# Monkeys Can Do Math

It looks like a standardized test question: Is the sum of two numbers on the left or the single number on the right larger? Rhesus macaques that have been trained to associate numerical values with symbols can get the answer right, even if they haven’t passed a math class. The finding doesn’t just reveal a hidden talent of the animals—it also helps show how the mammalian brain encodes the values of numbers.

Previous research has shown that chimpanzees can add single-digit numbers. But scientists haven’t explained exactly how, in the human or the monkey brain, numbers are being represented or this addition is being carried out. Now, a new study helps begin to answer those questions.

Neurobiologist Margaret Livingstone of Harvard Medical School in Boston and her colleagues had already taught three rhesus macaques (Macaca mulatta) in the lab to associate the Arabic numbers 0 through 9 and 15 select letters with the values zero through 25. When given the choice between two symbols, monkeys reliably chose the larger to get a correspondingly larger number of droplets of water, apple juice, or orange soda as a reward. To test whether the monkeys could add these values, the researchers began giving them a choice between a sum and a single symbol rather than two single symbols. Within 4 months, the monkeys had learned how the task worked and were able to effectively add two symbols and compare the sum to a third, single symbol.

To ensure that the monkeys hadn’t simply memorized every possible combination of symbols and associated a value with the combination—this wouldn’t be true addition—Livingstone’s team next taught the animals an entirely new set of symbols—Tetris-like blocks rather than letters and numbers. With the new symbols, the monkeys were again able to add—this time calculating the value of combinations they’d never seen before and confirming the ability to do basic addition, the team reports online today in the Proceedings of the National Academy of Sciences.

But when Livingstone and colleagues started analyzing the data in more detail—they had the results of hundreds of tests per day for months on end—they realized that the monkeys weren’t 100% accurate. They tended to underestimate a sum compared with a single symbol when the two were close in value—sometimes choosing, for example, a 13 over the sum of eight and six. The underestimation was systematic—when adding two numbers, the monkeys always paid attention to the larger of the two, and then added only a fraction of the smaller number to it.

The monkeys’ systematic errors argue against one theory of how the mammalian brain processes numbers. “What they’re doing is paying more attention to the big number than the little one,” Livingstone explains. But the altered values weren’t tied intrinsically to the symbols. If eight was the larger of two numbers in a sum, then its full value was considered, but if it was being added to a larger number, its value was diminished. One prevailing theory on number representation—dubbed logarithmic encoding—had proposed that the brain always underestimates the value of larger numbers in a systematic and unchangeable way. In such a case, the value of eight wouldn’t vary based on the situation as Livingstone observed.

“They’ve shown that it’s very unlikely that there’s some kind of logarithmic encoding of numbers,” says psychologist David Burr of the University of Florence in Italy, who was not involved in the new work. Further research on how humans and monkeys estimate the value of numbers, and how this plays a role in the brain’s ability to add two values, could shed light on dyscalculia—a human learning disability specific to mathematics. Children with dyscalculia often have trouble not only adding numbers, but quickly guessing how many objects are in a group. Together with the new results on rhesus macaques, this suggests that estimating values is key to the ability to add.

“Being able to estimate obviously has survival value; you want to be able to glance up and see how many lions are about to attack you,” Burr says. “The remaining goal is developing a model to explain how that happens in the brain.”

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