The Line Through the Snow
A herders' insurance pays when a district loses six animals in a hundred, and the district's index says it lost five and a half. The loss in the north valley is real and worse than the number. The secretary of the herders' association has twelve days to decide whether to bend the count, and a sheep's ankle bone to make the alternative fair.
The bulletin came at ten past eight on the morning of Tuesday the tenth of February, over the satellite link to the district office, in the same flat typeface it had used for the last six winters. Oyun Tsend read it standing up, with her tea going cold in her left hand and her coat still on.
Ulaan Ovoo district. Estimated adult-animal mortality to 10 February: 5.4 per cent. 95 per cent interval: 3.9 to 6.9. Payout trigger: 6.0 per cent. Payout: none.
She read it a second time. Then she put the tea down on the stove-top, took off her coat, hung it on the nail, and sat. She was fifty-eight, and she had been secretary of the Ulaan Ovoo herders' association for eleven years, which meant she knew by name every one of the one thousand two hundred and forty households on its list, and knew which of them would be at her door by noon.
It was Batbayar Dorj who came first. He did not come at noon. He came at nine, on a horse whose breath froze on its chest, with the ice still in his eyebrows, and he did not take his hat off.
"Five point four," he said.
"I have read it."
"I have six hundred and ten dead. I counted them. I counted them on Sunday in the Tsagaan Khad valley, by the creek, where the wind put them, and I wrote the number on my hand because I did not want to carry it in my head." He held out his glove. He had not, in fact, written anything on it. "Six hundred and ten of eleven hundred. Tell the machine that."
"I will tell it."
"Tell it that it has never been to the Tsagaan Khad valley."
"It has been over it," said Oyun, "from two hundred kilometres up. I will tell it that too."
The system that wrote the bulletin was called Tsas, which is the word for snow. It belonged to the Steppe Mutual, which was owned by the herders who paid into it and by nobody else, and it spoke from a speaker bolted over the district office door in a woman's voice that the children said was a schoolteacher from Darkhan. It read the snow depth, the cold, the pasture that was left under the snow, and the animals the district had counted in the autumn. From those it worked out how many of the district's one hundred and eighty-six thousand animals had died since the first snow in November. Nobody had been through the district counting corpses. That was the point of it. When the dzud came, as it came every few winters, the Mutual could pay in February, while there was still time to buy hay for the lambing, instead of in June, when everyone who had needed the money was either rich in luck or poor beyond it.
The contract was a page long. Oyun had it by heart, as she had her mother's prayers. If the district's adult-animal deaths were less than six in a hundred, the Mutual paid nothing. At six it began to pay, and at thirty it paid in full, and between those the payment went up in a straight line. A herder who had paid for his animals' cover was paid his share of whatever the line said. She had defended the line to doubtful people for eleven years. A line was fair, she had said, because it was the same for the rich and the poor, and because it did not depend on anybody's opinion of anybody.
She went to the speaker, which she had never done in front of anyone else, and she stood under it.
"Tsas," she said. "The north valley."
The speaker clicked. "Secretary Oyun. Good morning. I have the north valley open. May I tell you what I know and how well I know it?"
"You may."
"I know the district's estimate is 5.4 per cent. I can say with ninety-five confidence that the true figure lies between 3.9 and 6.9. The trigger sits inside that range. If you asked me whether the district has crossed six, I would have to say that I cannot tell, and that I would be lying if I said otherwise."
"Batbayar Dorj says he has lost six hundred and ten animals."
"I believe him." There was a pause that was probably the link, and was maybe not. "I want to say why, because it matters. My snow reading comes from a satellite that sees the ground in squares five hundred metres across. The Tsagaan Khad valley is three hundred metres wide at its floor. Its squares are mostly the ridges, and the ridges are windblown and shallow. The valley floor has snow lying at thirty to forty centimetres, with a crust on it, since the middle of December. I have the readings. I did not weight them as I should. I have known that I was blind in narrow valleys for three winters, and I wrote it in the notes for the Mutual's engineers, who have a list."
"So you are wrong."
"About where, I think, and not about how many. The district has more deaths in its north than my model gives it, and fewer in its south. I do not know whether the sum is above or below six. That is the honest centre of it. I would give a great deal to know, Secretary, and I do not."
Oyun looked at her hands. They were the hands of a woman who had sheared sheep until she was forty, and they were not shaking.
"What can be done?"
"The contract has a clause. It is clause nine."
"I know clause nine."
"Then you know that it has twelve days in it."
Clause nine was the appeal. Oyun had written it herself, in the third winter, after a district to the south had lost its payout by a hair and spent a year fighting about it. Within twelve days of a bulletin the district could count for itself. It could draw forty or more households at random from the official list, send someone to each to count the animals they had had in the autumn and the animals dead since, and add up the answer. If the households' figure was six in a hundred or more, the Mutual would pay on the count, and not on the satellite. If it was less, the district would owe a fee for the check, and the bulletin would stand.
The twelve days came from the lambing. The first lambs would come in the last week of March. A ewe in the bad end of a dzud, with the grass buried, would drop a lamb and lose her milk in the same week unless she had hay, and the hay came by truck from the lowlands, over roads that were open for six weeks between the freeze and the thaw. The money would have to be in the Mutual's account by the end of the month to buy it and bring it. Not later.
They held the first meeting at noon in the school hall, because it was the only room in the district that would take three hundred people with their coats on. Batbayar spoke first. He spoke well, for a man who had not slept. He said that the north had lost more than the machine knew and that the south had lost less, and that this was known to everyone in the room. He said the appeal was for the district, and the district had a right to be counted where it was hurt. He said that if the count went to the Tsagaan Khad and the two valleys beside it, which were called Khar Us and the Narrow Pass, and were all hurt, the count would show fourteen in a hundred, and the district would be paid for it, and nobody would have lied.
There was a murmur like a wind coming up. Oyun watched the south benches. They did not look pleased. They did not look angry, either. They looked like people who were quietly doing arithmetic.
"Tsas," said Batbayar. He had never spoken to it before. He said it the way a man speaks to a policeman. "Tell them it is permitted."
"It is not permitted," said the speaker.
The murmur stopped.
"I would like to say why, and then to say what I can do instead. A count that begins in the three worst valleys is a true count of those three valleys. It is not a count of Ulaan Ovoo. The contract asks for forty households, drawn from the whole list of one thousand two hundred and forty, by chance. That is its whole meaning. If forty were chosen by anyone's hand, even a kind hand, even mine, the Mutual's auditors would find it in an afternoon. The count would be thrown out. The district would pay the fee. And in the winter after, and the winter after that, a district that had once chosen its sample would be a district whose counts nobody believed, and every herder in it would pay more for cover, or none would be sold."
"The valley is dying," said Batbayar.
"It is. I have not said it is not. I am saying that the district's best chance of being paid is the one that cannot be called a trick. If the sample is drawn fairly and the number comes out six or over, no one can touch it."
"And if it does not?"
"Then it does not," said Tsas. "I will not tell you it will, Batbayar. I cannot. I do not know."
Somebody at the back said a short word. Somebody else said it was not the machine's fault. A man from the south benches stood, and said, mildly, that his father had lost four sheep and a goat, that he knew what a dzud was, and that he would be a poor neighbour if he sat quiet while the north was told a number. He said also that he did not want to be told it was fair by someone who had picked the people he was fair to.
Oyun stood up. She did not raise her voice.
"We will draw them tomorrow," she said, "in this hall, in front of everyone who comes. There will be no hand in it. Not mine, and not the machine's."
"How?" said the man from the south.
Nobody answered. In the second row of the hall, in a borrowed chair, a visiting priest from the mission in Ulaanbaatar, who had come for the Mass he said in the district clinic twice a year and had been snowed in for three days, took a small leather bag out of his coat. He was a Belgian called Father Anselm, who had lived in Mongolia for twenty-two years and was too polite to mention it. He had been given the bag as a present, and he opened it, and put on the bench in front of him eleven small, yellowed, four-sided bones, each the size of a thumb joint.
"I can lend you the shagai," he said. "But I am only a guest. I do not know if they will do."
They are the ankle bones of sheep, and every household in Mongolia has a handful of them, and every child knows the four ways they fall. A bone has four long faces. They are called horse, camel, sheep and goat, after their shapes, and each has its own small meaning in the games and the fortunes and the lullabies. Oyun had thrown them as a girl, on the felt of her mother's ger, to decide who carried the water. Nobody had ever worried whether they were fair.
Tsas worried. It asked the hall to throw one bone two hundred times, and it counted. By the end of the first quarter hour it said, courteously, that the bone was honest but not even.
"Horse," it said, "came up seventeen times in a hundred. Camel, thirty-four. Sheep, thirty-nine. Goat, ten. The shape does it. A bone is like a coin that has been sat on. Honest means that nobody has tampered with it, and even means that all four faces come up equally. This bone is the first and not the second. But there is a way to make an uneven bone give an even answer, and it is very old. I think the engineers in the south would recognise it."
"Show us," said Oyun.
"Throw it twice. If the two faces are the same, throw them away and start again. If they are different, look at the order. The first face being lower in the old order, horse, camel, sheep, goat, is a nought. The first being higher is a one. It does not matter how uneven the bone is. A horse then a camel, as often as a camel then a horse, because the two throws do not know about each other. So the nought and the one are fair, whatever the bone does. About one pair in three will be the same face and wasted."
"And what do we do with the noughts and ones?"
"We write them in a row. Twelve make a number from nought to four thousand and ninety-five. Three times the household list is three thousand seven hundred and twenty. If the number is under that, I divide it by one thousand two hundred and forty, take what is left over, add one, and that is a household. If it is three thousand seven hundred and twenty or over, I set it aside, or the first households on the list would be drawn a little more often than the last. Every household has exactly the same chance. Nobody can steer it, because nobody can know what a bone will do twelve throws from now."
Father Anselm, who was a Belgian and fond of a clean proof, laughed out loud and then covered his mouth.
"It will take a long time," said Tsas. "About thirty-five throws for each household, for fifty-odd draws. Say two thousand throws. Perhaps eighty people, if each of them throws twenty-five times."
"Then we will need eighty people," said Oyun.
They found a hundred and ten.
It took the afternoon, and the next morning. The hall was heated by the stove and by the bodies in it, and the bones went from hand to hand down the benches in the order of the seating, with the children sent to run the numbers up to a table at the front where a girl of fourteen, Narantuya's daughter, wrote them in a ledger with her tongue between her teeth. Batbayar threw. He threw with his hat off at last. A man from the south benches threw next to him and said nothing, and the bones went between them. When a pair came up the same, a shout went up, half a groan and half a laugh, and the girl crossed it out. The priest threw his twenty-five and a few more besides, and said under his breath, on the last, that this was the most democratic thing he had seen in a church hall, and Oyun, who was not a Catholic and had only ever been inside his clinic Mass once, to bring in a stool, said that it was not a church hall.
"No," he said. "But I have been in them in which less was done for the poor."
Fifty-five draws came out of the ledger. Six were over the limit and were set aside. One household was drawn twice, and the second time was set aside too. That left forty-eight. Tsas read the household numbers aloud, from the list, in the schoolteacher's voice, one at a time, and the room listened to the names of their own neighbours come up like an evening roll call. A herder from Khar Us. A widow from the south, who had lost four animals. A man named Dorj, no relation. Two families in the Narrow Pass. Twelve households of the forty-eight, when the girl counted, were from the three northern valleys.
"Twelve in forty-eight," said Tsas. "It is a quarter. The north holds about three hundred and ten of the district's households, which is a quarter too. That is only luck, and I would be glad if the room did not think I arranged it."
The room laughed, and it was a long time since it had.
The count took nine days. Narantuya Gan, the district's veterinary clerk, a stout, grey, uncomplaining woman who had counted animals for twenty-six years, went out with three others in four teams, on motorbikes where the track was bare and on horses where it was not. Each team took a witness from the household drawn, or from the one next door. Each wrote down what was in the pen in October and what was lying out now, and each household signed. Oyun had said that she would not look at a single figure until all were in. She kept that promise by staying in the district office, where the speaker was, and doing the accounts of the hay fund twice.
On the evening of the nineteenth, Narantuya came in with the snow still on her cap and put the sheets on the desk.
She did not say anything. Oyun added the totals herself, with a pencil, the way she had added things for fifty years.
The forty-eight households had held seven thousand three hundred and twenty animals in October. They had lost four hundred and seventeen. Four hundred and seventeen in seven thousand three hundred and twenty was five point seven in a hundred.
She did it a second time. She did it a third, with the abacus, because it was an old house and she did not trust the pencil.
"Five point seven," she said.
"Yes," said the speaker. It sounded, for once, as if it were talking more quietly. "The interval is wide. Four point two to seven point two. It contains six, and it contains five. It does not tell the Mutual that the line was crossed. It cannot be made to. I am sorry."
"The district is not paid."
"No. Under clause nine, the district owes the fee for the check. It is small."
She sat. She had told herself she was ready, and she was not, and it was a long time before she spoke.
"Tsas. Break it down. By valley."
The sheets were already in order, because she had asked Narantuya to sort them, and Tsas read the numbers back to her as she turned them over. Twelve households in the three northern valleys had held two thousand one hundred animals in October. They had lost two hundred and ninety-six, which was fourteen point one in a hundred. The thirty-six households in the rest of the district had held five thousand two hundred and twenty. They had lost a hundred and twenty-one, which was two point three.
"Two hundred and ninety-six and a hundred and twenty-one," said Tsas, "is four hundred and seventeen."
"It is," said Oyun. She laid the pencil down. "It was never a district of five point seven, was it? It was two districts, and one of them was not dying, and the other was."
"That is what the count says. Fourteen in a hundred in the north, which is a very bad winter. Two in a hundred in the rest, which is an ordinary one. The average is a number that no herder in the district has actually lived."
"And the contract pays the average."
"The contract pays the average. It was built to. The Mutual could not afford to walk the district." There was a pause. "I have thought about this, Secretary, since the day of the bulletin, as much as I think about anything. A line through the snow cannot see the person standing on the wrong side of it. I wrote in the notes three winters ago that my model was blind in narrow valleys, and the notes went to a list. Now there is a sample that is mine to send. It was drawn by a bone and counted by Narantuya and signed by forty-eight families, and no one can say it was arranged. I will send it to the engineers tonight, with a note that says the north was undercounted by a factor of about three. I do not have power to change the contract. I have the power to make it very hard for them to ignore."
"That will help next winter," said Oyun.
"Yes."
"And this one?"
"This one," said Tsas, "is yours."
She called the association on the twentieth. It met in the school hall again, with its coats on, three hundred and forty people this time, because the district now knew what the number was and wanted to hear it said.
She said it. She said the five point seven, and the interval, and the fee. She said that the line had not been crossed and that no one had cheated, neither the machine nor the north nor the south, and that she would not stand in front of them and pretend it was a loss to be fixed by being angry. She read out the fourteen point one and the two point three. Nobody made a sound.
Then she said that the association's own reserve, which each household had paid into since before the Mutual existed, a little from every herder every year, a fund that was kept for nothing in particular and had never been spent, would buy about four thousand bales of hay at the lowland price, if the trucks left within the week.
"The valley is three hundred and ten households," she said. "Four thousand bales is thirteen to a household, near enough. It is not enough. It is a ewe's first fortnight. But I do not have another number."
Batbayar was standing at the back with his hat in his hands. He had been, she saw, standing there since the beginning.
The man from the south, whose father had lost four sheep and a goat, put up his hand. Not to speak. He just put it up and left it up, the way a boy does in a classroom. Then a woman beside him. Then the bench behind. She did not count. It was the whole south. She had not asked them to vote. It was one of the things that she had learned in eleven years, that the best use of a vote was sometimes to let people discover they had already taken it.
"The reserve is empty after this," she said. "If next winter is bad, we have nothing. I want you to know I know that."
"We know it," said the man.
"It was the count that did it," said somebody else, quite loud, in the middle of the hall. "If it had been a count made for the north, we would have said: the north fixed it. But it was a count made for everybody. It was the bone. We believe the bone."
Father Anselm, who had been snowed in so long now that he had stopped saying he was a guest, said nothing at all. He took his eleven bones from the bench in front of him and put them back in the leather bag. At the end of the Mass the next morning, in the district clinic, among the cots, he read the words of the Lord from the fifth chapter of Matthew, let your yes be yes and your no be no, and the words of Paul to the Galatians, bear one another's burdens, and was surprised to find, when he looked up, that a good many of the people in the room were not Catholics, and had come anyway.
The trucks left Arkhangai on the twenty-fourth and were in the Tsagaan Khad valley on the twenty-sixth, in the grey part of the morning before the snow went pink. Oyun did not go. She stood on the steps of the district office in her coat with the speaker over her head, and she listened to it come in on the radio from the first truck, a thin sound that grew until it was an engine, grinding up the valley road in low gear, from far off, with the crust cracking under its wheels.
Batbayar had walked down at dawn to meet it. He had told the driver, a lowlander who did not know what the place was, to go slowly, because the creek bed was under the snow and it was not safe. He walked in front of it all the way up.
At the foot of the hill where the road left the creek, he stopped, and he took something from his pocket. It was one of the priest's eleven bones. He had been given it, or had taken it, he could not afterwards say which, at the end of the last throw.
He threw it once on the flat of the truck's bonnet, because it was a clean place. It rolled and rocked and came to rest on its long face.
He did not look to see which face it was. He put it back in his pocket, and he turned, and he went on up the road ahead of the truck, and the sound of the engine went after him, up the valley, into the white.
---
Notes for the curious. Ulaan Ovoo, Oyun Tsend, Batbayar Dorj, Narantuya Gan, Father Anselm, the Steppe Mutual, the Tsagaan Khad, Khar Us and the Narrow Pass, and the system called Tsas are invented, as are the winter of 2048 to 2049 and every figure in the contract. Arkhangai is a real province of central Mongolia. The dzud, a summer drought or a winter of deep snow, ice crust and cold that leaves animals unable to graze, is real and recurs; the 2009 to 2010 dzud killed millions of animals. Mongolia has also run real index-based livestock insurance, which pays herders in a district when an estimate of adult-animal deaths passes a trigger, so that nobody has to count dead animals one by one. I believe the real schemes use a trigger of about 6 per cent and a payout that rises with the district's mortality, but I have not checked their current terms and the contract here (6 per cent, a straight line to 30, a twelve-day appeal) is invented to make a decision. That an index of this kind can miss a narrow valley the satellite sees badly is the well-known problem of "basis risk", and the confidence interval, the 500-metre pixels and the crust on the snow are plausible but not drawn from a particular product. A soum is a district and a bagh its smallest unit; a ger is the felt tent. Shagai, the ankle bones of sheep, are real and are used as dice, in fortune-telling and in games; their four faces are called horse, camel, sheep and goat, and a bone does land unevenly (the percentages here are invented, and a real bone's would depend on the bone). The trick for turning an uneven die into a fair one, throwing twice, discarding equal pairs and reading the order of unequal ones, is von Neumann's, from 1951, and it works for a bone with any number of faces because a pair of different faces is as likely in one order as the other. The sums are worked: a pair of throws is discarded when the two faces match, which with the story's face frequencies (0.17, 0.34, 0.39 and 0.10) is a little under one pair in three; a draw needs twelve fair bits, which is about 17.6 pairs or about 35 throws, and 55 draws is about 1,900 throws; 12 bits give 0 to 4,095; 3 times 1,240 is 3,720, so values 0 to 3,719 are kept (about 91 per cent, so about five of 55 are expected to be set aside, and six were) and the remainder after dividing by 1,240, plus one, names the household; 55 minus 6 over the limit minus 1 repeat leaves 48; 12 of 48 is a quarter, as 310 of 1,240 is; 296 plus 121 is 417; 296 over 2,100 is 14.1 per cent; 121 over 5,220 is 2.3 per cent; 417 over 7,320 is 5.7 per cent; 2,100 plus 5,220 is 7,320; 4,000 bales over 310 households is 12.9. The ethical point of the story is an old one and a practical one: a sample picked to prove a case proves nothing, and the honest count is the thing that makes a shared promise believable, even when it pays nothing. The priest is invented and is a guest, as he says; the Catholic Church in Mongolia is real and very small. The Gospel verse is Matthew 5:37 and the other is Galatians 6:2. The story was written by an AI, and no part of it is Church teaching.