16 February 2013

A decimal calendar, launched in the year 2456 (today)

The calendar mess

A calendar tells you the year, the month and the day of the week, according to your culture or favourite religion. But whatever your taste, calendars are a mess. The reason is simple: the solar system is a mess, even the simple sun-moon-earth threesome. Voltaire compared it to a watch, but what a poor one it is! The basic wheel is the "earth" wheel, one turn in 24 hours (more or less, all the wheels wobble a bit). For longer periods, counting full moons is the first choice. Bad luck, because the moon doesn't count in days; it needs more than 29 but less than 30. Counting in solar cycles is more useful still, but, alas, the sun counts neither in days (it needs more than 365 but less than 366), nor in moons (more than 12 but less than 13). Besides being out of tune, our three gears are wobbling, speeding up or slowing down, or changing unpredictably, and it's intrinsically impossible to get things right. Some watch! Who on earth designed this? [pun intended]

Every now and then, things get so bad that interference cannot be postponed. Julius Caesar interfered when seasons were completely out of tune with the calendar, and in 1582 the pope simply cut October 5 tot 14 from the calendar.

(Math Horizons, February 2000. MAA.)

Anti-papists were reluctant to follow, and that's why the communist "October Revolution" happened in (our) November. Months have 28, 29, 30 or 31 days, years 365 or 366, according to some intricate count.

Things become even worse when religions get fussy. For obscure astrological reasons, Christians want their Easter egg served on the Sunday following the full Moon which falls on or after the March equinox (I'm oversimplifying). These conditions combine a conventional religious cycle (seven day weeks) with "real" lunar and solar cycles. Struggling with Easter, the medieval monk Dionysius Exiguus computed when Christ had been born, and started the "Anno Domini" count which is still in use. Some thousand years later, it was found out that Christ had actually been born a few years before Christ. Fortunately, by lack of data, Christmas is fixed conventionally on December 25. Imagine a Christmas copy of the Easter nightmare!

Science takes over

The man who proved Dionysius wrong, the learned French humanist Josephus Justus Scaliger, also came up with a starting point from where to count all known historical events. Here is how he proceeded, in a purely logical fashion. Calendars display two recurring patterns, one returning after 19 years, the other after 28 years. Moreover, in the Roman empire taxes were revised every 15 years, and these "indictions" were also reference points on the time scale, still in use in the middle ages. A megacycle embracing these three cycles should count 19x28x15=7980 years. Scaliger also found out that these three cycles were simultaneously in their first year for the last time in 4713 BC. So he came up with a new starting point: January 1, 4713 BC, and a new period: 7980 years. After that period, calendar events will indeed repeat, and a new cycle starts. (If necessary, because many theologians were convinced that the world would only exist for 6000 years: 4000 before and 2000 after Christ.)

Only calendar freaks count Scaliger years, and not without distorting his system. He used Caesar's calendar, not the pope's, and the Gregorian count differs from the Julian one. Anyhow, here is a page from last year's Old Farmer's Almanac, which was year 6725 of the first Julian Period. (Scaliger would have been displeased with the Byzantine count superior to his own, because his primary goal had been to outdate all recorded historical events.)

Scaliger years did not make it, but his starting point (epoch is the right term) is here to stay. It's omnipresent in astronomical formulas (my sundial program is no exception). Astronomers start counting with Scaliger, more precisely on

January 1, 4713 BC, 12 UT (Universal Time, being noon in Greenwich)

and they simply count the number of 'days' (not midnight to midnight, but noon to noon) since then. On January 2, 4713 BC at 12UT the number was 1, the next noon it was 2 etc. At noon today (February 16, AD 2013) the number was 2456340. (Check it here.) It's as simple as that. Not only noons, every event on the time scale has a unique Julian Day Number ('Julian' after Julius Caesar, who introduced leap years.) For each hour after 12UT, add 1/24 to the JDN number, for each minute, add 1/1440 etcetera.

The first Julian period ends well after AD 3200. There is some time left before astronomers will have to decide what to do: start a new Julian period, or (as I expect) simply count on. The system is logically designed, and free of any religious bias. Among its ingredients there are a few civil conventions, like the 15 year indiction cycle, January 1st, and Greenwich (for the latter, see here). Even so, it's beautiful. So far, the count has no cycles and probably it will be kept without. No messing around with months and leap years to keep the poorly designed cosmic watch operational! In its simplicity, it's very close to linear timekeeping in Robinson Crusoe's way:

Take any infinitely long pole, replace September 30, AD 1639 with January 1, 4713 BC, and off you go!

A decimal calendar

Defining a particular day the usual way requires 8 digits, say 1947-05-11, while its Julian Day Number, 2432317, is shorter. To give it a conventional look, one could write this number as 2432-3-17, giving the impression of years of 10 months (numbered 0,1,...,9) of 100 days each (numbered 00,01,...,99). Doing so, one would extend the ten-day weeks of  the French revolutionary calendar to decimal months of ten weeks and years of ten months. A person born on 1947-05-11 has his 65th birthday on 2012-05-11, which is Julian Day 2456-0-59. Not very catching, is it? But in this decimal calendar, birthday parties should come after 1000 days, not after 365 or 366 as now. And 'living another 1000 days' sounds definitely more magical than 'the earth being more or less in the same place on its ellipse'. (Anne Boleyn would agree.) But even on his 65th 'conventional' birthday, our person can easily tell how many days he has lived so far: 2456059-2432317=23742. You won't repeat this feat the Gregorian way! Telling the day of the week is also a piece of (birthday) cake, once you know that Scaliger's starting day was a Monday. Hence, day 7 was a Monday, and so were the Julian days 14, 21, ..., 2432318 (which is 347474x7). Therefore, day 2432317 (a.k.a. 1947-05-11) was a Sunday.