Galileo's Muse: Renaissance Mathematics and the Arts

by Mark Peterson
Harvard University Press, 338 pp., $28.95

 

 

Very often it takes the work of an outsider, with a fresh pair of eyes, to make an original contribution to any academic field—especially a field such as Italian Studies, whose tentacles reach into any imaginable branch of the humanities or sciences. Mark Peterson: a physicist, mathematician, and astronomer, is precisely that much needed outsider to the traditional dominion of italianisti. Peterson’s recent Galileo’s Muse offers a refreshing perspective on the great giant of Italian science, as well as on the very nature and genealogy of the scientific disciplines in Galileo’s age. The portrait of Galileo presented by Peterson is that of a great humanist, rather than his traditional and popular image as the very incarnation of scientific observation and experimentation, and in stark opposition to the oppressive ecclesiastic institutions of the Counter-Reformation. As the author puts it, “Galileo needs a public relations makeover.” And he is about to get it. Peterson’s first task is to analyze the state of mathematics during the Renaissance, which he describes as “weird” on more than one occasion—a weirdness resulting from its odd mixture of pure geometric abstraction, in the style of Euclid and the Alexandrians, and the moralizing, philosophical overtones of Aristotle and Ptolemy. This picture, though convincing as it is, is a convenient one for Peterson, as it allows Galileo to emerge from any side of the multifaceted and confused field of Renaissance mathematics. Yet perhaps more interesting than Peterson’s transformation of Galileo from scientist to humanist, is the transformation of other, earlier figures—above all Dante, who becomes a great mathematician. In tracing Galileo’s intellectual ancestry, Peterson turns to Dante’s puzzlingly abstract descriptions of the heavenly spheres in the final canti of Paradiso, in which the architecture of the heavens is described as what Peterson calls, in twentieth-century terms, a “3-sphere.” If a normal sphere (2-sphere), in three dimensions, is made of two attached hemispheres, a “3-sphere” is made of two spheres, attached on each concentric ring of latitude. Far from an easy concept to visualize, it exists in four dimensions, and most importantly, is a non-Euclidian space. Similarly, the Comedy’s final lines, which famously reference the impossibility of ‘squaring the circle,’ have Dante anticipating the mathematical concept of limit; and nearly four centuries before Newton and Leibniz invented the calculus required to articulate it effectively. This image of Dante as an expert geometer highly conscious of Euclid is quite seductive, and the argument seems generally well founded and equally well argued—but in a certain sense it almost gives too much responsibility to Dante. It could simply have been that he was exceedingly well-read in all number of disciplines, and that it was no specific mathematical expertise, but rather a general interest which prompted his seemingly advanced geometrical descriptions of the heavens. Piero della Francesca is likewise viewed as mathematician first, and painter second; but in this case Piero’s own published mathematical treatises lend support in this regard. For all his painterly talent, it was Piero’s geometric conception of perspective which allowed for the originality of works such as his Flagellation and Resurrection. If it seems Peterson’s narrative has turned away from Galileo himself, it is exactly the case, as the middle half of Galileo’s Muse focuses on the latter half of the title, exploring Vitruvius and Alberti, Pythagoras and Zarlino, Kepler and Tycho, while occasionally returning to Galileo’s writing to examine the influence of these figures on his thought. And their wildly diverse influences are essential to Galileo’s thought, often as complex as the state of Renaissance mathematics itself. Peterson’s book expertly demystifies this complexity, while simultaneously proffering a truly novel view of Dante the mathematician. Highly well-argued and impeccably written, Peterson effortlessly switches between mathematical, literary, and cultural registers in his explorations, and seems to master all three. A necessity for any level of interest in the subject, even for the most stubborn, traditionalist scholar of Galileo or Dante.