Suppose you say that you’re 99.99% confident that 2 + 2 = 4.
Then you're a dillbrain.
Then you have just asserted that you could make 10,000 independent statements, in which you repose equal confidence, and be wrong, on average, around once. Maybe for 2 + 2 = 4 this extraordinary degree of confidence would be possible
Yes, how extraordinary that I can say every day that the guy in front of me at the bodega won't win the Powerball. Or that [SystemRandom().random() >= 0.9999 for i in range(10000)] makes a list that is False in all but one spot.
P(x|y) is defined as P(x,y)/P(y). P(A|A) is defined as P(A,A)/P(A) = P(A)/P(A) = 1. The ratio of these two probabilities may be 1, but I deny that there's any actual probability that's equal to 1. P(|) is a mere notational convenience, nothing more.
Eliezer asks me to state my confidence that I won't roll a 1.
I say I am 99% confident I won't roll a 1, using basic math.
Eliezer says "AHA, you idiot, I checked all of your past predictions and when you predicted something with confidence 99%, it only happened 90% of the time! So you can't say you're 99% confident that you won't roll a 1"
I am impressed by the ability of my past predictions to affect the roll of a dice, and promptly run off to become a wizard.
Ah but the machine gods could be tinkering with your neural wiring to make you think you're rolling a die when in reality the universe is nothing but the color pink. That's right, reality is nothing but a shade of Fuchsia and dice don't actually exist. You should take this possibility into account when adjusting your priors for some reason.
Then you're a dillbrain.
Yes, how extraordinary that I can say every day that the guy in front of me at the bodega won't win the Powerball. Or that
[SystemRandom().random() >= 0.9999 for i in range(10000)]makes a list that isFalsein all but one spot.No, you kneebiter.
I roll a fair 100 sided dice.
Eliezer asks me to state my confidence that I won't roll a 1.
I say I am 99% confident I won't roll a 1, using basic math.
Eliezer says "AHA, you idiot, I checked all of your past predictions and when you predicted something with confidence 99%, it only happened 90% of the time! So you can't say you're 99% confident that you won't roll a 1"
I am impressed by the ability of my past predictions to affect the roll of a dice, and promptly run off to become a wizard.
Ah but the machine gods could be tinkering with your neural wiring to make you think you're rolling a die when in reality the universe is nothing but the color pink. That's right, reality is nothing but a shade of Fuchsia and dice don't actually exist. You should take this possibility into account when adjusting your priors for some reason.
Epistemic Status: Barbie.
Whom the gods would destroy, they first make Barbie.