Number sense in animals

Number sense in animals is the ability of creatures to represent and discriminate quantities of relative sizes by number sense. It has been observed in various species, from fish to primates. Animals are believed to have an approximate number system, the same system for number representation demonstrated by humans, which is more precise for smaller quantities and less so for larger values. An exact representation of numbers higher than 3 has not been attested in wild animals, but can be demonstrated after a period of training in captive animals.

In order to distinguish number sense in animals from the symbolic and verbal number system in humans researchers use the term numerosity, rather than number, to refer to the concept that supports approximate estimation but does not support an exact representation of number quality.

Number sense in animals includes the recognition and comparison of number quantities. Some numerical operations, such as addition, have been demonstrated in many species, including rats and great apes. Representing fractions and fraction addition has been observed in chimpanzees. A wide range of species with an approximate number system suggests an early evolutionary origin of this mechanism or multiple convergent evolution.

At the beginning of the 20th century, Wilhelm von Osten famously, but prematurely, claimed human-like counting abilities in animals on the example of his horse named Hans. His claim is widely rejected today, as it is attributed to a methodological fallacy, which received the name Clever Hans phenomenon after this case. Von Osten claimed that his horse could perform arithmetic operations presented to the horse in writing or verbally, upon which the horse would knock on the ground with its hoof the number of times that corresponded to the answer. This apparent ability was demonstrated numerous times in the presence of the horse's owner and a wider audience, and was also observed when the owner was absent. However, upon a rigorous investigation by Oskar Pfungst in the first decade of 20th century, Hans' ability was shown to be not arithmetic in nature, but to be the ability to interpret minimal unconscious changes in body language of people when the correct answer was approaching. Today, the arithmetic abilities of Clever Hans are commonly rejected and the case serves as a reminder to the scientific community about the necessity of rigorous control for experimenter expectation in experiments.

There were, however, other early and more reliable studies on number sense in animals. A prominent example is the work of Otto Koehler, who conducted a number of studies on number sense in animals between 1920s and 1970s. In one of his studies he showed that a raven named Jacob could reliably distinguish the number 5 across different tasks. This study was remarkable in that Koehler provided a systematic control condition in his experiment, which allowed him to test the number ability of the raven separately from the ability of the raven to encode other features, such as size and location of the objects. However, Koehler's work was largely overlooked in the English-speaking world, due to the limited availability of his publications, which were in German and partially published during World War II.

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