CLEVER HANS, THE MATHEMATICAL HORSE

IN THE EARLY YEARS of the twentieth century there was a horse in Germany who could read, do mathematics and exhibit a deep knowledge of world political affairs. Or so it seemed. The horse was called Clever Hans. He was owned by Wilhelm von Osten, an elderly Berliner whose character was such, everyone said, that fraud was out of the question. Delegations of distinguished scientists viewed the equine marvel and pronounced it genuine. Hans would reply to mathematical problems put to him with coded taps of his foreleg, and would answer nonmathematical questions by nodding his head up and down or shaking it side to side in the conventional Western way. For example, someone would say, “Hans, how much is twice the square root of nine, less one?” After a moment’s pause Hans would dutifully raise his right foreleg and tap five times. Was Moscow the capital of Russia? Head shake. How about St. Petersburg? Nod.

The Prussian Academy of Sciences sent a commission, headed by Oskar Pfungst, to take a closer look; Osten, who believed fervently in Hans’s powers, welcomed the inquiry. Pfungst noticed a number of interesting regularities. Sometimes, the more difficult the question, the longer it took Hans to answer; or when Osten did not know the answer, Hans exhibited a comparable ignorance; or when Osten was out of the room, or when the horse was blindfolded, no correct answers were forthcoming. But other times Hans would get the right answer in a strange place, surrounded by skeptics, with Osten not only out of the room, but out of town. The solution eventually became clear. When a mathematical question was put to Hans, Osten would become slightly tense, for fear Hans would make too few taps. When Hans, however, reached the correct number of taps, Osten unconsciously and imperceptibly nodded or relaxed—imperceptibly to virtually all human observers, but not to Hans, who was rewarded with a sugar cube for correct answers. Even teams of skeptics would watch Hans’s foot as soon as the question was put and make gestural or postural responses when the horse reached the right answer. Hans was totally ignorant of mathematics, but very sensitive to unconscious nonverbal cues. Similar signs were unknowingly transmitted to the horse when verbal questions were posed. Clever Hans was aptly named; he was a horse who had conditioned one human being and discovered that other human beings he had never before met would provide him the needed cues. But despite the unambiguous nature of Pfungst’s evidence, similar stories of counting, reading and politically sage horses, pigs and geese have continued to plague the gullible of many nations.^*