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army1987 comments on Failed Utopia #4-2 - Less Wrong
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Oh *please*. Two random men are more alike than a random man and a random woman, okay, but seriously, a huge difference that makes it necessary to either rewrite minds to be more alike or separate them? First, anyone who prefers to socialize with the opposite gender (ever met a tomboy?) is going to go "Ew!". Second, I'm pretty sure there are more than two genders (if you want to say genderqueers are lying or mistaken, the burden of proof is on you). Third, neurotypicals can get along with autists just fine (when they, you know, actually try), and this makes the difference between genders look hoo-boy-tiiiiny. Fourth - hey, I *like* diversity! Not just just knowing there are happy different minds somewhere in the universe - actually interacting with them. I want to sample ramensubspace everyday over a cup of tea. No *way* I want to make people more alike.
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?
Not necessarily -- for example, if all the members of both groups are on a one-dimensional space, both groups have the same mean, and Group B had much smaller variance than Group A... But still.
Most people are members of more than just one group.
So?
Soooooo, real humans might be a mite more complicated than that, such that your summary does not usefully cover inferences about people.
I don't see where I assumed that the groups were disjoint. My point was that "Two random men are more alike than a random man and a random woman", while technically true, isn't particularly informative about men and women.
Ah, my mistake. I thought you were saying that given your proposition is (asserted to be true), the idea that two random men are more alike than a random man and woman must be meaningfully true.
What about cases in which group B is a subset of Group A?
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.
I believe what Manon meant is that the difference in this case between two random members of the same class exceeds the difference between the average members of each class.