YOU get a leap year! And YOU get a leap year!

There’s no February 29 this year. My older daughter is starting to become aware of calendars and insisted on the 27th that it was the last day of February. I told her no, it’s not, but February is a shorter month – it only has 28 days. Except some years it has 29, but we’ll talk about that in three years.

But why is it now that the calendar gets weird? And why does it happen in both of the two calendars I pay some attention to? There’s a parallel between the Hebrew and Gregorian calendars (link goes to a comment I made at Hacker News). In both cases, the historic “new year” is in spring. In the Hebrew case, this is decreed in Exodus 12: “This month shall be unto you the beginning of months; it shall be the first month of the year to you.”

Passover, which takes place in Nisan, is supposed to occur after the spring equinox. But an ordinary year of twelve lunar months will be ~354 days, so when the end of Adar, the month before Nisan, starts getting too early, a second Adar is added. Similarly, the early Roman calendar originally had a year starting in March – supposedly because that’s when you can get around to going off to fight your wars – hence the names of the months “September” through “December” being off by two. And if March was going to come too early, they added an extra month, called Mercedonius. Somewhat confusingly, they stuck it in between the 23rd and 24th day of February, and also it was shorter than normal months, breaking the correspondence of the months with the phases of the moon. This evolved into the leap day in the Julian and later Gregorian calendar, but instead of having two 24ths of February, February now has 29 days.

So in both cases intercalation happens right before the start of the year in the spring – the Hebrew calendar has an extra month, and the Gregorian calendar has an extra day. But in both cases the year number increments at a different time – Hebrew Tishri in the fall, Gregorian January in the winter – so the intercalation appears to happen at some “random” moment within the year.

Incidentally, the Iranian Solar Hijri calendar has its new year at the spring equinox; the final month is 29 days, or 30 in leap years. Leap years are determined by astronomical observation; Nowruz begins at the midnight closest to the spring equinox according to Iranian time. So this is another intercalation that can only happen in the late winter / early spring. Other lunar calendars, including the Hindu and Chinese, can have their leap months at any time of year.

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