



"Figures of Thought" 

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 (left) from his "Treatise". 

“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 worldthe 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. 

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). 