It’s pretty easy to hoax people. We all want to be deceived, but only up to a point. Some hoaxes are fun and pleasant, others malicious and unpleasant. We’d like a way to tell the difference (Robert Carroll).

Sep 19, 2010

The Math Horse “Clever Hans” (Education level as for 14 years old student)

In the late 1800s, a German high school mathematics instructor named Wilhelm Von Osten was pushing a few scientific envelopes from his home in Berlin. Among other things, he was a student of phrenology, the now discredited theory that one’s intelligence, character, and personality traits can be derived based of the shape of one’s head. But it was his keen interest in animal intelligence that would ultimately win him fame.

Von Osten firmly believed that humanity had greatly underestimated the reasoning skills and intelligence of animals. To test his hypothesis, he took it upon himself to tutor a cat, a horse, and a bear in the ways of mathematics. The cat was indifferent to his efforts, and the bear seemed outright hostile, but the Arab stallion Hans from Russia, showed some real promise. With further tutelage, Hans the horse learned to use his hoof to tap out numbers written on a blackboard. Much to Von Osten’s delight, jotting a “3 on the blackboard would prompt a tap-tap-tap from his pupil, a feat which Hans could repeat for any number under ten.

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Encouraged by this success, Von Osten pressed his student further. The scientist drew out some basic arithmetic problems on his chalkboard, and attempted to train the horse in the symbols’ meanings. Hans had no problem keeping up with the curriculum, and soon he was providing the correct responses to a variety of math problems including basic square roots and fractions. Hans was proving to be a clever horse indeed.
It took about two years to complete the training which made the horse so famous. It mastered the four fundamental rules of arithmetic, changed common fractions into decimals and back again, and could give the day of the month. It knew how to tell the time by the clock and could, for example, answer the question, "Between which figures is the small hand when it is twenty-five to eight?" The horse also had an astonishing appreciation of music. If one played the dominant seventh chord D, F, A, C, it shook its head and indicated that the C should be left out to turn it into a more harmonious minor chord. (Katz, 1953)

Starting in 1891, Von Osten began parading “Clever Hans” all over Germany to show off the horse’s mathematical proficiency. As word of the spectacle spread, Hans’ free exhibitions began drawing larger and larger crowds of curious onlookers. They were seldom disappointed.

“If the first day of the month is a Wednesday,” Von Osten would ask Hans, who had learned to respond to verbal questions, “what is the date of the following Monday?” Six hoof-taps would follow. “What is the square root of sixteen?” Four taps. Von Osten also explained to the astonished crowds that Hans could spell out words with taps, where one tap is an “A”, two taps a “B”, and so on. Hans would then demonstrate this talent by spelling out the names of people he knew, and responding to simple questions. He could also tap out the time of day. Though he made mistakes occasionally, his accuracy was found to be roughly 89%. By some estimates, Hans’ grasp of mathematics was equivalent to a fourteen-year-old’s.

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Naturally there were many skeptics, particularly after the New York Times featured the crafty horse in a front-page story. Germany’s board of education asked to conduct an independent investigation into Hans’ abilities, and Von Osten agreed. He was a man of science, after all, and he knew that there was no fraud to expose. The board members assembled a number of scientific minds to join the Hans Commission, including two zoologists, a psychologist, a horse trainer, several school teachers, and a circus manager. Following extensive independent testing, the commission concluded in 1904 that there was no trickery involved in Hans’ responses; as far as they could tell, the horse’s talents were genuine.

The Hans Commission then passed the investigation on to Oskar Pfungst, a psychologist with some novel ideas on how to best unravel the mystery. Pfungst erected a large tent to house his experiments, thereby removing the contaminating effects of outside visual stimuli. In order to produce a sufficient data set, the scientist compiled a very large list of questions, and carefully outlined the different variables that were to be considered. Thus Pfungst began his interrogation of Hans.

As expected, Hans performed very well when questions were posed by his owner, Von Osten. He also received very high marks for accuracy with other questioners under normal conditions. But when the experiment called for the questioner to stand farther away, something interesting happened: the horse’s accuracy diminished somewhat, though it wasn’t immediately clear why.

It was the final two variables which proved to be the most revealing. In instances where the questioner didn’t know the answer to a question in advance, the accuracy of Hans’ responses plummeted to nearly zero. Likewise, when the questioner was completely concealed from him. It seemed that Hans’ cleverness hinged on his ability to have an up-close, unobstructed view of the person who knew the correct answer. The researchers also found evidence that hounding a horse with questions he can’t answer leads to painful horse-bites.

Pfungst continued his experiments, but with a new emphasis on observing the humans interacting with Hans. The psychologist immediately noticed that each questioner’s breathing, posture, and facial expression involuntarily changed each time the hoof tapped, showing ever-so-slight increases in tension. Once the “correct” tap was made, that subtle underlying tension suddenly disappeared from the person’s face, which Hans apparently took as the cue to stop tapping. Pfungst also noticed that this tension was not present when the questioner was unaware of the correct answer, which left Hans without the necessary feedback.

Though the experiment strongly indicated that the horse probably had no real grasp of math, it did uncover an extraordinary insight. Hans wasn’t dipping into a reservoir of intellect to work out the answers, he was merely being receptive to the subtle, unconscious cues which were universally present in his human questioners. There is evidence to indicate that horses may possess an enhanced sensitivity to inconspicuous body language, perhaps as a key part of their social interactions with other horses.

Once he became aware of these cues, Pfungst was able to rival Hans’ accuracy by placing himself in the “horse” role, tapping out his answers to researchers’ questions and keeping a sharp eye on their body language. Even more interestingly, he discovered that questioners seemed unable to suppress these subtle cues, even when made aware of them.

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In the intervening years, it has been found that many animals are sensitive to such cues from their human masters. Today, the term “Clever Hans Effect” is used to describe the influence of a questioner’s subtle and unintentional cues upon their subjects, in both humans and in animals. To prevent prejudices and foreknowledge from contaminating experimental results, modern science employs the double-blind method where researchers and subjects are unaware of many details of the experiment until after the results are recorded. For instance, when drug-sniffing dogs undergo training, none of the people present know which containers have drugs in them; otherwise their body language might betray the location and render the exercise useless.

Wilhelm Von Osten never really accepted the Clever Hans explanation, so he and his horse continued to put on their math-and-body-language show throughout Germany for some time. Throughout their career, the pair continued to draw large and enthusiastic crowds. Though Hans the horse knew nothing of math and had a flimsy grasp of German at best, his ability to fool so many people for so long clearly gives him a legitimate claim to cleverness. Considering his gifts in reading humans’ unconscious tells, there’s also little doubt that with some opposable thumbs and a stack of high society, Hans would have made one hell of a card player.


Unfortunately, Hans's exemplary case has also had more negative consequences on the development of psychological science. It has imposed an aura of suspicion onto the whole area of research on the representation of numbers in animals. Ironically, scientists now meet every single demonstration of numerical competence in animals with the same raised eyebrows that served as a cue to Hans! Such experiments are immediately associated, consciously or not, with Hans's story and are therefore suspected of a basic flaw in design, if not of downright forgery. This is an irrational prejudice, however. Pfungst's experiments showed only that Hans's numerical abilities were a fluke. By no means did they prove that it is impossible for an animal to understand some aspects of arithmetic. For a long time, however, the scientist's attitude was to systematically look for some experimental bias that might explain animal behavior without resorting to the hypothesis that animals have even an embryonic knowledge of calculation. For a while, even the most convincing results failed to convince anyone. Some researchers even preferred to attribute to animals mysterious abilities such as "rhythm discrimination" faculty, for instance, rather than admit that they could enumerate a collection of objects. In brief, the scientific community tended to throw out the baby with the bath water.

The Clever Hans effect

Pfungst made an extremely significant observation. After he had become adept at giving Hans performances himself, and fully aware of the subtle cues which made them possible, he discovered that he would produce these cues involuntarily regardless of whether he wished to exhibit or suppress them. Recognition of this striking phenomenon has had a large effect on experimental design and methodology for all experiments whatsoever involving sentient subjects (including humans).

The risk of Clever Hans effects is one strong reason why comparative psychologists normally test animals in isolated apparatus, without interaction with them. However this creates problems of its own, because many of the most interesting phenomena in animal cognition are only likely to be demonstrated in a social context, and in order to train and demonstrate them, it is necessary to build up a social relationship between trainer and animal. This point of view has been strongly argued by Irene Pepperberg in relation to her studies of parrots (Alex), and by Allen and Beatrix Gardner in their study of the chimpanzee Washoe.

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If the results of such studies are to gain universal acceptance, it is necessary to find some way of testing the animals' achievements which eliminates the risk of Clever Hans effects. However, simply removing the trainer from the scene may not be an appropriate strategy, because where the social relationship between trainer and subject is strong, the removal of the trainer may produce emotional responses preventing the subject from performing. It is therefore necessary to devise procedures where none of those present knows what the animal's likely response may be.

As Pfungst's final experiment makes clear, Clever Hans effects are quite as likely to occur in experiments with humans as in experiments with other animals. For this reason, care is often taken in fields such as perception, cognitive psychology, and social psychology to make experiments double-blind, meaning that neither the experimenter nor the subject knows what condition the subject is in, and thus what his or her responses are predicted to be. Another way in which Clever Hans effects are avoided is by replacing the experimenter with a computer, which can deliver standardized instructions and record responses without giving clues.

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