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The 21st Century will begin on January 1, 2001, not 2000. This is because the First (not the more logical zeroth) Century began in the year one, sort of.
The Christians used the Julian calendar (named for Julius Caesar). But they chose to make it begin with year one (not the more logical zero), at Jesus' birth. That was the change that they made to the calendar, a new starting date. Of course, they did not know when Jesus was born, not very accurately. So, they guessed.
The Julian calendar was not accurate. It had a year of 365 days, with a leap year every four years. This is close. But it is too long by one day every 128 years. In 1582, Pope Gregory (of Gregorian Chant fame) decreed that October 4, 1582 would be followed by October 15, 1582, dropping 10 days and correcting the accumulated error. Let's see; they dropped ten days, in 1582. Ten days error would accumulate after about 1280 years. So, Pope Gregory corrected only the 10 days error that had accumulated since about 302 A.D. I guess that was good enough.
Pope Gregory also instituted a new calendar, the Gregorian calendar. This calendar, which we now use, drops three leap days, every four centuries. 1600 was a leap year. 2000 will be a leap year. Other century years (1700, 1800, 1900) are not leap years. This makes the calendar pretty close to right (in synch with the earth's orbit). Further correction will not be necessary for many thousands of years.
Different countries did not switch to the Gregorian calendar right away. England, along with its American colonies, switched in 1752. George Washington was born under the Julian calendar. His birthday was Feb. 11, 1731. He converted his birthday to Feb. 22, 1732, under the Gregorian calendar. Russia did not adopt the Gregorian calendar until 1918.
Ancient Egypt used a calendar of a 365-day year, 12 months of 30 days, followed by five feast days that did not belong to any month. This calendar was off about one day every four years. And that calendar was used for thousands of years. So, at times, their calendar was very far off. Winter could occur during the summer months. They knew that their calendar was way off. And they just accepted it. They calculated when the floods would come, or when winter would arrive. And they didn't care that the season called Inundation (flood) might occur during the driest part of the year. They were ready for the real, physical floods, when they came.
People say that the Mayan calendar was much much more accurate than our calendar. Just how accurate could it be? Ours is right to the minute every few thousand years. Was theirs better than that? No. Theirs was nowhere near that accurate. The Columbia Encyclopedia also says that the corrected Mayan calendar (they also had another kind of calendar) had 18 months of 20 days and one month of five days. So, that was 365 days, same as the very inaccurate Egyptian calendar. The Columbia Encyclopedia says that that was more accurate than the Gregorian calendar. If so, then their description of the Mayan calendar is incorrect.
The myth of the great accuracy of the Mayan calendar probably comes from the fact that one of their calendars had cycles that repeated after millions of years into the past or future. So each day for millions of years would have a unique name based upon these cycles. This is not accuracy. It just comes from the fact that their cycles were relatively prime with each other and with the length of their calendar year. Our calendar has a unique name (date, month, year) for each date millions of years in the future, and we can even figure out what day of the week that date will be.
Anyway, don't celebrate the Millennium in 2000. You'll be worn out by the time the Millennium actually arrives, in 2001.
Comment: It is bad grammar to begin a sentence with a number (not spelled out). Years should not be spelled out. So, "1600 was a leap year," is incorrect. But I object. In my opinion, there is no good alternative to this very natural useage.
Addendum:
Above, I said that it would be more logical for the first century to be numbered zero instead of one. It is also more logical to begin a calendar with year zero instead of year one. A couple of readers object that we don't count things starting with zero. But we do measure intervals (time or distance) beginning with zero, and that is what we are doing here. In general, we can use simple arithmetic to calculate how many years or centuries there are between events. There are 4 centuries (400 years exactly) between the first day of the 9th century and the first day of the 13th century. How many centuries do you think there were between the first day of the 5th century B.C.E. (B.C.) and the first day of the 5th century C.E. (A.D.)? Ten is a good guess, but it is wrong, because there was no zeroth century. These are the centuries: -5, -4, -3, -2, -1, +1, +2, +3, +4 and then the next day is the one we are looking for, nine centuries. The arithmetic is ridiculous. The same thing happens with years. The ages of people born B.C.E, and dying in the C.E. are one off from what the simple arithmetic would suggest. Of course no one used our calendar back then, so they didn't have this problem (but they had similar problems with their calendars). This doesn't cause us great problems either, but it is illogical.
In The Star of Bethlehem I wrote this about the use of B.C.E. and C.E.:
The church created their calendar to begin in year one, not year zero (as is more logical), as the year of Jesus' birth. This was a guess. Jesus was apparently born during the rule of Herod the Great, who died in 4 B.C.E. ("before the Christian era"). So, Jesus was born some time before 3 B.C.E. That is one reason why historians now prefer to use "B.C.E." instead of "B.C." ("before Christ") and "C.E." ("Christian era") instead of "A.D." ("anno Domini" or "in the year of the Lord" which logically belongs before a date, not after) because using the starting point of Jesus' birth is a blatant error of at least four years, with Jesus being born before Christ, so to speak.