What number is halfway between 1 and 9? Is it 5 – or 3?

A new information-theoretical model of human sensory perception and memory sheds light on some peculiarities of the nervous system.

“There’s a whole bunch of different animal species,” says Adam Reeves, a professor of psychology at Northeastern University, “and a whole bunch of different sensory mechanisms, like hearing and vision, and different aspects of all of them, and then taste, and smell, and so on, all of which follow exactly the same law”—a logarithmic relationship between stimulus intensity and perceived intensity. “Biology is very variable, right? So how come all these organisms come up with the same law? And how come the law is so precise? It’s a major philosophical problem, actually.”

Ask adults from the industrialized world what number is halfway between 1 and 9, and most will say 5. But pose the same question to small children, or people living in some traditional societies, and they’re likely to answer 3.

Cognitive scientists theorize that that’s because it’s actually more natural for humans to think logarithmically than linearly: 3^0 is 1, and 3^2 is 9, so logarithmically, the number halfway between them is 3^1, or 3. Neural circuits seem to bear out that theory. Via What number is halfway between 1 and 9? Is it 5—or 3?.

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