Review of Between Raphael and Galileo: Mutio. Oddi and the Mathematical Culture of Late. Renaissance Italy by Alexander Marr

Transcription

1 Review of Between Raphael and Galileo: Mutio Oddi and the Mathematical Culture of Late Renaissance Italy by Alexander Marr Mark A. Peterson May 18, 2012 Mutio Oddi, recalled to life in this volume, will never again be confined to the marginal place in Renaissance mathematical cultural history that he has occupied until now. His story and his circumstances, in Alexander Marr s thoroughly professional study of him, have become a resource for understanding what it meant to be a mathematical practitioner at the time of Galileo, but without the peculiar distractions of Galileo s eventful history. The lives of Oddi and Galileo are in fact remarkably parallel. They were almost exact contemporaries, and if Galileo had never done anything but teach at Padua and peddle his geometric compass (not an entirely unfair description of his career, outwardly at least, into his forties), their careers would have been strictly comparable. Both were proteges of Guidobaldo del Monte, the Archimedes of Pesaro. And, like Galileo, Oddi ran afoul of authority, in a jealous court intrigue that he never 1

2 understood, suffering years of imprisonment and then nearly lifelong exile from his beloved Urbino. Oddi s need to re-invent himself during his enforced residence in Milan, and later in Lucca, gives remarkable insight into what the possibilities were for a man with mathematical training, aptitude, and connections. He acted as middleman for the procurement of mathematical instruments from Urbino s renowned Oficina di strumenti matematici on behalf of professional men, patrons, and even a countess. He published two books on sundials, one on a sighting instrument called the squadro, and one on a compass somewhat like Galileo s. He gave lessons in mathematics, both privately and as a professor at the Scuole Piattine in Milan. The records he left behind document all this activity in meticulous detail, and Marr has organized this information into appendices that shine a bright light into all these areas. An appendix on teaching shows us year by year whom he taught, and what subjects (military architecture being a popular one), described more discursively in Chapters 2 and 3. Another appendix, on the publication of one of his books, shows who he sent them to, while Chapter 4 on mathematical publishing describes his expenses, the paper, the woodcuts, the copperplate, and the printing. A third appendix lists the mathematical instruments that he ordered from Urbino, how many, and for whom, while Chapter 5 fleshes out the details of this history. One fact that emerges unmistakeably from this careful work is that the mathematical life did not exactly pay. Oddi gave away his books in remarkable numbers, and he also sometimes gave away the instruments that he had ordered. 2

3 The recipients were patrons, or potential patrons, who in return would be sure that Oddi was maintained. The dedicatee of Dello squadro trattato, for example, defrayed the expenses of the publication. This mutual exchange of gifts led to true friendships, amicizie, and Oddi s letter of gratitude and appreciation at the end of his life to his friend and patron Peter Linder is truly touching. Oddi and Linder each owned a copy of a double portrait of themselves depicting a lesson in geometrical optics, it is argued, because there is a mirror in the background that has been identified as most likely a parabolic mirror, the apparent subject of the lesson. This double portrait is the subject of Chapter 3 of the book s six chapters. When Oddi had had enough, after fifteen years, of depending on his patronage network for his living, he accepted the secure and well-paid position of chief fortifications engineer in Lucca, although he considered it a backwater. It is clear, though, that he never missed Milan as much as he missed Urbino. Before his fall from grace he had been Architetto Ducale in Urbino, and here in Lucca he was again an architect, once again practicing the craft that most obviously called upon both mathematics and the faculty of disegno, the subject of Chapter 6. Oddi s first training was in drawing and painting, and many architectural drawings from all periods of his life are reproduced in this lavishly illustrated book. With the death of Francesco Maria II della Rovere, the last duke of Urbino, Oddi was finally able to return to his patria, and with the wealth he had acquired he bought the Santini house, birthplace of Raphael, and restored it, organized 3

4 his affairs, and left his mathematical instruments and library to maintain, he hoped, the mathematical traditions of Urbino. This final act seems to put a seal on a point that this book has made throughout, the primacy of the material culture of mathematics, its artifacts and its instruments, the author s answer to the question raised in the introduction of what it meant to be a mathematician (and of what mathematics was) in the sixteenth and seventeenth century. One gets the feeling in this impeccably researched book that the material culture of Oddi s mathematics has been thoroughly sifted, but one also gets the feeling that something has been left out. Surely mathematics in the sixteenth and seventeenth centuries was more than drawing instruments, sighting instruments, and sundials. After all, it is a defining characteristic of mathematics that it is finally not material. Why should this have to be pointed out? Here and there are hints of something that never quite emerges into the light. Oddi s mathematical notes, we are told, in one startling sentence, reveal a lifelong commitment to the study of speculative geometry. In another place it is mentioned that Oddi undertook a thorough study of Books 7 and 8 of Euclid s Elements. These things seem quite unrelated to the material culture of mathematics or to anything else that we learn about Oddi. While so much surrounding material has been studied minutely, mathematics itself, which is also a cultural artifact, and ostensibly the reason that Oddi interests us at all, has been ignored. Can one learn what mathematics was without reading and understanding the mathematics? Chapter 3 may be a cautionary example in this connection. It is called Am- 4

5 icizia and Optics: A Mathematics Lesson Portrayed, but in fact the lesson has nothing to do with optics. The figure in the lesson is redrawn in Chapter 3 in an attempt to decipher what it means, and I have similarly redrawn it here. A preoccupation with material culture thwarted the decipherment, since in the end no satisfactory explanation for the enigmatic figure was found, but what it shows, in fact, is Oddi s beautiful construction of a parabola given its vertex D and its focal point K. Choose a point N on the axis DK, and construct a perpendicular to DK through N. Prolong DK in both directions, and find point L such that ND=DL. Then the circle with center K and radius KL intersects the perpendicular through N in C, a point on the parabola. The point I is also on this circle, as I have indicated by the dotted arc (not part of the original figure). That the point C is a point on the parabola is immediate, since NC is the geometric mean of IN and NL, and IN is twice the focal length, independent of the choice of N. In the lesson of the double portrait Oddi is about to explain, having drawn lines IC and AC, what is most beautiful about this construction, namely that it does not just construct the point C, it also finds the tangent to the parabola at C, namely the straight line LC. Thus the parabola is represented as the envelope of such lines, something that impressed Galileo s student Buonaventura Cavalieri, although he did not completely remember how it was done (note 20, p. 271). The line DM is included in the figure as the simplest (degenerate) case of such a line, being tangent to the parabola at D. Reading the mathematics changes the meaning of the double portrait, which does not at all allude to material culture, but rather to a purely geometrical idea. The 5

6 A B C G I K N D L H F E M Figure 1: Geometrical figure redrawn from the double portrait of Oddi and Linder mirror visible only darkly in the background contrasts with the bright geometry in the foreground, contradicting, if anything, the importance of material culture in Oddi s and Linder s notion of what they were doing together. To notice this is to raise anew the question of what mathematics was, but to be less confident of the answer. 6