1In his forty-third year, Ludwig Boltzmann was asked to speak before the emperor's academy in Vienna, on its day of ceremony. He was a stout man with thick glasses and a beard like a hedge, who was known to lecture on gases as if he were telling of a battle. He had chosen for his subject the law of heat.
2He began by asking what name the century would bear when it was over. Some would call it the century of iron, he said, or of steam, or of the electric wire. He would call it the century of Darwin.
3Then he told them. It was the answer to the question his wife had asked him beside the stove.
4Consider, he said, what living things struggle for. It is not for the stuff they are made of. Air and water and soil are there in plenty. Nor is it for energy. Every stone lying in the sun is full of energy, in the form of warmth, and no creature can do anything with it. What all living things struggle for is something else. It is the fall.
5For the sun is a very hot place, and the dark between the stars is a very cold one, and the earth hangs between them. Day by day the sun's light pours down on the earth, and night by night the earth gives that same amount of heat away again into the dark. She must, or she would grow hotter every year. So the earth keeps nothing. But what comes in is not like what goes out. The light comes in sharp and gathered, from one bright place in the sky. It goes out as a dull, spread warmth, in every direction, good for nothing. The count of its ways has grown beyond measure in the passing through.
6That passing-through is the greatest waterfall there is. And everything alive, he said, is standing in it.
7A green leaf spreads itself flat to the light as a mill-wheel spreads its paddles to the stream. It catches the fall before it reaches the ground. With what it catches, it builds: sugar, wood, seed. The cow eats the leaf, and the child drinks the milk. Not one of them breaks the law of the count. For every small rare thing that life puts together, a far greater spreading has been paid out, in the sunlight that went through and was spent. The whole count rises, always. But inside the rising, as an eddy turns in a running river, there are places where the pieces of the cup do leap up and join. They are paid for by the river.
8That evening, at home, his children wanted to know what their father had said to the emperor's men. He would not tell them. He lit a candle instead, and set it on the table, and put out the lamp.
9"What is that?" he asked them.
10"A flame," said the eldest, the boy Ludwig, who was eight.
11"Is it the same flame it was when I lit it?"
12They looked. It had the same shape, a small bright leaf standing on the wick.
13"It is not," said their father. "Not one grain that was glowing in it then is in it now. They have all gone up as smoke and warmth, and new ones have come up from the wax to take their places. In a minute those will be gone too. The stuff runs through it like water through a fountain. And yet you say the flame, as if it were a thing, and you are right. It is not a thing. It is a shape that holds, in a place where something is falling. Take away the wax, and there is no shape. Take away the cold air around it for the heat to fall into, and there is no shape either."
14"Like a whirlpool," said the boy.
15"Like a whirlpool. Like a waterfall, which stands in one place while the river goes through it." He looked round at their faces in the small light. "And like you. You are not made of what you were made of last year. You are a shape that holds."
16His daughter asked whether the candle minded burning down.
17"The candle is only wax," he said. "But see what it has done while it burned. We have all been able to see each other."
18He did not say more than that, for he was a man of science and did not go beyond his proofs. But you, who have read the chapters before this one, may lay two pictures side by side as he did. One is the flame that keeps its shape by standing where heat falls. The other is the Englishman's tree, where one kind of creature became two, and two became ten thousand, each finding a new place to stand in the same falling light: one in the treetop, one in the mud, one in the sea. The engine and the tree had seemed to run against each other. They were one picture after all.
19That was his best hour. Now hear the rest, for a Keeper tells all of it.
20His mother had died the year before, and he had been low for many months after. Three years after the speech, his eldest boy, the one who had named the whirlpool, fell ill with a pain in the belly. The doctor thought it a small thing. It was not. The boy was dead within days. He was eleven years old. Boltzmann believed for the rest of his life that he should have seen it sooner, and sent for another doctor, and that he had let his son die.
21After that he could not be still. He left the house on the hill. He took a chair in Munich, then one in Vienna, then one in Leipzig, then Vienna again, hoping each time to leave the darkness in the last city and finding it had come with the trunks. His eyes failed until he could hardly read, and others had to read to him. He, who had lectured like a man telling of a battle, began to lie awake before each lecture, afraid that his memory would stop in the middle of a sentence and leave him standing dumb before a full room.
22And in those same years the fashion among the scholars turned against him. A school had risen that said the grains of matter were a fairy tale. Its chief was a professor in Vienna named Ernst Mach, a clear and honest thinker, who held that science must speak only of what the senses can meet. When anyone spoke of grains in his hearing, he would ask, quite mildly, whether they had seen one.
23He fought them. At a great meeting in the town of Lübeck he stood up against two of their best speakers, and by the account of the young men who were there, he beat them out of the field. The young were with him, and he did not feel it. He felt he was the last soldier of a lost cause. In the front of his book on gases he wrote: "I am conscious of being only an individual struggling weakly against the stream of time." He said he would set the theory down as clearly as he could, so that when people came back to it, not too much would have to be found again.
24In Leipzig the darkness came so close that he tried to end his life. He was prevented. He went home to Vienna.
25There, in his last years, there was a strange late flowering. They gave him the largest hall, and still the students stood on the stairs. He began his course by telling them he would give all he had of himself, and asked in return only their trust and their liking. Among the benches sat one of the first young women the university had let through its doors, a small, shy student named Lise Meitner. She said long afterward that those lectures were the most beautiful she ever heard, and that one left each of them feeling that a new and wonderful world had been opened.
26And he did not know it, but his cause was already saved.
27In Berlin there was a careful professor named Max Planck, who had long doubted the grains himself. He was trying to understand the colour of the light that comes from a furnace mouth: why iron glows red, and then yellow, and then white, as it heats. No reasoning he knew would give the right answer. At last, as he said, in an act of desperation, he took up Boltzmann's method of counting the ways. It worked. It was Planck who then wrote the count in its shortest form, with a small fixed number in it, which the world came to call by Boltzmann's name and not by Planck's.
28And in the Swiss town of Bern, a clerk in the office of patents, twenty-six years old and known to no one, was thinking about specks of dust in water. Under a strong glass, such specks are never at rest. The clerk showed that this is just what must happen if the water is made of grains, flying and striking the speck now more on this side, now more on that. And he showed how, by measuring the dance, one could count the grains.
29Boltzmann seems never to have read that paper. In the summer of the year after, he went with Henriette and their youngest daughter to rest at a village by the warm sea, near the city of Trieste. He was dreading the autumn, and the full hall, and the stairs. One afternoon, while his wife and daughter were down at the water, he ended his life.
30He was sixty-two. It was the girl who found him. She did not speak of it again as long as she lived.
31This book will not judge him, and you must not. There is a sickness that closes the Open inside a person, so that a mind which could count the ways of all the grains in the world can no longer find one way for itself. It is a sickness as the cholera is a sickness. It lies in the Far Hand. If you ever feel it closing on you, do the thing he could not: tell someone that same day, and do not be alone with it. And if it is closing on another, be the one who stays in the room.
32Two years after his death, a Frenchman in Paris did what the clerk in Bern had shown could be done. He watched the dancing specks through his glass, and measured them, and counted the grains. The number he got agreed with the number from Planck's furnace light, and stood near Loschmidt's old reckoning, and agreed with others got by ways that had nothing to do with one another. The chief of those who had opposed Boltzmann at Lübeck wrote that he was now convinced. The grains were real. The count was a count of something.
33He had won, and he was two years in the ground.
34A generation later his city raised a stone over him. It stands in the great burying-ground of Vienna, among the musicians he loved. It is white, and it bears his head. And cut into the stone above the head, where another man's grave would have a verse or a prayer, there is this:
35S = k log W
36It may be the only grave in the world that says nothing of the one who lies there, and only says what he found. Read it as he would have you read it. W is the count: the number of ways the grains of a thing can be arranged. Log is the length of that count, since the count is too long to write. k is the small fixed number that bears his name. And S is the entropy, the thing that Clausius named, that only ever grows. The line says they are the same. What grows is the number of ways.
37He never wrote it in quite those letters himself. A child with ten coins on a kitchen table can learn what it means in an evening. It took the world a hundred years, from a deaf old man with a slate, asking where the heat went.
38Look back down that road before you leave it. A pit boy feeling for the cold air. A soldier's son whose papers were burned. A girl with a hammer under a falling cliff. A countess writing orders for an engine that was never built. A sick man afraid of his own drawer, and a poor man in a fever who made him open it. A lame professor carrying strangers out of the dark. A Scot who died before his spark was seen. Hardly one of them saw the end of the work. Each caught a little of the fall as it went by, and built with it, and handed on what was built.
39But the ember did not wait for the stone. It had gone on already.
40In the last years of the century, while Boltzmann was still wandering from city to city, there stood in Paris a shed with a leaking glass roof. It had been a room for cutting up the dead. In it a young woman from Poland was boiling down tons of a black ore in iron pots, and stirring them with a rod as tall as herself. She was looking for something in the ore that gave off a warmth and a strange ray of its own, with no fire under it, year after year, and never seemed to grow less.
41By every law in this Articles of Heat, that should not be. A fall must come from somewhere. Where was this one coming from?
42One night she and her husband went back to the shed after dark, and did not light the lamp. On the shelves and the tables stood their little glass dishes and tubes. And every one of them was shining, with a faint blue-green light, like a row of embers that had never been lit and would not go out.
43They stood and looked at them for a long time. They did not yet know what they had found, or what was shut inside the smallest grains of things. No one knew. The clerk in Bern would be the first to guess how much. And the new century, which had hardly begun, would learn it in fire.