It is commonly believed that the turn of the millennium takes place at midnight between New Year's Eve 1999 and New Year's Day 2000.
Let's consider the era as a one-dimensional coordinate system with a zero point and a positive and a negative part, the zero point neither being positive nor negative. This coordinate system is to be symmetric. The number +1 represents the point in time exactly one year after the zero point. The number -1 represents the point in time exactly one year before the zero point. If there were to be a year 0, it would have to be the year between 0 and +1 or between -1 and 0. However, the concept of a year 0 violates the symmetry and the principle of 0 neither being positive nor negative. Hence, there is no year 0. Thus, the first decade is the years 1 through 10. The first century is the years 1 through 100. The first millennium is the years 1 through 1000. The second millennium is the years 1001 through 2000. Hence, the millennium does not end at the end of December 31 of 1999, but at the end of December 31 of the year 2000.
A major cause of the misconception may be that we celebrate the milestones of the era slightly differently than we celebrate anniversaries. E.g., we celebrate someone's 30th birthday when he turns 30. So why shouldn't we celebrate 2000 years when the year turns to 2000? The explanation is simple. When one is 29 years old, one is going on 30. When it's the year 2000, the era is "going on 2000". When the year turns to 2000, it's alright to celebrate the year 2000, because that's how we celebrate the milestones of the era. However, one does not celebrate one's 30th birthday when one starts going on 30, i.e., when on one's 29th birthday. Similarly, as the year determines which year the era is "going on", it would not be right to celebrate the turn of the millennium before the end of the year 2000.
Or perhaps it's just because 2000 is too round a number to comprehend that its commencement is not the turn of the millennium?
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