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DanielLC comments on Harry Potter and the Methods of Rationality discussion thread, part 27, chapter 98 - Less Wrong Discussion
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I don't think paradoxes have much to do with it, but it's a limit of six hours into the past. Since negative a thousand is less than six, sending her a thousand hours in the future doesn't violate the six-hour limit.
It seems hard to believe that Harry managed to reverse engineer it in six hours with no special equipment.