Calendar follies

Here's an interesting side note on a case where the inventors of a commonly used facility should have used zero-based indexing, but didn't. We're still suffering from the annoyances of this one.

Long ago, there was no standard calendar, with year numbers progressing from one to the next, when January 1st came around. In fact, the year didn't begin on January 1st, but on March 1st. That's why the extra day in a leap year is at the end of February, and also why September, October, November and December are months 9, 10, 11 and 12 instead of months 7, 8, 9, and 10 as their names suggest.

Instead of using progressively increasing numbers, years were numbered relative to the reign of the current monarch; for example, the Bible might refer to "the third year of Herod's reign". This was fine in antiquity, when most people really didn't care what year it was. There were few retirement plans or 50th wedding anniversaries to celebrate anyway. However, it was quite annoying to historians to try to calculate the age of someone who was born in the fourth year of someone's reign and died in the tenth year of someone else's. According to Grolier's Multimedia Encyclopedia:

`About AD 525, a monk named Dionysius Exiguus suggested that years be counted from the birth of Christ, which was designated AD (anno Domini, "the year of the Lord") 1. This proposal came to be adopted throughout Christendom during the next 500 years. The year before AD 1 is designated 1 BC (before Christ).'

The encyclopedia doesn't state when the use of the term BC started, but the fact that its translation is English is a suspicious sign indicating that this was considerably later. In any event, this numbering system made matters considerably easier. Now, you could tell that someone who was born in AD 1200 and died in AD 1250 was approximately 50 years old at death.

Unfortunately, however, there was still a small problem. Zero hadn't yet made it to Europe from Asia when the new plan was adopted, so the new calendar numbered the years starting with 1, rather than 0; that is, the year after 1 BC was 1 AD. While this may seem reasonable, it accounts for a number of oddities of our current calendar:

1. Date ranges spanning AD and BC are hard to calculate, since you can't just treat BC as negative. For example, if someone were born in 1 BC and died in 1 AD, how old was that person? You might think that this could be calculated as 1 - (-1), or 2; however, the last day of 1 BC immediately preceded the first day of 1 AD, so the person might have been only a few days old.
2. The 20th century consists of the years 1901 to 2000; the year numbers of all but the last year of that century actually start with the digits 19 rather than 20.
3. Similarly, the third millennium starts on January 1, 2001, not 2000.

The reason for the second and third of these oddities is that since the first century started in 1 AD, the second century had to start in 101 AD; if it started in 100 AD, the first century would have consisted of only 99 years (1-99), rather than 100.

If only they had known about the zero! Then the zeroth century would have started at the beginning of 0 AD and ended on the last day of 99 AD. The first century would have started at 100 AD, and so on; coming up to current time, we would be living through the last years of the 19th century, which would be defined as all of those years whose year numbers started with 19. The second millennium would start on January 1, 2000, as everyone would expect.