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A neglected gem from Less Wrong:\\xa0Why The Tails Come Apart, by commenter Thrasymachus. It explains why even when two variables are strongly correlated, the most extreme value of one will rarely be the most extreme value of the other. Take these graphs of grip strength vs. arm strength and reading score vs. writing score:

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Grip strength is strongly correlated with arm strength. But the person with the strongest arm doesn\\u2019t have the strongest grip. He\\u2019s up there, but a couple of people clearly beat him. Reading and writing scores are even less correlated, and some of the people with the best reading scores aren\\u2019t even close to being best at writing.

Thrasymachus gives an intuitive geometric explanation of why this should be; I can\\u2019t beat it, so I\\u2019ll just copy it outright:

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I thought about this last week when I read\\xa0this article on happiness research.

The summary: if you ask people to \\u201cvalue their lives today on a 0 to 10 scale, with the worst possible life as a 0 and the best possible life as a 10\\u201d, you will find that Scandinavian countries are the happiest in the world.

But if you ask people \\u201chow much positive emotion do you experience?\\u201d, you will find that Latin American countries are the happiest in the world.

If you check where people are the\\xa0least depressed, you will find\\xa0Australia\\xa0starts looking very good.

And if you ask \\u201chow meaningful would you rate your life?\\u201d you find that African countries are the happiest in the world.

It\\u2019s tempting to completely dismiss \\u201chappiness\\u201d as a concept at all, but that\\u2019s not right either. Who\\u2019s happier: a millionaire with a loving family who lives in a beautiful mansion in the forest and spends all his time hiking and surfing and playing with his kids? Or a prisoner in a maximum security jail with chronic pain? If we can all agree on the millionaire \\u2013 and who wouldn\\u2019t? \\u2013 happiness has to\\xa0at least sort of\\xa0be a real concept.

The solution is to understand\\xa0words as hidden inferences\\xa0\\u2013 they refer to a multidimensional correlation rather than to a single cohesive property. So for example, we have the word \\u201cstrength\\u201d, which combines grip strength and arm strength (and many other things). These variables really are heavily correlated (see the graph above), so it\\u2019s almost always worthwhile to just refer to people as being strong or weak. I can say \\u201cMike Tyson is stronger than an 80 year old woman\\u201d, and this is better than having to say \\u201cMike Tyson has higher grip strength, arm strength, leg strength, torso strength, and ten other different kinds of strength than an 80 year old woman.\\u201d This is necessary to communicate anything at all and given how nicely all forms of strength correlate there\\u2019s no reason not to do it.