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COMPUTING SCIENCE

Dividing the Continent

Brian Hayes

It was the fourth day of a meandering coast-to-coast road trip. We were climbing through the Centennial Mountains along the Idaho-Montana border in an overloaded Toyota with a U-Haul luggage pod on the roof. As we crested Monida Pass, a sign at the roadside announced: Continental Divide, Elevation 6,823 Feet. "Well," quipped my traveling companion, "I guess it’s all downhill from here."

For miles afterward—as we climbed still higher hills and crossed the divide twice more—I pondered that remark. The great divide is the spine of the continent: Rain falling on one side trickles into the Pacific, and on the other side into the Atlantic. The concept is simple enough, but I kept wondering how we would have known we were crossing the divide if the highway department had not put up those helpful signs. The divide is not necessarily the high point of a cross-country journey, so what distinguishes it, geometrically or topologically? That morning in Idaho, it seemed even more enigmatic than other lines that people draw on the landscape. For example, a contour—a line connecting points of equal elevation—is something you could trace out by carrying around an altimeter, but there is no instrument that would help you find and follow the continental divide.

The long drive home offered us ample opportunity to noodle away at this puzzle. Being a computer-dependent person, my instinct was to address the question in algorithmic terms; I would know that I understood the answer when I could write a program to identify the divide. Out on the road, however, I could not put such a program to the test. I am also a library-dependent person, but the urge to go find out what others had to say was also frustrated. And thus for a week or so I had no choice but to actually think about the problem.





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