The Oddness of February

I understand why the calendar adds an extra day every four years.

The revolution of the earth around the sun is approximately 365 and one-quarter days. Every four years, that adds up to one additional day, plus some extra minutes. The modest rounding error in this calculation is offset by steps like dropping the extra day of leap year for years ending in “00.”

But my question is why February has only 28 days in other years. After all, January has 31 days and March has 31 days. If those two months each donated a day to February, then all three months could be 30 days long, three years out of four, and February could be 31 days in leap years. Every other month is either 30 or 31 days. Why does February only get 28 days?

The answer to such questions leads to a digression back into the history of calendars. In this case, Jonathan Hogeback writing at the Britannica website tells me, it seems to settle on the Roman king Numa Pompilius back around 700 BCE, before the start of the Roman Empire. The ancient Roman calendar of that time had a flaw: it didn’t have nearly enough days. As Hogeback writes:

The Gregorian calendar’s oldest ancestor, the first Roman calendar, had a glaring difference in structure from its later variants: it consisted of 10 months rather than 12. In order to fully sync the calendar with the lunar year, the Roman king Numa Pompilius added January and February to the original 10 months. The previous calendar had had 6 months of 30 days and 4 months of 31, for a total of 304 days. However, Numa wanted to avoid having even numbers in his calendar, as Roman superstition at the time held that even numbers were unlucky. He subtracted a day from each of the 30-day months to make them 29. The lunar year consists of 355 days (354.367 to be exact, but calling it 354 would have made the whole year unlucky!), which meant that he now had 56 days left to work with. In the end, at least 1 month out of the 12 needed to contain an even number of days. This is because of a simple mathematical fact: the sum of any even amount (12 months) of odd numbers will always equal an even number—and he wanted the total to be odd. So Numa chose February, a month that would be host to Roman rituals honoring the dead, as the unlucky month to consist of 28 days.

This discussion does explain why February would be singled out, since it was the month of rituals honoring the dead. In Numa’s calendar, the 355-day year would be made up of 11 months that had the lucky odd numbers of 29 or 31 days, plus unlucky February.

The discussion also explains why months that start with the prefix “Oct-” or eight, “Nov” or nine, and “Dec-” or ten, are actually months 10, 11, and 12 in the calendar. Those names were originally part of a 10-month calendar year.

But questions remain unanswered: Why did the Romans of that time view odd numbers as lucky, compared with unlucky even numbers? I suppose that explaining any superstition is hard, but I’ve never seen a great explanation. In a Dartmouth course on “Geometry in Art and Architecture,” some course describes Pythagorean feelings about odd and even numbers. For those of you keeping score at home, Pythagoras lived about two centuries after Numa Pompilius. The Dartmouth course material summarizes aspects of “Pythagorean Number Symbolism”:

Odd numbers were considered masculine; even numbers feminine because they are weaker than the odd. When divided they have, unlike the odd, nothing in the center. Further, the odds are the master, because odd + even always give odd. And two events can never produce an odd, while two odds produce an even. Since the birth of a son was considered more fortunate than the birth of a daughter, odd numbers became associated with good luck.

Various mentions of the luckiness of odd numbers recur over time. A few centuries later in the first century BCE, the poet Virgil has the character Alphesiboeus (a shepherd who sings about love rituals) say in Eklogue VIII (from the A.S. Kline translation):

Bring Daphnis home, my song, bring him home from town.

First I tie three threads, in three different colours, around you

and pass your image three times round these altars:

the god himself delights in uneven numbers.

Bring Daphnis home, my song, bring him home from town.

Or leaping ahead a millennium-and-a-half, at the start of Act V of the The Merry Wives of Windsor, Shakespeare has Falstaff say:

Prithee, no more prattling. Go. I’ll hold. This
is the third time; I hope good luck lies in odd numbers.
 Away, go. They say there is divinity in odd
 numbers, either in nativity, chance, or death.
Away.

While I acknowledge this history of a belief in odd numbers, as a person born on an even day of an even month in an even year, I’m not predisposed to accept it. But it’s interesting that modern photographers have a guideline for composing photographs called the “rule of odds.” Rick Ohnsman at the Digital Photography School, for example, describes it this way:

This is where the rule of odds comes into play, a deceptively simple yet powerful tool in your photographic arsenal. It’s all about arranging your subjects in odd numbers to craft compositions that are naturally more pleasing to the eye. Unlike more static guidelines, the rule of odds offers a blend of structure and organic flow, making your images both aesthetically pleasing and impressively compelling.

The revised calendar of Numa Pompilius couldn’t last. With only 355 days, it didn’t reflect the actual period of the earth revolving around the sun, and thus led to further revisions which are a story in themselves.

But when you think about it, the question of February having 28 days all goes back to Numa Pompilius and the superstitions about odd numbers. The modern calendar has 365 days in a typical year. You might think that the obvious way to divide this up would be to start off with 12 months of 30 days, and then add five days. Indeed, the ancient Egyptians had a calendar of this type, with five “epagomenal” or “outside the calendar" days added each year.

The preference over the last two millennia, at least since the time of Julius Caesar, is to have 12 months, with a few of them being a day longer. But even so, why not in a typical year have five months of 31 days, and the rest with 30? The “problem,” I think, is that most months would then have unlucky totals of an even number of days. By holding February to 28 days rather than 30, you can redistribute two days from February and have 31 days in January and March. Thus, you can have only four months with an even total of 30 days every year (“Thirty days hath September, April, June, and November …”), and seven months always with the luckier odd total of 31 days. In leap years, when February has 29 days, then eight months have an odd number of days. I think this makes February 29 a lucky day?