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army1987 comments on Failed Utopia #4-2 - Less Wrong

52 Post author: Eliezer_Yudkowsky 21 January 2009 11:04AM

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Comment author: [deleted] 26 December 2012 09:03:39PM 1 point [-]

Two random men are more alike than a random man and a random woman

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?

Comment author: [deleted] 27 December 2012 11:20:16PM 0 points [-]

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.

Comment author: [deleted] 28 December 2012 01:23:20AM *  0 points [-]

Most people are members of more than just one group.

Comment author: [deleted] 28 December 2012 02:08:52AM 0 points [-]

So?

Comment author: [deleted] 28 December 2012 03:55:05AM 0 points [-]

Soooooo, real humans might be a mite more complicated than that, such that your summary does not usefully cover inferences about people.

Comment author: [deleted] 28 December 2012 04:29:45AM 0 points [-]

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.

Comment author: [deleted] 28 December 2012 04:45:22AM 0 points [-]

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.

Comment author: J_Taylor 28 December 2012 05:45:11AM 0 points [-]

What about cases in which group B is a subset of Group A?

Comment author: Nominull 28 December 2012 08:12:43AM 4 points [-]

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.

Comment author: ygert 28 December 2012 09:16:32AM *  0 points [-]

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.

Comment author: Kawoomba 28 December 2012 09:43:33AM 0 points [-]

What I think army1987 intended to talk about is "real" sets

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.

Comment author: [deleted] 28 December 2012 11:57:58AM *  1 point [-]

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.)

Comment author: ygert 28 December 2012 12:09:47PM 0 points [-]

Ah, okay then. That makes sense.

Comment author: Oligopsony 28 December 2012 11:27:34AM 1 point [-]

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.