Friday, March 07, 2008

Math instinct?

Check out this really fascinating article by Jim Holt about humans' ability to learn and do serious math. Here's a very brief summary:

According to Stanislas Dehaene, humans have an inbuilt “number sense” capable of some basic calculations and estimates. The problems start when we learn mathematics and have to perform procedures that are anything but instinctive.

Here's an excerpt about a theoretical prediction about "number neurons" that was later confirmed experimentally:

Dehaene has been able to bring together the experimental and the theoretical sides of his quest, and, on at least one occasion, he has even theorized the existence of a neurological feature whose presence was later confirmed by other researchers. In the early nineteen-nineties, working with Jean-Pierre Changeux, he set out to create a computer model to simulate the way humans and some animals estimate at a glance the number of objects in their environment. In the case of very small numbers, this estimate can be made with almost perfect accuracy, an ability known as “subitizing” (from the Latin word subitus, meaning “sudden”). Some psychologists think that subitizing is merely rapid, unconscious counting, but others, Dehaene included, believe that our minds perceive up to three or four objects all at once, without having to mentally “spotlight” them one by one. Getting the computer model to subitize the way humans and animals did was possible, he found, only if he built in “number neurons” tuned to fire with maximum intensity in response to a specific number of objects. His model had, for example, a special four neuron that got particularly excited when the computer was presented with four objects. The model’s number neurons were pure theory, but almost a decade later two teams of researchers discovered what seemed to be the real item, in the brains of macaque monkeys that had been trained to do number tasks. The number neurons fired precisely the way Dehaene’s model predicted—a vindication of theoretical psychology. “Basically, we can derive the behavioral properties of these neurons from first principles,” he told me. “Psychology has become a little more like physics.”


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