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D_Malik comments on Query the LessWrong Hivemind - Less Wrong
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Idea: play a game of chess against someone while in a lucid dream.
If you won or lost consistently, it would show that you are better at chess than you are at chess.
If anyone actually does this, I think you should alternate games sitting normally and with your opponent's pieces on your side of the board (i.e. the board turned 180 degrees), because I'd expect your internal agents to think better when they're seeing the board as they would in a real chess match.
My favorite moment along those lines was at work years ago, when a developer asked me to validate the strategy she was proposing to solve a particular problem.
She laid out the strategy for me, I worked through some examples, and said "OK... this looks right to me. But you should ask Mark about it, too, because Mark is way more familar with our tax code than I am, and he might notice something I didn't... like, for example, the fact that this piece over here will fail under this obscure use case."
Then I blinked, listened to what I'd just said, and added "Which I, of course, would never notice. So you should go ask Mark about it."
She, being very polite, simply nodded and smiled and backed away quickly.