Why Leap Years?

Mar 3 JDN 2460374

When this post goes live it will be March 3, not March 4, because February had an extra day this year. But what is this nonsense? Why are we adding a day to February?


There are two parts to this answer.

One part is fundamental astronomical truth.

The other part is historically contingent nonsense.

The fundamental astronomical truth is that Earth’s solar year is not an even multiple of its solar day. That’s kind of what you’d expect, seeing as the two are largely independent. (Actually it’s not as obvious as you might think, because orbital resonances actually do make many satellites have years that are even multiples of or even equal to their days—the latter is called tidal locking.)

So if we’re going to measure time in both years and days, one of two things will happen:

  1. The first day of the year will move around, relative to the solstices—and therefore relative to the seasons.
  2. We need to add or subtract days from some years and not others.

The Egyptians took option 1: 365 days each year, no nonsense, let the solstices fall where they may.

The Romans, on the other hand, had both happen—the Julian calendar did have leap years, but it got them slightly wrong, and as a result the first day of the year gradually moved around. (It’s now about two weeks off, if you were to still use the Julian calendar.)

It wasn’t until the Gregorian calendar that we got a good enough leap year system to stop this from happening—and even it is really only an approximation that would eventually break down and require some further fine-tuning. (It’s just going to be several thousand years, so we’ve got time.)

So, we need some sort of leap year system. Fine. But why this one?

And that’s where the historically contingent nonsense comes in.

See, if you have 365.2422 days per year, and a moon that orbits around you in every 27.32 days, the obvious thing to do would be to find a calendar that divides 365 or 366 into units of 27 or 28.

And it turns out you can actually do that pretty well, by having 13 months, each of 28 days, as well as 5 extra days on normal years and 6 extra days on leap years. (They could be the winter solstice holiday season, for instance.)

You could even make each month exactly 4 weeks of 7 days, if for some reason you like 7-day weeks (not really sure why we do).

But no, that’s not what we did. Of course it’s not.

13 is an unlucky number in Christian societies, because of the betrayal of Judas (though it could even go back further than that).

So we wanted to have only 12 months. Okay, fine.

Then each month is 30 days and we have 5 extra days like before? Oh no, definitely not.

7 months are 30 days and 5 months are 31 days? No, that would be too easy.

7 months are 31 days, 5 are 30, and 1 is 28, unless it’s 29? Uh… what?

Why this is so has all sorts of reasons:

There’s the fact that the months of July and August were created to honor Julius and Augustus respectively.

There’s the fact that there used to be an entire intercalary month which was 27 or 28 days long and functioned kind of like February does now (but it wasn’t February, which already existed).

There are still other calendars in use, such as the Coptic Calendar, the Chinese lunisolar calendar, and the Hijri Calendar. Indeed, what calendar you use seems to be quite strictly determined by your society’s predominant religious denominations.

Basically, it’s a mess. (And it makes programming that involves dates and times surprisingly hard.)

But calendars are the coordination mechanism par excellence, and here’s the thing about coordination mechanisms:

Once you have one, it’s really hard to change it.

The calendar everyone wants to use is whatever calendar everyone else is using. In order to get anyone to switch, we need to get most people to switch. It doesn’t really matter which one is the best in theory; the best in practice is whatever is actually in use.

That is much easier to do when a single guy has absolute authority—as in, indeed, the Roman Empire and the Catholic Church, for the Julian and Gregorian calendars respectively.

There are other ways to accomplish it: The SI was developed intentionally as explicitly rational, and is in fact in wide use around the world. The French revolutionaries intentionally devised a better way to measure things, and actually got it to stick (mostly).

Then again, we never did adopt the French metric system for time. So it may be that time coordination, being the prerequisite for nearly all other forms of coordination, is so vital that it’s exceptionally difficult to change.

Further evidence in favor of this: The Babylonians used base-60 for everything. We literally only use it for time. And we use it for time… probably because we ultimately got it from them.

So while nobody seriously uses “rod“, “furlong“, “firkin“, or “buttload” (yes, that’s a real unit) sincerely anymore, we still use the same days, weeks, and months as the Romans and the same hours, minutes, and seconds as the Babylonians. (And while Americans may not use “fortnight” much, I can assure you that Brits absolutely do—and it’s really nice, because it doesn’t have the ambiguity of “biweekly” or “bimonthly” where it’s never quite clear whether the prefix applies to the rate or the period.)

So, in short, we’re probably stuck with leap years, and furthermore stuck with the weirdness of February.

The only thing I think is likely to seriously cause us to change this system would be widespread space colonization necessitating a universal calendar—but even then I feel like we’ll probably use whatever is in use on Earth anyway.

Even when we colonize space, I think the most likely scenario is that “day” and “year” will still mean Earth-day and Earth-year, and for local days and years you’d use something like “sol” and “rev”. It would just get too confusing to compare people’s ages across worlds otherwise—someone who is 11 on Mars could be 21 on Earth, but 88 on Mercury. (Are they a child, a young adult, or a senior citizen? They’re definitely a young adult—and it’s easiest to see that if you stick to Earth years. Maybe on Mars they can celebrate their 11th rev-sol, but on Earth it’s still their 21st birthday.)

So we’re probably going to be adding these leap years (and, most of us, forgetting which centuries don’t have one) until the end of time.