### "Figures of Thought” is a literary study of one of the great works of the physical sciences–

James Clerk Maxwell’s “Treatise on Electricity and Magnetism”. Careful study of Part IV of the “Treatise” reveals many ways in which mathematics has its rhetoric just as other forms of language do, and that the shaping of equations and diagrams in turn gives shape to the thoughts which they convey. Maxwell is an artist with numbers and figures, and uses his skills to open his readers’ minds to a new way of looking at the natural world-the way of the “field”.

Maxwell is very conscious of his debt to Michael Faraday, to whom, he insists, the idea of the field is due. Part IV of the “Treatise” takes truly dramatic form as Maxwell leads us along Faraday’s path as far as that path was able to go. We meet an impasse, however, with a fundamental problem Faraday had been unable to solve. Only by standing with Faraday at that dark place can we recognize the power of the new mathematical form Maxwell invokes to capture the idea of the field. This is Lagrange’s calculus of variations, capable of addressing the electromagnetic system as a single, fully connected entity.

It would have been easy to leave Faraday’s methods behind at this point, but in something akin to an act of love Maxwell makes sure to interpret this new view of the field in ways Faraday would have understood. By the same act, the new field idea becomes for Maxwell by no means a formal, merely symbolic abstraction. He reads his field equations as expressing a real entity, whole and filling space, and bearing true momentum and energy. In this way his “Treatise” emerges as a mathematical work whose symbols are filled with meaning, a true example of natural philosophy in a sense we would do well to remember today.

The cover image of "Figures of Thought" is the stairway of the house on India Street in Edinburgh in which Maxwell was born and where he spent much of his time while a student in Edinburgh; it is now the home of the Maxwell Foundation. Maxwell was always fascinated with curious spatial configurations, especially those associated with the magnetic fields of current flows. It seems inescapable that this stairway must have made an early impression on him, as suggested by this image from his "Treatise":

### Review of "Figures of Thought"

by Diane Greco Josefowicz

Thomas K. Simpson. Figures of Thought: A Literary Appreciation of Maxwell's Treatise on Electricity and Magnetism. xix + 169 pp., figs., bibl., index. Santa Fe, N.M.: Green Lion Press, 2006. $17.95 (paper).

Here, at last, is an answer to those who think mathematical physics has nothing to do with poetics. Although Thomas K. Simpson's Figures of Thought is modestly billed as an "appreciation" of James Clerk Maxwell's monumental Treatise on Electricity and Magnetism (1873), it is really a tour-de-force reading, one that lavishes on the Treatise the sort of scrupulous formal attention usually reserved for the masterpieces of Western literature. Simpson thinks Maxwell's Treatise, in fact, is literature-and he wants you to see it that way too. A trained classicist as well as a physicist, Simpson looks closely at ten chapters of book 4 of the Treatise, showing how Maxwell introduced rhetorical figures and tropes to articulate and formalize his intuitions about the electromagnetic field. Simpson's presentation of the relevant rhetorical, poetic, mathematical, and physical concepts is clear and graceful. Like Maxwell's Treatise, however, the book is not for the mathematically faint of heart. Although Simpson explains just about every symbol and expression that might trip up his reader, some familiarity with the mathematics of differential equations is helpful.

Simpson's treatment of Maxwell is not especially historical; he approaches the Treatise as if the conditions of its production are basically irrelevant to what it has to say. This narrow focus is perhaps the result of the book's curious history. Although it was published only this year, Figures of Thought, which was originally Simpson's dissertation, has circulated in manuscript since 1968. As an underground classic of nearly forty years' vintage, Figures of Thought was written when the New Criticism-a school of literary criticism that approached all texts as autotelic, or complete in themselves, just as Simpson approaches Maxwell's Treatise- was, if not exactly new, still worthy of serious consideration. While Simpson does not explicitly acknowledge the New Critics as models for his approach to Maxwell, his debt to them seems obvious, at least to me. But Simpson's focus on the work itself, rather than its contexts of production or reception, is not a fatal flaw. Rather, it is a choice-and the choice is interesting. Historians looking for a novel approach to Maxwell, or to mathematical physics in general, will find much that is provocative and interesting here; those interested in the rhetoric of science may be surprised to discover just how rhetorical the mathematical sciences can be. In its attention to the nuances of Maxwell's thought, Simpson's book recalls Jed Z. Buchwald's From Maxwell to Microphysics (Chicago, 1985) and Daniel Siegel's Innovation in Maxwell's Electromagnetic Theory (Cambridge, 1991). But while Buchwald and Siegel restrict their studies to Maxwell's physics, Simpson wants to show how Maxwell's Treatise is, in its rhetorical complexity, on a par with such touchstones of Western civilization as the Oresteia. Simpson's genius is that, by the end of the book, we believe him.

DIANE GRECO JOSEFOWICZ

Published in ISIS 2007