Friday, January 2, 2015

One Year plus 0.242190 Days

Moore's Memorial Park, Ames, IA (January 10, 2014)

New year, new post, the first update of this blog since the last summer. The fall has come and gone: a cold November spell, with the only snow we got so far in this season, and an unusually warm December with autumnal weather through the solstice into the new year. The photo above? A snowfall from last year. This year's weather looks more like the small iphone photo below on the left.

January 1st, 2015
It is customary at the beginning of a new year to look back at the 364.242190 spins that the planet did in its last revolution around the Sun. I will refrain from that... you are welcome to go to +Massimo Marengo and read all my rants about the never ending (but very much enjoyed) new course I had to teach this semester (in summary: lots of work to prepare new classes, and not much sleep to recover between one lecture and the next), discovering how I live in the only populated place on earth that is seemingly cooling as a consequence of climate change, the continuing disappointment of a society that for each step forward in equality seems to make three step backwards in racial and economic inequality. Let's talk instead about the calendar itself, and the consequence of these 0.242190 extra days at the end of each year. 

Wishful thinking
Unless you live on a celestial body that is locked in some period resonance with some larger mass (e.g. the moon always shows the same face to Earth, hence the duration of its day is the same as the length of a month; Mercury rotates three times every two of its years), the length of the day and the length of the year are totally random. So it happens that if you want to have a calendar with an exact number of days for each year you are pretty much out of luck, because the seasons would drift by one day every fourth year, and you would soon be celebrating harvest in the middle of spring. That was the situation in antiquity, at the time Julius Cesar went to Egypt to biblically meet the queen Cleopatra. Egypt at the time was the cultural center of the Mediterranean, thanks to the famous library in Alexandria where the summa of all knowledge was kept. It was in Alexandria that Cesar consulted with the local astronomer Sosigenes, and figured out the need to add one extra day every four years to take into account the extra time that kept accumulating at the end of each year. This is how the leap years were born.

More like it
The celestial spheres, however, are indifferent to the desires of humankind, and 0.25 (one day every four year) is not the same as 0.242190. The seasons kept shifting, albeit more slowly and in the opposite way, even after the Julian calendar correction. So was the situation in the middle ages, when the calendar was again out of sync by 10 days. This was not good for the Church, since it completely messed up the complicated calculations that were used to determine the calendar date of Easter. As a result, Pope Gregorius XIII decreed that the day following October 4, 1582 was to be October 15, 1582, obliterating from existence 10 full days from the history of the world, and removing one leap year every century (but not if the century was divisible by 400). With these changes the calendar was forced to sync again with the seasons, with an accuracy better than 0.002%. Not all countries, however, adopted the Gregorian calendar right away: not everybody was very keen to follow the dictates of a Catholic pope. The orthodox Russia, for example, didn't fix their calendar until 1918: as a result, the October bolshevik revolution actually happened in November!

Moore's Memorial Park, Ames, IA (January 10, 2014)

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