Your strength as a rationalist is your ability to be more confused by fiction than by reality. If you are equally good at explaining any outcome, you have zero knowledge.

What people really believe doesn't feel like a BELIEF, it feels like the way the world IS.

You couldn't changed history. But you could get it right to start with. Do something differently the FIRST time around. This whole business with seeking Slytherin's secrets... seemed an awful lot like the sort of thing where, years later, you would look back and say, 'And THAT was where it all started to go wrong.' And he would wish desperately for the ability to fall back through time and make a different choice. Wish granted. Now what?

The people I know who seem to make unusual efforts at rationality, are unusually honest, or, failing that, at least have unusually bad social skills.

If you are equally good at explaining any outcome, you have zero knowledge.

Okay, so either (a) I just teleported somewhere else entirely (b) they can fold space like no one's business or (c) they are simply ignoring all the rules.

You will find ambiguity a great ally on your road to power. Give a sign of Slytherin on one day, and contradict it with a sign of Gryffindor the next; and the Slytherins will be enabled to believe what they wish, while the Gryffindors argue themselves into supporting you as well. So long as there is uncertainty, people can believe whatever seems to be to their own advantage. And so long as you appear strong, so long as you appear to be winning, their instincts will tell them that their advantage lies with you. Walk always in the shadow, and light and darkness both will follow.