An unfortunate beginning: The story of Clever Hans’ mathematical abilities
An initial attempt to study numerical abilities in animals is the famous story of Clever Hans. In the early twentieth century, Wilhelm von Osten trained his horse Hans, to perform a variety of arithmetic calculations, which ranged from adding, subtracting, long divisions and square roots. When von Osten presented Hans with a mathematical operation, the horse responded by tapping its hoof on the ground the correct number of times. Initially, the majority of scientists were convinced by Hans’ mathematical skills. Some years later, it turned out that the horse returned the correct answer only when the trainer knew the answer. Nevertheless, the horse failed when the trainer did not know the correct outcome or when Hans could not see the trainer while responding. Hans was surprisingly skilful in perceiving subtle behavioral signals made by his trainer as he reached the correct count with his hoof tapping. Hans had no mathematical intelligence — but social intelligence!
Related scientific publications
Pfungst, O. (1907). Der Kluge Hans. Ein Beitrag zur nichtverbalen Kommunikation. Frankfurter Fachbuchhandlung für Psychologie, Frankfurt am Main.
Rugani R. (2017). Towards numerical cognition’s origin: insights from day-old domestic chicks. Phil. Trans. R. Soc. B 373: 20160509.http://dx.doi.org/10.1098/rstb.2016.0509
Vallortigara, G., Chiandetti, C., Sovrano, V. A., Rugani, R., and Regolin, L. (2010a). Animal Cognition. Wiley Interdisciplinary Reviews. Cogn. Sci. 1, 882–893. doi: 10.1002/wcs.75
Vallortigara, G., Regolin, L., Chiandetti, C., and Rugani, R. (2010b). Rudiments of mind: number and space cognition in animals. Comp. Cogn. Behav. Rev. 5, 78–99. doi: 10.3819/ccbr.2010.50004