Maxwell's Equations, Written by a Man of Prayer

The lamps in that basement room at King's College never gave enough light, not for close work, and I remember blowing on my fingers between drafts because the cold came up through the stone floor no matter how many coals we fed the grate. I copied for him three winters running. Fair copies, mostly — pages of his slanted hand turned into something a printer could set without cursing. I knew the loops of his letters better than I knew my own signature by the end of it.

He worked the way a man works who has already seen the shape of the thing and is only waiting for his pen to catch up. Coils on the bench, a galvanometer with its needle trembling, and Mr. Maxwell bent over it all with his sleeves rolled and his spectacles pushed up on his forehead, muttering to himself in that soft Galloway voice that never quite lost its border burr no matter how many years of London and Cambridge tried to sand it down. He would write for an hour without lifting his eyes. Then he would stop, set the pen down flat across the inkwell's lip, and go still for a moment before starting again. I did not understand, at first, what that stillness was.

Before that winter, the world kept electricity and magnetism and light in three separate rooms, so to speak. Men who studied one rarely trespassed on the others. Mr. Newton's universe of hard little points pushing and pulling across empty space had held for a hundred and fifty years, and it held well enough for planets. But Mr. Faraday, over at the Royal Institution, had spent decades insisting that the space itself was doing something — that there were lines of force running through the air between a magnet and a wire, real as rope, though no one could weigh them or touch them. Most of the mathematical men treated this as poetry. Beautiful, maybe. Not physics.

Mr. Maxwell did not treat it as poetry. He set himself the task of putting Faraday's lines of force into the language of equations, and that meant building a mathematics for something nobody could see. Night after night I watched him wrestle notation into shapes it did not want to hold, crossing out whole sheets, muttering that the symbols were fighting him. Once he told me, not looking up from the page, that a man who tries to write down what the aether is doing had better be humble about it, because the aether does not consult him first.

By December of 1864 the paper had a shape he trusted enough to read aloud. I carried the folder to the Royal Society myself, tied with tape gone soft from handling, and I sat at the back of the room while he stood and read it to men who had known him since he was a boy prodigy at Edinburgh Academy answering questions about ovals that grown mathematicians could not answer. He read in that same unhurried voice. No flourish in it. Just a man walking his listeners, step by careful step, through equations that described how a current in one wire could tug at a current in another across empty space, and how that tug propagated — not instantly, but at a speed, like a ripple crossing a pond.

That speed was the part that stopped my breath, copying it out afterward. He had built the electromagnetic field as a thing with its own dynamics, its own energy stored in space itself rather than in the wires and magnets that seemed to cause it. And when he worked through what a disturbance in that field would do — how fast it would travel — the number that came out of his equations matched, near enough to make a man's hand shake, the measured speed of light. Light, he wrote, was nothing more nor less than a wave in this same electromagnetic field. Two sciences that had never spoken to each other in three thousand years of study turned out to be one science wearing two coats.

He was careful with the number. I remember him checking it twice, comparing it against the best measurements of the day, the ones from optics, and finding the agreement close enough that he allowed himself, in that dry way of his, to call it more than a coincidence. Not to shout it. He was not a man who shouted anything. But there was a kind of settled satisfaction in him for days afterward, the satisfaction of a man who has been climbing in fog and suddenly feels solid ground where he expected another ledge.

It was in the margins of those same working notes, the scraps I copied from before the fair draft, that I first saw the other side of him. Small lines, tucked between a derivation and a crossed-out attempt at the next. Not equations. Words. A plea, brief and plain, for steadiness in the work, for the mind to be kept honest, for the labor to serve some purpose beyond his own name. I did not speak of it to him. It did not seem a thing a copying clerk was meant to remark upon, a man's prayers caught sitting beside his mathematics like two lodgers who had agreed to share a room without complaint.

I asked myself, more than once, sorting those sheets by lamplight, what kind of man prays in the same hand he uses to calculate the velocity of light. I came to think there was no contradiction in it for him at all. He treated the universe as a made thing, ordered by a mind, and he seemed to feel that finding its order was itself a kind of listening. He was not hunting for God in the gaps where equations ran out. He found nothing strange in kneeling and calculating in the same evening, as if both were forms of the same attention.

The paper went to the printers under the title he had settled on, "A Dynamical Theory of the Electromagnetic Field," and it ran to some seventy pages in the Philosophical Transactions, volume one hundred and fifty-five, 1865. I held one of the early printed copies before he did, fresh ink still faintly sharp off the page, and I remember thinking it looked smaller in type than it had felt in the room where it was written.

The world did not fall over itself to embrace it. Most of the men who read it that first season found the mathematics thick going, and a few found the whole notion of a field with its own reality faintly absurd — space itself, doing work, storing energy, as though the emptiness between a lodestone and a nail were somehow alive with strain. Mr. Maxwell knew what he had put down on paper better than his critics did, and I heard him say once, in a letter he was dictating rather than reading aloud, that he held the paper to be great guns — said with a small dry laugh, as if surprised at his own daring in saying it, and then he went quiet and returned to correcting a proof sheet as though he had not spoken at all.

He left King's College not long after, worn thin by lecturing and administration both, and went home to Glenlair, to the low stone house among the Galloway hills where he had grown up, to write and to farm and to think without the London soot pressing on his chest. I did not go with him. I heard from him now and again, in the way a man hears from someone who was once close and then is not, letters growing shorter as the years did their work. He was drafting his great Treatise in those years, the full architecture the 1865 paper had only sketched, and later still he was drawn back out, this time to Cambridge, to build and to run the laboratory that would carry his name after he was gone.

News of his illness reached me the way such news always does, secondhand and late, softened by whoever passes it along so that you do not feel the whole weight until you are alone with it. He was dying slowly, the way men his age do not usually die, and among those who came to sit with him near the end was his cousin, Colin Mackenzie, who talked with him in those last quiet stretches about the things a man talks about when the ledger of his life is nearly closed.

Mackenzie carried what passed between them to Lewis Campbell, Mr. Maxwell's old schoolfriend from the Edinburgh Academy days, the one who would later write his life down properly for the rest of us to read. And it was through that chain — cousin to friend, friend to page — that the rest of us learned what Mr. Maxwell had said near the end of his working through of every system he could find, every philosophy that claimed to explain the world without leaving room for a maker of it. He had looked into most of them, he said, and he had seen that none of them would work without a God.

I did not need Campbell's book to believe it. I had copied the margins of his notebooks years before anyone thought to ask him a deathbed question, and the answer had been sitting there in his own hand the whole time, small and unremarked, tucked beside a calculation of electromotive force.

He died that autumn, not old as men count age in a long life, the mathematics of the field still working its way slowly into laboratories that had not yet learned to trust it. In the same year, across the sea in a town called Ulm, a child was born who would grow up to finish, in his own way, what those equations had started — a boy who did not yet know he would spend a career standing, as he put it much later, on Mr. Maxwell's shoulders rather than merely on Newton's.

That was Einstein's own phrase, offered decades on when someone tried to trace his lineage back only as far as gravity and falling apples. He said it plainly, correcting the record as a man corrects a small injustice done to someone he admires. He said, too, that before Mr. Maxwell, physicists had thought of the world as made of little points of matter pushing on each other across a void, the way billiard balls do, and that after him, they thought instead of continuous fields filling all of space, doing real work in the emptiness Faraday had first sensed and Maxwell had first written down in symbols. Einstein called it the deepest change in the notion of reality since Newton's own century. I do not think Mr. Maxwell, bent over his coils in that cold basement room, ever imagined the word deepest attached to anything he did. He imagined, mostly, getting the equations right.

They got taught everywhere eventually — compressed, over time, by other hands into four tidy statements that any student now scrawls across the flyleaf of a first notebook without a second thought for the man who spent whole winters wrestling them out of Faraday's lines of force. When the California Institute of Technology asked a younger physicist, Richard Feynman, in 1962, to lay the whole foundation of physics for a new class of undergraduates, he did not begin with falling bodies or orbiting planets. He began with Mr. Maxwell's equations, as though there were no other honest place to start a course meant to explain how the world holds together.

I think sometimes of the two things sitting side by side on those working sheets I copied so long ago — the long chain of symbols describing how a field bends and propagates and carries a wave of light across the dark between the stars, and beside it, cramped into the margin where there was barely room for it, a short line asking to be kept honest in the labor. Neither one crossed out the other. Neither one, in his hand, seemed to need defending against the other's company.

The equations are cut now into the stone and glass of laboratories and lecture halls that never knew his voice, distilled down from seventy pages to four short lines that a student can hold in one glance. Nobody troubles to print the margins alongside them. But I was there when both were still wet ink on the same page, in a cold room, by a poor lamp, in the hand of a man who believed the order he was uncovering had been put there on purpose, and who did not think it strange to ask, in the smallest possible script, for help in reading it rightly.

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