Do Dogs Know Mathematics?

Some people doubt that dogs are capable of even the most rudimentary form of quantitative thinking. The most basic form of analyzing the world in a quantitative way involves the judgment of size, namely, answering the question of whether one thing larger than another. Early researchers would put out two balls of hamburger, one large and the other small, and when they found that dogs were as likely to choose the small one as the large, they concluded that dogs could not estimate size. However there is a flaw in this test. Dogs think in an opportunistic manner, a sort of "A bird in the hand is worth two in the bush" mentality. If the two plates were a different distances, the dog would always grab the closest. However if they were at equal distances, the dog would show that he understood the notion of size by going after the larger one. Norton Milgram, at the University of Toronto confirmed that dogs can judge size well using a tray which contains two objects of different sizes. If the dog pushes the correct object, then underneath it he will find a food treat. Dogs can be taught always to pick the larger (or smaller) of two objects, regardless of the shape or identity of the objects, and they learn this fairly easily..

A slightly more difficult aspect of quantitative reasoning is the judgment of numerosity. This simply refers to the ability to compare two groups of items. We do this when we judge which of two crowds contains more people, and this can be done without counting or any idea of the specific number of people in either group. Thus a dog who runs to a pile containing ten pieces of kibble, rather than to the pile next to it that contains only two pieces of kibble, may have made that decision based upon his judgment of the number of kibbles in each pile. In the laboratory dogs prove that they can judge numerosity by learning to press a panel which has more (or fewer) dots painted on it for a food reward.

The next level up is simple counting, and this is an ability which dogs frequently demonstrate, especially working and sporting dogs. For example in field trials for retrievers, to successfully complete the higher-level tasks the dog must be able to count to at least three. This is because, if three ducks have been dropped, and he has already retrieved two, the dog must know that there is still one more out in the field to retrieve.

If dogs can count, it seems natural to ask whether they can do simple arithmetic. Robert Young of the Pontifical Catholic University in Brazil, and Rebecca West of the University of Lincoln in the UK, attempted to test this idea by modifying a test that has been used to prove that human infants have the ability to count. The procedure involves something called "preferential viewing" which simply measures the amount of time that infants spend looking at things. Research confirms that infants (just like adults) will stare at something unexpected or unusual for a longer time. The human test for counting is quite simple. First the child is a shown a small doll on a table and then a low screen is put in front of it to block the child's view. While he watches the experimenter takes another doll, shows it to the child and then puts it behind the screen. If the child can count he should expect that when the screen is raised he should see two dolls-and sometimes he does. However sometimes the experimenter secretly removes one of the dolls so that now when the screen is raised there is only one doll visible. When this occurs, the babies stare at what is on the table for much longer after the screen has been raised. Psychologists believe that this confirms that infants have made the mental calculation and now surprised to find that the number of dolls that they are seeing is different than what they expected it to be.

In the canine version of this test the dog was shown a single large treat and a low screen was put in front of it. Then the dog watched as the experimenter obviously placed another treat behind the screen. If the dog can do the math he knows that 1 + 1 = 2 and he should expect that when the screen was raised there should be two dog treats. However, just like in the case of the babies, sometimes the experimenters surreptitiously removed the second treat so that when the screen was raised the dog saw only one. As in the case of the babies, the dogs stared at this unexpected outcome for a longer time than they did when the arithmetic came out correctly, apparently "surprised" at what they saw. Similarly, if an extra treat was secretly added so that the dogs saw three instead of the expected two, the dogs appear to be equally surprised. This suggests that dogs can not only count, but can also do simple addition and subtraction.

The ability to count and do simple arithmetic might seem to be a superfluous skill for dogs, but it is a useful ability that would have been vital to dog's wild ancestors. For example, it would be useful for a female to know if all of her pups were present in the den or if one of them had somehow gone astray and required a search and rescue mission to be launched.

Despite this display of arithmetic ability in dogs, I wouldn't give one my pocket calculator since he is still apt to view it as a chew toy rather than as a mathematical tool.

Stanley Coren is the author of many books including: Born to Bark, The Modern Dog, Why Do Dogs Have Wet Noses? The Pawprints of History, How Dogs Think, How To Speak Dog, Why We Love the Dogs We Do, What Do Dogs Know? The Intelligence of Dogs, Why Does My Dog Act That Way? Understanding Dogs for Dummies, Sleep Thieves, The Left-hander Syndrome

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