Basic math in monkeys and college students

Abstract

Adult humans possess a sophisticated repertoire of mathematical faculties. Many of these capacities are rooted in symbolic language and are therefore unlikely to be shared with nonhuman animals. However, a subset of these skills is shared with other animals, and this set is considered a cognitive vestige of our common evolutionary history. Current evidence indicates that humans and nonhuman animals share a core set of abilities for representing and comparing approximate numerosities nonverbally; however, it remains unclear whether nonhuman animals can perform approximate mental arithmetic. Here we show that monkeys can mentally add the numerical values of two sets of objects and choose a visual array that roughly corresponds to the arithmetic sum of these two sets. Furthermore, monkeys' performance during these calculations adheres to the same pattern as humans tested on the same nonverbal addition task. Our data demonstrate that nonverbal arithmetic is not unique to humans but is instead part of an evolutionarily primitive system for mathematical thinking shared by monkeys.

Figure 1. The Addition Task

Monkeys and humans were presented with one set of dots (set 1), followed by a brief delay after which a second set of dots was presented (set 2). Then, two choices (the sum and the distractor) were presented, and monkeys were rewarded for touching the choice that represented the numerical sum of the two sets.

Figure 2. Monkeys' Acquisition of the Addition Task

Each session was approximately 250 trials, divided equally among the three problem types (1 + 1, 2 + 2, and 4 + 4). Feinstein and Boxer required two and six sessions, respectively, to reach above-chance performance on all three trial types (binomial tests of accuracy versus chance: Boxer: 1 + 1, n = 62, 0.85 versus 0.5, p < 0.001; 2 + 2, n = 127, 0.58 versus 0.5, p < 0.05; 4 + 4, n = 61, 0.75 versus 0.5, p < 0.001. Feinstein: 1 + 1, n = 149, 0.92 versus 0.5, p < 0.001 ; 2 + 2, n = 184, 0.64 versus 0.5, p < 0.001; 4 + 4, n = 167, 0.93 versus 0.5, p < 0.001).

Figure 3. Monkeys' Addition Performance Was Ratio-Dependent

Both monkeys' accuracy on each of the addition problems was modulated by the numerical ratio between the correct sum and the distractor choice. Solid lines show the predicted data from Equation 1. R ² values reflect the fit between the predicted and actual data. w represents the precision with which monkeys selected the correct sum from the distractor choice based on the best fitting predicted data. As the ratio (small/large) between the sum and the distractor approached one, accuracy declined. Chance = 50%.

Figure 4. Monkeys Can Solve Novel Addition Problems

Both monkeys performed significantly above chance on the novel and familiar addition problems, and their performance was similarly modulated by the ratio between the numerical values of the sum and distractor choices. Solid lines represent the predicted data from Equation 1 at the best-fitting w. R ² values reflect the fit between the predicted and actual data for familiar trials (black) and novel trials (gray; all p's < 0.0001).

Figure 5. Monkeys Perform Addition like Humans

Monkeys and humans exhibited ratio-dependent accuracy and response time when solving addition problems. For accuracy (left panel), solid lines show the predicted data from Equation 1 for humans (red) and monkeys (gray) at the best fitting w. The R ² values for accuracy show the strength of the fit. Response times (right panel) are fit with a linear function, and the corresponding R ² values are reported. Error bars reflect the standard error among subjects.

Figure 6. The Effect of the Magnitude of the Sum on Accuracy for Addition Trials

Monkeys and humans performed less accurately as the numerical magnitude of the sum of the sample sets increased. Bolded lines show the predicted data from Figure 5 presented as a function of sum size. Error bars reflect the standard error among subjects.