I am halfway through The Man Who Changed Everything, a biography of James Clerk Maxwell, written by Basil Mahon. As a physical chemist, I know something about Maxwell’s scientific achievements. The Maxwell-Boltzmann distribution shows up in multiple places because chemistry is about the movement of zillions of tiny particles, meaning you have to apply statistical methods to bridge the microscopic world to macroscopic phenomena that we large lumbering humans observe. Maxwell’s 1873 paper titled “Molecules” is marvelous, showcasing his lucid writing and insightful though; I have on occasion assigned it to first-year undergraduates along with light annotations to help them read along. I mentioned this in my very first blog post!
What I didn’t know much about, and am delighted to learn from Mahon’s book, is who James Clerk Maxwell was as a person. I learned about his rural upbringing that made him initially stick out as a weirdo in a more urban school, and how his geniality, generosity and genius eventually won over his classmates. While his mother had passed away in his early life, he had a loving extended family, and in his early twenties, he devoted much of his time to caring for his ailing father. He was beloved by his friends, an occasional prankster, liked to exercise, and wrote poetry. Given his fame for conjuring mathematical relationships of physical phenomena, I was surprised to learn that he frequently made lots of math mistakes in his derivations, but his scientific intuition was brilliant and almost always on the mark. A famous contemporary scientist said: “He is a genius, but one has to check his calculations.”
Maxwell was also a devout Christian but did not get sucked in to the many debates pitting science against religion. In declining to join an eminent society discussing such matters, he replied: “I think that the results which each man arrives at in his attempts to harmonise his science with this Christianity ought not to be regarded as having any significance except to the man himself, and to him only for a time, and should not receive the stamp of a society. For it is in the nature of science, especially those branches of science which are spreading into unknown regions, to be completely changing.” Maxwell’s views on the relationship between theory and experiment in science are also immensely quotable, for example: “I have no reason to believe that the human intellect is able to weave a system of physics out of its own resources without experimental labour. Whenever the attempt has been made it has resulted in an unnatural and self-contradictory mass of rubbish.”
I confess that I never took a physics course in college or beyond. How I became a professor who teaches physical chemistry still amazes me. My weak physics background, and perhaps lack of effort to improve my mediocre mathematical ability, means that I don’t really understand Maxwell’s famous equations although I do have the gist of its broader impact. I was heartened to read that Maxwell made great effort to find physical analogies to explain seemingly mysterious phenomena such as lines of force. Even now, I find it challenging to think through the lens of a field approach, and I use Maxwell’s ideas of fluid flow as a crutch to think about flux. Maxwell’s analogy of potential difference and hydrostatic pressure is also helpful; I use it when I teach electrochemistry in General Chemistry. (In fact, I will use it in my class tomorrow morning!)
What jumped out at me in reading the account of Maxwell’s struggle to derive a mathematical framework for Faraday’s lines of force was the ability to bring together insights from one area of physics to solve another. The jumping off point was a discovery by William Thomson (later Lord Kelvin) who found that the equations for the strength of electrostatic force looked similar to those describing the rate of steady heat flow. This seems odd: why would static equations resemble dynamic ones? But Maxwell made it work by imagining the flow of an “ideal” weightless incompressible fluid through pipes. I’m presently covering kinetics in my Physical Chemistry, and was looking ahead at my lecture on molecular collision theory. With Maxwell in my mind, one of the equations looked suspiciously familiar. I flipped back to a lecture I had given in the second week of the semester on the Lennard-Jones potential energy curve (for two-body molecular interactions), and sure enough, the mathematical expression for the static temporary dipole attraction looked analogous to the rate equation in collision theory. Wow!
I was impressed to read about the breadth of problems Maxwell tackled. His work on optics and colour vision culminating in his famous colour triangle is brilliant. He even devised spectacles for those with red-green colour-blindness. I did not know that Maxwell won a prestigious award for deriving mathematical equations to describe the conditions of stability of Saturn’s rings. When tackling the possibility that the rings are a fluid rather than a solid, he showed they would break up into smaller entities. But how would a hodgepodge of particles maintain an orbit? Maxwell showed that such rings vibrate in different ways and could be stable at low enough average densities. When he considered multiple rings, “he found that some arrangements were stable but others were not: for certain ratios of the radii the vibrations would build up and destroy the rings.” This sounds like the remarkable Bohr orbits of quantum mechanics where the electron orbiting the nucleus is treated as a standing wave to be stable.
Another surprising thing I learned was that despite his lucid and clear writing, Maxwell’s success in classroom teaching was mixed. Mahon writes: “For all his talents, he never mastered the technical part of teaching. He would prepare a lesson beautifully, do fine for a time while he stuck to his script, and then fly into analogies and metaphors which were intended to help the students but more often than not mystified them. He was not expert on the blackboard, where he made algebraic slips which took time to find and correct. And yet the students liked him and some found him truly inspiring… It seems paradoxical [for] such a fine scientific writer… as he believed fervently in the value of good education… Appreciating that people learn in different ways, he may have tried too hard to bring in helpful illustrations and analogies, confusing his audience with a welter of rapidly changing images… And perhaps he was too much of an idealist. All good teachers aim, as he did, to teach people to think for themselves, but most also recognize that all some students want is to gain a second-hand smattering of the subject so they can pass exams, and make a specific effort to help them succeed in this limited ambition. Maxwell never did.”
Those are sobering words for me as an educator who is also very excited about imparting chemistry to my students. I certainly try to give metaphors and analogies which I hope are helpful. Given my theoretical bent (a product of both my training and my interests), I have noticed that I now spend more time trying to impress upon my students the key frameworks on which my discipline builds its foundations. And I do this unprompted; it’s not in my lecture notes. It’s almost as if, like Maxwell, I can’t help myself. I feel compelled to make those connections to the broader edifice of how chemists think about the world. One progresses from novice to expert by first glimpsing and then progressively seeing more clearly the abstract categories that undergird chemical knowledge. I pontificate more than I used to. When I first started teaching, I couldn’t see some of the hidden frameworks; my focus was getting the students through the material in a systematic way that allowed them to (hopefully) provide them the basics to solve chemical problems on an exam to prove they understood what I was trying to teach. I am still aware that the majority of students in my classes are interested in the “second-hand smattering of the subject so they can pass exams”, and make efforts to help them along, but I also want to truly inspire the minority to see the beauty and depth of chemistry. Maxwell cannot help me resolve this tension, but I am inspired by his efforts. I look forward to sinking my teeth into the second half of his biography!
