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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I think 1-H(p) but with a single question it’s hard to think what this really means for a human.
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.
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H is the usual name for Shannon Entropy: https://en.m.wikipedia.org/wiki/Entropy_(information_theory) … for a variable like this: -p*log(p)-(1-p)*log(1-p). Your formula is a well known upper bound on 1 - H(p).
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Nice! Bedtime reading! ;)
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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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