Canine Calculus

All dogs measure their existence by their distance between you and what matters. A dog will position himself at the apex of equidistant purposes. For instance, he will sit in the hallway between you and the door. If, perchance, you were to decide to leave, he would know. Or, in case of danger, if some predator were to enter, he'd be the first to attack and alert. If he has yet to be fed, he will position himself at the exact angle between you, the food dish and the food container.

Our dog, Rubin, has sentry posts throughout the house. Using an astonishing knowledge of calculus, he measures the exact point between us and curls up, at the ready. If one of us moves, he opens one eye and recalculates, shifting enough to maintain the most efficient and exacting equation. If one of us goes upstairs and the other is downstairs in the kitchen, he rests on the landing of the stairs, angling himself so that if one of us moves, he can see it without turning his head.

When we are together, when we on the couch to watch television, he has one of two algebraic locations -- under our outstretched legs or stretched out just before the door. The first is his security position -- it marks the end of a long day and a surrendering of sorts. The second is the position of possibility that perhaps the day is not quite over and we might go for one more spin around the block or, better yet, go out to the big field and play fetch.

He, like all dogs, is imbued with an order of operations. There is no need to rise until the coffee is done. Then, one must go out and take care of morning business. Too early for any real activity, there's a short nap while the paper is read and the coffee consumed. The day truly begins once the showers are complete and the clothes on. Even during these simple tasks, he finds the geometry of alertness, curling up just outside the shower -- a fuzzy, breathing rug, or lies sphinx-like on the top step ready to race down the stairs toward the front door.

Shoes are a signal of great importance ranking up there with the jangle of keys. A dog will always position himself at the exact location between front door and leash and in his excitement, let out a whine of anticipation that he might be invited along. The rest of the day is spent pondering the equations and manipulating the spatial relations using an inbred protractor and innate calculator. There are the walks, with a measured leash. There are the moments of waiting, clicking off the 60 seconds in every 60 minutes of every hour. More food, some treats, and a recalibration of purpose when it rains or visitors come by. Assistant to the house chef, he knows the angle and velocity of fallen food, the amplitude of its wavelength. There is speed and distance and the acute accuracy of the shortest distance between two points.

A dog's math mind rests only with the final measuring of the circumference of sleep better known as Rubin's Theorem-- circle three times to the left and two the right, curl up in a perfect sphere for a long night's sleep.