Tech UPTechnologyHans the Wise, the mathematician horse

Hans the Wise, the mathematician horse


Horses , in general, show a more than acceptable intelligence. They are able to learn more or less complex tricks and remember them for a long time. They are very perceptive animals, which can easily respond to gestures and commands from their human owners, even when they are very subtle . And as it happens among people —or among any animal of any species—, there are individuals more capable than others.

At the beginning of the 20th century, of all the horses, there was one that broke all the moulds. His owner, a retired school teacher, Wilhelm von Osten , tested various teaching methods for four years on Hans , a horse who assimilated knowledge with unusual speed and even more surprising efficiency.

The exploits of Hans the Wise

For years, von Osten taught the horse to count, add, subtract, multiply, and divide . To perform operations with fractions. He taught him the times of the day and to read them on a clock, to read calendars, musical notes, he even learned the cards of the deck. Hans apparently assimilated all this knowledge as if it were a child.

Obviously, the horse had no way of responding to the questions in a spoken way, but instead responded with head movements or knocks on the ground , the meanings of which were previously defined. Thus, if von Osten presented him with the “3 + 4” operation, Hans would hit the ground seven times. If von Osten played a note pitched in C on his harmonica, the horse would nod three times—corresponding to the letter “C” in Anglo-Saxon notation—and if they asked him what day would be next Friday, he would answer. The questions could be both oral and written, and the horse answered correctly up to 89 % of the time ; and when he didn’t, he stayed amazingly close.

Of course, the news of Hans the Wise —as he was known— spread like wildfire until it reached the scientific circles of the time. The horse aroused the interest of the philosopher and psychologist Carl Stumpf , who convened an investigative committee made up of 13 people, including a veterinarian, several school teachers, a cavalry officer, a circus administrator and the director of the gardens. Berlin zoos. The commission concluded, in the year 1904, that Wilhelm von Osten did not do any tricks at the exhibitions with Hans . They were before a genius among horses.

The secret of the horse Hans

Biologist and psychologist Oscar Pfungst , who was a volunteer assistant in Stumpf’s lab at the time, was not very convinced by these results. So he started running more tests on the horse.

He began by substituting for the person asking the question , to ensure that the committee’s conclusions were true, and that von Osten was not cheating. The horse continued to answer the questions correctly.

But that didn’t prove it was because he knew the answers. So he tried something else.

He had Hans answer certain questions , of the same level of difficulty, but whose answer von Osten did not know in advance . For example, placing an operation on the board, but preventing the handler from seeing it while asking the horse to solve it. The 89% of success in the answers was reduced to a bare 6% ; a result that, since he was never asked questions about numbers that were too large, could well be explained by random answers.

This proved that the questioner was giving Hans the correct answer , when he knew it. However, it happened even when it wasn’t von Osten.

It’s not that he cheated, it’s that the person who was there, whoever it was, was giving him the solution unintentionally . This was the conclusion that Pfungst reached when he did yet another test: asking the horse without making eye contact with the handler, in a method that was called “blind”.

Reading the ideomotor effect

The artifact that happened in the process is called the ideomotor effect . Hans was not answering the questions by an intellectual act, but was observing the reactions of the questioner . When the horse got closer to the correct answer, the person showed changes in body language, caused by the expectation of success; Hans interpreted such changes as the right time to stop hitting the ground, and he was right . Without von Osten, or whoever asked the question, knowing that he was providing those clues.

Because, as has already been indicated, horses are very perceptive animals, which respond easily to gestures and orders from their owners, even when they are very subtle . Hans , without a doubt, was an exceptional animal, but not because he knew how to solve mathematical equations, but because he was capable of capturing such subtle signals that not even humans were aware of emitting them.

The perception of these small involuntary movements and reactions that make up the ideomotor effect can be trained; In fact, certain deduction techniques such as cold reading take advantage of the identification of this type of reaction to give the impression of guessing things about someone , when only the reactions are being read. These people do a slightly more sophisticated version of what Hans did, but with the same base.

The danger of anthropomorphization

When it became clear that Hans did not possess complex mental ability, but used simple stimulus-response interaction during his performances, reading human reactions, many people were very disappointed, especially von Osten.

However, on many occasions we humans continue to fall into the same bias when we observe animals.

Many of the mental abilities attributed to animals in popular culture have no solid scientific backing and are based on biased interpretations of anecdotal observations. The Wise Hans effect adds to the confirmation bias, making us believe that our expectation is true based on an anecdote, ignoring all the times it was not met.

What happened over a century ago with Hans the Wise is still happening today. Many assume that the animal acts as they would, solving the equation, ignoring that the animal may have other abilities than human ones, such as reading body language. This anthropomorphization of animals , attributing to them capabilities, and even human thoughts and feelings, leads to misunderstandings and can have negative repercussions on them , by performing actions or sympathizing with images that we would think would be for their benefit, and that in reality they are not. .

Let’s remember that terrible viral video from 2018 of a rat that seemed to be taking a shower, rubbing himself with the soap ; rodent behaviorists were pretty sure that the protagonist—not a rat, but a pacarana— was greatly stressed , and her movements weren’t to wash herself, but to try to get rid of the soap. That video did not show more than a form of animal abuse .

To avoid falling into the effect of Hans the Wise , it is necessary to carry out interactions with animals in very specific conditions, which minimize direct contact. There is very good science studying the cognitive abilities of animals using methodologies that minimize or even eliminate these biases. After all, in reality, they have their own abilities, thoughts and feelings , and they do not have to be the same as ours.


Anders, C. J. et al. 2022. Finding and removing Clever Hans: Using explanation methods to debug and improve deep models. Information Fusion, 77, 261-295. DOI: 10.1016/j.inffus.2021.07.015

Ladewig, J. 2007. Clever Hans is still whinnying with us. Behavioural Processes, 76(1), 20-21. DOI: 10.1016/j.beproc.2006.10.014

Pfungst, O. 1911. Clever Hans (the horse of Mr. von Osten): a contribution to experimental animal and human psychology. (C. L. Rahn, Trad.). Henry Holt and Company.

Prinz, W. 2006. Measurement versus appearance: Oskar Pfungst examines clever Hans. Psychological Review, 57(2), 106-111. DOI: 10.1026/0033-3042.57.2.106

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