Reforms that never happened

Every one of these machines fixes the calendar. None of them survived the week. ← Calendar Contraptions

Since Pope Gregory XIII steadied the drift in 1582, reformers have kept submitting upgrades: calendars where every year is identical, every quarter is square, every date keeps its weekday forever. Several came close to winning. This page runs your date through three of the runners-up — the World Calendar that reached the United Nations, Comte's Positivist calendar of great men, and the Hanke–Henry calendar still collecting signatures — plus the arithmetic patch that would have mended the French Republican calendar before France abandoned it. Pick a date; each machine will tell you what it would have called it.

The number that ruins everything

A common year is 365 days. Fifty-two weeks take 364 of them, and the leftover day is the whole problem. Every proposal on this page is an answer to that remainder, and there are only two honest answers.

The first: throw the extra day out of the week. Make it a blank day — a year-end holiday with no weekday name — so the week always restarts in step with the year and every date keeps its weekday forever. The World Calendar, the Positivist calendar and Asimov's seasons all work this way. The second: keep the week unbroken and let whole years be 364 or 371 days — one leap week every five or six years, dates sliding against the seasons by up to a week. The Pax and Hanke–Henry calendars work this way.

The first answer is where the fighting starts. Three of the world's largest religions fix their worship to the seventh day — Friday, Saturday or Sunday, depending on the house. A blank day makes the week eight days long, once a year, twice in leap years: either the holy day slips onto weekdays, or the faithful keep counting sevens privately and drift away from the civil weekend. To communities whose calendar is a commandment, neither is acceptable. The second answer spares the week and charges the month instead: the 31sts vanish, anniversaries migrate a few days, and the software never quite recovers. The Gregorian calendar survives because it promises nothing about weekdays at all.

Comte's calendar of great men

Auguste Comte, the philosopher who founded positivism, designed a calendar as a sermon. Thirteen months of 28 days, four identical weeks each, plus a festival day (two in leap years) outside the week. 1 January is always a Monday; the 17th of every month is always a Wednesday. What made the machine unrepeatable was the naming. The months run in historical order through the people Comte thought had built civilization: Moses, Homer, Aristotle, Archimedes, Caesar, Saint Paul, Charlemagne, Dante, Gutenberg, Shakespeare, Descartes, Frederick, Bichat. Every one of the 364 days got a patron too — 558 names in all — starting with Prometheus on 1 Moses and ending with the anatomist Franz Joseph Gall on 28 Bichat. Villains were not omitted: Comte assigned them days of "perpetual execration", Napoleon in particular.

The scheme descends from the Reverend Hugh Jones's Georgian calendar of 1745 (published under the pen name Hirossa Ap-Iccim, its months named for George II) via Marco Mastrofini's eternal calendar; its great descendant, Moses B. Cotsworth's International Fixed Calendar, got further than Comte ever did — the Eastman Kodak Company ran it for sixty-one years — but no 13-month calendar ever converted a nation. Comte called his own design "a provisional institution" for an exceptional century, and it never saw widespread use. The historian of calendars Duncan Steel dryly notes the month names alone were enough to sink it: it would seem strange to give the date as the third day of Homer.

The World Calendar and the eighth day

The closest the world came. Elisabeth Achelis of Brooklyn founded the World Calendar Association in 1930 to promote a design older than she was: the Abbot Marco Mastrofini had proposed a year of four equal 91-day quarters beginning on a Sunday, and around 1887 the French astronomer Gaston Armelin published a near-identical plan. Twelve months, each quarter 31–30–30 days: 91 days, 13 weeks, every quarter starting on a Sunday and ending on a Saturday. The 365th day is Worldsday, dated "W", after the last Saturday of December; leap years add a Leapyear Day after 30 June. Both sit outside the week — a 24-hour waiting period between Saturday and Sunday, as the association liked to say. Every quarter is identical, so April, July and October are the same month with different names; the calendar prints once and never expires.

Achelis published the Journal of Calendar Reform for twenty-five years, and after the Second World War the question reached the United Nations, which had inherited the League of Nations' file on the subject. In 1955 the United States shut the door: it would withhold support for any study "unless such a reform were favoured by a substantial majority of the citizens of the United States acting through their representatives in the Congress". Congressman Gerald Ford relayed the State Department's opposition to his constituents that spring. Jewish, Christian and Muslim leaders objected to the blank days for the same reason they had objected to every blank day: worship fixed to every seventh day cannot share a calendar that inserts an eighth. Achelis dissolved the association in 1956; successors kept the file open into this century — its last director died in 2020 — and the World Calendar remains the most-cited calendar never adopted. One footnote for the modern reader: it is incompatible with ISO 8601, which counts weeks from Monday and has no way to write a date that sits outside one.

The reform of the reform

The French Republican calendar — the one reform that actually happened, for twelve years — carried a flaw its own decree built in. A four-year period called the Franciade was to close with a leap day, "the fourth year of the Franciade is called Sextile"; but the same law pinned the new year to the autumn equinox in Paris, and the equinox does not obey four-year schedules. In practice An III, VII and XI were sextile (366 days), An XV and XX were planned that way five years apart, and about three times a century the leap years had to stretch. Piece one of this corner runs the real astronomical rule live.

In 1795 the commission's own mathematician proposed the obvious patch. Delambre's rule, presented to the Committee of Public Education by Gilbert Romme on 19 Floréal An III (8 May 1795), applied the Gregorian leap arithmetic to the Republican years themselves — An IV, VIII, XII and so on sextile, with An 4000 held common as a concession to the sky. The point was predictability, not accuracy. The committee knew the equinox rule depended on astronomy that could not be trusted hours from midnight: their own ephemeris put the equinox of An 144 (1935 in our counting) at 11:59:40 pm Paris apparent time, closer to midnight than the three or four minutes their tables could resolve. A calendar whose leap years need a live astronomer is a calendar waiting for an argument.

The patch never ran. Shortly after presenting it, Romme was sentenced to the guillotine and killed himself on the way to the scaffold; the proposal died with him, though the astronomer Lalande pressed it for years afterwards. Reconstruct the arithmetic calendar — An 1 stays 22 September 1792, lengths follow the rule — and you can watch it work: the table below, computed live from the same observatory machinery as piece one, shows the two rules never disagree on the date of the new year by more than a single day in six centuries. What the patch changes is not the sky but the ledger: which years count as sextile. The law had made An III, VII and XI leap; the rule makes IV, VIII and XII leap instead. Adopting it would have relabelled years France had already lived — one more reason the argument mattered. The reconstruction passes a neat test of its own: every year of the third Republican century (An 201–300, or 1992–2091) begins on 22 September, exactly as accounts of the proposal record.

Apart = arithmetic new year minus equinox new year, in days; positive means Romme's calendar runs ahead of the sky. Rows where the two rules disagree on sextile status are shaded. Computed in your browser; the equinox column is the Paris-observatory rule that governed the actual calendar.

The echo that keeps coming back

The blank-day calendars lost in the 1950s, and the lesson stuck: the next generation of reformers kept the week sacred and charged the month instead. Richard Conn Henry, a Johns Hopkins astronomer, proposed the Common-Civil-Calendar-and-Time in 2004, building on a scheme by Robert McClenon; the economist Steve Hanke joined for the 2011 revision that gave the design its current name and moved its leap week from mid-year (Henry had christened it Newton) to the end. The Hanke–Henry Permanent Calendar is four square quarters of 30–30–31 days — 364, with a 371-day year every five or six years, exactly the years that already run 53 ISO weeks. Its Xtra week sits between the end of December and the new year, and 1 January falls on a Monday, every year, forever.

The pitch is the Fourth Commandment kept: no day is ever inserted into the week, so Saturday stays Saturday and no worship day drifts. The price appears in the month column. The 31sts of January, May, July, August and October cease to exist, and Halloween has to move — the authors' own suggestion is the 30th, or "a random day of one's choosing". A birthday on the Xtra week arrives once in five or six years, about five times as common, oddly, as February 29 birthdays are now. There is a business appendix, too: equal quarters would have prevented Apple's Q4 2012 reporting surprise, when a fourteen-week quarter made a healthy year look like a miss. And in the spirit of fixing time itself, the proposal would abolish time zones — one clock for the whole planet. Like every machine on this page, it remains unadopted. The week, it turns out, is the easy part; the dates are the hostage.

Hall of the unreformed

The family is larger than this page. A few more machines that never ran the world:

The Georgian calendar (Rev. Hugh Jones, 1745) — thirteen 28-day months named for the glory of George II; 364 days and no apology, so the seasons walked slowly around the year. The Pax Calendar (James Colligan, 1930) — thirteen 28-day months with a leap week in 71 of every 400 years: no blank days ever, dates adrift by up to a week. The World Season Calendar (Isaac Asimov, 1973) — months abolished altogether; four seasons of 91 identical days plus a blank day or two. Symmetry454 (Irv Bromberg) — months of 4, 5 and 4 weeks and a 293-year leap cycle, the most mathematically patient of the family.

Why none of it happened

Every machine on this page is arithmetically better than the one you use: perpetual, square, printable once. Each lost to the same two enemies. The first is the week — break it by a day and the faithful refuse; keep it and the month breaks instead, and the anniversaries move. The second is indifference: a calendar is infrastructure, and infrastructure only changes when it fails. The Gregorian calendar does not fail. It merely annoys, quietly, one leftover day a year. The leftover day keeps winning.