Why Zeus Smoked a Pipe, or The Legitimization of Mathematics

October 21, 2006

Frontispiece, Arithmeticae libri duo et Geometriae libri Vi (1626), by Adriaan Metius.

Book Review
Philip J. Davis

Widmung, Welterklärung und Wissenschaftslegitimisierung: Titelbilder und ihre Funktionen in der Wissenschaftlichen Revolution. [Dedications, Explanations of the World, and the Legitimization of Science: The Function of Title-Page Frontispieces During the Scientific Revolution.] By Volker Remmert, Harrassowitz Verlag, Wiesbaden, 2005, 267 pages, €89.

Wouldn't it be great if applied mathematics could be celebrated visually with a lavish display of gods and goddesses, muses, graces, angels, putti, mythical animals, symbolic personifications, Illustrious Departed, patrons, scrolls, triumphal arches, slogans, instruments of the trade, and miscellaneous symbols, all strewn about not with the random order of a yard sale, but according to the artistic criteria of the Baroque Age? Well, that's what went on during the 17th century, and Volker Remmert's unique (to me at least) volume displays these elements in full measure.

Remmert is a historian of mathematics and science at Johannes Gutenberg University in Mainz. To do full justice to the contents of his book---about a hundred title-page etchings from scientific works, together with extensive interpretive and perceptive comments---would require the knowledge and the talents not only of a historian of science and of art, but also of a semioticist, a rare book aficionado, and a bibliographer. The bulk of the book is devoted to works of astronomy and their promulgators---Copernicus, Galileo, Tycho Brahe, Kepler---but it also includes 21 pages on applied mathematics, with 19 title-page engravings. Feeling a bit more comfortable with these pages, I have limited my review to them.

One has to understand that the word "legitimiztion" in Remmert's title has several intertwined meanings. The first relates to the acceptance of scientific ideas in the face of alternative and competing explanations, descriptions of the universe, ethical norms, and prejudices. The second relates to the support of science---who pays for it and why. "Plus ça change, plus c'est la même chose," as the French saying has it, and the legitimization of science in both senses goes on today on the front pages of mainstream newspapers. I'm thinking not only of, say, the stem-cell and the intelligent-design controversies, but also, in the philosophy of science, of the question as to whether a theory that cannot be verified experimentally has any validity or meaning. The third meaning of "legitimization" is implicit in the dedications (i.e., thanks) of many of today's scientific papers not to princes, as in the 17th century, but to foundations and governmental institutions.

And now to Remmert's pages (103–124) on mathematics. This is by no means a definitive collection of title-page figures in mathematics books, and the mathematics is limited to applied mathematics. Thus, for example, you will not find here the title page of the first English translation of Euclid (1570). Graphical elements of the sort mentioned above appear in full fig in Euclid, but the text, as I recall it, is devoid of applications. (A fine reproduction can be found on page 304 of Boyer and Merzbach's A History of Mathematics.)

The promulgation and legitimization of applied mathematics as illustrated and described here fall into two large categories: war and business (author's choice!), and war is the more prominently covered. In several of the engravings, there is no reluctance in admitting that mathematics feeds into war through military architecture (fortifications) and ballistics. Thus, in the Arithmeticae libri duo et Geometriae libri Vi (1626) (Arithmetic in two volumes and Geometry in six) of Adriaan Metius, a grinning soldier, fully clad in Roman military style, sits atop a military turret in the midst of a large cannon, spears, battleaxes, helmets, maps, trumpet, and drum.

In the frontispiece of Jacques Ozanam's notable Dictionaire Mathématique (1691), reproduced full-size, the military motif is present but a bit subdued. The central figure, amidst a clutter of puttis and so forth, is a young woman personifying geometry. In her left hand she holds a carpenter's angle; in her right is a large compass with which she points to a large drawing of the ground plans of a fortification. She is crowned with a tiara that displays battlement crenellations, and her headdress, in turn, is topped off by the mystic pentagram that---in the standard interpretation suggested by Remmert---puts military constructions under the aegis of the kabbalistic forces of the universe. But we need to look again: In the distance, seen through a series of arches, an artillery action is taking place, fully as bloody as any of the explosions that go on today.

As to business and trade, Remmert provides essentially only one etching: the title page of Sir Jonas Moore's A New System of Mathematicks (1681). (A slightly modified copy of this figure appears in the Dutch De Geheele Mathesis of Wiskonst (The Whole of Mathematical Science), from 1694.) Moore, as the Surveyor General of His Majesty's (Charles I) Ordnance, surveyed the drainage system of the Fens; he was a mathematician and a Fellow of the Royal Society, and a person interesting enough to attract the notice of John Aubrey (with an appearance in Aubrey's famous and delightful Brief Lives).

Title page from A New System of Mathematics (1681), by Sir Jonas Moore.

In the central ornamental frame, a group of prosperous investors, importers, navigators huddle around a large globe. In their hands are mathematical and navigational instruments; others are strewn about the floor before them. Above this frame, the personification of geometry and cartography on the right side and that of astronomy on the left legitimize the enterprise below.

Directly above the assemblage of men, four boats float on a shining sea, protected and ap-proved on the right by Poseidon with trident in hand and on the left by Zeus smoking a pipe, or a mini-calumet. Remmert points out that in the 17th century the importation of tobacco from Virginia to London, and thence to Amsterdam, was big business. Thus we have smoking in the service of legitimizing mathematics.

By contrast to the title pages presented in this book, title-page art in the 21st century has shifted to the front covers or the dust jackets of books, where it is intended to attract buyers. The art itself is for the most part abstract or consists of collages or overlays of mathematical symbols. Among the recent books I've seen whose dust jackets get anywhere near the spirit of the 17th century is King of Infinite Space, a biography of Donald Coxeter by Siobhan Roberts. A shirtsleeved Professor Coxeter crowns himself with a large non-convex polyhedron; a second polyhedron appears beside him at waist level, and a diagram with triangles overlays it all.

My baroque imagination suggests that something better is possible, assuming that a skilled engraver can be found today. Which of the dozens of contemporary applications of mathematics shall I select for my graphical rhapsodizing? Baseball, about which most American know something and which through its reliance on statistics, has become the most mathematized of our sports. (See "Playing Ball Probabilistically, SIAM News, Vol. 35, No. 3, www.siam.org/news/news.php?id=415.) As an overlapping topic, I select medicine, in which statistics are a constant source of concern.

The engraving I have in mind would depict a baseball stadium, both the field and the grandstand. At the top, the Illustrious Person of Abner Doubleday sits among a scattering of bats, balls, cages, helmets, chest protectors, and pairs of socks. Below, to the right, the figure of Babe Ruth at bat points to the right-field wall. At the left, Jackie Robinson comes to the plate swinging three bats. On the field, a player is sliding into third, while in the bullpen, a reliefer is warming up.

I need now to bring in a personification of the statistical element. Who shall it be? I've got it: Florence Nightingale, who was tutored in mathematics by the great James Joseph Sylvester, was a member of both the Royal and the American Statistical Societies, and did much to promote medical statistics. Florence would be depicted with a lamp in her left hand; to her right, a polar area chart of her own devising would exhibit statistics on injuries in the sport. As a female, she would lend balance and grace. At the very top of the engraving would be a ceremonial scroll bearing the immortal words: "It ain't over till it's over." The whole would be framed in velvet drapery with tassels.

Enough of this. Remmert's splendid collection of engravings and his accompanying text will suggest to readers that mathematics constantly requires legitimization, in all senses of the word. Each generation will find its own graphical or computer-graphical solution for this necessity.

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at philip_davis@brown.edu.

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