A neglected gem from Less Wrong: Why 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:
In a pinch, the second graph can also serve as a rough map of Afghanistan
Grip strength is strongly correlated with arm strength. But the person with the strongest arm doesn’t have the strongest grip. He’s 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’t even close to being best at writing.
Thrasymachus gives an intuitive geometric explanation of why this should be; I can’t beat it, so I’ll just copy it outright:
I thought about this last week when I read this article on happiness research.
The summary: if you ask people to “value 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”, you will find that Scandinavian countries are the happiest in the world.
But if you ask people “how much positive emotion do you experience?”, you will find that Latin American countries are the happiest in the world.
If you check where people are the least depressed, you will find Australia starts looking very good.
And if you ask “how meaningful would you rate your life?” you find that African countries are the happiest in the world.
It’s tempting to completely dismiss “happiness” as a concept at all, but that’s not right either. Who’s 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 – and who wouldn’t? – happiness has to at least sort of be a real concept.
The solution is to understand words as hidden inferences – they refer to a multidimensional correlation rather than to a single cohesive property. So for example, we have the word “strength”, which combines grip strength and arm strength (and many other things). These variables really are heavily correlated (see the graph above), so it’s almost always worthwhile to just refer to people as being strong or weak. I can say “Mike Tyson is stronger than an 80 year old woman”, and this is better than having to say “Mike Tyson has higher grip strength, arm strength, leg strength, torso strength, and ten other different kinds of strength than an 80 year old woman.” This is necessary to communicate anything at all and given how nicely all forms of strength correlate there’s no reason not to do it.
