Wednesday, February 29, 2012

LEAP

Oh lord, leap is a four letter word.

Today is leap day. That day, almost every four years, where those who follow the Gregorian calendar stick an extra odd day on a typically odd month. There are many odd traditions associated with this date, and many computer bugs have come out of the leap day rules, but why does it exist at all? And why at the end of February?

As with everything having to do with the calendar, we have a leap day because the Earth moves somewhat imprecisely in its orbit around the sun when compared to how long it takes to revolve around its axis.  In order words, in order to return to the exact same point in its orbit takes 1 year... but slightly more than 365 days. How much more? About a quarter of a day more. So roughly every four years, it has fallen one more day "behind" in its orbit around the sun. The Gregorian Calendar system addresses this by adding a day almost every four years - leap day.

I did a lot of hedging and fudging there. "About a quarter"... "roughly every four years"... "almost every four years". Well... truth be told, it isn't exactly a quarter of a day. It is more like 0.242374 of a day. To adjust for that, every 100 years, we don't have a leap year. So although 2096 will be a leap year, 2100 will not be.  But if you do the math, thats not quite close enough still.  That brings us to 0.24 (one quarter less one one-hundredth). To make it more accurate, we further refine the rule so that every 400 years, when we would normally expect there not to be a leap year, instead we will have a leap year.  Such was the case in the year 2000.  This brings us still closer to our goal - adding another 1/400th brings us to 0.2425 of a day.

As a child, I was very worried about the remaining 0.000126 of a day (about 11 seconds) and thought that this meant that every 8000 years we should, again, add a leap day when we would not normally expect one.  And then again every million years. Apparently I need not worry, however, since our orbit may not be this precise in the long run.

But why February? The Gregorian Calendar was derived from earlier Roman Calendars, ultimately going back to the Roman Calendar from around 750 BCE. In this early calendar, the first month was Martius, which eventually became known as March.  (As an aside, this explains why later months in the year have prefixes that don't match their position. October has the prefix oct-, meaning eight, although it is now the tenth month. December has the prefix dec-, meaning ten, although it is now the twelfth month. Something else that bugged me as a child.) The months of January and February were added later, and it made sense to add the "extra" day at the "end" of the year, which was first done under the Julian Calendar.

So no matter if you're going to leap for joy or take a flying leap, take comfort in the fact that we've adjusted ourselves to cosmic time once more.