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DanielLC comments on Harry Potter and the Methods of Rationality discussion thread, part 16, chapter 85 - Less Wrong
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Because you would have sent that information back in time. It didn't block them "then" because they weren't going to send the information further back. The effect could be more subtle - instead of preventing you from succeeding, it could prevent you from trying (don't mess with time) or even make you not think of trying.
No, you can't "fix" it, you can only reduce the effect. If a signal is weak, you can amplify it. But that only works up to a point. And apparently, that point is six hours, even with magical amplification and correction.
I remember a short story by Larry Niven - Rotating cylinders and the possibility of global causality violation. The short story first appeared in Analog, was reprinted in CONVERGENT SERIES, and it contains the immortal line "I imagine the sun has gone nova". Because the universe protects its cause-and-effect basis with humorless ferocity.
They weren't planning on it, but the information was sent nonetheless. P(Someone is going to go back and stop them from going back|They came back) < P(Someone is going to go back and stop them from going back|They did not came back)
Not really. The amount of time you can send back increases exponentially with the number of people sent back. If you only get it right a third of the time, sending one guy back only works a third of the time, but sending a hundred people back, you'd get about 67 +- 5 people sending the right bit, and you'd get it right about 99.98% of the time. If you have two hundred people, you'd get it right about 0.9999997% of the time.
That presupposes that P(Bob came back) is not affected by your decision to send the information further on. I'm postulating that IF you would have sent the information further back, THEN P(Bob came back) = 0. Of course, it might not actually work that way, but if my supposition is correct, then Bob not coming back tells you nothing. The event only carries information if you aren't going to make use of that information.
No. I gave an example in which it was not decided to send information back. It's simply impossible to go back in time without proving that you weren't killed by a time-travelling assassin.