The origins of counting algorithms

Abstract

Humans' ability to count by verbally labeling discrete quantities is unique in animal cognition. The evolutionary origins of counting algorithms are not understood. We report that nonhuman primates exhibit a cognitive ability that is algorithmically and logically similar to human counting. Monkeys were given the task of choosing between two food caches. First, they saw one cache baited with some number of food items, one item at a time. Then, a second cache was baited with food items, one at a time. At the point when the second set was approximately equal to the first set, the monkeys spontaneously moved to choose the second set even before that cache was completely baited. Using a novel Bayesian analysis, we show that the monkeys used an approximate counting algorithm for comparing quantities in sequence that is incremental, iterative, and condition controlled. This proto-counting algorithm is structurally similar to formal counting in humans and thus may have been an important evolutionary precursor to human counting.

Keywords: animal cognition; cognitive development; counting; mathematical cognition; nonhuman primate.

Figure 1

Example Trial. Baboons were presented with a choice between two sequentially-presented sets of food items. We observed that they frequently committed to a choice after the first set was completely baited but before the second set was completely baited. The baboons indicated that they had reached an early decision by physically moving from the first set to the second set in the middle of a trial.

Figure 2

Ratio Effects. Both monkeys showed evidence of approximate quantification in that they showed ratio effects in their ability to choose the larger quantity of food items. As the ratio between quantities increased (and became finer), monkeys’ accuracy at choosing the larger quantity decreased.

Figure 3

Probability of a switch behavior. Monkeys were increasingly likely to switch to Set 2 as the difference between Set 1 and Set 2 approached zero and the value of Set 2 began to exceed that of Set 1.

Figure 4

Average Switch Point. The value of Set 2 at which monkeys typically executed a mid-baiting switch behavior (the switch point) was correlated with the total value of Set 1. Monkeys exhibited larger switch points for larger values of Set 1.

Figure 5

Posterior distributions on model parameters for a) the sensitivity of the accumulators for Set 1 (left) and Set 2 (right), measured by the Weber fraction, b) baseline probability of a switch, c) the probability of a switch when Set 2 was greater than Set 1, and d) the probability of attending to a trial.