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Number Sense In Primates
There have been a plethora of studies done on primates’ understanding of numbers. However, the process of training primates to complete even the most simple experimental tasks is extensive and involved work that can take years to complete. Through these experiments, it has become apparent that there are two possible ways of handling numbers mentally, the approximate number system (ANS) and the parallel individuation system (PNS).

Approximate Number System
The approximate number system (ANS) of processing numbers is fairly imprecise and relies heavily on estimation and comparison. This system does not give numbers individual value, but compares quantities based on their relative size. The efficiency of this ANS depends on Weber’s law which states that the ability to distinguish between quantities is dictated by the ratio between two numbers, not the absolute difference between them. In other words, the accuracy of the ANS depends on the size difference between two quantities being compared.

In a study on rhesus macaques (Macaca mulatta), it was found that when given certain images of objects with multiple properties i.e. colors, shapes, and numbers, the monkeys were quick to match the image with another of the same number of items regardless of the other properties. This result is an example of the ANS at work. The monkeys aren't defining numbers individually, but are matching sets of items of the same number using comparison of quanitites.

The most basic example of the ANS in primates exists during natural confrontation within and between groups. For instance, in the case of chimpanzees (Pan troglodytes), an intruder on a group’s territory will only be attacked if the intruder is alone and the attacking party is composed of at least three males. This social numerical superiority concept exists across most primate species and displays the understanding of power in numbers, at least in a comparative way.

One study done on the ANS in 2012 made chimpanzees listen to food that they were unable to see be thrown individually into containers then had to choose which container to eat from based on which had the higher amount. They were fairly successful with the task suggesting that they have some capability to not only compare quantities, but also keep track of those quantities within their minds. The experiment did however break down at certain similar numbers of individual food items according to Weber's Law.

Parallel Individuation System
The other number system to consider is the parallel individuation system (PIS) which requires that numbers to possess individual and exact properties without the need to compare them. The PIS allows for each number to exist on its own, without comparing its quantity to other quantities, and with a specific value defined by arithmetic. In order to use the PIS, one must have some understanding of numerals, or specific symbolic representations of quantities that relate to other symbolic representations of quantities in definite ways.

It is extremely difficult to support the presence of the PIS in primates. This is because once a primate has been trained on a task long enough to display a true PIS, the results are usually attributed to mere associative learning rather than exact number comprehension. In order to provide unequivocal evidence of the existence of the PIS in primates, researchers must ideally find a situation where a primate performs some sort of arithmetic calculation in the wild.

While this has yet to be discovered, there are some laboratory experiments that may support the beginnings of a PIS in primates such as one well known study known as the “chimp challenge”. This study was more aimed at testing the working memory of primates however, involved teaching chimpanzees to memorize the correct order of Arabic numerals from 1-9 then press them in that order once they’ve disappeared scattered on screen. While they didn’t necessarily need to know how to do math problems with the numerals, they did have to understand the sequential order of the numbers and that they always remained in that increasing order regardless of other variables. This understanding does require the PIS to some degree and the rate at which the chimps did this was in many cases faster than humans.

Another study that might also support the existence of the PIS in primates was done again with Rhesus macaques. In this study, the macaques were proven to associate auditory stimuli of a certain number of individual vocalizations with the correct number of individuals. While this didn’t require them to learn arabic numerals it required the ability to choose an exact quantity for the voice number they heard rather than merely comparing quantities by sight.

Subitization
A final important phenomenon to consider regarding primates understanding of numbers is subitization. Subitization is a phenomenon where the brain automatically groups small numbers of objects together without requiring it to go through mental counting. This is common in humans and allows us to notice for instance the number shown on a pair of dice is three without having to count one dot on one die and two dots on the other. Essentially, it can give one a number sense without really needing to understand the numerical system at least at low quantities.

One study done on over 200 semi-free-ranging rhesus monkeys proved that to an extent, the monkeys could differentiate between numbers of apples in a container even when the sizes of the apple slices were manipulated (some larger but fewer slices). However, this experiment broke down once the numbers reached above about four, suggesting that the subitization phenomenon was likely at play.