Read the Introduction
Two clocks keep time in the world, and they have never agreed. One of them is fastened to the wall, and the other is written across the sky, and the distance between them is the subject of this book.
Begin with the wall. Its minute holds sixty seconds, its hour holds sixty minutes, its day holds twenty-four hours, and the whole of it comes to one thousand four hundred and forty minutes between one midnight and the next. That figure governs every statute, every contract, every accrual, and every timestamp in daily use, and nothing in the firmament corresponds to it. The number was agreed and published and handed down, and it holds whether the day it measures runs long with summer light or short with winter light. Such is its virtue. It belongs to the counting houses, and its keepers say so plainly: sixty seconds to the minute, sixty minutes to the hour, twenty-four hours to the day. That is their stuff, entire, and no honest count of the sky can be stated in its units without saying so.
The other clock is the count the record itself keeps. Reading it takes patience more than instruments, because its parts return at two different speeds. Stand outside at dawn and mark where the sun comes up, then return a year later and mark it again, and the second mark falls almost on the first. Almost, because the sun has two returning places and they sit at different distances from one another. One is the equinox, where daylight and darkness stand equal and the season turns. The other is a fixed star, which a year brings back to the same place in the sky. Count from equinox to equinox and the year runs 365.2421897 days. From the star to the star the year runs 365.2563630 days. Twenty minutes and twenty-four and six tenths seconds a year separate the two, and that gap is the precession of the equinoxes written in time. One whole day of it gathers in seventy point six years, one degree in seventy-one point six, and the full circuit closes in twenty-five thousand seven hundred and seventy-one. A count that answers to the seasons and a count that answers to the stars are therefore two instruments, and each one drifts against the other.
The record keeps a year of its own as well, and that year is built on the week rather than on the sun alone. Three hundred and sixty-four days stand in it, laid out as four seasons of ninety-one days, each season thirteen weeks long, so the whole year comes to fifty-two exact weeks. Four days complete the frame, and one of them stands at each quarter, outside the months and outside the count of weeks, which is why the Sabbath never moves under that reckoning. Twelve months of thirty days plus those four standing days give the same three hundred and sixty-four. Thirteen months of twenty-eight days give it again. Each reading is a different way of laying out one year, and only one of them is used at a time, because the two are two shapes of the same figure and not two figures to be added.
Set that year beside the year the counting houses price their money on and a subtraction appears. The banker's convention runs three hundred and sixty days, and it stands behind commercial paper, discount math, and margin interest, printed in the handbooks and named in the agreements. Three hundred and sixty-four less four is three hundred and sixty. The commercial year is the year of the record with the four days of the quarters struck out, and the striking is structural rather than accidental.
Then there is the smaller ledger, kept by a man and his own hand, and it is where the arithmetic begins to bite. Take four seconds off every minute. Sixty seconds less four is fifty-six seconds to the minute. Take the same four seconds off each of the sixty minutes in an hour and the saving is two hundred and forty seconds, which is four minutes, which leaves fifty-six minutes to the hour. Four seconds off every minute, four minutes off every hour, and fifty-six to the hour are one statement in three forms, and a man who says any one of them has said all three.
That reduction is not a preference. It is a working engine, and it runs in either direction. Four seconds taken off each of the one thousand four hundred and forty minutes of a day comes to ninety-six minutes. Build the day instead from twenty-four shortened hours and the same ninety-six minutes appear, since twenty-four times fifty-six is one thousand three hundred and forty-four, and one thousand four hundred and forty less one thousand three hundred and forty-four is ninety-six. The two roads meet. Ninety-six minutes a day stand outside the statutory grid, and they are the first figure in this book that belongs to a ledger no one else is keeping.
Across a year of three hundred and sixty-four days the leak compounds into something a man can hold. Ninety-six minutes a day for three hundred and sixty-four days is thirty-four thousand nine hundred and forty-four minutes. Divide that by fifty-six, the length of the shortened hour, and the quotient is six hundred and twenty-four with nothing left over. Six hundred and twenty-four over twenty-four gives twenty-six, exactly. The annual leak is twenty-six whole days of a man's own time, whole down to the minute, and no ledger of men has ever entered them. State the same quantity on the other clock and it reads differently, twenty-four and a fraction days in their hours, and the two figures describe one quantity and are never to be spoken as one figure.
Why the count matters is not a question about minutes. A day in a calendar is a term of an instrument before it is a label for light. Rent falls due on a day, wages accrue by the day, interest runs by the day, a lease is measured in years, and the time allowed a man to bring his claim is a count of days that some statute set. A count that drifts does not fail loudly. Its entries keep their force while their meaning decays, and a date written under a count that has since moved must be translated before it can be read. That is why the arithmetic here is worth following all the way down. A count that closes on whole numbers can be checked by anyone with a pencil, and a count that can be checked can be held to.
The history of the Western calendar is that same problem told in three acts. Rome fixed the year at three hundred and sixty-five and a quarter days, which runs long of the seasons by eleven minutes and fourteen point eight seconds a year and pays off one whole day of error in one hundred and twenty-eight years exactly. A council at Nicaea in the year three hundred and twenty-five fixed the spring equinox at March twenty-first and anchored the feast of the Resurrection to it, which gave the drift a datum to be measured against and nothing with which to stop it. Twelve and a half centuries later the separation had reached nine point eight two days, ten days were struck out of October of fifteen eighty-two, and the rule that withholds three leap days in every four hundred years was written to hold the equinox where the council had left it. Three more days have been struck since, out of seventeen hundred, eighteen hundred, and nineteen hundred, and the next falls in twenty-one hundred. The reformed year misses the seasons by twenty-six point eight seconds, one day in three thousand two hundred and twenty-three years, and it still is not the sky. It is the sky's year as closely as a stated fraction can be made to fit.
One thread runs under all of it, and it is the thread this book follows out. A count is a decision before it is a measurement. Nobody voted the seven-day week into being; it falls out of the day itself, since twenty-four is three sevens and a remainder of three, and the remainder of three walks the ruler three places forward in the old order of the hours. The names the days carry are that arithmetic, still legible after two thousand years of use. Nor were the hours of the oldest dials empty spans. They carried names and keepers, a gate and a guardian for every one, which is what makes an hour an office rather than a length. The clock that divides tells how long. A clock that assigns tells who, and only the one that assigns can be charged.
An office is what this book is finally about, and the office is the reason the count matters more than the minutes. Every count in the world was declared by somebody, in writing, with a date on the paper, and every declared count can be read by anyone who can reach the record. Even the wall clock was declared. The two machine zeros that govern the age, one at midnight on the first of January of nineteen seventy and one at midnight on the sixth of January of nineteen eighty, stand ten years and five days apart, and the seconds that reconcile them were entered by hand. So was the reformed calendar, and it printed its own reason in the open. A declaration is a document, and a document can be checked, which is the whole defense available to a man whose days are counted by somebody else. Read the record, and the hours no ledger has ever entered are the hours that remain his.