If you could ask a single yes/no question of someone from the year 2050, and get a truthful response, what would it be?
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What's H? If they lie with probability 1, that's as good as telling the truth. And p = ½ gives no information. Ok, so let's assume the person from 2050 is omniscient enough to answer, "was reducing our emissions by X enough to save the planet?" And we have to pick X.
So, should we choose X to be the value for which current science believes there's a 50/50 chance it will be "enough"? Or would it make more sense to pick a smaller X, while expecting the answer to be much more likely "yes" than "no", but *if* we get a "no", we learn much more.
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Yep. We want to pick the point where we think we have a 50/50 chance of yes/no to maximize our information.
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To put it another way, imagine there are ten envelopes (0-9). Five are empty, four contain money, and one contains instant death. I would rather ask the question, "does envelope 9 contain instant death?" than "is instant death in one of the first five envelopes?"
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