# Fun with calendar arithmetic

This page lets you calculate your own whimsical anniversaries. For example, you can work out when you will be (were) 10,000 days old, or a billion seconds old. Simply enter your birth date and time in the left column, the anniversary in the middle column, and click the equals button. (If nothing happens, you probably need to enable JavaScript on your browser.)

If you enter an invalid date the program will try to interpret it sensibly; for example 29 Feb 1900 is read as 1 Mar 1900.

 year month day hour min sec
+
 lunar years lunar months days hours min sec

 year month day hour min sec

All this might make you want to muse on the origin of calenders....

Calendars are a compromise between three different cycles that the sky presents to us: a day averaging 24h, a lunar month averaging 29d 12h 44m 3s, and a tropical (or seasonal) year averaging 365d 5h 48m 45s. Each of these cycles is simple enough in itself, the trouble is their ratios are irrational.

The standard civil calendar is a Roman invention which was tweaked during the Renaissance. Through its system of leap years, it gets the equinoxes to fall on the same dates each year and this stays in step with the seasons. But it practically ignores the moon.

The Roman version, called the Julian calendar, actually lets the equinoxes slide backwards a little, about a day per century. The Renaissance Catholic church didn't like that, and in 1582 the then Pope Gregory XIII disappeared the dates from 5 Oct and 14 Oct of that year to bring the equinoxes forward again. (The children's novel Tibaldo and the Hole in the Calendar tells the story through the eyes of a boy whose birthday would be disappeared as a result.) Gregory also decreed that 1700, 1800, 1900, and so on would not be leap years; that will keep the equinoxes from drifting for another few millennia.

The standard calendar now used, and which the calculator here follows, jumps from 4 Oct 1582 (Julian) to 15 Oct 1582 (Gregorian). The missing days were, if you like, consumed by 29 Feb 1500, 1400, and so on.

The Hijri (or Muslim) calendar follows the opposite strategy from the Gregorian: it follows the moon, defines its year as 12 lunar months, and completely ignores the seasons! That makes it easy to keep track of dates and festivals (you just watch the moon) but makes farming harder. You can use the lunar month and lunar year features in the calculator to compare Hijri and Gregorian dates. You'll need to input the zero point of the Hijri calendar, which is 16 July 622. Then adding lunar years will give you the Gregorian date of the Hijri new year (Muharram). Add eight months more and you'll get the beginning of Ramadan, and add one more month and you'll get the Gregorian date of Eid.

In the Julian-Gregorian transition there are some more complications which the calculator disregards. One is that January and February were originally the last two months of the year rather than the first two. So a year number in an old book may be one less than you'd have expected. Also there is the small issue that not everybody liked Gregory XIII [and not because of Gregorian chants---that was a different Gregory] so some countries and institutions stayed with the Julian calendar long after 1582, and Eastern Orthodox churches still use it. Which is how Cervantes and Shakespeare both died on 23 April 1616, but not the same day. And how the October Revolution really happened in November.

Yet both Gregorian and Hijri are probably exceptional, because most classical calendars try to compromise with both sun and moon. The general idea is to add leap months every so often (such as 7 leap months every 19 years, called the Metonic cycle) to keep lunar months in step with solar years.

And then there are calendars which dream up new cycles of their own. One of these days I'll code up the Maya katuns: place-value notation with a mixture of base 18 and base 20, negative numbers written as 13's complement---those are fun!