Gregorian calendar

[weavercs]

In the explanation of the Gregorian calendar, shouldn’t it say that years divisible by 400 are leap years, not years divisible by 4000? For example, 2000 was a leap year.

[C_K_Dexter_Haven]

Welcome to the Straight Dope Message Board, weavercs, glad to have you with us.

When you start a new thread, it’s helpful if you provide a link to the Staff Report that you’re commenting on – helps keep everyone on the same page, avoids people repeating what’s already been stated, etc. In this case, I presume, it’s Why do we have leap years?

And, to answer your question, the Staff Report says:

The Gregorian correction is that every hundred years, we make it NOT a leap year. Thus, 1700, 1800, and 1900 were not leap years, even though they would have been in the normal four year cycle. Thus, every 100 years, there are 24 leap years, not 25. So that lets the calendar year average 365.24 days each year.

Does that do it? Sadly, no. There are still those extra seconds–the astronomical year is 365.2422 days. So every 400 years, we DON’T NOT add the extra day (double negative intendedl). So 1700, 1800, 1900 were NOT leap years, but 2000 was.

If you’ve followed the math, that gets us very close. Over a 400 year period the calendar will contain an average of 365.2425 days per year.

Every 4,000 years (the first will be the year 4000, then 8000, etc.) we make the century years NOT leap years again.

So I think you’re misreading. The Staff Report says that years evenly divisible by 4000 are NOT leap years. In fact, any year evenly divisible by 100 would NOT be a leap year, with the exception that years divisible by 400 ARE leap years, with the exception that years divisible by 4000 are NOT leap years.

The odds of y’all being around to see another century year (2100)are slim, and the odds of this Board being around to see the year 4000 are even slimmer, so it’s not something anyone needs to worry about overmuch.

[weavercs]

Yes I realized that after I posted the question. I am not sure I ever heard the 4000 year part before.

[C_K_Dexter_Haven]

Well, it probably doesn’t come up very often.

Among the great disappointments of my life was that 2000 WAS a leap year. I thought it would be so cool to have a year-divisible-by-four that WASN’T a leap year, and I could explain to people why not. No such luck. It was a leap year because it’s an exception, and no one even thought that, they just thought it was the typical every-four-years.

[weavercs]

It sure saved a lot of computer programmers though. They had enough trouble with the year 2000 as it was.

[bonzer]

*Originally posted by C K Dexter Haven *
It was a leap year because it’s an exception, and no one even thought that, they just thought it was the typical every-four-years.

Not everybody overlooked its exceptionality. Writing in the December 1999 edition of History Today about myth that the switch to the Gregorian led to ‘Calendar Riots’ in Britain, Robert Poole made the following cute observation:

An adjustment was made to the leap year cycle to keep the dates in line. Previously, the year at the end of every century had been a leap year; now, there was to be a leap day every fourth century year. When this first comes into practice, on February 29th, 2000, it will mark the implementation of the longest delayed action piece of legislation ever passed in Britain, 248 years and three months after receiving royal assent.

Who says governments can’t plan ahead?

[Musicat]

Wanna bet that some software will still be around in 4000, and misfire?

Every 4,000 years (the first will be the year 4000, then 8000, etc.) we make the century years NOT leap years again.

So set your computer’s clock to 4000 and see what happens.

[RM_Mentock]

*Originally posted by bonzer *
**Not everybody overlooked its exceptionality. Writing in the December 1999 edition of History Today about myth that the switch to the Gregorian led to ‘Calendar Riots’ in Britain, Robert Poole made the following cute observation:

An adjustment was made to the leap year cycle to keep the dates in line. Previously, the year at the end of every century had been a leap year; now, there was to be a leap day every fourth century year. When this first comes into practice, on February 29th, 2000, it will mark the implementation of the longest delayed action piece of legislation ever passed in Britain, 248 years and three months after receiving royal assent.

Who says governments can’t plan ahead? **

Interesting article, but I think that’s a misinterpretation. Instead of “Previously, the year at the end of every century had been a leap year,” I think the actual situation was that “previously, every fourth year had been a leap year.” So the implementation actually took place the first time that a leap year was skipped–48 years later, in other words.

[bonzer]

Yes, Poole’s wording could be a lot better, but his point is clearer if you look at the way the 1751 Act expresses the change.
Most provisions of the Act - eliminating the 11 days, legislating the start of the year, etc. - had their first effect in 1752. The section relating to the exceptions is:

II. And for the continuing and preserving the Calendar or Method of Reckoning, and computing the Days of the Year in the same regular Course, as near as may be, in all Times coming;

Be it further enacted by the Authority aforesaid,

That the several Years of our Lord, 1800, 1900, 2100, 2200, 2300, or any other hundredth Years of our Lord, which shall happen in Time to come, except only every fourth hundredth Year of our Lord, whereof the Year of our Lord 2000 shall be the first, shall not be esteemed or taken to be Bissextile or Leap Years, but shall be taken to be common Years, consisting of 365 Days, and no more;

and that the Years of our Lord 2000, 2400, 2800, and every other fourth hundred Year of our Lord, from the said Year of our Lord 2000 inclusive, and also all other Years of our Lord, which by the present Supputation are esteemed to be Bissextile or Leap Years, shall for the future, and in all Times to come, be esteemed and taken to be Bissextile or Leap Years, consisting of 366 Days, in the same Sort and Manner as is now used with respect to every fourth Year of our Lord.

The first of the two clauses sets up the new 100-year cycle of exceptions to the 4-year cycle of leap years; this clearly first has an effect in 1800, as you note. However, while they’ve been touched on in the previous one, the second clause deals with the cases like 2000 by explicitly confirming that these are exceptions to the new cycle.
When Dex described 2000 as “a leap year because it’s an exception” and not a “typical” leap year, it was this final clause that makes him correct. And Poole was commenting on the unusually long period before this particular clause was ever implemented.

[RM_Mentock]

*Originally posted by bonzer *
When Dex described 2000 as “a leap year because it’s an exception” and not a “typical” leap year, it was this final clause that makes him correct.

No it doesn’t. He overstated his case for effect. Otherwise, such clauses as “in all Times coming” mean that we are experiencing a continual delayed effect of the law–and that also shows he’s incorrect, in that the period of delay is much longer than 249 years.

But thanks for the link, very interesting reading.

[C_K_Dexter_Haven]

<< No it doesn’t. He overstated his case for effect. >>

Well, I guess it depends on where you come from.

(1) The logic is that every fourth year is a leap year, EXCEPT century years, EXCEPT century years divisible by 400. Thus, 2000 is the exception to the exception, which is the way I was taking it.

(2) The other logic is that every fourth year is a leap year except the century years not divisible by 400.

I thought the first approach was easier to explain. It’s not “overstating the case for effect” so much as phrasing the case in a logical (i.e., mathematical) frame.

[Musicat]

*Originally posted by Musicat *
So set your computer’s clock to 4000 and see what happens.

I took my own advice, just for kix, and found out my Windows/PC-based computer can only handle years from 1980 thru 2099.

Darn. Pretty soon I’ll have to change my BIOS again.

[RM_Mentock]

Sorry Dex I wasn’t trying to indict you. I thought you were joking when you said it was one of the great disappointments of your life that everybody else treated 2000 as just another leap year.

Poole, on the other hand, didn’t seem to be joking.

[aktep]

:cal 2 4000

February 4000
S M Tu W Th F S
1 2 3 4 5
6 7 8 9 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29

I guess we’ll have to upgrade our HP-UX system sometime in the next 1,997 years

[C_K_Dexter_Haven]

Does it do 2100 correctly?

[RM_Mentock]

I’m not so sure the 4000 rule is official yet. Dex, you have a citation handy?

[C_K_Dexter_Haven]

No, sorry, RM, I did that report ages ago, and I don’t recollect where I got the info from.

[Musicat]

According to Calendopaedia,

It has been suggested (by the astronomer John Herschel (1792-1871) among others) that a better approximation to the length of the tropical year would be 365 969/4000 days = 365.24225 days. This would dictate 969 leap years every 4000 years, rather than the 970 leap years mandated by the Gregorian calendar. This could be achieved by dropping one leap year from the Gregorian calendar every 4000 years, which would make years divisible by 4000 non-leap years.

This rule has, however, not been officially adopted.

I guess it is tied up in committee. Figures.

[Tim_T-Bonham.net]

I had to do a fair amount of re-programming pre-2000, and I found the following the most memorable description of the Gregorian Leap-Year algorithm:

• every 4th year (divisible by 4) is a leap year.
• except that every 100th year is NOT a leap year.
• except that every 400th year IS a leap year.
• except that every 1000th year is NOT a leap year.
  P.S. regarding the English “calendar riots”, my understanding is that they were quite justifiable, given the way this law (like most laws?) screwed over the poor people.

Most english workers of that time were hired by the day, and so they were paid only for the actual days they worked during that shortened month. But they were also renters, and were required to pay a full months’ rent for the month of September, which was in fact only 19 days.

So the landlords got a full months’ rent, while the workers took a nearly 40% pay cut for the month.
I think I’d riot, too!

[C_K_Dexter_Haven]

<< So the landlords got a full months’ rent, while the workers took a nearly 40% pay cut for the month. >>

Parliament must have got that idea from the current U.S. congress…