Number Sense in Animals

From horses that do math (not really) to ants that count, here's a compilation of some of my favorite research on the numerical abilities of animals.

Transcript | References | Media Credits

Recommended Books

The Number Sense: How the Mind Creates Mathematics

What Counts: How Every Brain is Hardwired for Math

More about Number Sense in Animals


Do you think horses can do math? Because there was this one horse named Clever Hans who supposedly could solve problems like 2/5 + 1/2. I don’t know how, but he gave the correct answer 9/10 by tapping his hoof 9 times and then 10 times. And he even answered questions posed by random audience members, not just his master. He was a bit more shy around strangers, but that’s understandable, because “of affection on the part of Hans, who for the last four years had had intercourse only with his master” (Pfungst, 1911, p. 19). I’m so immature. :D (Note: I just had to highlight this perfect example of how words develop new meanings over time! Isn’t language interesting?)

Anyway, this horse was quite a sensation. He was featured in the New York Times in 1904, and then a commission was formed to see if Hans really could do math. And as the New York Times published later in 1904, “Expert Commission Decides That the Horse Actually Reasons”. You have to read that article. I can’t believe that 13 smart people all thought this horse could actually solve problems like 2/5 + 1/2! I mean, I can’t even do that! I haven’t gotten to fractions yet. (Note: I will make a future video on fractions once I do get there!)

Luckily, one person was not convinced. His name was Oskar Pfungst, and he tested this horse much more thoroughly and wrote a 200-page book on his findings. He found that people were unconsciously giving the horse subtle cues when he got close to the correct answer, like jerking their head up a little bit or looking tense. So, if the person asking the question didn’t know the answer, Clever Hans didn’t know the answer either.

And guess what? The trick is still done today. (Video of a horse on Animal Planet answering “what’s six plus six?” by tapping its hoof 12 times. Then a video of a dog on Opera tapping its paw to answer “what’s two times three?”)

For a long time after this Clever Hans incident, all the scientists were very skeptical about animal intelligence. Maybe if this Clever Hans thing never happened, more research would’ve been done by the time Jean Piaget was around, and Piaget wouldn’t have thought children were born blank slates, and his theories wouldn’t have influenced educators, and educators wouldn’t have ruined math for an entire generation of students! But that was my last video. (Note: Piaget’s theories did influence educators, but there were many other factors that contributed to the New Math movement and its failure. This was just an exaggerated, hypothetical example to make the point that Clever Hans had an influence that lasted for many years.)

Anyway, here’s what Monsieur Piaget has to say about animals doing math:

"if [mathematics] was pre-formed [...] we would have to go back to invertebrates to find the source of mathematics." (Piaget on Piaget: The Epistemology of Jean Piaget (1977) by Yale University Films)

I’m so glad you said that, Piaget. And I really wish you were still around to see this:

(Video clip of an experiment showing a honeybee differentiating two from three. See study for details.)

Invertebrates can do math. Uh, OK, sort of. They have a sense of numbers, though, just like us. Honeybees “can not only differentiate between patterns containing two and three elements, but can also use this prior knowledge to differentiate three from four, without any additional training” (Gross et al., 2009).

And a weird experiment on desert ants suggests that they actually count how many steps they take to get to their food and then use that knowledge to walk the same number of steps to get back to their nest. How do we know that? Well, you have to watch this dorky cartoon from NPR:

The scientists put some ants on stilts (I didn’t know you could put ants on stilts!), so that way they would take longer steps. And for another group of ants, they cut off part of their legs so they would take shorter steps! The ants on stilts took the same number of steps back home and walked past their nest, while the stumpy-legged ants took the same number of steps and stopped before they got back home, and so the best explanation we have is that apparently ants can count!

(Video clip from NPR’s ant video posted above, in which one ant says, “I want my legs back.”)

Oh, and here’s another one of my favorite studies. They compared guppies to college students and found that “the students and guppies showed almost identical performance patterns” (Agrillo, Piffer, Bisazza, and Butterworth, 2012).

Oh OK, maybe not identical; the student test didn’t involve any swimming. It was actually very similar to the test I took at Panamath, where you have to choose the larger of two sets of dots. The fish, on the other hand, were placed in a tank like this and tended to swim to the group with more fish. Both students and fish can distinguish numbers up to four, and beyond that we both rely on the ratio between the groups; distinguishing 6 from 24 is easier than 6 from 8.

And with training, some animals can do way, way more than that, like Ayumu the chimpanzee and even Alex the African grey parrot.

(Learn more about Alex the parrot and Irene Pepperberg’s incredible research in this PBS video and this video on YouTube.)

"This system, this gut sense of number, is something evolutionarily very old. I mean rats have it, pigeons have it..." (Dr. Justin Halberda, in What Makes a Genius?)

Ants have it, bees have it, fish have it, and lions, birds, monkeys, apes, dogs, cats, dolphins, bears, raccoons, elephants, and sea lions have it. Salamanders try to eat the video showing more flies. Baby chicks choose the larger group of balls. Horses can’t add fractions but they can tell the difference between two and three. And I bet that penguins and giraffes and velociraptors and all other animals have it too! It’s not just us.


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