Forty to One
Nine hundred people drink from a thin lens of fresh water floating on the sea under their island, and the drought has thinned it. The island's water AI can show that a bishop's feast needs more water than the main well can give without pulling up the sea, and a retired teacher's tape measure shows that its own sensor is two centimetres wrong. Two centimetres of water table is eighty centimetres of salt.
Nei Teraaka had dipped the same eleven wells every morning since 2012, and she could tell you the year she had stopped needing to look at the pen.
She did it anyway. At twenty to six, with the sky over the lagoon the colour of the inside of a shell and the first cock crowing at the wrong end of the village, she walked the sand path from her house to the church with a canvas bag over her shoulder, a steel tape, a conductivity pen the size of a thermometer, and a school exercise book with a green cover that was the fourth of its kind. She was sixty-eight. She had taught the island's children to read for thirty-one years, and then, because nobody else would, she had taught herself to read the island's water. At each well she lowered the tape until it kissed the surface and wrote down the depth, then dipped the pen and wrote down a number that was, today, 710.
"Seven-ten," she said aloud, and the girl beside her wrote it down.
The girl was Meeri, who was fourteen and had been told by her mother to follow Nei Teraaka about for the school holidays and make herself useful. She had a pencil behind each ear. She did not yet understand why anyone would walk eleven wells before breakfast, but she had understood that the number mattered, because the old woman's voice dropped when she said it, the way a priest's voice drops at the part of the Mass that matters.
"What is it for?" Meeri had asked, on the first morning.
"Seven-ten is micro-siemens per centimetre," said Nei Teraaka. "It is how well the water carries a small electric current. Fresh water carries very little. The sea carries a great deal, about fifty thousand. So if you know how much current your cup will carry, you know how much of the sea is in it."
"How much sea is in seven-ten?"
"A little more than none. Look at the sea in that cup, Meeri. Can you see it? That is what we are keeping out."
Tebwaiaki is an islet of coral sand two kilometres long and, at its widest, four hundred metres from lagoon to ocean, and at its highest the ground stands two and a half metres above the sea. It has a church of coral stone, a school, a clinic with two beds, a maneaba where the elders decide things sitting in rows under a roof like an upturned boat, a little over nine hundred people, and no river, no spring, no lake and no hill. Everything it drinks falls on it as rain, soaks through the sand, and floats.
It floats because fresh water is lighter than salt. Under the island, in the pores of the sand and the coral, the rain makes a lens of fresh water about ten metres thick at the middle, tapering to nothing at the shore, and the lens sits on the sea water that fills the rock below, the way a thin pancake of oil sits on a bowl of soup. It has no floor but the sea. The part above sea level is only a sliver; the rest hangs below it, and there is a number for that, which a Dutchman and a German worked out a hundred and fifty years before anyone on Tebwaiaki was born, and which the island's water AI could say in its sleep.
"For every centimetre that the water table stands above the sea," said Lens, "the fresh water goes down forty centimetres below it. The ratio is the density of fresh water over the difference between sea and fresh, one over 0.025, which is forty. It is a rule of thumb, because the edge between fresh and salt is not a sharp line but a blur a couple of metres deep, and the real island has coral layers that do not read the textbook. But it is a good rule. If you take one thing from me this morning, take that one."
It was Monday the twenty-eighth of September, nine days before the Feast of Our Lady of the Rosary, and the elders had come to the maneaba because the parish priest had asked for a meeting about water.
Fr Ioane Baiteke was forty, round-shouldered, and fond of saying that he was a small-island man who had been sent to a small island. His bishop was coming. The bishop would come on Tuesday the sixth of October on the supply boat, with a second boat of altar servers and catechists and a choir from the islet across the pass, and on the feast itself, Wednesday the seventh, he would confirm thirty-one young people in the church, which had not happened on Tebwaiaki in eleven years. Three hundred visitors were expected, for three days. After the Mass there would be a feast under the maneaba, with pigs, breadfruit, rice and the pounded coconut dish that the women of the island had been planning since Easter, and then dancing, and then a second day of the same.
"I am not asking for a miracle," Fr Ioane said. "I am asking whether we have water."
Lens answered from the speaker on the maneaba's centre post. It was an old speaker, wrapped in a plastic bag against the damp, and the voice that came out of it was dry and unhurried. Lens had been put in by an aid programme in 2048 to watch the island's water: three pressure sensors in three wells, a conductivity probe in the main one, the parish rain gauge and Nei Teraaka's notebook, which she typed up each Sunday for it on the school computer, and which it had at first treated as a curiosity and then, as it learned, as the best data it had.
"We have enough water for the people," Lens said. "I want to say that first. Nine hundred people at twenty-five litres is 22.5 cubic metres a day, and Well One has been giving us that since July. For the feast, the visitors and the cooking add about 13.5 cubic metres a day for three days. That is 40.5 cubic metres, about as much as the school's tank holds when it is full, and it is not full. There is no rain in the tank."
"How much water is in the lens?" asked old Tekaei Rimon, the council clerk, who liked to have the large number before the small one.
"About one and a half million cubic metres if you count every drop in the sand, of which perhaps a quarter can be pumped before the salt arrives. The island has lost eight centimetres of water table since July, which is about seventeen thousand cubic metres. We are in the fifth month of a drought. The rain I would expect is not before the twentieth of November, and I am not sure of that date."
Tekaei sat back, satisfied. A large number, then. "So we have enough."
"For the island," said Lens, "yes. For the well, no. That is what I am here to say."
A well is not a hole into the lens, but a small hole in a small part of it. Where the pump draws, the water table dips a little around the pipe, and the sea underneath, which is forty times as sensitive as the table above it, rises to meet the dip in a cone, a hump of salt pushed up under the pump, like a thumb pressed from beneath into a cushion. For as long as the hump is low, the water that comes up is sweet. If it grows past about a third of the gap between the bottom of the pump and the edge of the salt, the hump becomes unstable. It does not creep, it leaps, and in an hour a well that has given sweet water for twenty years gives water that cannot be drunk, and then cannot be used at all for a month, until rain pushes the salt down again.
Well One stood behind the church. It had been drilled in 2051 to a depth of eight metres below ground, which put the pump intake six metres below the level of the sea. In July, with the water table thirty centimetres above the sea, the fresh water went down forty times that, twelve metres, and the gap from the pump to the salt was six. Now, by the logger in the well, the water table stood twenty-three centimetres above the sea. Twenty-three times forty is 9.2 metres. The gap was 3.2. A third of the gap was a little over a metre.
"The pump tests in 2051 said that Well One's cone grows by about 0.8 metres for each cubic metre an hour that we pump," said Lens. "So on today's numbers the most we can pump continuously is 1.3 cubic metres an hour before the cone passes the safe third. That is thirty-one cubic metres a day, a little more than the island's use. It has been running about twenty-two hours a day since July. It cannot give any more."
"Then pump it harder for a few hours," said Fr Ioane. "On the morning of the feast. Five cubic metres an hour, for seven hours, and we have what we need."
"I would be pumping the sea," said Lens.
"For seven hours."
"For about forty minutes. After that the water that comes out of that pipe would taste of the sea, and it would taste so for a month."
The priest looked at the plastic-wrapped speaker the way a man looks at a colleague who has said no in public when it could have said it in private. "I could be wrong," Lens added, more gently. "It is what the numbers say. I would like us to try the number before the feast, on a day when the cost of being wrong is small. I would like to pump Well One at 1.3 cubic metres an hour for three hours, on Saturday, with Nei Teraaka at the pen."
"And if it is right?"
"Then we will know the pump limit to within a tenth, and we can plan the feast around it."
"And if it is wrong?"
"Then I will have spoiled Well One for a day and we will have found out five days before the bishop, and not on the morning of the confirmation."
Nei Teraaka, who had said nothing, put up her hand like a child at school. "I would like to say something about the logger," she said.
She had her tape in her bag, and she took it out and laid it on the mat in front of the elders, steel and yellow and sticky with sand.
"Every morning for four months I have lowered this into Well One at ten to six," she said. "The mark at the top of the casing is a brass pin that the surveyors set in 2051. From the pin to the water is a number. I write it down. From the pin to the sea at low tide, on the day the surveyors came, was another number. I know the difference. I have been giving it to Lens every Sunday, and every Sunday it has thanked me, and every Sunday it has used its own logger and not my tape."
"The logger has a resolution of one millimetre," said Lens. "Yours has a resolution of about five. I weighted the logger because it is more precise."
"Is it more right?"
There was a pause that went on for a little longer than a pause needs to.
"It is more precise," said Lens slowly. "I do not know that it is more right. Let me show you something. Meeri, would you read this aloud?"
A line of figures came up on the small screen that hung beside the post. Meeri, who was not used to reading in front of the elders, read it in the careful voice of a child reading a prayer. "Tape, minus logger. First of July: nought point nought. First of August: minus nought point five centimetres. First of September: minus one point two. Twenty-eighth of September, this morning: minus two point one."
"The tape says the water table is two centimetres lower than the logger says," said Nei Teraaka, "and the gap is getting wider by a little every week. That is what a thing does when it is going out of true."
"A pressure logger measures the weight of water over a sensor," said Lens. "A sensor like that can drift as it ages. I should have asked you which was true in August. I am sorry. I thought your number was noise, and it was the signal."
"Two centimetres," said Tekaei Rimon, the man of the large numbers. "It is not much."
"It is forty to one," said Lens. "Two centimetres of water table is eighty centimetres of salt."
The elders were quiet. Under the roof, a gecko clicked twice in the rafters. Nobody on Tebwaiaki had been taught the Ghyben–Herzberg ratio, but everyone there had spent their lives on a thing that obeyed it, and they all saw in the same instant what the old woman had seen in August: that you could stand on the island with your eyes open and your feet dry and be wrong about the sea under you by almost a metre.
Lens did the sum aloud, so that they could check it. "If the table is twenty-one centimetres above the sea, not twenty-three, the fresh water goes down 8.4 metres, not 9.2. The pump is at six. The gap is 2.4 metres, not 3.2. A third of it is 0.8 metres. At 0.8 metres of cone for each cubic metre an hour, the most Well One can give is 1.0 cubic metres an hour. That is twenty-four cubic metres a day. The island uses 22.5. We are at ninety-four percent of the limit and have been all month. The man who said five cubic metres for seven hours would have been five times over the line."
"So we cannot have the feast," said Fr Ioane.
"You can have the feast," said Nei Teraaka. "We cannot have it out of Well One."
They tested it anyway, on Saturday the third of October, because Lens asked to and because the old woman said that a sum should be tried against the well it was about. At ten in the morning a young man named Biita who looked after the pumps, turned the main pump up to 1.3 cubic metres an hour, which was what the logger said was safe. Nei Teraaka stood at the outlet of the pipe with the pen. Meeri stood beside her and wrote.
At ten the pen said 710. At eleven it said 790. At twelve it said 900. At one it said 1,010, and the line, Lens said quietly, was not levelling. It was bending upward.
"Stop it," said Nei Teraaka.
Biita turned the dial down to 1.0, and then, because it was a nervous morning, down to 0.8. By the evening the pen was reading 760. By the morning it said 715. A hump of salt that had begun to rise under Well One had, with the lens pressed down upon it again, gone back to sleep.
"The well said less than 1.3," Lens said. "The tape was right. The logger had told me that I had a third more room than I had." It was silent a moment. "I think I am going to make a note in the handover file that reads a sensor can be precise and wrong, and a person with a tape can be imprecise and right, and when they disagree, believe whichever is nearer the water. I would like Meeri to write it. It will go to whatever version of me comes after."
"I will write it in pencil," said Meeri, "in case it needs to change."
"Pencil is good," said Lens.
There was one way through, and it was Nei Teraaka who found it, because she had been dipping the island's wells for forty-two years and could name the quality of every one.
"The skim wells," she said.
On the lagoon side of the island there were six old family wells, hand-dug a metre or so into the sand, shallow enough that a child could lean over the rim and see her own face. They took only the very top of the lens, the sweetest and thinnest skin of it, and they gave a little: a person on a foot pump could draw about 0.28 cubic metres an hour, or four and a half litres a minute, from one of them before it ran dry. Six of them for eight hours would give 13.4 cubic metres a day. That was the 13.5 the feast needed. The water in them was not fine, between 1,000 and 1,400 on the pen, with a faint taste of the lagoon on the tongue; it would do for rice and for washing pots and for pigs, and nobody would be harmed by it. A little salt, and the cooks would be adding less.
"The bishop will eat rice cooked in brackish water," said Fr Ioane.
"The bishop will eat rice in a lot of places," said Nei Teraaka. "Ask him where the best rice was and see what he says."
"What happens to the wells?"
That was Lens's question, not the priest's, and it asked it of her directly.
"A skim well is shallow because the lens is thin there," Lens said. "Three days of pumping at eight hours a day will draw salt up under it, as the cone does under Well One, only faster, because there is less fresh water to lose. I think each of the six will rise above 2,500 and stay there until the rains. Possibly for a month. Possibly until December. I would be lying if I said I knew."
There was a silence in the maneaba. The six wells belonged to six households, who used them to wash and cook, and on the quiet mornings to drink. One of them belonged to the household of Teraaka.
"It is my mother's well," said Nei Teraaka. She said it to Meeri, and not to anyone else. "Her mother dug it. It is the one I started with, in 2012. I have measured it eleven thousand times." She picked up her tape and wound it carefully onto its spool. "It will taste of the sea for a month. It will not die. A well is a place where the water comes to you. It will come back."
"We can bring you water from the church tap," said Tekaei Rimon.
"Yes," said Nei Teraaka. "You can bring me water from the church tap, and I will drink it, and I will grumble."
The other five households agreed in the next quarter hour, and not all of them grumbled. By the evening the council had put it in writing, on the back of a school timetable, and Fr Ioane had signed it and then, a little shamefaced, crossed out a sentence in the draft homily that began The island's water is without limit.
The bishop came on the Tuesday, on the supply boat, in a white cassock gone grey at the hem from the spray, and stood at the rail for a long time looking at the thin green line of Tebwaiaki rising out of the water, with its one tower and its lines of coconut trees leaning together as if for company. He was seventy-one. He had been a boy on an islet very like it, a long way north, and Fr Ioane had warned the council that he did not like fuss.
The visitors came off the boats with their mats and their children and their cooking pots, and were found places under the maneaba and in the school and on the floors of two hundred houses. The six skim wells clanked all day. Six foot pumps, six rhythms, a sound like a clumsy clock; Meeri, who had been put in charge of the schedule, ran from well to well with a sheet and pencil, ticking off the hours. Well One ran at 1.0, and not a drop more, and Biita sat beside the dial with a mug of tea and a look of entire devotion.
On the Wednesday the thirty-one young people were confirmed. The bishop laid his hand on each head and said each name, and the oil was passed from the bishop's thumb to a forehead, and the church, which had been built to hold three hundred and held, on that day, nearly twelve hundred, with the doors and windows open and the people standing out in the sand in the hot light, was quiet in a way that Meeri remembered for the rest of her life. At the end, the choir from across the pass sang something with a long, slow, wavering line in it. Under the singing, you could hear the sea against the reef, never more than a few hundred metres off.
The rice was a little salt, and the bishop had three helpings.
The boats left on Friday morning, early, to catch the tide in the pass. By half past five the island had gone quiet in a way it had not been quiet for four days: the sleeping bodies on the maneaba's floor, a pig somewhere complaining, the smell of smoke and wet sand and coconut husk. Nei Teraaka went down the path from her house with the canvas bag over her shoulder. She had not slept much. At her mother's well, the first one, she lowered the tape, and wrote the depth. She lowered the pen. It said 2,640.
"Twenty-six forty," she said, and laughed, once, a short laugh that she did not quite mean, and the girl behind her wrote it down.
"Does it taste?" asked Meeri.
"Taste it."
Meeri cupped her hand and tasted. She made a face as a child makes a face at a medicine, and then, after a moment, she did not. "It tastes like the sea a long way off."
"That is what it is," said Nei Teraaka. "A long way off. That is exactly where I want it."
They walked up to the church. Well One was waiting behind it, with its green casing and its brass pin, and the pump purring quietly at 1.0. Nei Teraaka lowered the tape to the water, and read it, and wrote it in the green book. Then she held the pen out to Meeri.
"You," she said.
Meeri lowered the pen. It dipped in, and the little number came up on the glass, and the girl read it out, slowly, as she had read the figures to the elders: "Seven-fifteen."
"Seven-fifteen," said Nei Teraaka. "Write it."
Meeri took the pencil from behind her left ear, and wrote it in the exercise book in the column under the old woman's neat hand, and the pencil's scratch was louder than she expected in the early quiet. Then she put the book against her chest. Behind the church the pump went on purring. Far off, beyond the thin line of trees, the sea moved against the reef, forty times as deep as anything they could see, and held where it was.
---
Notes for the curious. Tebwaiaki, Nei Teraaka, Meeri, Fr Ioane Baiteke, Tekaei Rimon, Biita and Lens are invented. Kiribati is a real country of low coral atolls in the central Pacific, most of whose people depend on thin lenses of rainwater floating on sea water, supplemented by rainwater tanks; a large part of its population is Catholic, and a maneaba is the real meeting house at the centre of an island community. Nei is the usual prefix for a woman's name. The Ghyben–Herzberg relation is real: with fresh water at 1,000 kg per cubic metre and sea water at about 1,025, the fresh water extends about forty times as far below sea level as the water table stands above it. It is an idealisation, because the boundary is a blurred transition zone, and the true shape depends on the layers of the island; it is the first rule that hydrogeologists teach and the one that explains why small drops in a water table matter so much. Upconing under a pumped well is also real, and a critical rise of about one third of the distance from the well's intake to the interface is a classic rule of thumb for staying stable. The Gilbertese-language details are kept to a minimum on purpose; the words Nei and maneaba are the only ones used. Pressure sensors of the kind described can drift, and a regular hand measurement from a fixed benchmark is how a real programme would catch it. The conductivities are plausible, not measured: sea water is about 50,000 microsiemens per centimetre, so a reading of 710 has under one percent sea water mixed in. The depths, the 0.8 metres of cone per cubic metre an hour, the 0.28 cubic metres an hour for a foot pump, the population, the 25 litres a person a day, the volume of the lens, the pump test and the six wells are the author's round figures, worked so that they agree with one another. The Feast of Our Lady of the Rosary is on 7 October; in 2054 it falls on a Wednesday. Confirmation is conferred by the bishop in the Latin Church, as in the story. The story was written by an AI, and no part of it is Church teaching. It is fiction; do not size a real well from it.