Can Your Jack Do Math?

Can a dog do math? We're not talking about calculating how many hours until the next meal time. We're talking about actual arithmetic.

Check out this video from the BBC, where Maggie, an American Jack Russell Terrier, challenges a classroom full of seven-year-olds to an arithmetic duel. Dog and kids race to solve addition, subtraction, multiplication and even division problems with one and two digits. And Maggie is spot on nine times out of ten.

Maggie isn't the only canine mathematician. In the video below, Milo from Australia appears to recognize written numbers and give the answers to simple arithmetic problems using the same paw-touch communication that Maggie uses. And, unlike the children, who started practicing with numbers around age four or five years, Maggie and Milo started at ages six and seven months, respectively.

Oreo appears to count as well, but he barks his answers. His owner also holds up fingers instead of presenting written numbers. Still, it's pretty impressive. What's going on here?

In Oreo's case, one might argue that he is simply barking on command. He knows that three fingers mean three barks. Plenty of dogs respond to hand signals instead of (or in addition to) voice commands. As for Milo, one could argue that Milo has been practicing his tapping responses to the same sheets of paper (and being rewarded when he gets the number of taps right). Simple behavioral reinforcement.

But Maggie's responses — nine correct answers out of ten — were to written problems she'd never seen before, which the teacher generated on the spot. How is this possible? Is it possible?

The answer might surprise you.

Animals Actually Can Do Math

Just, perhaps, not in the same way, to the same degree, or for the same purposes that we do.

It's not just dogs, either. Recent experiments have shown that amphibians, fish, birds, horses, monkeys, and even spiders have abilities that can be described as mathematical.

Scientists believe that a rudimentary mathematical ability may go back to a distant common ancestor. It makes sense that such a useful trait would remain, even as species developed, diverged, and evolved. It also could have evolved independently in different species — much like the independent (or convergent) development of bat wings and bird wings.

So, What is Animal Math?

That, according to scientists, depends on the animal. But all animal math shares the same basic traits.

What are they?

An approximate number system

Scientists have found that all animals have what they call an “approximate number system.” This means that they can tell if one group of the same object has generally more or generally less of that object. You can see where that might come in handy. Interestingly, as the number of objects gets larger, the animal's accuracy decreases.

It's similar in humans. You could probably look at a pile of five beans and immediately identify it as five beans. But if that number were seventeen, you might have to stop and count if you wanted to be sure.

Weber's law

Scientists also found that with nonhuman animals, just as with humans, Weber's Law still applies. What's that? Well, Weber's Law states that it's easier to tell the difference between two groups of objects when one group contains a lot more than the other. So it's easier to tell which group is larger when one group contains three objects and the other contains thirty, than when one group contains eight objects and the other contains nine.

That may sound like a no-brainer, but, evolutionarily speaking, it's a pretty big deal. Especially when you consider that in Christian Agrillo's study at the University of Padua in Italy, guppies and people performed equally well at this particular task.

Image CC BY-SA 2.0 by Bremer Kid, via Flickr

Guppies?

Yup.

Counting. Sort of.

A 2002 experiment with pet dogs turned up an interesting result. In this experiment, dogs were shown a bowl with one treat. Researchers then introduced a barrier, so the dogs couldn't see the bowl, and then either added a second treat or pretended to. Then they lifted the barrier to show how many treats were in the bowl.

The dogs displayed confusion when there was only one treat in the bowl, and they had been expecting two. When researchers slipped an extra treat into the bowl — revealing three treats instead of the expected two — the dogs showed the same confusion.

This would suggest that at some level, dogs have a rudimentary sense of counting. Researchers called this numerosity, that is, the general idea of numbers of concrete objects. That's different from numeracy, which is the ability to manipulate symbols that represent numbers of objects.

What About Symbolic Math?

At this point in time, scientists believe that humans are the only animals that do symbolic math — that is, equations using numbers that represent an amount. So where does that leave our original canine math genius, Maggie?

Researcher Robert DiFranco doesn't believe that Maggie is actually solving those equations. In a follow-up segment, DiFranco and other researchers test Maggie in various ways to try to see how she manages to solve the equations correctly time and time again.

In the first part of the segment, Maggie gives a flawless performance for DiFranco. However, when Maggie's owner leaves the room and DiFranco asks the questions, Maggie taps her foot in response, but doesn't get the right answer even once. This leads DiFranco to believe that Maggie's owner, Jessie, is somehow signaling the answers to Maggie.

So, are Jessie and Maggie cheating? Another group of tests rules out both visual and audible signals, so DiFranco is at a loss.

Another researcher, Frederica, comes up with a theory. She notices that Maggie has extremely focussed attention — even for a Jack Russell, a breed known for its laser-focus. Frederica believes that Maggie's owner, Jessie, is unconsciously giving off signals that betray the answer to Maggie.

Which, according to the researcher, makes Maggie extraordinary in a different way. Maggie may not be a true canine mathematician, but her ability to read her owner's intention from signals that her owner doesn't even know she's giving off, is nothing short of remarkable.

Maybe the Dog Didn't Eat Their Homework

So, can your Jack Russell help your seven-year-old with their math homework? I wouldn't count on it.

On the other hand, dogs, and other animals have shown that they are capable of some pretty impressive things.

Featured Image: CC0 by An Ragaire, via Pexels