make the Potterverse a great deal more sophisticated. Things like Harry and Hermione being sorted into Ravenclaw obviously aren’t compatible with the original work, but some of the other ideas improve the canonical story:
- Slytherin is not a house of cartoon villains, but where the most cunning are sorted. It’s not about power so much as control and manipulation, skills which can be turned to evil but then so can any of the other virtues celebrated by the houses.
- evil is not limited to Slytherin. In particular, bullies come from Gryffindor just as much as Slytherin.
- self-consistent explanations for magical artifacts and creatures. From the invisibility cloak to Dementors to the Mirror of Erised, magical things are explored and defined coherently. I particularly like the Philosopher’s Stone, but the examination of horcrux technology is impressive too.
- a plausible analysis of the Dark Mark.
The story can be a little dark sometimes but not gratuitously so, to the point where anyone who was comfortable with the goings on in books six or seven should be fine with the events here.
It is long, though. It took me about two weeks to work through it, and there are a lot of scenes with characters arguing: there are intense action sequences, but a lot of talking in between.
But as I say, this fanfic improves my appreciation of the original work, and that is something to celebrate.
 and canons can be changed. To use another Star Wars example, the Star Wars Extended Universe used to be canon, but after the Disney acquisition it was deprecated. Presumably they didn’t want to be weighed down by thirty years of continuity with the new stories they wanted to tell.
 Fifty Shades of Grey notwithstanding. After all, it was published as original work with no connection to the Twilight Universe.
 not the only change, but the one which is most significant.