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Sarunas comments on Crazy Ideas Thread, Aug. 2015 - Less Wrong Discussion
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This is a crazy idea that I'm not at all convinced about, but I'll go ahead and post it anyway. Criticism welcome!
Rationality and common sense might be bad for your chances of achieving something great, because you need to irrationally believe that it's possible at all. That might sound obvious, but such idealism can make the difference between failure and success even in science, and even at the highest levels.
For example, Descartes and Leibniz saw the world as something created by a benevolent God and full of harmony that can be discovered by reason. That's a very irrational belief, but they ended up making huge advances in science by trying to find that harmony. In contrast, their opponents Hume, Hobbes, Locke etc. held a much more LW-ish position called "empiricism". They all failed to achieve much outside of philosophy, arguably because they didn't have a strong irrational belief that harmony could be found.
If you want to achieve something great, don't be a skeptic about it. Be utterly idealistic.
Am I correct to paraphrase you this way: maximizing EX and maximizing P(X > a) are two different problems.
Yeah, that's one part of it. Another part is that some irrational beliefs can be beneficial even on average, though of course you need to choose such beliefs carefully. Believing that the world makes sense, in the context of doing research, might be one such example. I don't know if there are others. Eliezer's view of Bayesianism ("yay, I've found the eternal laws of reasoning!") might be related here.
What are the meanings of these symbols "EX", "P(X>a)"?
X is a random variable, E is expected value (a.k.a. average), P is probability. For example, if X is uniformly distributed between 0 and 1, then EX=0.5 and P(X>0.75)=0.25.
Sarunas is saying that some action might not affect the average value, but strongly affect the chances of getting a very high or very low value ("swing for the fences" so to speak). For example, if we define Y as X rounded to the nearest integer (i.e. Y=0 if X<0.5 and Y=1 if X>0.5), then EY=0.5 and P(Y>0.75)=0.5. The average of Y is the same as the average of X, but the probability of getting an extreme value is higher.
This is probably obvious for others, but it wasn't obvious for me that by paying 0.1 to go from the first game to the second one you both decrease your average earnings and increase the probability of high earnings.
Good point. It's worth noting that you can use Markov's inequality to relate the two.