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g comments on Typicality and Asymmetrical Similarity - Less Wrong

25 Post author: Eliezer_Yudkowsky 06 February 2008 09:20PM

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Comment author: g 07 February 2008 11:58:34AM 5 points [-]

Tiiba, I don't think what I described is a bias, but perhaps I didn't explain it well. I'm proposing that in phrases like "X is approximately Y" and "X is like Y", the connectives are not intended to be taken as symmetrical relations like "differs little from"; rather, they mean something like "If you want to know about X, it may be useful to think about Y instead". And I don't see anything wrong with that, as such.

Let me give an analogy from a field where bias is quite effectively eliminated: pure mathematics. Mathematicians have various notations they use to express relationships of the form "this function is bigger than that one for large x". One of them, written something like "f ~ g", means "the ratio f/g tends to 1 in whatever limiting case we're interested in" (n -> oo, x -> 0, whatever). This really is a symmetrical relation; f ~ g if and only if g ~ f. But if you ask mathematicians which of "x^3+17x^2-25x+1 ~ x^3" and "x^3 ~ x^3+17x^2-25x+1" is more *natural* then I bet they'll quite consistently go for the former.

Now, if you want to call it a "bias" every time some term that looks symmetrical is used asymmetrically as a matter of convention or convenience, fair enough. I'd prefer to reserve "bias" for cases where the asymmetrical usage actually causes, or is a symptom of, error. As I say, I'm sure there's plenty of error caused by typicality heuristics; but I don't see that the asymmetry in the use of phrases like "is like" is, or indicates, an error.

(What "wrong question" do you think is being answered here?)