Dr. Walter Huddell
Over the winter recess I was able to read UCLA historian Amir Alexander’s Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. Well known are the battles for the soul of the European continent in the 16th and 17th centuries: the Protestant provocation of Church authority, Galileo and Kepler’s challenges of the geocentric universe (and man’s place in it), Hobbes’s rousing political philosophy and Descartes, Locke and Bacon’s epistemic innovations all played into a kind of upheaval unlike the West had seen prior. Less well known is the dispute over the mathematical controversy surrounding infinitesimals.
Informally, infinitesimals are geometric objects with zero (or very close to zero) magnitude in a given dimension. Infinitely many such objects arranged adjacent to one another could be understood to sum to something with nonzero magnitude in that dimension, or so the speculation went. A simple example which gives the flavor of infinitesimals would be the pages that make up the thickness of a book. The trouble was, early on, most of the work which employed infinitesimals lacked the kind of rigor that is typically associated with mathematics. In particular, the theory of infinitesimals led to all kinds of strange results and paradoxes, not in keeping with the tried and true axiomatic system found in Euclid’s Elements, which was central to so much of Western education, built on Aristotelian syllogism.
Alexander looks at the juxtaposition of the arguments over the infinitely small alongside the aforementioned ecclesial, cosmological and political disputes mentioned above. He paints a picture wherein Euclidean geometry represents order, stability and authority over and against the fast and loose “rules” that many early advocates of infinitesimals used. The tensions here parallel those in the broader intellectual and theological community. The study of infinitesimals was considered such a threat that their study in Jesuit schools was banned in 1632 by the Revisors General. Alexander goes so far as to suggest that the Jesuits believed if the certainty of Euclidean geometry had not been threatened, “the Reformation and all the chaos and subversion that flowed from it would have never taken root.” In fact, the argument goes, the more liberal approach to the study of infinitesimals in England set the stage for her leading role (think Newton and Locke) in the scientific revolution vs. the decline that occured in Italy on that score after Galileo. As overstated as this premise may be, this interdisciplinary historical analysis seems to be right on the money.
Leah Sioma ’14
Sometimes the worst thing about a book is that it’s just too short. Thankfully, The Thinking Women’s Guide to Real Magic is not afflicted with this problem. Even 563 pages isn’t nearly enough space to explore the world Emily Croy Barker has built in any satisfactory manner. Part Ivy-league graduate fiction, part George MacDonald, and part Tolkien, this novel is a delight. The main character Nora is swept out of her graduate school life into a fairy land of romance and beauty. But not all that shimmers is true and good, and when Nora is rescued by the Snape-looking magician named Areundiel, an exploration of magic, the nature of things, and knowing thyself ensues.
One theme of the book I’ve been reflecting on is how evil can afflict us long after we no longer participate in it. How are you wed to your mistakes? In what ways can you break ties to the things that have led you to where you now stand? And how can other people know you truly when you have invisible or maybe very visible scars of your errors? I should tell you that Barker leaves a major plot line concerning this theme unresolved, though (thank goodness!) there is a sequel in the works.
Emily Croy Barker is a delightful author, and this debut novel is stuffed with intriguing ideas and references to well-loved literature. If you’re looking for a world to fall into for a little while, I highly recommend The Thinking Women’s Guide to Real Magic.