doubt that is not investigated still serves as a placeholder in one’s mind
This seems to be popular opinion in the comments, and I’m inclined to agree that doubt can still be useful even if not investigated further. Yudkowsky pointed out above that the word “doubt” seems to have 2 meanings. It can refer either to an emotional state (such as the emotions a child feels when doubting Santa), or to a mathematical uncertainty (when you’re not sure your conclusions are statistically significant).
In both cases, I can think of counterexamples where merely doubting without having the opportunity to act on those doubts still proves useful. In the mathematical sense, doubting provides an upper bound for how much you would trust a possibly-erroneous concision without investigating it. The emotional aspect cements this knowledge in your mind, and makes it come to mind much easier if it is needed in the future.
Perhaps doubting can best be thought of as having diminishing returns. The first time you think to doubt a statement, it is tested, and if it has no obvious flaws one can assign it a higher probability than one which hasn’t been doubted. Additional thought returns less and less additional certainty, since it is less and less likely to disprove the statement. Eventually, the only value left is as a marker. Even then, the purpose of a red flag is to point out something that is actually uncertain, so the total value of a lingering doubt should go to zero if investigated forever.
...so the total value of a lingering doubt should go to zero if investigated forever.
Very well written, I just wanted to confirm something, I was under the impression that since nothing has 100% certainty, nothing can have a 0% uncertainty, you could get closer and closer, but you can never actually reach it. If I’m wrong or misunderstanding this I would appreciate it if someone would correct me, thanks.
nothing has 100% certainty, nothing can have a 0% uncertainty
That’s my understanding as well. I was trying to say that, if you were to formalize all this mathematically, and took the limit as number of Bayesian updates n went to infinity, uncertainty would go to zero.
Since we don’t have infinite time to do an infinite number of updates, in practice there is always some level of uncertainty > 0%.
There are some forms of doubts that you can easily reduce by simply adding more observations but not all. Seeing an infinitive amount of white swans doen’t help you to completely rule out the black one.
MarsColony_in10years: Yeah, thanks. Sorry about the nitpicking.
ChristianKl: I think an infinite number would allow you to rule out the possibility (of a black swan that is). I thought that the problem was simply that we could never get an infinite number of them, but then again: I’m not certain.
This seems to be popular opinion in the comments, and I’m inclined to agree that doubt can still be useful even if not investigated further. Yudkowsky pointed out above that the word “doubt” seems to have 2 meanings. It can refer either to an emotional state (such as the emotions a child feels when doubting Santa), or to a mathematical uncertainty (when you’re not sure your conclusions are statistically significant).
In both cases, I can think of counterexamples where merely doubting without having the opportunity to act on those doubts still proves useful. In the mathematical sense, doubting provides an upper bound for how much you would trust a possibly-erroneous concision without investigating it. The emotional aspect cements this knowledge in your mind, and makes it come to mind much easier if it is needed in the future.
Perhaps doubting can best be thought of as having diminishing returns. The first time you think to doubt a statement, it is tested, and if it has no obvious flaws one can assign it a higher probability than one which hasn’t been doubted. Additional thought returns less and less additional certainty, since it is less and less likely to disprove the statement. Eventually, the only value left is as a marker. Even then, the purpose of a red flag is to point out something that is actually uncertain, so the total value of a lingering doubt should go to zero if investigated forever.
Very well written, I just wanted to confirm something, I was under the impression that since nothing has 100% certainty, nothing can have a 0% uncertainty, you could get closer and closer, but you can never actually reach it. If I’m wrong or misunderstanding this I would appreciate it if someone would correct me, thanks.
That’s my understanding as well. I was trying to say that, if you were to formalize all this mathematically, and took the limit as number of Bayesian updates n went to infinity, uncertainty would go to zero.
Since we don’t have infinite time to do an infinite number of updates, in practice there is always some level of uncertainty > 0%.
There are some forms of doubts that you can easily reduce by simply adding more observations but not all. Seeing an infinitive amount of white swans doen’t help you to completely rule out the black one.
MarsColony_in10years: Yeah, thanks. Sorry about the nitpicking.
ChristianKl: I think an infinite number would allow you to rule out the possibility (of a black swan that is). I thought that the problem was simply that we could never get an infinite number of them, but then again: I’m not certain.
To the extend that the word infinitive makes sense, you can see an infinitive number of white swans without seeing a black swan.