I think I must be the odd one out here in terms of comfort using probabilities close to 1 and 0. Because 90% and 99% are not “near certainty” to me.
How sure are you that the English guy who you’ve been told helped invent calculus and did stuff with gravity and optics was called “Isaac Newton”? We’re talking about probabilities like 99.99999% here. (Conditioning on no dumb gotchas from human communication, e.g. me using a unicode character from a different language and claiming it’s no longer the same, which has suddenly become much more salient to you and me both. An “internal” probability, if you will.)
Maybe it would help to think of this as about 20 bits of information past 50%? Every bit of information you can specify about something means you are assigning a more extreme probability distribution about that thing. The probability of the answer being “Isaac Newton” has a very tiny prior for any given question, and only rises to 50% after lots of bits of information. And if you could get to 50%, it’s not strange that you could have quite a few more bits left over, before eventually running into the limits set by the reliability of your own brain.
So when you say some plans require near certainty, I’m not sure if you mean what I mean but chose smaller probabilities, or if you mean some somewhat different point about social norms about when numbers are big/small enough that we are allowed to stop/start worrying about them. Or maybe you mean a third thing about legibility and communicability that is correlated with probability but not identical?
I think I must be the odd one out here in terms of comfort using probabilities close to 1 and 0. Because 90% and 99% are not “near certainty” to me.
How sure are you that the English guy who you’ve been told helped invent calculus and did stuff with gravity and optics was called “Isaac Newton”? We’re talking about probabilities like 99.99999% here. (Conditioning on no dumb gotchas from human communication, e.g. me using a unicode character from a different language and claiming it’s no longer the same, which has suddenly become much more salient to you and me both. An “internal” probability, if you will.)
Maybe it would help to think of this as about 20 bits of information past 50%? Every bit of information you can specify about something means you are assigning a more extreme probability distribution about that thing. The probability of the answer being “Isaac Newton” has a very tiny prior for any given question, and only rises to 50% after lots of bits of information. And if you could get to 50%, it’s not strange that you could have quite a few more bits left over, before eventually running into the limits set by the reliability of your own brain.
So when you say some plans require near certainty, I’m not sure if you mean what I mean but chose smaller probabilities, or if you mean some somewhat different point about social norms about when numbers are big/small enough that we are allowed to stop/start worrying about them. Or maybe you mean a third thing about legibility and communicability that is correlated with probability but not identical?