Eliezer, can you clarify what you mean by
“You’ll note that I don’t try to modestly say anything like, “Well, I may not be as brilliant as Jaynes or Conway, but that doesn’t mean I can’t do important things in my chosen field.”
Because I do know… that’s not how it works.”
He didn’t reply to this, so I’ll take a stab at unpacking/justifying that statement.
For the number of people in the world, smaller numbers are more conservative, so suppose that number is 6 billion. For the number of truly distinct things that there are to be good at, larger numbers are more conservative, so let us suppose that number to be 600,000. (I doubt if any reader can come up with even 10,000 such things, even allowing trivial variations like “experimental high energy physicist with subspecialty A” and “experimental high energy physicist with subspecialty B”.) Under those conservative assumptions, it is mathematically necessary that AT LEAST 99% of people are not in the top 100 at anything. Further, that boundary only happens with the additional conservative assumptions that 1) literally everyone pursues the exact career (among 600,000 choices!) that an infallible oracle told them they were the best at, and 2) people match careers in such a way that each one is assigned by the oracle to at least 100 people. The farther reality is from those, the more the percentage gets closer to 100%, or the rank required to be at the top of something dips lower than 100.
Because of the preceding argument, it seems likely that most people are not very important to the field to which they are the most important. Therefore, it seems irrational to believe “I am important to my chosen field” without specific, relatively strong evidence that this is the case. Certainly “lots of people say that that’s true of everyone” isn’t strong enough, since that evidence has the more-plausible alternate explanation that people say that because it’s comforting to them to believe it, in ignorance of whether it’s actually true.