1In the days of the third Ptolemy, when the library at Alexandria had grown past counting, there lived in Egypt a man named Nakht whose trade was walking.
2He was one of the king's pacers. A pacer is a man trained from boyhood to take steps of one length and never lose count of them. Kings need such men. A king must know how far it is from this town to that, how many days an army will be on the road, and how much land a village has, so that he may tax it.
3Nakht had walked for the king for twenty years. He had measured fields from which the grain was then taken. He knew what the villagers called him behind his back, and sometimes to his face. He thought of himself as a pair of legs that belonged to the palace. He had no wife, for he was never anywhere long enough.
4He had one friend, and that was old Senu, who had taught him the trade. They walked as a pair. Each kept his own count and told it to no one until the day's end. If the two counts agreed, it was written. If they did not, the pair walked the stretch again. In twenty years they had quarrelled over many things, and never once over a number.
5One spring the keeper of the library sent for them.
6The keeper was a man from Cyrene named Eratosthenes. He knew a great deal about a great many things, about stars and poems and numbers and the shapes of lands. The other scholars had a nickname for him. They called him Second, because they said he was the second-best man alive at everything and the best at nothing. He did not seem to mind it.
7"I want the distance from this city to Syene," he said, "on the southern edge of Egypt, where the river comes down over the rocks. I want it as true as two men can make it."
8"The king has that distance," said Senu. "The tax boats have gone up and down for a thousand years."
9"The king has a boatman's guess," said Eratosthenes. "I want a count. And I want one of you standing beside a certain well in Syene at noon on the longest day of the year. You must look down it and tell me what you see."
10"Why?" said Nakht.
11The keeper smiled. "If I tell you now, you will think me mad and walk carelessly. Walk well. I will tell you when you come back."
12So they went south, along the edge of the fields, where the black earth stops and the red land begins. Each had a bag of pebbles at his left hip and an empty bag at his right. Every hundred paces a pebble went across. Every time the left bag was empty, a knot went into a cord. A boy with a donkey came behind with water and bread.
13It is a long land. They walked through the heat of spring into the heat of summer. The river lay always on their left hand, and the desert always on their right, and the sun went over them from one to the other, day after day.
14In the middle country they came to a village where the tax men had been the month before. The people there knew what pacers were. To them, two men counting steps along the edge of their fields could mean only one thing.
15It began with children throwing clods. Then it was men, and the clods were stones. Nakht took one on the shoulder. Senu took one on the side of the head. He went down on his knees and got up again, still moving his lips. He had not lost his number.
16They got clear of the village and went on. But Senu's head ached from that day. In the next week his eye on that side grew dim. Then a fever came. Near the old city of Thebes he lay down in the shade of a wall and said he would get up in the cool of evening.
17In the evening he gave Nakht his knotted cord. "Mine says the same as yours," he said. "I checked at noon. Do not let them write a guess, boy." He had called Nakht boy for twenty years. He did not get up.
18Nakht buried him in the red land above the fields, as well as a man can with a borrowed hoe. He set a stone on the place. Then he hung both cords at his belt, and walked on south, alone.
19He was bitter, and he had time to be. He thought: Senu died for a number. A number for a clever man in a cool room, who would not even say what it was for. And before that we walked twenty years so that kings could take grain from people who hate us. That is what we were. That is all the size we were.
20Six days below Syene, where the road runs between cliffs, three men came down out of the rocks at dusk. They had knives. They took the donkey and the bread. They took the bag from Nakht's right hip because it was heavy and they thought it was silver. They cut the bag from his left hip too. And one of them, for spite or for the worth of the cord, tore the knotted strings from his belt and carried them off into the dark.
21They left him his life. The donkey boy had run and did not come back.
22Nakht sat in the road that night with nothing. He knew to within a day's walk how far he had come. But the count since the last marked town was gone, pebbles and knots and all. It was four days of steps.
23He thought about it clearly. No one else was alive who knew the true count. If he walked on to Syene and gave a number, any likely number, it would be written, and no man on earth could say it was false. The clever man in the cool room would never know. Senu would never know.
24Do not let them write a guess, boy.
25He sat until the stars turned. Then he got up and walked north, back the way he had come. He walked four days without bread, drinking from the river, to the last town where the count had been written down. There he begged pebbles from the bank and a cord from a fisherman. He turned around and paced those four days again.
26He did not altogether know why. Only that the number was the one thing on that road that was his. The stones had not been his to stop, nor the fever, nor the knives. The count was his. If he spoiled it himself, the robbers would have taken everything after all.
27He came to Syene thin as a rope, three days before the longest day.
28The well was on an island in the river, an old deep shaft cut straight down through the rock. The people there showed it to him without wonder. Everyone in Syene knew about the well.
29On the longest day he stood beside it and waited. The sun climbed. The shadows of the walls drew in toward the walls. The shadow of a man drew in under his feet. At noon Nakht looked around him, and nothing in that town had a shadow at all. The posts had none. The palm trunks had none. He held out his staff upright and there was only a bright ring of dust around its foot.
30He looked down the well. Far below, at the bottom of the dark, the whole round sun looked back at him out of the water. The light went straight down the shaft and touched nothing on the way.
31He stood there until it slid off. He had walked the length of Egypt to see it, and he did not know what he had seen.
32He came home by boat, with the current. It took a month. He passed Thebes by night and did not sleep.
33Eratosthenes received him in a court of the library, beside a bowl of bronze. It was a deep round bowl like half of a hollow ball, and from the very bottom of it rose a thin upright pin.
34Nakht gave the count. It came to five thousand stades, as near as two men and then one could make it. He told about the well, and the staffs with no shadow. He did not tell about Senu. He found he could not.
35"Now I will pay you what I owe," said Eratosthenes, "which is the reason. On that same longest day, at that same noon, I stood here by this bowl. Here the pin did cast a shadow. A short one. See, I marked where its tip fell."
36There was a scratch on the inside of the bowl, a little way up from the pin.
37"The sun is very far off," said the keeper. "So far that its light comes down on Syene and on Alexandria in lines that run side by side, like the furrows of one field. Yet at Syene the light fell straight down the well, and here it fell a little aslant. The same light, the same hour. How can that be?"
38Nakht looked at the bowl. He was a man who had spent his life on the ground, and he knew ground. "The ground is not flat between here and there," he said slowly. "It bends away."
39"It bends," said Eratosthenes. "Wise men have long said the earth is a ball. They said it from the round shadow it throws on the moon, and from ships going down behind the sea. But no one knew how big a ball. Now look. That shadow covers one fiftieth part of the circle of this bowl. I measured it nine times. So the road you walked is one fiftieth part of the way around the whole earth."
40He knelt, as geometers do, and drew a great circle in the dust of the court. On its rim he marked off a short piece, no longer than a finger.
41"That is Egypt," he said. "That is your walk. Fifty of them make the circle. Fifty times five thousand. Two hundred and fifty thousand stades around. We are the first who have ever known it, you and I."
42Nakht looked at the finger's length on the rim of the circle.
43All of it was in there. The village with the stones was in there, too small to see. The palace was in there, and the king, and the king's granaries, and every field Nakht had ever measured, and every man who had ever cursed him. The cliffs where the robbers waited were in there. The four days he had walked twice were in there. And somewhere along that finger of dust, at a place he could have touched, was a stone in the red land above Thebes.
44Outside that finger was all the rest. Forty-nine parts of it, which no pacer had walked and no king had taxed. Lands and seas with no names.
45Something happened in Nakht then that he had no word for. It was as though he had gone straight up into the air, higher than a hawk, higher than a mountain, until he could see the river as a green thread and himself as a speck upon it. From there his bitterness was a very small thing. It had filled the whole road, and now it would not have filled a thimble.
46But this was the strange part. Senu did not grow small. Senu, who had kept his count with a broken head, was part of the first true measure of the world. The speck had measured the ball it stood on.
47"And the king?" Nakht said. His voice was not steady. "How much of the circle is the king's?"
48Eratosthenes looked at the mark, and then toward the palace wall, and he lowered his voice, though he was smiling. "The king has a part of the fiftieth part," he said. "I would not tell him so at dinner."
49Then Nakht laughed, for the first time since Thebes. And then he sat down in the dust of the court beside the circle and wept. The second-best man alive at everything sat down beside him and waited, and asked no question. That may be a thing he was best at.
50After a while Nakht told him about Senu, and the stones, and the knives, and the four days.
51Eratosthenes heard it all. Then he took the reed pen from behind his ear, and on the record of the measure he wrote two names where there would have been none. "A number is only as good as the men who would not guess," he said.
52The measure went out from Alexandria to every place where people cared about such things. It was not perfect. A stade was not the same length in every land, and the well is not quite under the sun's road, and the river road is not quite straight. But it was close. It was far closer than anyone had a right to expect from a stick, a well, and two pairs of legs.
53Eratosthenes went on to draw a map of the whole known world, with lines across it to find places by. He lived to be very old.
54Nakht did not walk for the tax men again. He stayed at the library and taught the young pacers. He taught them Senu's rule, that two counts must agree or the stretch be walked again. And he taught them a rule of his own.
55"When they throw stones," he would say, "and they will, go up. Not with your feet. Go up in your mind until the village is a dot. Look at how much there is besides this. Then come down and keep your count."
56The young ones did not understand him. But some of them remembered it later, on bad roads, and found that it worked.