In the late 1800s in Berlin, there was a horse named Clever Hans that could do math. His owner, a high school math teacher named Wilhelm Von Osten, spent four years teaching the horse not just math, but spelling, music, colors, the calendar, and other things a well-educated horse should know.

Clever Hans would tap a hoof to answer questions put to him. And 90 percent of the time, he got the right answer.

“What is three plus three plus two?” The horse would give eight taps.

“If today is Monday the first of September, what is Friday’s date.” Five taps.

“What is the square root of 16?” Four taps.

Spelling by the tap method was slow, but Clever Hans could do it, giving one tap for A, two for B, and so on.

If Von Osten sang a bit of a classical music theme and asked Hans to name the composer, the horse would patiently tap out the name.

Von Osten and Clever Hans began touring Germany giving demonstrations. Even though the crowds that gathered to witness this phenomenon grew larger and larger, no entrance fees were charged.

There has to be a trick to it, everyone said. No horse could be that smart. Von Osten must somehow be giving Clever Hans the answers. To prove that there was no hoax, Von Osten would leave the room and let someone else, anyone else, ask the questions. Hans still got the answers right.

The German Board of Education formed a group called the Hans Commission to study the horse. The group included two zoologists, a psychologist, a horse trainer, several school teachers, and a circus manager. After a year of testing, the commission concluded in 1904 that there was no trickery involved. Clever Hans was indeed clever.

Yes, the horse was clever, but not in the way everyone thought. A psychologist named Oskar Pfungst managed to solve the mystery. He noticed that if the questioner didn’t know the answer, then neither did Hans. If the questioner was placed further away, Hans’s accuracy dropped. And when the face of the questioner was covered, Hans couldn’t answer correctly.

Pfungst noticed that there was a slight tension in a questioner’s breathing, posture, and facial expression as Hans was tapping. When the correct number of taps was reached, the tension disappeared. Clever Hans was taking subtle visual clues from the questioner — Von Osten or whoever — to know when the correct number of taps had been given.

Today, the term “Clever Hans Effect” is used to describe the ability in both animals and humans to perceive and be influenced by a questioner’s unintended clues.

In research, a procedure called the double-blind method is often used, in which neither the researchers nor the subjects know the details of an experiment until it is over. Is this person receiving the medication or the placebo? Someone knows, of course, but not the researcher assigned to hand out the pills. That way, no unintended signals can be sent, and the subject can’t Clever-Hans a reaction.