Hmm. Perhaps.. but notice how the experimenter heads for the bucket with fewer apples to remove them. Is the elephant just watching this? Remember Clever Hans!
Von Osten’s method was quite elementary. He began by demonstrating counting to Hans, using spoken words in the company of objects. After a time Von Osten dispensed with objects and simply used numerals on a blackboard. Hans concentrated intently on his task, tapping numbers out with his hoof. By the end of his schooling, Hans could tap out correct answers for questions ranging from addition, simple square roots and even the names of people he knew by tapping out letters in a simple code. Hans could also tell the time when asked. A great many investigators, including a special commission of thirteen people of varied background in 1904 led by Carl Stumpf, director of the Berlin Psychological Institute, were absolutely convinced of the startling intelligence of Hans the horse. Even if Von Osten was absent, Hans would still come up with the correct answers.
The Big Disappointment
Stumpf’s commission was followed up by a very carefully planned investigation conducted by Oskar Pfungst. Pfungst began his testing of Hans by using numbered flash cards with which Hans was already familiar. Pfungst controlled the situation very carefully: first, Von Osten was allowed to see each number before Hans did – and Hans continued to be very clever. Then Pfungst instructed Von Osten to show Hans the cards without looking at them. Suddenly Hans’s answers became random. What happened?
Pfungst concluded that somehow Von Osten, when he knew the answer, was giving it to Hans. This hypothesis was confirmed when Pfungst had Von Osten stand behind Hans and ask him to count. Again, the horse was stumped. Somehow, Hans was figuring out the correct answer by looking at the interrogator.
Next, Pfungst turned to Von Osten and watched the teacher’s behaviour. Through careful observation, Pfungst was able to create a sort of dictionary of Von Osten’s unconscious physical cues that were being read by Hans. Von Osten, or any other interrogator of Hans, would subtly change posture as Hans’s tapping was expected to start and would change again as Hans approached the correct answer. Pfungst gave the final demonstration of the accuracy of his conclusions by cueing Hans to count without speaking, and to provide answers to questions not asked.
Conclusion? Clever Hans was a clever horse, but he was not a mathematician. – bbc