How Did Calendars Develop? Fitting a Year Into Whole Days

A society designing a calendar picks which astronomical cycle to follow, and the choice determines what goes wrong:

• •Lunar calendars follow the moon, with twelve months of twenty-nine or thirty days totalling about 354 days, so they drift against the seasons by eleven days a year and a given month moves through the whole year in about thirty-three years. The Islamic calendar works this way deliberately, which is why Ramadan occurs in every season over a lifetime
• •Solar calendars follow the sun and the seasons and ignore the moon, so the months have no relationship to lunar phases. The Egyptian and later the Roman and Gregorian calendars are solar
• •Lunisolar calendars follow the moon and correct periodically by inserting an extra month, keeping both cycles roughly aligned. The Hebrew, traditional Chinese and Hindu calendars do this, adding a leap month in seven years out of every nineteen, which is the Metonic cycle noticed in Greece in the fifth century BC and in Babylon before that
• •Some calendars ignore astronomy altogether for their counting unit: the Maya long count simply counts days from a fixed origin, which avoids every drift problem and tells you nothing about the season

The calendar Rome inherited had 355 days and required priests to insert an extra month at intervals to keep it aligned. Because those priests were also politicians, and because the insertion could extend a term of office or shorten an opponent's, the system was manipulated until the calendar had drifted by months from the seasons. Julius Caesar, advised by the Alexandrian astronomer Sosigenes, fixed it in 46 BC by abandoning lunar months entirely, setting the year at 365 days with a leap day every four years, and inserting enough days into that single year to realign it with the seasons, which made 46 BC 445 days long and earned it the name the year of confusion. The Julian calendar was a substantial improvement and was slightly wrong: a year of exactly 365.25 days is about eleven minutes longer than the actual solar year, an error of one day every 128 years.

By the sixteenth century the accumulated Julian error had reached ten days, which mattered to the Church because the date of Easter is calculated from the spring equinox and the equinox had moved away from its assumed date of 21 March. Pope Gregory XIII issued a reform in 1582 with two parts: drop ten days immediately, so that 4 October was followed by 15 October, and refine the leap rule so that century years are leap years only if divisible by 400, which reduces the error to about one day in 3,000 years. Catholic countries adopted it at once. Protestant and Orthodox states refused for a long time, since accepting a papal decree was politically impossible, so Britain and its empire changed only in 1752, by which time eleven days had to be dropped, and Russia not until 1918, by which time it was thirteen, which is why the October Revolution happened in November. The story that English crowds rioted demanding their eleven days back appears to derive from a Hogarth painting and an election slogan rather than from any recorded riot, though there was genuine confusion about rents, wages and interest.

Several familiar features have no astronomical basis at all. The seven-day week corresponds to nothing in the sky and appears to derive from Babylonian practice and the seven visible moving bodies, and it has been remarkably resistant to change: both the French Republican calendar, which tried ten-day weeks from 1793, and the Soviet five-day and six-day weeks of 1929 to 1940 were abandoned, in the Soviet case partly because a continuous production week that gave workers different rest days destroyed family and social life. The uneven month lengths are Roman accretions, and the names of the last four months mean seventh through tenth because the year once began in March, which is also why the leap day is added in February, the last month of the old year. The start of the year has been placed at various times including Christmas and 25 March, which is why the British tax year still begins on 6 April, being 25 March plus the eleven days dropped in 1752.

Calendar reform proposals continue and none has succeeded. The World Calendar and the International Fixed Calendar, both promoted in the twentieth century, would make every year identical by inserting a blank day belonging to no week, which religious groups opposed because it breaks the seven-day cycle. The deeper problem is that any change requires simultaneous global adoption, which is far harder now than in 1582. Meanwhile a smaller adjustment causes continuing trouble: leap seconds, inserted irregularly since 1972 to keep atomic time aligned with the Earth's slightly irregular rotation, break computer systems that assume a minute has sixty seconds, and in 2022 the international body responsible voted to stop adding them by 2035 and let the discrepancy accumulate instead. The underlying situation has not changed since Babylon: the Earth's rotation, its orbit and the moon's cycle are independent and none is a whole number of the others, so every calendar is a managed approximation.

A year is about 365.2422 days and a lunar month about 29.53, and neither divides the other, so every calendar chooses to follow the moon and drift through the seasons, follow the sun and abandon the moon, or follow both and insert a leap month. Caesar's solar reform in 46 BC left an error of a day every 128 years, which Gregory corrected in 1582 by dropping ten days and changing the century leap rule, a change Protestant and Orthodox states resisted for centuries. The seven-day week and the month lengths have no astronomical basis at all.