It is tempting to think of 2000 as the first year of the next millennium. But if it is the start of the next millennium, the first millennium must have been numbered year zero, so that year 1 began one year after the supposed date of the birth of Christ. This has 2 difficulties (possibly 3).
First, zero as a number was not known to mathematics until much later than the first year of the modern era. By about 500 BC, Babylonian astronomers had a notation for a null value, so that they could signify a fractional amount which was less than 1 (but greater than 0). They had a place-value system of numbering, so in order to represent a quantity such as one sixtieth, they had to have a null value in the first position (0 plus one sixtieth). However, even the Babylonian astronomers did not have the concept of zero as a value which lay between -1 and +1: their zero was a mark of an absence, not a numerical concept.
We know that the ancient Roman and Greek mathematicians did not know of zero as a number.The best research suggests that zero as a numerical concept was discovered in the 8th century AD by Indian mathematicians. If any contemporary Roman citizen or Judean citizen had been asked “In what year was Jesus Christ born?”, they would have very likely denied the significance of his birth, and would have given the date using the old calendar. But assuming the question had been asked at a time when Christ’s birth was seen as the beginning of a new era (say, by the 3rd century AD), they would have answered “Year 1” not “Year zero”, because year zero would have been, to them, a meaningless concept and a numerical nonsense.
It must follow that the first year of the Christian era ended on 31 December year 1, the first decade ended on 31 December year 10, the first millennium ended on 31 December year 1000, and so on. That is how things would have been reckoned until at least 900 AD, by which time it was much too late to adjust the entire history of the world by one year. The millennium celebration is, on this view, one year early.
The second problem is different. We seem to have fallen into the gravitational pull of the soothsayers and cabalists who see profound significance in the turn of the millennium – 2000 years since the birth of Christ, etc, – but all the evidence points to the probability that Christ was born in the year we would now call 4 BC. So the big celebration is either 3 or 4 years too late, depending on your views about my first argument!
In addition, 31 December 1999 is not exactly 2000 years after 31 December year 0: the calendar has been adjusted several times since then, to keep it consistent with the undeniable fact of the equinoxes. Adjustments made to the calendar in 1582 as a result of a Papal bull, resulted in 10 days being skipped: the next day after 4 October 1582 was 15 October 1582. Similarly, in the shift from the old style calendar to the new style, the next day after 2 September 1752 was 14 September 1752. These 2 groups of omitted days have no more reality than 29 February in an ordinary year.
So, if you want to celebrate the day which falls exactly 2000 years after 31 December in the probable year of Christ’s birth, you should have done it on the day we called 21 January 1996; and if you want to mark the 2000th anniversary of the end of year 0, perhaps you should do it on 21 January 2000; and if you want to celebrate the end of the millennium, you should wait until 31 December 2000.
As for me, I like watching the odometer tick over to all zeroes – I don’t really care whether the odometer is accurate, or how many kilometers it showed when I bought the car – so I reckon the time to celebrate is 31 December 1999.
Incidentally, in computing terms, K is conventionally 1024 (ie 2 raised to the 8th power).So Y2K presents its own difficulties of interpretation …