Killspeak

“Maybe if you know what you’re doing, you get it wrong.” Kellogg Booth stood up and made his way to the white board. Our discussion had reminded him of a test question he once had to answer. “It was for the draft,” he said.

On the white board he sketched a rough plot: two curves, with amps along the x axis and voltage along the y. “Which of these would you say has the greatest power, the green or the orange?”

Green because it’s taller. Duh. Next question.

If you know what you’re doing, you’re not going to fall for that. You know that power can be found by taking the area under the curve. From the look of it, the broader orange curve will have a greater area, so you put orange down as your answer.

Now, if you’re really paying attention, you’ll notice that the scale along the y axis isn’t linear, but logarithmic. This means that, while the green curve doesn’t seem to be any more than two times taller than the orange one on paper, it’s actually representative of a much greater difference between the two. Since the green curve reaches far higher than the orange one, it covers a greater area. You answer green.

Green is the correct answer. If you’re dumb or lazy you get it and if you’re smart you get it, but if you’re in between, you know just enough to get it wrong.

Kelly’s punchline: “But I think that’s what they were going for. They wanted to get people who were smart enough to trust with guns, but dumb enough to go to Vietnam.”

We could call this kind a porridge filter: it selects those that are not too ignorant, not too knowledgeable, but just right.

How common are porridge filters in the real world? Are they more often products of design (as Kelly suspects of the above case) or accidents? What other cases could they be useful?

By the way, if I’ve messed up my physics, let me know.

Update: I came across the following in Neal Stephenson’s The Confusion.

“What is the Intelligence Test?” he demanded to know, and swept the curtain aside.

“A private joke,” said the annoyed Padraig.

But Jack saw good reasons to explain it, and so he said, “Cast your memory back to when Fortune had set us ashore in Surat—”

“I remember it every day,” said Surendranath.

“You stayed there to pursue your career. We fled inland to get away from the diverse European assassins who infested that town, and who were all looking for us. Soon enough, we came upon a Mogul road-block. Hindoos and Mohametans were allowed to pass through with only minor harassment and taking of baksheesh, but when it became known that we were Franks, they took us aside and made us sit in a tent together. One by one, each of us was taken out alone and conducted to a field nearby, and handed a musket—which was unloaded—and a powder-horn, and a pouch of balls.”

“What did you do?” Surendranath demanded.

“Gaped at it like a farmer.”

“I likewise,” said Padraig.

“So you failed the Intelligence Test?”

“I would rather say we passed it. Van Hoek did the same as we. Mr. Foot tried to load the musket, but got the procedure backwards—put the ball in first, then the powder. But Vrej Esphahnian and Monsieur Arlanc loaded the weapon and discharged it in the general direction of a Hindoo idol that the Moguls had been using for target practice.”

“They were inducted,” said Surendranath.

“As far as we know, they have been serving in the armed forces of the local king ever since that day,” Jack said.