Could a horse really do arithmetic? The Clever Hans story

No: Clever Hans was not doing arithmetic. He was reading people. In 1907 the psychologist Oskar Pfungst demonstrated that the horse was watching the reactions of his trainer, and was responding to involuntary cues in human body language that the trainer was entirely unaware he was giving.

Hans belonged to Wilhelm von Osten, a mathematics teacher and amateur horse trainer. Von Osten would ask something like "If the eighth day of the month comes on a Tuesday, what is the date of the following Friday?" and Hans would answer by tapping his hoof eleven times. The public of the day was especially curious about animal minds, largely because of Charles Darwin's recent publications, and a commission with a veterinarian, a circus manager, a cavalry officer, schoolteachers and the director of the Berlin zoological gardens concluded in September 1904 that no tricks were involved.

Pfungst went further. Using a substantial number of trials, he found Hans could answer correctly even when von Osten himself did not ask, which ruled out fraud. But when Hans could see the questioner he got 89 percent of the answers right, and when he could not, only 6 percent. The horse was right only when the questioner knew the answer and Hans could see them.

The giveaway was tension. As the taps approached the right number, the questioner's posture and face changed, and the tension was released at the final correct tap. That was Hans's signal to stop. Nobody was lying: people were simply leaking the answer without knowing it.