## Things about the year 2000

Subject: Things about the year 2000
From: Stan Brown <stbrown -at- NACS -dot- NET>
Date: Mon, 5 Feb 1996 02:00:29 -0500

In TECHWR-L Digest, skrev John Wilcox <wilcox -at- PCD -dot- NET>:

>The addition of an extra day (oops, there's a superfluous modifier) every
>four years to correct for the fact that a day is slightly less than 24
>hours long results in a tiny overcorrection. So supposedly each year
>that is divisible by 400 is NOT supposed to be a leap year. In spite of
>this, a zillion programs have been written to use the standard leap year
>algorithm. Simply to avoid patching so many programs, I suppose 2000
>will indeed be a leap year. Have you heard anything definite?

I was going to send this to just John, but there seems to be
widespread misunderstanding so I'll post to the list.

First, the executive summary: 2000 is a leap year because Pope
Gregory planned it that way. And it's the last year of the 20th
century because of logic: there was no year 0, so 100 was the last
year of the first century.

Now, details: Inserting February 29 is required not because a day is
not 24 hours but because a year is not 365 days. In fact a year is
almost 365.25 days; hence an extra day must be inserted almost every
fourth year. I haven't got the exact value of "almost" to hand, but it
turns out that we'll be close enough for some thousands of years into
the future if three out of four century years (XX00) are _not_ leap
years.

Hence a year divisible by 400 is a leap year, other years divisible by
100 are not leap years, and other years divisible by 4 are leap years.
Specifically, 1600 was a leap year; 1700, 1800, 1900 were not; 2000
will be; 2100, 2200, 2300 will not be; 2400 will be, and so on.

John's "Simply to avoid" has things exactly backwards: computer
programs (and persons!) that naively assume years divisible by 4 to be
leap years have the correct answer for 1901 through 2099 inclusive,
but fail for 1900 or 2100. We're lucky that programming was invented
in the twentieth century so that we have an extra hundred years to get
the programs right.

By the way, you may wonder why we care: why not just have every year
be 365 days? The folks who decide these things -- "Some person in
authority; I don't know who: very likely the Astronomer Royal" --
thought it would be a good idea to keep the dates of the seasons
roughly the same from year to year so that farmers could plant the
same crops in, say, the second week of May every year. Without leap
by about a week every generation and Northern Hemisphere farmers would
eventually be doing their spring planting in October.

Regards,
Stan Brown, Oak Road Systems Cleveland, Ohio USA +1 216 371-0043
email: stbrown -at- nacs -dot- net Web: http://www.nacs.net/~stbrown

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