Calendar Contraptions

The machines we count days with. ← Workbench

A day, a moon and a year never divide evenly, so every calendar in history is a contraption: a hack that balances arithmetic, astronomy and politics — and breaks somewhere interesting. Each piece in this corner takes one way of counting days apart: a working converter, and the story of where it cheats.

Pieces

• One day, five counters the same date as a Julian Day Number, Julian date, ISO week, Maya Long Count and French Republican date — live
• The days have names all 360 named days of the French Republican year — plants, minerals, animals, tools — find yours · live
• Ten days that never happened October 1582, the Gregorian reform, and why the Orthodox Christmas is in January · live
• Weeks don't fit the ISO week calendar, its secret year, the 53-week trap and the three attempts to build a week that fits · live
• Mayan arithmetic the long count as a machine: five dials, one bent gear, zero as a shell — push the odometer yourself · live
• Reforms that never happened the World Calendar, Comte's great men, the Hanke–Henry echo and the arithmetic patch France never ran · live
• Unix time is a calendar seconds since 1970: the epoch, the 27 vanished leap seconds, the 2038 cliff — the day counter in every computer · live
• Easter, the moving target the 1,700-year-old machine with a moon that isn't there, a bug Gauss shipped and two Easters most years · live
• The year that wanders the Islamic calendar: 354 days, no seasons, an arithmetic moon, a crescent that must be seen · live
• The calendar that waits the Jewish calendar: a moon too old, weekdays with a veto, years of 353 and 385 days — the waiting machine · live
• The sixty-year wheel the Chinese calendar: months from the moon, a leap month picked by the sun, and 2,700 unbroken years of counted days · live
• Thirteen months of sunshine the Ethiopian calendar: twelve months of thirty, a thirteenth of five or six, a leap day that never skips, and seven years behind everyone · live
• Nineteen months of nineteen the Badíʿ calendar: nineteen months of nineteen days, a festival parked outside time, and a new year that waits for the equinox in Tehran · live
• The 33-year spring the Solar Hijri calendar: no leap formula at all, a new year decided at Tehran noon, and a 33-year rhythm that only looks like a rule · live
• The agreeable calendar the Indian national calendar: five months of 31, six of 30, a leap day borrowed wholesale from the Gregorian — the calendar that cannot drift · live
• The doomsday trick a dozen dates and a little arithmetic — name any weekday in your head, with a drill to train it · live
• The Sunday letters dominical letters: one letter pinned to the year, every Sunday known — the medieval twin of the doomsday trick · live
• The calendar on a stick runic calendars and primstavs: golden numbers, Sunday runes and saints' marks carved on wood — the staff carved for any year · live
• Ten weeks at once the Balinese pawukon: a 210-day wheel running ten concurrent weeks, days repeated to make them fit, and no year anywhere · live
• The New Fire every 52 years the Mexica calendar: a 260-day count of names and numbers, eighteen months and five nameless days, years named Rabbit, Reed, Flint and House — and the fire that had to be drilled fresh every 52 years · live
• The year with two names Japanese era names: a year number decreed by committee, years that last a week, and a registry of just 73 characters · live
• The month that never existed Japan's old lunisolar calendar: the rokuyō fortune cycle in every datebook, the moon arithmetic behind it — and autumn 2033, when the rules for naming months break on schedule · live
• The rules that can't break China's lunisolar calendar: the leap rule that has never crashed since 1645, the same moon read in Hanoi, Beijing and Seoul — and 1985, when one hour of longitude put Vietnam's new year a month before China's · live
• The month that gets skipped India's lunisolar calendars: where the rules can not only insert a month but delete one — the adhika months that repeat and the kṣaya months that vanish, and the two rule-books that disagree about which name dies · live
• The day that happens twice the tithi machine: India's lunar days, where a single day can repeat at two sunrises or never happen at all — the day-scale version of the kṣaya · coming next

Why bother

Because a calendar is the rare machine that everyone uses and nobody looks at. Its gears are leap rules and moon phases and a pope's arithmetic; its bugs caused riots; its version history includes guillotines and ten vanished days. None of the counters here is wrong — that is the quiet lesson. They are all counting the same days, and they all had a good reason.