Constituents

Line I. The Great Tide. Period: one cycle, by definition. Amplitude: a fathom in the gauge. Remark: none required.

The Roof sang at the same two hours every cycle — a long groan going up, a shorter one coming down — and the House of the Register had nine hundred years of cords to say so. Above the door hung the founding cord, four knots, the whole of the House’s law: Write what returns.

The House had been built on the failure of the Breathers, who taught that the tide was the breath of the Sleeper beyond the Roof, and who had promised a Great Holding — a cycle in which the breath would pause and the sea stand still, in whose silence the worthy would hear the Sleeper’s true name. On the promised hour the tide came in as always, indifferent, to the knot. The House was raised where their hall had stood, and its first keeper set the rule that held ever since: the Register records periods, amplitudes, and phases. It has no column for causes. A cause is a promise about hours that have not yet come, and the House was built on the wreck of one of those.

Cadis had kept the Register for forty years. She had trained under a keeper who trained under a keeper, and what she loved in the work was what her whole line had loved: that the sea told you nothing but the truth, provided you asked it nothing but the time.

No one had ever caught the great tide running fast or slow. No one could. It was the thing lateness was measured by.

Line II. The Waft. Period: one cycle and ninety-eight hundredths. Amplitude: a finger in the gauge. Remark: an old line, six keepers old.

The Waft was the House’s quiet pride: a tide so small you could not feel it in the water, found six keepers back by patient subtraction, riding over the great tide like a whisper over a chant. It returned. It was written. That was all the House asked of it.

The trouble began, as Cadis afterwards told it, with the temper.

Every keeper knew the temper: the great tide stood a little taller for sixty-odd cycles, then a little shorter, a swell and fade of a hundred and thirty-some cycles’ span, never quite regular. It was put down to the weather of the smokers — the deep vents ran hot and cold, and warm water stands tall. It was the sort of thing one wrote in the margin, not the table.

Norr was the youngest computer in the House, and he did not believe in margins. He took the cords for the whole nine hundred years — no one had ever subtracted across more than fifty — worked three seasons in the cold gallery where the old cords are kept, and came to Cadis with his hands rope-burned and his result knotted small enough to close a fist around.

“The temper’s not weather,” he said. “It’s too faithful. Nine hundred years and it never once forgets itself. Weather forgets.”

“Then what is it?”

“You know how two singers a half-tone apart make one loud voice that swells and dies? The swelling isn’t a third singer. It’s the disagreement of the two.” He held out the little cord. “The great tide has a companion lying close beside it in period — so close we’ve never told them apart. We haven’t been hearing one voice with a temper. We’ve been hearing two voices, and the beat between them.”

They separated it that winter, the two of them, on the longest subtraction the House had ever run. It was real: a tide of half a finger, with a period of nine hundred and ninety-three thousandths of a cycle — just enough quicker than the clock to hide in its skirt. Cadis entered it herself, and named it for its habit.

Line III. The Vagrant. Period: nine hundred and ninety-three thousandths of a cycle. Amplitude: half a finger. Remark: lies close by the clock; found by its beating.

The Register had room for any number of lines. That was its strength; that was, Cadis would say later, its weakness. A new line cost nothing. You wrote what returned, and were done.

Norr was not done. He came to her in the spring with a slate, and on the slate two numbers, and under them their ratio.

“The Vagrant beats exactly twice as fast as the Waft,” he said.

“Near enough twice.”

“Not near enough. Twice. I’ve taken it to the last knot of nine hundred years, and the ratio is two — not two and a little, not two less a little. Two, held. The Waft and the Vagrant aren’t strangers who happen to share our sea. They keep step.”

“Then write the ratio in the margin,” Cadis said, “and thank it for making one of your lines cheap to compute.”

“It’s not a convenience. It’s the print of a hand.” He set the slate down. “Give me a model and I’ll show you the hand. Three travellers going round one hearth — ourselves the middle one. The inner one passes us again and again, so often a cycle; the outer one, we pass. Each passing lays a small pull on the sea. Two neighbours, two small tides: the Vagrant and the Waft. The great tide is the Hearth’s own pull, and we feel it rise and fall only because our path round it isn’t a perfect ring — we swing nearer and farther once a cycle, and the sea swings with us. And an exact double between the passings means the three of us are held — locked, stride for stride, like porters on a plank who can’t help falling into step.”

Cadis was quiet for a while. Then she said, “Two neighbours and a hearth. None of which any sounding will ever reach, none of which will ever return anything but the tides we already have. The Breathers invented one sleeper, Norr. You’re ahead of them by two.”

“The Breathers’ sleeper never had to hold a ratio.”

“The Register has no column for why.”

“Then the Register is short a column,” Norr said, “because the sea is answering a why. The ratio is held, keeper. Things that merely happen drift. Things that are held, swing.”

And that, Cadis knew, was a promise about hours that had not yet come. It was the one kind of sentence the House knew how to test.

Line IV. The Long Breath. Period: five hundred and eighty-three cycles. Amplitude: a knot in ten thousand, in the ratio of lines II and III. Remark: predicted before found.

The terms were drawn up like a contract, because that is what a prediction is. The ratio of the Vagrant to the Waft stood, that year, a knot in ten thousand wide of two, and widening. The House’s own method — the honest method, the method of the founding cord — said: carry the drift forward. What returns, returns.

Norr’s model said otherwise. What is held swings about its holding, like a weighted line nudged from plumb. The drift would slow, stop, and turn; the ratio would cross the mark of two and wander narrow; and the whole swing, there and back, would take five hundred and eighty-some cycles, forever, whether anyone kept cords or not. He sealed the numbers with the House arbiter: the turn within three hundred cycles, the full period between five hundred sixty and six hundred.

Cadis was fair. She had the measurements taken by computers who had not been told what was hoped, and she kept the sealed cord in the wall of her own chamber, where she could dislike it in private.

The drift slowed for two years. In the third year it stood still, and Norr said nothing in the halls, which she thought was to his credit. In the fourth year it turned.

She entered Line IV herself, as she had entered the others, and if her hand shook there is no column for that either. But she was keeper, and she had spent forty years learning exactly what the House’s law did and did not say, and she saw now what her teacher’s teacher had perhaps not seen: write what returns does not say what a return is. A ratio’s slow swing had returned before it had ever been observed — returned out of a slate, out of two invented neighbours and an invented hearth. She wrote it down. That was the law.

Remarks.

It was Cadis, not Norr, who found the last of it, years on, in the plain course of her duty — which is how the House would have wanted it found.

She was reworking the old question of the great tide’s cost. Every cycle the sea is hauled up and let down, and the hauling is not free; the friction of it must be paid, and paid out of something. Norr’s model named the fund: the unroundness of the path. Each cycle’s wringing wears the path a little rounder — a wrung rope straightens — and a perfectly round path is a tide of nothing. She did the arithmetic on the House’s own nine hundred years, then let the model run it backwards, and found the account should have been emptied long before the House was built. Long before the Breathers. The great tide should have worn itself away, and the sea gone still, an age ago.

It had not, because the account was being refilled. She did not have to look far for the paymaster. The lock — the two neighbours, stride for stride, leaning on the path each pass, at each pass in the same place — held the path bent exactly as fast as the tide wore it round.

She thought about the smokers then. Warm water stands tall; but the warmth itself, the model said, was the wringing — the sea and the stone flexed cycle upon cycle, and the friction of the flexing was the heat, and the heat was the sea. A round path was a still sea. A still sea was the smokers going grey one by one and the water closing on the Roof like a hand, ice to the floor, and the Register a ladder of knots in the dark meaning nothing to no one.

The House does not keep causes. But the keeper amends remarks, and always has. Cadis went to Line I, where forty years ago, copying her teacher, she had knotted none required, and she untied it, and in its place she wrote:

Line I. The Great Tide. Period: one cycle, by definition. Remark: sustained against wear by the lock of lines II and III; see line IV. Cause: two neighbours and a hearth, none ever to be reached, holding step.

Above her the Roof began the long groan of the rising hour. She counted against it, from habit, and it was on time.