IMAGES AND REVERSALS
Vol.32 No.1 February 1999
James Clerk Maxwell, Working in Wet Clay
“If you can visualize the shape, you can understand the system.” 
James Clerk Maxwell, acknowledged by many to be the most important physicist of the nineteenth century, knew how to be a supremely competent scientist and mathematician. Yet, when necessary, he could draw on the talents of the artist and sculptor — for he knew if he could find a way to “visualize the shape,” then he could begin to really “understand” the vast complexity of the “system.” Accordingly, when he wanted to understand some deep and complex pattern in nature, he often dismissed conventional analysis and notation. Instead, he used the visual and spatial tools of the craftsman, mechanic and artist — modeling clay with wet hands to mold a tangible sculpture of the 3D image in his mind’s eye.
First Color Photograph
The fame of “Maxwell’s Equations” has meant that the name of James Clerk Maxwell is familiar to most persons having any form of scientific training. However, the full extent of his work and accomplishment is relatively little known. Members of SIGGRAPH may be especially interested to note that as early as 1860, Maxwell had began the scientific study of color — and had projected the first color photograph. In addition to developing the electrodynamic theory of light, he also began the systematic application of statistical methods in physics — including original methods to explain the nature of Saturn’s rings.
SIGGRAPH members may also be interested to note that in 1868, he wrote the first important paper on the cybernetic and control theory so central to computer technology — through an analysis of the common spinning ball governor. Along with important contributions to the geometry of optics, he also developed certain mathematical terms and coined terminology related to the study of vectors (familiar to many as the arrows used to represent the direction and magnitude of a force). 
Maxwell’s accomplishments were indeed remarkable. But it is also apparent that he had a number of the distinctive and mixed traits often seen in very strong visual thinkers. He seemed to have an unusual capacity to think in two ways: both visually and mathematically — and many of his considerable accomplishments may be traced to this ability. However, like many strong visual thinkers, Maxwell also had language difficulties.
On the one hand, he had no difficulty with reading or writing and was generally an excellent student for most of his life. However, on the other hand, he often had difficulty collecting his thoughts in order to answer on demand and under pressure an unexpected question. In addition, he was a severe stutterer and this continuing difficulty adversely affected his career as lecturer and professor.
As a child, he had shown a great love of drawing and had near relatives who were artists. He had a hearty and whimsical humor. And as an adult, he seemed to retain a childlike curiosity about everything, often seeing similarities and making connections among the most diverse and apparently unrelated things.
Gibb’s “Graphical Method”
An important illustration of the operation of Maxwell’s visual-spatial thinking is his early appreciation of the work of the American physicist, J. Willard Gibbs, one of the major figures in the development of the study of thermodynamics. In the 1870s, Gibbs published a series of papers addressing the complex thermodynamic behavior of water and other fluids — using an unusual and innovative “graphical method,” as he called it.
This method involved a three-dimensional mental model comparable to what we would now call a “surface plot” — a kind of 3D graph that shows a number of points covering an undulating surface with rises and depressions like small mountains, hills and valleys. As any point (representing a particular temperature, volume, pressure, etc.) moves over the surface plot, the conditions change in certain predictable ways, giving a deep understanding of the behavior of the complex system — based on being able to visualize the complex shape.
Gibbs wrote about his new method and described it mathematically, yet he made no effort to make a diagram of what was, apparently, clearly seen in his own mind’s eye. The new method and the difficulty in having to visualize such complex material resulted in little attention from Gibbs’ scientific colleagues, especially in the United States.
Maxwell’s Sculptured “Fancy Surface”
Yet, when Maxwell read Gibbs’ papers in Britain, he immediately saw the power and the potential of the new graphical method. Indeed, so great was his interest, that “he spent an entire winter” constructing a 3D clay model of a surface using Gibbs’ data.  As Maxwell explained in a letter to a scientist friend, “I have just finished a clay model of a fancy surface showing the solid, liquid, and gaseous states, and the continuity of the liquid and gaseous states.” 
What Maxwell had made, then, was a kind of sculpture — patiently calculating the approximate position of each point in 3D space and then adjusting the shape of the clay surface to correspond to the array of points in different positions (just as a sculptor or stone cutter would check his own work with a series of caliper measurements from an original model).
Maxwell sent a plaster of Paris cast of the clay model to Gibbs and kept two more in his own laboratory at Cambridge University. Gibbs’ copy is still on display in a glass case outside the Yale University Physics Department — while Maxwell’s own copy remains on display at the new Cavendish Laboratory just outside Cambridge in England. Sculpture is a reproducible and durable medium, even in plaster.
What is most important for our discussion, then, is the way the highly visually oriented Maxwell immediately seized upon Gibbs’ unusual but strikingly apt visual-spatial approach. Because Maxwell by this time was famous among scientists while Gibbs was entirely unknown, Maxwell was eventually able to move a whole generation of American and European scientists to appreciate the true value of Gibbs’ novel approach.
However, while Gibbs’ method and approach in mathematical form came to be fully appreciated over time, the visual and spatial model on which the method was based has been almost completely ignored for more than a century — until very recent times. That is, for more than a century, Gibbs’ equations have been memorized by students of nearly every technical occupation, yet the visualizations on which these equations are based received virtually no attention at all during this period.
Rediscovering the Geometry of Thermodynamics
As explained by University of Iowa Chemistry Professor Kenneth R. Jolls, “for those who could not follow the elaborate verbal manipulation of lines and planes in space that permeates [Gibbs’] writings, the physical meaning and the artistic beauty of these brilliant analogies were lost. Indeed, the interesting connections between thermodynamics and geometry, which were the essence of Gibbs’ theoretical development, have all but vanished from the literature.”
Recently, however, with the development of computer-generated 3D graphics, all this has started to change. Professor Jolls and his graduate student Daniel Coy developed a means of doing what Maxwell had done — but this time rapidly on a powerful graphics computer rather than over several months in modeling clay and plaster. According to Jolls, “there can be no doubt in the mind of any serious thermodynamicist” that images like those being produced on their computer screen “were vividly in Gibbs’ mind as he wrote his famous trilogy [of papers] in the mid 1870s.” 
So it is that the visual-thinking Maxwell immediately perceived the value of a visual-spatial approach which he could model in clay — but which we can now see modeled on a computer screen or in a virtual reality display. The technology and the speed are enormously different, but the concept and the visual image in the mind’s eye are exactly the same.
With Limited Words, Anticipating Pixar and the NSF
The reference to the art of sculpture is especially apt in the case of Maxwell. As I have noted in previous columns, strong family connections can often be observed between those with some form of dyslexia or learning disability and strong talents in the visual or performing arts. Also, it is commonly observed that many inventors have been artists or closely related to artists.
This connection is of particular interest to one of Maxwell’s biographers as he attempts to gain a better understanding of Maxwell’s extraordinary abilities: “The persistence of the artistic gift in a family so practical in outlook is a striking fact, one that must be born in mind in analyzing Maxwell’s genius. Each generation threw up clever artists, among whom not the least able was Maxwell’s cousin Jemima . . . whose brilliant water-color paintings of Maxwell’s childhood are a perpetual delight to Maxwell scholars.” 
It is of perhaps no small import that the display case at the New Cavendish Laboratory outside Cambridge that holds Maxwell’s plaster model also holds two rotating drums with slits designed by Maxwell with images painted in watercolor with his own hand. One animation portrays a man and woman dancing; the other animation visualizes two smoke rings interacting. Accordingly, we can easily say that in one glass case we have concrete evidence that Maxwell anticipated, with all else, the basics of the animated cartoon (brought to full computerized 3D feature length a short time ago by Pixar and Disney) as well as the first scientific visualization (long promoted at the Supercomputer Centers and elsewhere by the National Science Foundation).
Maxwell “In a Prop”
Maxwell’s early biographers, Campbell and Garnett (1882), describe the period from 1847 to 1850, when Maxwell was between the ages 16 and 19: “When he entered the University of Edinburgh, James Clerk Maxwell still occasioned some concern to the more conventional amongst his friends by the originality and simplicity of his ways. His replies in ordinary conversation were indirect and enigmatical, often uttered with hesitation and in a monotonous key…
“When at table he often seemed abstracted from what was going on, being absorbed in observing the effects of refracted light in the finger-glasses, or in trying some experiment with his eyes — seeing round a corner, making invisible stereoscopes, and the like. Miss Cay [his aunt, the sister of his late mother] used to call attention by crying, ‘Jamsie, you’re in a prop’ [a mathematical proposition]. He never tasted wine; and he spoke to gentle and simple in exactly the same tone. On the other hand, his teachers… had formed the highest opinion of his intellectual originality and force… “ 
The brief description of Maxwell at the dinner table is particularly telling in establishing his relative disinterest in conventional table conversation and his persistent preoccupation with observing the operation of light and other natural phenomena, whatever the situation.
It is also notable that all these examples are of a visual nature (“trying some experiment with his eyes — seeing around a corner, making invisible stereoscopes”). These examples lend themselves to building mental models of optical interaction and spatial relationships, which are, in turn, closely related to the mathematics of area, field, line and force.
Maxwell relied heavily upon visual, mechanical and geometric approaches in his mathematical and scientific work. As one biographer observed: “Maxwell’s starting point in mathematics was Euclidean geometry. Euclid is now so out of fashion that few people know the excitement of his intellectual rigor…. With Maxwell the love of geometry stayed… The love of geometry also helped interest Maxwell in Faraday’s ideas about lines of force.” 
The common thread throughout the great variety of Maxwell’s accomplishments is the interplay of force and substance in a largely visual-spatial arena. The visual-spatial dominated his work. However, from the stories of his daily life we might also infer that he was thinking in geometric terms much of the time, wherever he was and whatever he was doing.
Thomas G. West was recently interviewed for a video documentary called The Unwrapped Gift. Made primarily for dyslexic university students in Britain, the documentary deals with the implications of moving from a culture based mostly on words to a culture where high level work will increasingly involve the rediscovered integrative power of the image. Currently, he is working on a conference and associated research agenda concerning visual thinking and visualization technologies for the U.S. National Library of Medicine and other organizations.
Maxwell’s writing and research show an unusual flexibility of mind, which seems to be characteristic of some strong visual thinkers. Maxwell could move from any given structure to another quite different one with relative ease, retaining underlying similarities of approach. “Maxwell…was continually changing his outlook. His five leading papers on electromagnetic theory written between 1855 and 1868 each presented a complete view of the subject, and each viewed it from a different angle. It is this variety that makes Maxwell’s writings, in Jeans’ words, a kind of enchanted fairyland: one never knows what to expect next.” 
Maxwell was a professional scientist, but he was able to see well beyond the conventional science of his day. He was as fully at home in the intuitive and visual world as he was with the world of the “professed mathematicians.” He knew mathematics, but did not think in the same way as the conventional mathematicians of his time. He knew their ways but was not restricted by them.
He approached physical phenomena with complex mechanical models, yet when he was finished, all such analogies were made impossible (at least for a time). The consequences of his work were so extensive and profound that they set the research agenda for the next half century. Yet, he never received, during his lifetime, the recognition given his contemporaries of lesser stature.
He was well educated, but his career was only modestly successful. His speech difficulties limited professional advancement throughout his life. Although he was eventually appointed head of the new Cavendish Laboratory at Cambridge University, it was only after two other preferred candidates had declined the position.
He died too young to elaborate his work fully or to gain full recognition for his accomplishments. Yet, in the physical sciences his work came to be acknowledged as the most important product of the entire nineteenth century. Maxwell never was able to lecture well, and yet he taught generations — sometimes because he was willing to renounce troublesome words and notation and attempt to visualize complex patterns in nature by molding wet clay with bare hands.