Clever Hans: The Horse Who Could Do Math

May 29, 2020 0 comments

Clever Hans

In a paved courtyard surrounded by high apartment houses in the northern part of Berlin, a small crowd had gathered to watch an old high school mathematics teacher demonstrate the brilliance of one of his precocious pupil. The sixty-something math instructor stood proudly with a black, slouch hat covering his thinning white hair. To his left, stood the pupil—an impressive Russian trotting horse.

For more than a decade, Wilhelm von Osten, the instructor, had helped Clever Hans, the horse, to develop a number of cognitive skills. von Osten would ask a question, and Hans would answer, correctly, by nodding his head, for a “yes” or a “no”, or by tapping his foot to indicate numbers. Clever Hans could show directions by turning his head, could differentiate between “left” and “right”, identify colors, read the clock, recognize and identify playing cards, and understand a large number of different concepts. Not only could Hans count, he could perform arithmetic far beyond the fundamentals.

“How much is 2/5 plus 1/2?”, von Osten would ask. Hans would answer with nine taps followed by another ten to indicate that the answer was 9/10. “What is the square root of sixteen?” Hans would make four taps. “What are the factors of 28?” Hans would tap consecutively 2, 4, 7, 14, 28.

Hans could even pick up cleverly worded questions: “I have a number in mind. I subtract 9, and have 3 as a remainder. What is the number I had in mind?”. Twelve hoof-taps.

“In the number 365287149, I place a decimal point after the 8. How many are there now in the hundreds place?” von Osten would press on. Hans would reply promptly with five taps.

Clever Hans intelligence wasn’t just limited to arithmetic. The horse would astonish crowds by spelling out words and names of people with taps, where one tap is an “A”, two taps a “B”, and so on.

Clever Hans

Clever Hans shows a number on the footboard.

Hans also gave evidence of excellent memory, and apparently carried the entire yearly calendar in his head. You could ask him: “If the eighth day of a month comes on Tuesday, what is the date for the following Friday?”, and he would tell you.

The versatility of Hans in other directions was baffling. He could recognize tones, recognize people in photographs, tap out the time of the day, distinguish between straw and felt hats, known the different colors, and so on. By some estimates, Hans mental development was similar to a child of 13 or 14 years.

Naturally, Hans aroused curiosity among many psychologists, zoologists and experts in various other fields. This was a time when studies on animal cognition and their mental processes were few and far between. The general consensus was that animals were incapable of exhibiting anthropomorphic intelligence.

“In no case is an animal activity to be interpreted in terms of higher psychological processes,” warned C. Lloyd Morgan, a respected 19th-century British psychologist. Morgan believed that higher mental faculties should only be considered as explanations if faculties that stand lower in the scale of psychological evolution and development could not explain a behavior. This is known as Morgan's Canon, and it is a fundamental precept of comparative animal psychology.

Clever Hans

Clever Hans and Wilhelm von Osten.

In the face of rising media attention, the German board of education appointed a commission to investigate von Osten's scientific claims. This Hans Commission consisted of a veterinarian, a circus manager, a cavalry officer, a number of schoolteachers, and the director of the Berlin zoological gardens. Following extensive testing, the commission concluded in 1904 that no tricks were involved in Hans's performance. As far as they could tell, Hans’s mental abilities were real.

The commission then passed off the evaluation to Oskar Pfungst, a young psychologist who worked in the laboratory of the man who headed the commission. Pfungst designed a careful set of experiments and began testing Hans.

To rule out the possibility that von Osten was secretly feeding Hans the answers, he removed von Osten from the scene and was pleasantly surprised when Hans was able to get the correct answer even when von Osten wasn’t the one asking the questions. With the likelihood of fraud out of the way, von Osten began examining whether the horse was getting clues, unknown to the questioner, by reading subtle changes in the questioner’s demeanor, posture, tone, etc. To confirm this, Pfungst kept the answers hidden from the questioner. At once, Hans’ accuracy dropped.

Clever Hans

Clever Hans demonstrating his arithmetic skills.

Oskar Pfungst explains the procedure of this test:

Mr. von Osten whispered a number in the horse's ear so that none of the persons present could hear. Thereupon I did likewise. Hans was asked to add the two. Since each of the experimenters knew only his own number, the sum, if known to anyone, could be known to Hans alone. Every such test was immediately repeated with the result known to the experimenters. In 31 tests in which the method was procedure without knowledge, 3 of the horse's answers were correct, whereas in the 31 tests in which the method was procedure with knowledge, 29 of his responses were correct. Since the three correct answers in the cases in which procedure was without knowledge evidently were accidental, the results of this series of experiments show that Hans was unable to solve arithmetical problems.

Pfungst also found that when the questioner stood farther away from Hans than normal, the horse had trouble correctly answering the questions.

Oskar Pfungst wrote:

The usual distance was one-quarter to one-half meter. This holds for all tests hitherto described. Seventy tests which were made for the purpose of discovering the influence of change in distance showed that the reaction of the horse upon the customary signal of the head-jerk was accurate up to a distance of three and one-half meters. At a distance of three and one-half to four meters there suddenly occurred a fall of 60-70% in the number of correct responses. At a distance of four to four and one-half meters only one-third of the responses were correct, and at a distance beyond four and one-half meters there were no correct responses. The greater number of these tests were made in our presence by Mr. von Osten, who was under the impression that we were testing the accuracy of the horse's hearing, whereas we were really testing the accuracy of his perception of movements.

Every test Pfungst conducted, Hans failed miserably. Even his memory—some people tried to explain Hans’ supposed intelligence on muscle memory—was found to be average, and unsuitable of performing the astonishing feats that had been claimed for him.

Clever Hans

Clever Hans before an audience in 1904.

After it became evident that the horse was entirely dependent on external stimuli from the questioner, Pfungst began observing the questioners instead to understand what kind of clues humans subconsciously gave away. The psychologist immediately noticed that a questioner’s breathing, posture, and facial expression involuntarily changed each time the hoof tapped. Pfungst observed a marked tension in the muscles of the questioner’s face and neck, as the horse approached the correct answer. As soon as the final, correct tap was made, the tension was suddenly released. This provided a cue for Hans that he should stop tapping.

Once Pfungst learned to read these barely perceptible cues as good as Hans did, he carried out further tests in which he played the part of the horse. Pfungst asked his subjects to concentrate upon a particular number. Pfungst would then tap out the answers solely by observing the body language of his human subjects. Even more incredible was that the subjects seemed unable to suppress these subtle cues, even when made aware of them.

Oskar Pfungst’s research proved that Clever Hans was an excellent observer who could read the microscopic signals in the face of his master, and this ability greatly exceeded that of the average man. But his intelligence, by no means, approached that of a human.

Clever Hans

Clever Hans in 1910.

Oskar Pfungst’s conclusions, that researchers can unknowingly lead a subject, is now recognized as widespread in research involving human subjects as well as animals. This is known today as the “Clever Hans Effect”. To prevent prejudices and foreknowledge from contaminating experimental results, many experiments in the fields of perception, cognitive psychology, and social psychology are “double-blind” where many information about the experiments are withheld from both the researchers and the subjects until after the experiment is complete. The Clever Hans Effect has also been observed in drug-sniffing dogs, where cues from the handler are transmitted to the dogs resulting in false positives.

Despite Pfungst’s exposé, Clever Hans never stopped being a sensation. His owner, von Osten continued making tours throughout Germany drawing crowds wherever he put up a show. von Osten never charged a dime for these exhibitions. He genuinely believed in Clever Hans’ unmatched intelligence.

Wilhelm von Osten died in 1909, after which Hans changed owners several times, until he was drafted as a military horse at the beginning of World War I in 1914. His fate is unknown, but some believe that Hans was killed in action in 1916.

Wilhelm von Osten

Wilhelm von Osten.

# Oskar Pfungst, “Clever Hans (The horse of Mr. Von Osten): A contribution to experimental animal and human psychology”,
# Laasya Samhita and Hans J Gross, “The “Clever Hans Phenomenon” revisited”,
# Alan Bellows, 
# NY Times,
# Karin-D’Arcy, M. Rosalyn, “The Modern Role of Morgan’s Canon in Comparative Psychology”,


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