I stumbled on it some years ago on a rambling hike down a dry streambed in Driggs, Idaho. I found a perfect bend in a river. A 180-degree change in direction, carved from the alluvial plain. The gravel bank was perhaps eight feet high; it was plumb vertical, and had a perfectly walled arc, perhaps 100 feet in diameter. From every angle it was astoundingly geometrically perfect. It grabbed my eye and carried it around its curve. I had never seen such mathematical perfection in nature before.
Luna Leopold felt that same sense of awe in nature. As the son of Aldo Leopold, the famous pioneer of wilderness ethics and land protection in the United States, Luna Leopold was the first to set out to study rivers in a manner unheard of—he measured them… in great detail. In fact he spent a lifetime creating formulas to explain just how rivers work, and how it was possible for them to carve the perfect bend.
By and large, he was successful.
He was the creator of what is now called quantitative hydrology, and in doing so re-established much of the fundamental assumptions of modern engineering.
Starting in 1953 with his obscure (to most readers) text, The Hydraulic Geometry of Stream Channels and Some Physiographic Implications, Leopold pulled rivers apart, feature by feature, and scratched out the formulas that explain their behaviours. Some of his findings are uncanny. Consider these, if you haven’t before: the wavelength a river meanders is, on average, 12 times its width; the Sine coefficient for those meanders is the same coefficient for the compression waves that form on a stream’s surface; and the riffle-pool interval is one half the wavelength of the meanders.
Fascinating.
He created formulas to explain helical flow, wave creation, hydraulics, sediment load and watershed flood rates. The list goes on and on. In my search to explain the perfect bend all roads lead to Leopold’s work. He was incredibly prolific and clearly a genius. While mathematically dazzling, his formula for the perfect bend left me spiritually unfulfilled.
A year later I was handed Barry Lopez in a used bookstore in Smithers, B.C., Lopez lives on the other end of the Sine curve from Leopold; if Leopold is pure science, Lopez is pure poetry. River Notes is Lopez’s river dissection, via a series of short stories so descriptive the book drips with water. His swirling eddies suck you in, carry you into the current, then delicately and surprisingly drop you in the literary ocean of deep thought with his famous single-sentence endings.
Lopez explores the idea of how a river can so seamlessly and completely change direction, while looking for instruction that may be useful to his own life.
Mired in depression, he laboured to examine every aspect of the bend in the river behind his home. If he could figure out this bend, then maybe he could figure out how to turn his own life around. Bed-ridden and feeling no hope at all, he hauls himself down to the stream and dips his hand in the water. The essence of the turn, he realizes, is not in the details (nor in any of Leopold’s formulas), but in some bigger connection between himself and the river.
Lopez’s exploration of the fine details of rivers is in a way an exploration of the human soul, but his life-changing river bend metaphor did not speak to me any more than Leopold’s algebra.
I’ve since returned to the sharp and blocky Canadian Shield rivers, rivers with turns seemingly unaffected by water and time pushing against them. In my lifetime I’m unlikely to find another bend so geometrically perfect.
With every new river I paddle I realize it was not the bend that was so intriguing, it was how the perfectly bending arc grabbed my eye, smoothly railing it around the corner in a new direction. It was not the bend in the river, it was what lay beyond that was so intriguing and so important. The perfect bend is not a complex equation. For me now, the perfect bend is the one just downstream, the one luring me to explore what is just beyond.
This article first appeared in the Summer 2007 issue of Rapid Magazine.
