"Outside the laboratory, scientists are no wiser than anyone else." Sometimes this proverb is spoken by scientists, humbly, sadly, to remind themselves of their own fallibility. Sometimes this proverb is said for rather less praiseworthy reasons, to devalue unwanted expert advice. Is the proverb true? Probably not in an absolute sense. It seems much too pessimistic to say that scientists are literally no wiser than average, that there is literally zero correlation.

But the proverb does appear true to some degree, and I propose that we should be very disturbed by this fact. We should not sigh, and shake our heads sadly. Rather we should sit bolt upright in alarm. Why? Well, suppose that an apprentice shepherd is laboriously trained to count sheep, as they pass in and out of a fold. Thus the shepherd knows when all the sheep have left, and when all the sheep have returned. Then you give the shepherd a few apples, and say: "How many apples?" But the shepherd stares at you blankly, because they weren't trained to count apples - just sheep. You would probably suspect that the shepherd didn't understand counting very well.

Now suppose we discover that a Ph.D. economist buys a lottery ticket every week. We have to ask ourselves: Does this person really understand expected utility, on a gut level? Or have they just been trained to perform certain algebra tricks?

One thinks of Richard Feynman's account of a failing physics education program:

"The students had memorized everything, but they didn't know what anything meant. When they heard 'light that is reflected from a medium with an index', they didn't know that it meant a material such as water. They didn't know that the 'direction of the light' is the direction in which you see something when you're looking at it, and so on. Everything was entirely memorized, yet nothing had been translated into meaningful words. So if I asked, 'What is Brewster's Angle?' I'm going into the computer with the right keywords. But if I say, 'Look at the water,' nothing happens - they don't have anything under 'Look at the water'!"

Suppose we have an apparently competent scientist, who knows how to design an experiment on N subjects; the N subjects will receive a randomized treatment; blinded judges will c...

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