The jury's still out on the other two Rs, but many animals practice arithmetic, though in different, often less precise ways than humans, according to new research and summary data presented at APA's 2007 Annual Convention.
At Georgia State University, for example, researchers have taught chimpanzees to recognize Arabic numerals on a computer screen and to touch an equivalent number of dots from a field of many dots lower on the screen, said psychologist Michael Beran, PhD. He found that although the chimps did pretty well with lower numbers, their performance deteriorated as the numbers got higher. Eight seemed to be the upper threshold, Beran said.
Another experiment examined the chimps' ability to parse numbers far apart but not numbers close together: Beran dropped different numbers of M&Ms in two different cups while the chimps looked on. They then selected the cup with the most candies in it. When there was a big difference between the amount of M&Ms in the two cups, they did well at this task. Otherwise, they performed more poorly.
"As the difference between the sets gets bigger, performance increases," Beran said. "It's easier to tell the difference between six versus two than it is three versus two."
But the question remained whether the chimps were maintaining a numerical representation of the number of M&Ms in each cup, or if they were just keeping track of the relative amounts. So Beran and his team added a third option: an open platter of M&Ms. If the chimps had been actually counting the M&Ms as they dropped into the cups, they would know whether or not it was a better deal to pick door number three. In fact, in three-quarters of these trials, the chimps chose the option with the most M&Ms, which led Beran to conclude that they were keeping approximate quantities in their heads while they watched and not just relying on which cup seemed like it had the most poured into it.
Jessica Cantlon, a psychology graduate student at Duke University, had more to say about these approximate quantities from her work with Rhesus macaque monkeys. In her research, she found that these approximate values follow a simple rule of ratios: The "fuzziness" monkeys experience between the numbers two and four is the same as between four and eight because the ratios are the same, Cantlon said.
The idea that numbers exist on an approximate scale where quantities close together blend into one another is known as an analog representation of numbers. Cantlon performed an experiment testing monkeys' abilities against humans in a counting task. Two sets of dots appeared on a screen, and both human and monkey participants had to pick the set with more dots. The humans were also explicitly told to perform this task as quickly as possible.
After analyzing the results, Cantlon found that humans were only 5 to 10 percent better than the monkeys. And when she compared the monkeys with the fastest humans, the difference basically vanished, she said. To her, this indicated that, at least in this task, the humans and monkeys were using the same analog representation mechanism.
"These are mathematical abilities that appear to be part of a primitive mathematical toolkit for reasoning about numerical values," Cantlon said.
This toolkit, however, may not be limited to primates, said Irene Pepperberg, PhD, a psychologist at Harvard University. She was on hand to talk about her findings related to a well-known African Grey parrot, Alex, who died just after APA's convention.
For the past 30 years, Pepperberg has conducted a large amount of research into birds' numerical abilities. Alex knew numbers-both the Arabic numerals and abstract quantities-up to eight and could add with about 75 percent accuracy, Pepperberg said.
What's more, Alex seemed to have a "zero-like" concept. In the lab, the bird could identify the color of a given number of objects on a tray, Pepperberg said. For example, if there were six blue blocks, five red blocks and four green blocks, Pepperberg could ask, "What color is six?" Alex would respond, "Blue." But if Pepperberg asked Alex about the color of a number not present on the tray, he squawked, "none." Occasionally in other trials involving "sham" addition-asking him to add together visible objects and absent spaces where an object would be-Alex would misidentify zero as "one," Pepperberg said. But this mistake is also common among children, who use a mental "number line"-like system, where one and zero are close together.
"I think he's at the stage of very young children who are just beginning to understand zero-ness and absence-ness," Pepperberg said.
Alex's performance suggests that the evolutionary roots of mathematics run deep, she said.
"Given that parrots' and primates' evolutionary history dates back from the dinosaurs, I think number concepts are very likely to be widespread across a lot of species," Pepperberg said.