Gregorian calendar

• 1. Introduction

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  The Gregorian calendar governs nearly every appointment, deadline, and birthday on Earth, yet it was born from a single religious puzzle: when exactly is Easter? On Thursday, the 4th of October 1582, people went to bed in one world and woke up in another. The next morning was not the 5th of October. It was Friday, the 15th. Ten days had vanished overnight, by order of Pope Gregory XIII. The question the rest of this documentary will answer is how a calendar could drift so badly that ten days had to be erased, who did the mathematics to fix it, and why it took more than three centuries for the world to agree.

• 2. The Problem With Julius Caesar

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  Julius Caesar gave his name to the calendar that preceded Gregory's, and he gave the world a beautiful simplification: every year is 365 days, and every fourth year gets a leap day. The Julian year therefore averaged exactly 365.25 days. The trouble is that the actual solar year is approximately 365.2422 days long, about 11 minutes shorter than the Julian estimate. Eleven minutes sounds trivial. Across a single lifetime it amounts to less than three days. Across thirteen centuries it adds up to ten full days of drift.

  Bede, writing in the 8th century, had already detected that the accumulated error in his time exceeded three days. Roger Bacon, writing around 1200, put the error at seven or eight days. Dante, writing around 1300, was aware that the calendar needed fixing. The drift was no secret; what was lacking was the political will and the mathematical precision to act.

  The urgency was not abstract. The date of Easter is calculated from the spring equinox, and the First Council of Nicaea in AD 325 had specified that all Christians must celebrate Easter on the same day. Easter falls on the Sunday after the ecclesiastical full moon on or after the 21st of March. But the calendar's slow creep meant the March equinox was actually falling on the 10th or the 11th of March by the time Gregory took up the question. The Church's most sacred date was slipping through the year.

• 3. The Architects of Reform

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  Pope Sixtus IV made an early attempt at correction in 1475, inviting the astronomer Regiomontanus to Rome for that purpose. Regiomontanus died shortly after arriving, and the project collapsed with him. It would not be seriously revived for another six decades, until the Council of Trent in 1545 formally authorized Pope Paul III to pursue a reform, with the explicit requirement that the vernal equinox be restored to where it had stood at the Council of Nicaea.

  The mathematics that finally made reform possible came largely from a Calabrian doctor named Aloysius Lilius. His proposal had two interlocking parts. The first addressed the length of the year: by skipping three leap days out of every 400 years, the average year would shrink from 365.25 days to 365.2425 days, a figure that matched the mean tropical year to a precision that earlier tables could not distinguish. The specific leap-year rule he proposed, later encoded as "years divisible by 100 are not leap years unless also divisible by 400", had actually been published earlier by Petrus Pitatus of Verona in 1560; Pitatus had noted that it was consistent with the Alfonsine tables and with the work of Copernicus and Erasmus Reinhold.

  The second part of Lilius's contribution was a practical scheme for recalibrating the Church's lunar tables, which were used to find Easter's date. At the time of the reform, astronomical new moons were occurring four days earlier than the tables predicted. His solution required adjusting the lunar cycle by one day every 300 or 400 years.

  Lilius's proposals were expanded by Christopher Clavius, a German mathematician who wrote a closely argued, 800-page defense of the new system. In 1577, a summary document called a Compendium was circulated to expert mathematicians outside the reform commission. Some of them, including Giambattista Benedetti and Giuseppe Moleto, argued that Easter should be calculated from the true motions of the Sun and Moon rather than from tables. That recommendation was not adopted. Clavius also had a decisive influence on one crucial practical question: whether to correct the ten-day drift gradually over forty years, as Lilius had suggested, or all at once. Clavius argued for immediate correction, and Gregory followed that advice.

• 4. The Bull and the First Calendars

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  Pope Gregory XIII issued the papal bull Inter gravissimas on the 24th of February 1582. The bull carried the full solemnity the Church could muster, but Gregory was realistic about his authority. He ruled the Papal States directly and led the Catholic Church as its supreme authority, but civil calendars required civil adoption. A pope could not compel Protestant or Orthodox kings by papal decree.

  A month after the bull, Gregory granted Antoni Lilio, a relative of the late Aloysius Lilius, the exclusive right to publish the new calendar for ten years. One of the first calendars printed in Rome under this arrangement was the Lunario Novo secondo la nuova riforma, printed by Vincenzo Accolti. It bore a note at the bottom recording both the papal authorization and the Lilio name. The printing monopoly did not last long: the papal brief was revoked on the 20th of September 1582 because Antonio Lilio could not keep pace with demand.

  On the 29th of September 1582, Philip II of Spain decreed the switch for his territories, which at the time included Spain, Portugal, and much of Italy. In Spain, Portugal, France, the Polish-Lithuanian Commonwealth, and the Papal States, the calendar was implemented exactly as the bull specified. In France the sequence was slightly different: the 9th of December was followed by the 20th of December, not the 15th. The Spanish and Portuguese colonies followed somewhat later, delayed by the time it took for news to cross oceans.

• 5. Centuries of Resistance

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  Protestant countries did not welcome a Catholic innovation. Some feared the new calendar was a scheme to draw them back under Rome's authority. Britain found a characteristically English solution: the Calendar (New Style) Act 1750 mandated a calculation for the date of Easter that produced exactly the same result as Gregory's rules, without ever mentioning Gregory by name. Britain and the British Empire, including the eastern portion of what is now the United States, adopted the Gregorian calendar in 1752, a full 170 years after Catholic Europe. Sweden followed in 1753.

  Eastern Orthodox countries waited even longer. Russia held out until 1918. Greece, the last European country to adopt the calendar for civil use, did so in 1923. Many Orthodox churches continued to use the Julian calendar for religious purposes regardless. Saudi Arabia did not adopt the Gregorian calendar until 2016, making it one of the most recent countries to do so.

  Turkey's transition illustrates how gradual adoption could be. Before 1917, Turkey used the Islamic lunar calendar for general purposes and the Julian calendar for fiscal matters, with a fiscal year beginning on the 1st of March. From the 1st of March 1917, the fiscal calendar became Gregorian. Then, on the 1st of January 1926, Turkey extended Gregorian dating to all general purposes.

  The gap between Julian and Gregorian dates does not stay fixed. It grows by three days every four centuries, whenever a centurial year is a leap year in the Julian system but not in the Gregorian. From the 15th of October 1582 through the 28th of February 1700, the two calendars differed by 10 days. By the period from the 1st of March 1900 to the 28th of February 2100, that gap has grown to 13 days.

• 6. The Puzzle of Year Beginnings

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  Adopting the Gregorian calendar and agreeing on when the year starts turned out to be separate questions, and countries resolved them at different times. During the Middle Ages, Catholic influence pulled many Western European countries toward starting the year on one of several Christian festivals: the 25th of December, the 25th of March, or Easter.

  In England, the legal year began on the 25th of March, known as Lady Day, from the 12th century until 1751. This produced historical anomalies that still confuse readers today. The Parliamentary record lists the execution of Charles I on the 30th of January as occurring in 1648, because the year had not yet ended by Lady Day. Later historians, working from a January-first convention, place the same event in 1649. Scotland changed its New Year to the 1st of January as early as 1600, meaning 1599 was a short year in Scotland. England, Ireland, and the British colonies did not make the same shift until 1752, at which point 1751 ran for only 282 days.

  The Roman Republic itself had once begun its year on the 1st of May before 222 BC, then on the 15th of March from 222 BC, and finally on the 1st of January from 153 BC. The Julian calendar, launched in 45 BC, kept the 1st of January convention. The full Gregorian calendar cycle, ignoring lunar and Easter calculations, repeats every 400 years, which equals exactly 146,097 days, or 20,871 complete weeks.

• 7. Months, Memory, and Accuracy

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  The Gregorian calendar kept the Julian month names intact, and those names carry the debris of Roman religion and Roman power. January honors Janus, the god of doorways and beginnings. March recalls Mars, the war god. July was instituted in 44 BC to honor Julius Caesar in the month of his birth. August followed in 8 BC, named for Augustus after several events key to his rise to power fell within it. September through December preserve the numerical names of the old ten-month Roman year attributed to Romulus around 750 BC: seventh, eighth, ninth, tenth. Both September and October now hold positions two months beyond their original numbering.

  The earliest currently known text of the verse "Thirty Days Hath September" appears as a marginal note in a calendar of saints dated to around 1425. The knuckle mnemonic, which treats raised knuckles as 31-day months and the valleys between them as shorter months, offers a nonverbal alternative. A piano keyboard version also exists: moving up from an F key in semitones, white keys represent longer months and black keys the shorter ones.

  On the question of accuracy, the Gregorian calendar is substantially better than the Julian, which accumulated an error of one day every 128 years. The Gregorian system's error with respect to the mean tropical year is roughly one day every 3,030 years by one estimate, or one day every 3,333 years by NASA's figure. Against the astronomical vernal equinox, using the average interval near the year 2000 of 365.24237 days, the error is closer to one day every 7,700 years.

  Sir John Herschel, in the 19th century, proposed a further refinement: 969 leap days every 4,000 years instead of 970, which would make the year 4000 a common year rather than a leap year. That would shorten the mean year to 365.24225 days. The proposal has circulated widely but has never been officially adopted.