In a recent input with Richard we were faced with the question “do you think animals can count?”, after a few moments of silence and deep thought this sparked a very interesting discussion on whether or not we thought animals have any form of numerical understanding. Some of us making suggestions like “my dog knows to wait for a count of 3 before he gets a treat” or “if your cat knows exactly when you will get home every night, is that an understanding of time?”. All of these questions left me unsure of my opinion on the question, but as am very big animal lover myself I would love the idea of my cat being able to do times tables or being a secret maths genius, but I was sceptical. The issue came up in discussion that animals probably don’t have the same mathematical understanding that humans do but perhaps just are just trained by owners to appear to understand simple mathematics. For example a dog can just be trained to know that after the sound “one, two, three” this is when they are given a treat rather than being aware this is counting. We then went on to look at a few studies of animals who appeared to have the ability to count.
Clever Hans
The First animal we looked at and discussed was a horse names ‘Clever Hans’. In the early 1900s Clever Hans was touring with his owner Wilhelm Van Osten who was claiming the horse had the ability to count, he claimed he was able to teach it basics sums including addition, division even square roots. Hans would be able to give the answer to any question by signalling the correct number with taps of the hoof , in fact 86% of the time Van Osten asked Hans a question he was able to give the correct number of taps. It really does sound quite incredible, doesn’t it. Well after many scientists became sceptical of the horses knowledge, they began to test the legitimacy of this in various ways. One way they used to test if the horses knowledge was real or whether it was to do with something the trainer was signalling, was they made it so that the horse was unable to see Van Osten when he was asking the question. This test along with others in fact found that the reason the horse was able to tap its hoof the correct amount of times was that its owner with giving it very subtle ques of when to start and stop tapping its hoof in order to get the correct answer. So rather than being a mathematical genius Hans was simply following commands given by his owner, much like a dog being told to “sit”.
Ayumu the Chimpanzee
After Clever Hans’ unsuccessful attempt at convincing us that animals can understand numbers, we then looked at some other examples including; ants, lions, chicks and bees. Yet all of these were still unable to provide me with an answer to the lingering question “can animals count?”, but potentially the most convincing of all of these was the example of Ayumu the chimpanzee.
This study showed that when shown numbers from 1-9, the chimps were able to put them in order(to be rewarded with a peanut if they were correct). Although this initially seems to be very impressive, I then began to think surely if the chimp was just able to remember the correct order of the visual symbols they click when they receive a peanut, this doesn’t really have anything to do with the numbers or values the hold. It then goes on to show that when the numbers are flashed and then covered up quickly, the chimps can still remember and correctly order the numbers from 1-9 (this particular chimp Ayumu only got this wrong once!!). Again I was very impressed by this, but I still don’t see how this proves mathematical understanding rather than just an extremely good memory. The last test they did on Ayumu and the other chimps is what had me almost convinced, in the final test not all of the 9 numerals were shown and were covered up the same as the previous test, again the chimps were able to put the numbers in the right order despite there being some missing. This is what has me more convinced that these animals may be able to understand numbers or the idea of counting, when their is some missing it proves that the chimps are aware that some numbers always come before others .. so does this count as being able to count?
Even after looking at this within the class input and then also further in my own time, as much as I wanted to believe it I still am not quite sure if I’m quite convinced that animals can count or understand maths the way in which us humans do. I feel “can animals count?” would be a great question to ask a class of children, allowing them to use their mathematical understanding to discuss and share their own opinions and come to their own conclusions about if they think animals can understand maths, whilst still being a fun and light hearted way to approach mathematics.
