Leap day coming on Monday. Here are a “common” year and a leap year side by side.
(Actually they are the small “block calendars” in the Astronomical Calendars for the years, with blue color denoting Moon-free nights.)
You can see that January 1 is a Thursday, then becomes in the next year a Friday; and this one-day jump is what ordinarily happens to all the dates in the year, because 365 days make 52 weeks plus one day. But after the inserted Feb. 29, all the dates take a two-day “leap”: March 1 leaps from Sunday to Tuesday, and so on. That is the presumed reason for this usage in English of the word “leap,” though it seems unproved. There are other terms for the added day: bissextile day (which takes some explaining), intercalary day.
The leap day is stuck into every 4th year (except century years not divisible by 4 – thus, 97 times in each 400 years). Why? To bring the average calendar year to 365.2425 days, closer to the solar year of 365.2422: the true seasonal year, measured by astronomy from one point in our journey around the Sun to our next arrival at that point.
If you’re born on a leap day, do you have birthdays only once every four years? We can bet that such people claim to be only 15 when they’re 60, yet have it both ways by accepting birthday gifts and greetings arpund the ends of the leapless Februaries too. The number of leap-day babies is presumably about 97/(400*365.2425) = 0.0006663942 of the world’s population; something like 4 million. Or more, if conception is above average in May.
Not rare, anyway. Rarer is for the birth on a leap day to be twins; rarer again, triplets. Or for a mother to bear a baby on a leap day, and again on another leap day. Rarer again, on a third leap day. Rarer again, for those births to be twins; rarer again, triplets. I read somewhere that Mrs. Henriksen, Norwegian, bore triplets on 1960 Feb. 29, 1964 Feb. 29, and 1968 Feb. 29. And Mrs. Louise Estes of Provo, Utah, achieved the same on the leap days of 2004, 2008, and 2012.
And beyond? What is all but impossible for physiology is easy for imagination. Quadruplets would be more appropriate, since February is the month of four weeks. Once upon a time, there was a queen who… And her children set out to find the four corners of the world. They had time to reach their goals, since they each lived to be 280.
I have a book called “How Round Is Your Circle? Where Engineering and Mathematics Meet” by John Bryant and Chris Sangwin. The book discusses questions like, how do you determine roundness? How do you draw a straight line without a straightedge? etc. In it they make a suggestion for the calendar (I don’t know if it’s original to them). They suggest that every four years be a leap year, except for years divisible by 128. 4 being 2^2 and 128 being 2^7, if you write the year in binary, every year ending in 00 is a leap year, except for years ending in 0000000.
This gives 97 common years and 31 leap years every 128 years, for an average calendrical year of (97*365+31*366)/128 = 365.2421875 days, which is closer to the solar year of 365.2422… than our current 365.2425 days.
Chris Sangwin wrote me: “I first heard James Davenport mention the idea in passing (CS prof. in Bath, UK) but I don’t know if it is published. I certainly didn’t invent it!”
Given that our current approximation of 365.2425 days per year is slightly longer than the true value of 365.2422 days, if I’m doing the math right, in 3333 years and four months after the establishment of the Gregorian calendar — 4915 CE– the calendar will fall a full day behind Earth in her orbit around the Sun. Who will get us back in sync?
The figure of 365.2422 days for the tropical year is actually an approximation for a number found, for any given year, by a long equation taking into account the gravitational perturbations by the other planets, so it undergoes gradual change. It also will undergo gradual and unpredictable change from the slowing of Earth’s rotation (the notorious factor called Delta-T). So the exact length of the tropical year in the far future will oscillate slightly and with slight unpredictability, and this is why there is no point in fiddling with the calendar any more to approximate to it.
Thanks Guy. After I posted my comment, I realized that over many centuries the duration of the tropical year would probably vary by more than 26 seconds, so our current Gregorian approximation is good enough for now. And we sporadically add leap seconds to the clock, anyway. I guess adding a second isn’t enough to get you memorialized as were Julius and Gregory. Nobody refers to the Chuck second, or the Jennifer second. And then there are those scientists who want to disassociate timekeeping from Earth’s rotation and orbit, and just use the vibration of the Cesium atom as our fundamental unit of time. A very bad idea, in my opinion.
By the way, This morning National Public Radio broadcast a story about how people who were born on February 29 celebrate their birthdays — one woman is expecting her child to be born tomorrow, February 29.
Actually, the number of leap year babies is closer to 1/(4*365) = 0.0006849315 of the world’s population because no living person was, in fact, born on 01 March 1900, a person who would have been born on 29 February 1900 if 1900 were divisible by 400.
Most people don’t realize that leap years aren’t always every four years because no one living remembers 1900 not being a leap year*, and 2000, the last century year, was a leap year.
There are two people alive who lived through the lack of a 29 February 1900, but they were infants less than a year old. https://en.wikipedia.org/wiki/List_of_oldest_living_people
A delightful statistical refinement!
And now there’s one, Emma Morano, born 29 November, 1899. She is, in fact, the only living person born in the 1800s. (There are three living people who were born in the 19th century, the other two being born in 1900. A philosophy professor, Bill Wisdom (no kidding), was insisting to me around the turn of the century and the millennium that the 20th century and second millennium ended 31 December 2000. I told him that was pedantic. He said it was correct. I said pedantry *is* correct, but in this case it missed the central point, that what really mattered to people was the end of the 19__s and the start of the 20__s.)
The 1st century was the hundred years 1-100 (there was no year 0), so the 20th century was the years 1901-2000. I had to discuss this in the cover picture story for Astronomical Calendar 2001, about Ceres, which was discovered in the night between 1800 and 1801.
Yes, except around those bordering years, we do naturally equate or conflate “the twentieth century” with “the 1900s”. The latter kind of expression is more immedate. (But has the disadvantage that it could mean 1900-1909.) The “-th century” kind of expression is liable to that “Two-Way Hazard” I mentioned in one of these blog posts: I, and perhaps other not-instinctively-mathematical people, always have to hesitate at least a fraction of a second before being sure which century is the “fourteenth”: is it the 1300s or the 1500s?
Just as, tonight, I have to think before I remember to turn the British clock an hour forward or an hour back.