The Curves of Life

Theodore Andrea Cook (1867–1928), with a deep background in sport and literature, traveled in Europe during the early twentieth century and published authoritative works on French and English history, Leonardo da Vinci, and sculpture. In 1910, he became editor of The Field: The County Gentleman’s Newspaper, remaining until his death in 1928. In his passionate sleuthing of the open-ended spiral curve, he describes in this book what he sees as a beautiful truth foundational to the structure of plants, shells, physiology, the periodic table, animal horns, and galaxies. (Sometimes the horns of goats are morphological indications of domestication, a physiological indicator that always strikes me whenever I encounter it.) The Curves of Life explores these ideas through 426 illustrations, from a Narwhal’s tusk to rare seashells to exquisite architecture. No less than Martin Gardner said of this work, “This is the classic reference on how the golden ratio applies to spirals and helices in nature.”

Spirals in Shells and Staircases could be an alternate title for this overt love affair with the logarithmic studies of Leonardo da Vinci. A fourth of the chapters in this book are devoted to that pair of topics, as well as much of the material in the rest. Da Vinci leads Cook through drawings and writings, like Beatrice guiding Dante through Heaven.

Cook finally gets hold of the physical traces of his ideal in the non-pareil spiral staircase of the Château de Blois. Like a triumphant detective, Cook is breathless in the telling:

a staircase whose form and construction so vividly recalled a natural growth would, it appeared to me, be more probably the work of a man to whom biology and architecture were equally familiar than that of a builder of less wide attainments. It would, in fact, be likely that the design had come from some great artist and architect who had studied Nature for the sake of his art, and had deeply investigated the secrets of the one in order to employ them as the principles of the other.

Cook sees the master’s hand, and it is indeed possible da Vinci was the designer.

This exploration first unfolded serially in the pages of The Field. Numerous correspondents replied to Cook’s musings. Relevant and thought-provoking responses are reproduced at the end of chapters, whether they support or contradict Cook’s evaluations. This expert back-and-forth of detail-oriented collectors with time on their hands is like an early twentieth century crowdsourced survey of global biota and architecture, resulting in hundreds of images and a fair consensus on the spiral as axiomatic to a wide gamut of organic form.

In this headlong jaunt arm and arm with his comrades, there is no room for mathematics. Says Cook, “This is not the place in which to introduce those cumbrous forms of scientific nomenclature in which specialists usually delight to communicate their researches to one another.” Cook is keen on hands-on understanding. For him, being able to draw the seashell’s curve is more revelatory than a descriptive formula

because I believe very strongly that if a man can make a thing and see what he has made, he will understand it much better than if he read a score of books about it or studied a hundred diagrams and formulae. And I have pursued this method here, in defiance of all modern mathematical technicalities, because my main object is not mathematics, but the growth of natural objects and the beauty (either in Nature or in art) which is inherent in vitality.

Cook is seduced, however, by the compact efficiency of scientific language, drawing him to something more precise and formal: “these curious words may be considered as a convenient form of shorthand in which a few syllables — however barbarous they sound — may express a meaning which often needs a lengthy sentence in ordinary language.” So, he will use “homonymous”, “autogenic”, “leiotropic” (sinistral), and more plucked from the mouths of scientists to more efficiently curate this many-roomed museum.

Says Cook in his “Final Results” chapter:

One of the chief beauties of the spiral as an imaginative conception is that it is always growing, yet never covering the same ground, so that it is not merely an explanation of the past, but is also a prophecy of the future; and while it defines and illuminates what has already happened, it is also leading constantly to new discoveries. This, therefore, is that unspent beauty of surprise which Nature can always offer her best lovers.

Having so poetically expressed the idea that had so enraptured him, he finds that he has also become enamored of mathematics: “In mathematics we have the most supple and beautifully precise instrument by which the human mind can fulfil its need of cataloging, labelling, defining the multifarious facts of life around us.” Thus ends a fascinating and engrossing investigation into the geometry of the natural world, a very special book profuse with illustrations and a spirited search for a winding truth.

Tom Schulte teaches mathematics at Oakland Community College in Michigan and hopes he leaves a few of his students enamored of the subject, as well.