Have you ever added a bill or figured a tip and gotten a number that just didn't look right? That feeling may not have been a figment of your imagination. The human brain appears to have two modes of mathematical reasoning, which take place in different brain regions--one verbal and exact, the other nonverbal and approximate, according to a study in today's Science . The alarm bell was probably the nonverbal part of your brain disagreeing with what your calculator came up with after you had pushed a wrong button.
Stanislas Dehaene, a cognitive neuroscientist at INSERM in Orsay, France, first proposed the two-mode theory in 1991, after treating a former schoolteacher who suffered from an unusual kind of "innumeracy." After a stroke, the patient lost her ability to recite the alphabet or solve the simplest arithmetic problem--she literally could not add two plus two. Nevertheless, she was quite certain that two plus two was closer to three than to nine, which suggested that her ability to approximate figures was still intact.
Now Dehaene and cognitive psychologist Elizabeth Spelke of the Massachusetts Institute of Technology have found that in normal people, too, exact and approximate math are separate abilities. Spelke trained a group of college students who were fluent in both English and Russian to do unfamiliar arithmetic tasks, some exact and some approximate. The training took place in only one language. The students learned to solve the problems in a little over 2 seconds on average, in the language they had trained in. Exact problems took them about a second longer to solve in the language they had not trained in--even if it was their native tongue. But when solving the approximate problems, Spelke says, "there was zero slowdown. They were equally fast in both languages."
The reason, as revealed in brain scans Dehaene ran on different volunteers, is that approximate problems activate a part of the brain that deals with visual and spatial relationships rather than words. The students do not need to translate these problems to a different language to solve them, says Dehaene; instead, they appear to represent numbers mentally as if they were distances along a line--so that two units plus two units look about like four units.
"These results fit very well with evidence from human infants and from nonhuman animals," says Karen Wynn, a psychologist at the University of Arizona, Tucson. Previous studies have shown that monkeys  and babies also seem to have an approximate number sense. "The message is that when you think numerically, you should trust your instincts," says Wynn. No matter how expensive that calculator is.