# Bill and Miguel’s Calendrical Adventure

## When is the same date not the same day?

It’s 23rd April, World Book Day, as I write this.

Miguel de Cervantes and William Shakespeare both died on 23rd April 1616. They did not, however, did not die on the same day. There is no paradox, but there is an assumption: these dates of death do not come from the same calendar.

In 1616 Spain was following the Gregorian calendar, introduced by and named for Pope Gregory XIII in October 1582, and England was still following the Julian calendar, based on Julius Caesar’s calendar reforms in 46 BCE. Shakespeare died 10 days after Cervantes, which was in May 1616 in the Gregorian calendar.

The difference between the two calendars is defined by their leap-year calculation rather than by a fixed number of days. With (almost) every passing century the calendars drift a little further apart. By the time England (now part of the United Kingdom) adopted the Gregorian calendar in 1752, the accumulated difference between the calendars was 11 days.

A calendar is an attempt to read some order into the universe while connecting it to the world and quirks of human affairs. Sometimes the heavens can be quite tidy and harmonious.

The Moon is tidally locked to the Earth, so that the Moon takes as long to rotate as it does to orbit the Earth, thus keeping the same face towards us. Mercury has a 2:3 ratio of its day (~58⅔ days) to its year (~88 days). Three of Jupiter’s Galilean moons — Ganymede, Europa and Io — are locked into a heavenly harmony of 1:2:4, an orbital resonance that tidally squeezes Io into being the most volcanically active body in the Solar System. Overall, however, the cosmos is more messy than tidy. And orbits and rotations certainly don’t clock in to follow our calendrical fancies:

The Earth’s orbit around the Sun is not an exact multiple of the Moon’s orbit around the Earth, so lunar months to not square neatly into years, and the Earth’s day is not tidally locked to its orbit around the Sun, so the solar year is not a convenient integer count of the solar day. Although embedded into so many brand names, URLs, etc., the familiar 365 is just not enough to make a full turn around the Sun.

Hence, a given calendar year will be one of two day counts: 365 days for common years; 366 days for leap years. The ratio between common and leap years is adjusted to ensure that calendar years and solar years maintain a close alignment. The frequency of the intercalary day (29th February) is one feature that distinguishes the Gregorian calendar from the Julian calendar.

The Julian calendar introduces a leap day in years that are divisible by 4, giving a mean year of 365.25 days. This can be coded simply in, for example, Python:

`def is_leap_year(year):    return year % 4 == 0`

The logic here reads as a year is a leap year if the remainder of dividing it by 4 is 0. This is close enough for government work and, was indeed, the official administrative calendar of European nations for centuries. It’s close, but not close enough: the solar year is around 365.2422 solar days. The Gregorian calendar was introduced in 1582 to address the gradual drift of the Julian calendar from seasonal alignment. It adds an exception for centuries (so that 1900 was not a leap year) with an exemption every fourth century (so that 2000 was a leap year):

`def is_leap_year(year):    return year % 4 == 0 and year % 100 != 0 or year % 400 == 0`

The logic here reads as a year is a leap year if the remainder of dividing it by 4 is 0 unless the remainder of dividing it by 100 is 0, or if the remainder of dividing it by 400 is 0. This gives a mean year of 365.2425 solar days. Not bad. It may need tweaking again it in a thousand years or so.

Logical as the Gregorian reform was, however, it took over three centuries for the Gregorian calendar to be adopted in preference to the Julian calendar. Humans are not particularly rational creatures and, like any measure of the world or heavens, calendar reform is tied in — and up, and down — with religion and politics, which is a sure way to decelerate progress and subvert any logic and reason that might have been in play.

The slow roll-out leaves us with calendar-shearing oddities such as Shakespeare and Cervantes’ non-coincident but identical dates of death and, as observed by most of the rest of the world in 1917, placing Russia’s October Revolution in November. Flush with revolution, Russia switched calendars in 1918. Turkey, in 1926, was the last country to adopt the Gregorian calendar.

Now, I said that calendar years have one of two day counts: 365 and 366 days. In the Gregorian and Julian calendars this is true… but when jumping from one system to another, truth is more fluid.

1752 in the UK and its dependencies was 355 days long. Although a leap year, 11 days were ‘lost’ in going from Wednesday 2nd to Thursday 14th September. Note that the claim of civil unrest “Give us our eleven days!” — is an urban myth. This calendar adjustment followed hot on the heels of another: 1751 was 282 days long, which began — as years did up until then — on 25th March but this time ended on 31st December. What was considered the start of the year changed, with 1751 being shortened so that 1752 began on the now familiar 1st January.

Sometimes, the years really do pass more quickly.

consultant · father · husband · itinerant · programmer · speaker · trainer · writer

## More from Kevlin Henney

consultant · father · husband · itinerant · programmer · speaker · trainer · writer

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