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Gurkenglas comments on Harry Potter and the Methods of Rationality discussion thread, part 23, chapter 94 - Less Wrong
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Ah, I believe you have misunderstood me. Lets say that in Yudcanon, either Dumbledore stole the map or Quirrel stole the map or Harry stole the map or Hat&Cloak stole the map or Mr. X stole the map. If Harry makes sure that Harry never steals the map, there is one less person who might have had a reason to steal the map, and the probability of the map being stolen versus it not being stolen goes down, even though he already knows that the map was stolen when he makes that decision; just like when Omega presents you the two boxes, you should retroactively precommit to one-box to receive a million, even though the content of the boxes is already determined.
Imagine Harry saw that the map was stolen, and thinks immediately of stealing it himself so as to acquire it. Naturally, he then plans to precommit to invisibility-cloak deposit it right behind Fred and George in 5 seconds. He might then go further and precommit instead to never having stolen it in the first place, so that it never leaves the grasp of the Weasley twins and Harry doesn't have to go to the effort of stealing it. Therefore, he now knows that the map was stolen by someone else, and that the probablity of the map being stolen in the first place has lessened, which is a good thing.
This is the point that I think is escaping many people in this thread. The options aren't as simple as A/A+B in Newcomb.
The map has been stolen. Everything we know about how Time Travel works in this universe indicates that this is a fixed fact that cannot be altered. Who took the map however is an unknown, and while it cannot be 'altered' either, the Effect can in this case precede the Cause. 'Map has been taken' can happen before 'Harry takes map because someone had to' such that B causes A and A leads to B. If Harry doesn't commit to it, B is still true, and so the Map is lost to him. His choices are (Map is Gone, I have it.) or (Map is gone.) The choice 'Map is still here and Hermione lives' is not a valid choice and should be discounted. So, his choices are to benefit or not benefit from the Map being gone.
The interesting question is, if the Twins forgot the Map entirely, how did they remember 'Deligitor Prodi'? Admittedly not perfectly.
Why would the two be linked?
They learned the phrase from Dumbledore when they gave him the map. The fact that they don't remember the map but imperfectly remember the phrase does support the "poorly done obviation" hypothesis. (either because the obliviator missed removing the phrase or the obliviator intended for them to keep the phrase but accidentally messed it up)
(or, less likely, 'Deligitor Prodi' would not have worked for the twins and the obliviator intentionally altered it so that it would)
I'd completely forgotten that!
But, y'know, procedural versus declarative memory. It's perfectly possible to remember to say something like "deligitor prodi" when you want the Sorting Hat, while forgetting all sorts of associated details. Er, like I did myself.