I have a pet theory that some biases can be explained as a mix-up between probability and likelihood. (I don’t know if this is a good explanation.)
At least not clearly distinguishing probability and likelihood seems common.
One point-in-favour is our notation of conditional probabilities (e.g. P(X|Y)) where ⋅|⋅ is a symbol with mirror-symmetry. As Eliezer writes in a lecture in plane crash, this is a didactically bad idea and an asymmetric symbol would be a lot easier to understand:
P(X|Y)≠P(Y|X)
is less optically obvious than[1]P(X◃Y)≠P(Y◃X).
Of course, our written language has an intrinsic left-to-right directional asymmetry, so that the symmetric ⋅|⋅ isn’t a huge amount of evidence[2].
Some maths symbols where the symmetry does match their meaning: =,+,×,/,∪,<,→,⇒ and lots more. Some where it doesn’t: |,−,∘,[⋅,⋅] (the latter two stand for function-concatenation and commutation).
At least not clearly distinguishing probability and likelihood seems common. One point-in-favour is our notation of conditional probabilities (e.g. P(X|Y)) where ⋅|⋅ is a symbol with mirror-symmetry. As Eliezer writes in a lecture in plane crash, this is a didactically bad idea and an asymmetric symbol would be a lot easier to understand: P(X|Y)≠P(Y|X) is less optically obvious than[1] P(X◃Y)≠P(Y◃X).
Of course, our written language has an intrinsic left-to-right directional asymmetry, so that the symmetric ⋅|⋅ isn’t a huge amount of evidence[2].
I am not sure that I remember the symbol that Eliezer used correctly
Some maths symbols where the symmetry does match their meaning: =,+,×,/,∪,<,→,⇒ and lots more. Some where it doesn’t: |,−,∘,[⋅,⋅] (the latter two stand for function-concatenation and commutation).