Clever Hans: The Horse That Can Perform Arithmetic Operations

Do you think a horse can do square root calculations?
What would your first reaction be if you had the chance to watch a horse that is claimed to be able to perform arithmetic operations? Would you think that horses are very intelligent animals and can perform such performances with a little training?
Have you ever thought about how our reactions and facial expressions can affect the thought system of the other person?
Let’s look for answers to these questions. and meet the legendary horse “Clever Hans”…

Let’s Meet Clever Hans…

Wilhelm von Osten, a mathematics teacher at a high school in Germany in the early 1900s, had an unexpected experience in his routine and regular life. One day, he realizes that his horse, Hans, recognizes the numbers written on the board. The horse recognized the number on the board and hit the ground with his hoof up to that number. Realizing the situation, Osten excitedly began to introduce the symbols to Hans one by one. Their communication had become stronger. Hans the Horse, on the other hand, was an enthusiastic student who followed Osten carefully. He was improving himself almost every day and was a quick learner.

Osten trained Hans for four years, and at the end of this training, he claimed that Hans the horse can perform arithmetic operations and traveled all over the country to participate in shows with Hans. As The reputation and the interest of Hans the Horse increased, so did the suspicions. How can a horse do the four mathematical operations that are challenging even for us when we were learning them in elementary school and indicate the answers to the other person by hitting the board with his hoof?


Smart Hans

What Else Could Hans Do?

Encouraged by the rapid progress of Hans the Horse in mathematics, Osten also taught him the alphabet. Hans tapped as much as the letters were placed in the alphabet, as he was learning the letters. For example, when he learned the letter “B”, the second letter in the alphabet, he learned that he had to hit the ground twice. This was a miraculous development! Hans had learned not only numbers but also letters.

Recognizing the numbers and making as many hoof kicks as the numbers, Osten decided to take Hans’ training a step further. Addition, subtraction, multiplication, and division were the next lesson. Osten even managed to teach fractional operations. Hans was good even at square root numbers. He had learned to take the square root and make as many hoof strikes as the result of the operation.

Developing his skills day by day, Hans became able to track day and hour. Hans was able to tell what day of the week they were on with hoof kicks and not only that,  he could allegedly understand the time and tell it as well.

Hans, whose fame spread all over the world, was increasing his abilities day by day. It was even claimed that he once knew the composer of the melody he heard and was able to convey the composer’s name through syllables. All the questions that were addressed to the horse in the performances that were in front of a large audience were answered!


Osten und Hans
Clever Hans and Wilhelm von Osten

Was Hans Really Talented?

The number of people who came to watch Hans was increasing as his fame was growing bigger. The audience couldn’t believe what they saw, they were almost mesmerized. Of course, there were those who supported Hans and Osten, as well as those who did not believe and tried to prove the contrary. Osten allegedly cheated. A commission was established, the source of Hans’s success was investigated and the theory was tried to be disproved. Indeed, in 1904 the commission admitted that no cheating had been done.
However, this issue was still not closed in the scientific community. Those who did not believe what happened were not convinced that there was no cheating involved. Oskar Pfungst, the assistant of German philosopher and psychologist Carl Stumpf, who studies animal psychology, decided to examine Hans in 1907. As a result of these investigations, striking facts emerged. In fact, Hans, contrary to popular belief, does not perform arithmetic operations. He was completing his strokes according to the movements, facial expressions, and reactions of the person in front of him.
Osten was unaware of this fact, so he was not sny an accusation that could be called cheating. His involuntary gestures and reactions, reinforced by his excitement, gave Hans a clue. As a result of this awareness, Pfungst wanted questions to be asked by different people, not by Osten. He also preferred to observe Hans in the absence of his sitter and spectators, avoiding taking cues from them.



Seeing that Hans also gave correct answers to questions asked by strangers from the audience eliminated the possibility of cheating. At this point, a different issue emerged. If the person asking the question knew the correct answer, Hans could know the answer too, but if the person asking the question didn’t know the answer, Hans couldn’t give the right answer either! When Pfungst studied this incident, he noticed that as Hans’ hoof approached the right number of knocks on the ground, there were minor changes in the pose and facial expression of the questioner, which could be considered clues for Hans. Hans, who was able to analyze these changes, realized that he was getting close to the right number. Similarly, Hans couldn’t answer the question if he couldn’t see the questioner. In short, the involuntary signals given by the questioner were clues telling Hans what number to stop.
The clever horse’s life was not easy after Hans’ teacher Osten passed away in 1909. Unfortunately, the incredible observer “Clever Hans” served as a military horse during World War I and died in 1916.

What is the Clever Hans Effect?

After Pfungst’s work, it became clear that the audience’s expectations and small changes in their response, which used to be thought to be imperceptible, had a serious impact on the results. Of course, Hans couldn’t sense and answer math questions or tell us the time, but he could read the other person’s body language with care and precision. Pfungst, who published his research results in 1909, proved this.

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While communicating, our mouth, eyes, in short, our entire face, make many involuntary movements and reactions. These involuntary contractions do not escape the horse’s extremely keen visual perception, thereby enabling it to respond as we hoped for. As the research shows, when we do not know the answer, we cannot give any signal to it, so it will not be possible for the horse to perceive it and respond accordingly.

In our previous article titled “Self-Fulfilling Prophecy: The Pygmalion Effect”, you can find the opportunity to examine this subject in more detail from a psychological perspective, as well as high expectations, which can help a person perform better in a certain area.
Therefore, we can analyze the thoughts of the other person to a certain extent, thanks to mimics and micro-expressions that are displayed unconsciously. It seems that Clever Hans made his name known to the world by performing mimic analysis better than any of us, even if he can’t do math operations…

References and Future Readings

Samhita, L., & Gross, H. J. (2013). The “Clever Hans Phenomenon” revisited. Communicative & integrative biology6(6), e27122.

Wikipedia. (2022). Clever Hans. https://tr.wikipedia.org/wiki/Ak%C4%B1ll%C4%B1_Hans

The proofreading has been done by Asu Pelin Akköse and Mete Esencan.

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Sima Türküner

Hello there! I'm Sima Turkuner. I am a Political Science and Public Administration student at METU. I love to research, learn and share what I have learned. I would like to share with you my articles on topics that I find interesting.

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