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Pole gets ready to play at the Duke Canine Cognition Center.

If you show a child a red block and a green block, and then ask for the chromium block, not the red block, most children will give you the green block, despite not knowing that the word "chromium" can refer to a shade of green. Children infer the name of the object. They know that you can't be referring to the red block.

In 2004, Juliane Kaminski from Britain's University of Portsmouth and her colleagues published the results of a similar experiment with a dog called Rico who knew the names of hundreds of objects.

Dr. Kaminski showed Rico an object that he had never seen before, along with seven other toys that he knew by name. Then she asked Rico to fetch a toy using a word that was new to him, like "Sigfried." Just like human tots with the word "chromium," Rico was immediately able to infer that "Sigfried" referred to the new toy. Since the report on Rico, several other dogs have also been shown to make inferences this way. Dogs are the only animals that have demonstrated this humanlike ability.

Based on the ability of cats to hold a grudge, you might think that they have better memories than dogs. Not so. Several years ago, Sylvain Fiset of Canada's University of Moncton and colleagues reported experiments in which a dog or cat watched while a researcher hid a reward in one of four boxes. After a delay, they were allowed to search for the treat. Cats started guessing after only one minute. But even after four minutes, dogs hadn't forgotten where they saw the food.

Still, dog owners should not be too smug. In 2010, Krista Macpherson and William Roberts of the University of Western Ontario published a study that tested navigational memory, in which dogs had to search for food in a maze with eight arms radiating out from a central position. The researchers then looked at rats previously given the same test. They beat dogs by a wide margin.

Even the dog's closest relative, the wolf, beat its cousin when food was placed on the opposite side of a fence, as shown in a 1982 study by Harry and Martha Frank of the University of Michigan. In 2001, Peter Pongrácz and colleagues from Eötvös Loránd University in Hungary published a study with an important qualification to this earlier finding: When the experimenters showed dogs a human rounding the fence first, the dogs could solve the problem immediately.

This is the secret to the genius of dogs: It's when dogs join forces with us that they become special.

Nowhere is this clearer than when dogs are reading our gestures. Every dog owner has helped her dog find a lost ball or treat by pointing in the right direction. No other animal—not even our closest relatives, bonobos and chimpanzees—can interpret our gestures as flexibly as dogs.

So are dogs smarter than cats? In a sense, but only if we cling to a linear scale of intelligence that places sea sponges at the bottom and humans at the top. Species are designed by nature to be good at different things.

And what might the genius of cats be? Possibly, that they just can't be bothered playing our silly games or giving us the satisfaction of discovering the extent of their intelligence.