toner comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 113 - Less Wrong Discussion
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Here's a flawed solution, but maybe someone can fix it.
Harry performs partial transfiguration on his brain, to transform it into a state where he thinks that he's booby-trapped the universe (for example, by transfiguring some strangelets along with a confinement field that will expire before the strangelets do). Then he just explains honestly to Voldemort why the universe will end if he dies.
Does transfiguring your brain work in a setting implied to have Cartesian dualism?