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Nominull comments on Failed Utopia #4-2 - Less Wrong
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Comments (247)
For any two groups A and B, two random members of A are more alike than a random member of A and a random member of B, aren't they?
No. A is [1,3,5,7], B is [4,4,4,4]. A random member of A will be closer to a random member of B than to another random member of A.
I probably would say that that is because your two sets A and B do not carve reality at its joints. What I think army1987 intended to talk about is "real" sets, where a "real" set is defined as one that carves reality at its joints in one form or another.
There will be some real sets that are similar to Nominull's (well, natural numbers are a subset of reals, eh?), however army1987 did emphasize the any, so Nominull's correction was well warranted.
Er, no, I was just mistaken. (And forgot to retract the great-grandparent -- done now.) For a pair of sets who do carve reality at (one of) its joints but still is like that, try A = {(10, 0), (30, 0), (50, 0), (70, 0)} and B = {(40, 1), (40, 1), (40, 1), (40, 1)}.
(What I was thinking were cases were A = {10, 20, 30, 40} and B = {11, 21, 31, 41}, where it is the case that “two random members of A are more alike than a random member of A and a random member of B”, and my point was that “Two random men are more alike than a random man and a random woman” doesn't rule out {men} and {women} being like that.)
Ah, okay then. That makes sense.