Eliezer Yudkowsky, “Harry Potter and the Methods of Rationality”

To change the future

Harry’s thoughts flashed back to possibly the worst moment of his life to date, those long seconds of blood-freezing horror beneath the Hat, when he thought he’d already failed. He’d wished then to fall back just a few minutes in time and change something, anything before it was too late...
And then it had turned out to not be too late after all.
Wish granted.
You couldn’t change 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 going wrong.’ And he would wish desperately for the ability to fall back through time and make a different choice...
Wish granted. Now what?

Harry slowly smiled.
It was a rather counterintuitive thought... but...
But he could, there was no rule saying he couldn’t, he could just pretend he’d never heard that little whisper. Let the universe go on in exactly the same way it would have if that one critical moment had never occurred. Twenty years later, that was what he would desperately wish had happened twenty years ago, and twenty years before twenty years later happened to be right now. Altering the distant past was easy, you just had to think of it at the right time.