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# How Monkeys Do Math

## Humans appear to have an instinct for math, but they're not the only primates that can count.

Apr 21 2014, 8:20pm
##### Image: Shutterstock

Humans appear to have an instinct for math, but they're not the only primates that can count—others, like chimpanzees, have been shown to have a basic grasp of arithmetic. But are primates actually performing calculations, or are they just good at deciphering the difference between large and small numbers?

Rhesus macaques can indeed do math, according to new work published in Proceedings of the National Academy of Sciences today. The Harvard-Yale research team, led by Margaret S. Livingstone of Harvard Medical School's Department of Neurobiology, found that the macaques "could combine symbolically represented magnitudes, and they transferred this ability to a novel symbol set, indicating that they were performing a calculation, not just memorizing the value of each combination."

The tests involved three sets of A/B tests on a pair of touchscreens; when a macaque selected a touchscreen, the total value of the symbols it displayed would be paid out in the form of drops of a reward liquid. The first test involved simply showing a number of dots—say, 5 on one side, and 10 on the other.

Second, researchers used a set of 26 symbols corresponding with between 0-25 drops of reward liquid—the set used the Arabic numerals 0–9 to represent 0–9 drops, and the letters X Y W C H U T F K L N R M E A J to represent 10–25 drops—that, according to the researchers, the monkeys have been learning for years.

Finally, a second symbol set "was made by filling 4–5 squares in a 3 × 3 square array: 0–25 drops were represented by the symbols." To the human eye—or at least mine—this code is the most abstract:

The first round of tests were straightforward A/B tests. If a macaque selected the higher of the two numbers, it would get a larger reward. The macaques were surprisingly successfully, even with the second symbol set, which they had less experience with:

##### Image: PNAS

The graphs above show the percentage at which macaques chose one number over another; they uniformly chose the higher of the two options. But one thing stands out: Macaques did comparatively worse when the numbers weren't very far apart. For example, in the middle graph above, the monkeys only chose the number 8 over the number 7 around 60 percent of the time.

This is an important finding. Humans' understanding of math is based on our number sense. We can learn the relationship between numbers of varying sizes, and how they can operate on each other. It's a sense we must develop; a 2003 study found that 6-month-old infants were only able to distinguish between two numbers if one was at least twice as large as the other, while 9-month-old infants were able to discriminate between numbers that were half as large as each other.

In this case, macaques didn't seem to have much trouble discriminating between numbers whose values varied widely. But as the symbol sets became less familiar—counting dots would be the most elementary, while the grid-based symbol set was the hardest—their ability to distinguish between numbers of relatively close value diminished pretty heavily.

To test how those differences were being distinguished, the researchers comprised a different test, in which one touchscreen showed a single symbol, while the other showed two, with their total value being the total reward.

##### Image: PNAS

While the results aren't quite as clean (in this case, the graphs are the same, but reversed), the macaques still chose the the pair of symbols when they were the higher value option. While the authors note that this could simply be the monkeys assuming that two symbols is more valuable than one, they did find evidence to the contrary.

When looking at a pair of numbers, the macaques consistently valued the larger number correctly, while they consistently undervalued the smaller of the two numbers. This happened regardless of the number's actual magnitude: If a 9 was the high number of the pair, it was valued correctly, and if it was the low number, it was assigned a real value of about third that.

But over time, the macaques began to assign the lower half of the sum pair more correctly, which suggests they had learned to take this number into account. So, when faced with a 9 and a 4, the macaque didn't simply calculate the value as "9 plus a bit more," but began to actually assess things more coherently. This result even applied to the second, grid-based symbol set, even though the macaques were less familiar with it.

##### A Rhesus monkey picking a letter in the test. Image: Margaret S. Livingstone

So while it's not clear proof that a rhesus monkey can add 4+15 and know the answer is exactly 19, the evidence does suggest that they are capable of learning approximate addition quite successfully. Or, as the authors write, "symbol-literate monkeys can be trained to combine, or add, pairs of large numbers," and "their addition behavior indicates an underlying relative scaling of magnitude."

That last point is key, as the goal was to shine light on how the brain actually processes basic differences in quantities. As the authors write in their intro, "although it is easy to recognize the difference between 2 and 4 items, it is more difficult to distinguish 22 from 24 items. This dependence of accuracy on magnitude is a property that the approximate number sense shares with more basic sensory processes​."

In other words, the monkeys' assessment of numbers was context-dependent—if it was the smaller of the two values, they placed less emphasis on evaluating it accurately. On its own, this isn't a surprise, as context-dependent assessment is key to much of our understanding of scale. (For example, a \$100 keychain seems like a lot less of a rip-off if you're also buying a \$50,000 car.)

But what is interesting is that, unlike a pair of theories that are central to psychophysics, the scaling observed was neither directly linear or logarithmic. Instead, Livingstone and company found that such scaling is more dynamic, which they argue corresponds more directly with observed models of neuronal responsiveness. "Our result brings the coding of symbolically represented magnitude into agreement with direct measurements of neuronal coding of value," they write. Or, in simple terms, monkeys' abilities to discriminate numbers is reflective, not just of their own intelligence, but of how their brains physically function.