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The day after (Thursday) October 4th 1582 was (Friday) October 15th 1582!

The short story

It’s all about Easter Day!

Too short perhaps….

Well: the date of Easter has been agreed in the First Council of Nicaea in 325 and is tied to the spring equinox; but the Julian calendar – introduced in 46 BC by Julius Caesar – was drifting the Easter day away year on year. Undesirably, from the Roman Catholic Church perspective. So, Pope Gregory XIII (after whom the Gregorian calendar was named) by papal bull Inter gravissimas (dated February 24th 1582), adjusted the Julian calendar in order to correct that. The Easter date was drifting by about three days every four centuries, so the adjustment had to be approximately of ten days: so what should have been October 5th became October 15th, AD 1582.

The process for this change has actually been quite long. After the Council of Trent in 1563 approved a plan for correcting the calendrical errors and preventing future drift, a Compendium was sent in 1577 to expert mathematicians for comments. The approach suggested by the Calabrian doctor Aloysius Lilius (later expanded and slightly modified by Christopher Clavius) was finally adopted: a one-off correction of the at-the-time situation was required and, from that moment onwards, in order to prevent future drifts, years divisible by 100 would be leap years only if they were divisible by 400 as well.

The Gregorian calendar was soon adopted by most Catholic countries (e.g. Spain, Portugal, Poland, most of Italy). Protestant countries followed later, and the countries of Eastern Europe adopted the new calendar even later. In the British Empire (including the American colonies), it was adopted in September 1752. For 12 years from 1700, Sweden used a modified Julian calendar and adopted the Gregorian calendar only in 1753. Russia remained on the Julian calendar until 1918, while Greece continued to use it until 1923.

The long story of counting days

All of this looks terribly complicated but the matter of counting days and ensuring the consistency with seasons is far from being trivial.

In order to understand properly, we probably need to go back to the Paleolithic’s lunar calendars – as early as 6,000 years ago – of either 12 or 13 lunar months (either 354 or 384 days). Without intercalation to add days or months to some years, seasons were quickly drifting: so a thirteenth month was added to some years to make up for the difference between a full year and a year of just twelve lunar months. This is roughly what was enforced in the Roman calendar before Julius Caesar’s reform (Numa Pompilius, etc.), where an intercalary month (Mensis Intercalaris) was sometimes inserted between February and March to a 355-days lunar calendar. With this addition of 22 or 23 days to some years, the average Roman year would have had 366.25 days over four years. A further refinement would average the length of the year to 365.5 days over 24 years.

In practice, these intercalations did not occur schematically, but were determined by the Pontifices. Since the Pontifices were often politicians, this power was abused, e.g. lengthening a year in which political allies were in office. Not only these adjustments were missing, but they were often determined quite late, and the average Roman citizen often did not know the date, particularly if he was far from the city! For these reasons, the last years of the pre-Julian calendar were later known as “years of confusion”….

The approximation of 365.25 days for the tropical year had been known for a long time but was not used directly since ancient calendars were not solar, except in Egypt where a fixed year of 365 days was in use, drifting by one day against the sun in four years. Julius Caesar probably experienced the solar calendar in that country and, once returned to Rome in 46 BC, according to Greek-later-Roman historian Plutarch, called in the best philosophers and mathematicians of his time – like Sosigenes of Alexandria – to solve the problem of the calendar. Eventually, it was decided to establish a calendar that would be a combination between the old Roman months, the fixed length of the Egyptian calendar, and the 365.25 days of the Greek astronomy.

The first step was to compensate for missed intercalation and realign the calendar year to the tropical year: this meant that 46 BC had 445 days. The first year in the new calendar was then 45 BC. Ten days needed to be added to the usual 355-days Roman calendar: two extra days were added to Januarius, Sextilis (changed to Augustus in 8 BC) and December, and one extra day was added to Aprilis, Junius, September and November. Februarius was not changed in ordinary years, and so continued to be the traditional 28 days long. All of this still holds today. The old intercalary month was abolished. The new leap day was dated as ante diem bis sextum Kalendas Martias: the bissextile day. Although the new calendar was much simpler than the pre-Julian calendar, the Pontifices initially added a leap day every three years, instead of every four. After 36 years, this resulted in three too many leap days. Augustus remedied this discrepancy by restoring the correct frequency. He also skipped three leap days over 12 years in order to realign the year.

Though improving significantly from the previous calendar, the Julian scheme was a bit too “fast” (approximately 11 minutes) with respect to the astronomical seasons. As a result, the calculated date of Easter gradually moved out of alignment with the March equinox. While Hipparchus and presumably Sosigenes were aware of the discrepancy at the time (not of its correct value, though), it was evidently considered of little importance. In reality, it accumulated significantly over time: at the pace of about one day every 134 years, by 1582, it was ten days out of alignment!

The ten-days correction is still not enough….

Left like this, the Gregorian algorithm will anticipate the astronomical season by three days in 10,000 years (which ends up bringing Christmas in the middle of the Northern hemisphere summer in about 600,000 years). In order to remedy this problem, we should consider as leap all the end-of-millenuim years only if they are divisible by 4000, this would limit the difference to a day every 20,000 years (which ends up bringing Christmas in the middle of the Northern hemisphere summer in about 3,600,000 years).

For such precision, the Gregorian calendar was (wrongly) judged the most perfect solar calendar but, in the centuries before the Gregorian reform, an Islamic-originated calendar designed an algorithm for a change to the Julian calendar which would approach the seasonal cycle to the actual length of the tropical year with amazing accuracy!

But that’s a story for another post….

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