2006-04-05 / Columnists

Pets, Pets, Pets...

by Joanne Anderson

Sushi, Siamese Sushi, Siamese "If you think dogs can't count, try putting three dog biscuits in your pocket and then give him only two of them." -Phil Pastoret

Canine math skills may far surpass this humorous warning. One math professor claims his dog uses calculus to figure out the fastest way to retrieve at the beach. In 2003 Dr. Tim Pennings of Hope College discovered the analytical talents of his Welsh Corgi, Elvis, while tossing a ball into Lake Michigan. Elvis, much more like Sir Isaac Newton than his "Hound Dog" King namesake, seemed to grasp that the shortest route is not always the quickest way to get from Point A to Point B. Perhaps the dog intuitively sensed that the lake puts a damper on Euclidean geometry.

This Corgi didn't use a formula or slide rule. No one taught Elvis that calculus is the study of the rates of changes, crucial to solving some practical problems by finding minimum and maximum values. The shortest way would be to dive right in, but that doesn't take into account the difference between his running speed and swimming speed. With a knowing look, stubby legged Elvis ran along the shore part of the way, plunged into the lake at a point of his choosing, and swam diagonally to the ball. End resultthe optimal path for fast fetching, the route that minimizes travel time.

Bandid, Labrador Bandid, Labrador Pennings was impressed. He assumed that Elvis unconsciously found the most efficient retrieval route, much to the envy of his calculus students who depend on the help of drawings and equations. To test his theory, Pennings clocked his best friend's running and swimming speeds. Later while throwing the ball at varying angles to the shore line, the professor measured Elvis's paths with a long, (wet) tape measure and a screwdriver as a marker at the spots in the sand where the dog shot off into the water. Bringing all the data back to the math lab, Pennings plotted the dog's points on a graph, andeurekahis precocious pet's chosen trajectories were in line, or very close, to the calculus based solution.

When the mathematician published his findings in the May '03 College Mathematics Journal, Elvis (aka Elvis Bogart Wales) joined academia. The dog earned an honorary degree"Litterarum Doctoris Caninarum" from Hope College and accompanied his owner on a speaking tour. Elvis is also mentioned in Keith Devlin's bookThe Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs).

Devlin says there are two kinds of mathnatural and symbolic. Natural math has evolved in animals over millions of years to fine tune survival tasks like navigation and catching prey. For example, the Tunisian desert ant finds its way across the barren sands using the same mathematical techniques the Apollo crew depended on to land on the moon, while bats have a bug catching sonar system so accurate the Navy and robotic engineers have tried to emulate its precision .


Elvis et al have their critics. A pair of Paris professors, who made slight changes in the fetching experiment with Salsa, their Lab, argues that Pennings pre-supposes that a dog knows the entire route in advance, and that a dog actually adjusts its behavior on a moment to moment basis. Voila! Pennings insists his Corgi's decisions are more global. By reversing the retrieval, and throwing a stick from the water to the shore, the Michigan duo countered the French.

Both Pennings and the Parisians utilized symbolic math, the other kind in Devlin's book. Symbolic math is unique to humans and has only been around about 3,000 years. Grantedmost folks aren't thinking about higher mathematics when they romp with their pups at the park. However, what if Professor Pennings is on to a canine conspiracy? People everywhere need to be warned. During a game of fetch, devious dogs might take advantage with this calculating sixth sense that streamlines their efforts while tiring us out. Although the idea is mind boggling, I'm too rusty to prove their plot. It's been over 35 years since I've sat in a calculus class (at Massapequa High). 35, oops, that's merely 5 in dog years. Darn, there goes my excuse. Quick, Fido, fetch me the slide rule.

Visit Oyster Bay Town Shelter (677-5784) 150 Miller Pl. Syosset to adopt a 4-legged friend (or math tutor). "Bandit" #060207 is "The Natural" when it comes to fetching. This purebred Labrador retriever is 1 year old and personality plus. "Sushi" is an exquisite seal point Siamese cat#000189. She's front declawed on her fancy snowshoe paws. All adopted animals leave the shelter already neutered and vaccinated. The shelter's dog fee of $67.50 includes a NYS license while the cat fee is $59.

Female: former POST poster pets"Bonnie" # 060176-the Schipperke/Lab & "Squirt" #060156 the Sheltie mix. Also "Trini"#051123a Rottweiler mix; "Gussie" #051102a Chow mix.

Male: "Bonnie's" buddy-"Clyde "#060175the handsome Catahoula/ Dalmatian mix; "Buddy" #060091a purebred Siberian husky.

Low Cost Spay/Neuter for your pet(516)364-PAWS.

Return to top