Finally Fixing That Calendar

The phases of the moon: the golden part shows ...
An earlier, failed attempt at calendrical simplification

In many ways today is already the first day of a new year. Christmas is the de facto midwinter festival after all, and we’re already a week into the actual solar year. I wonder aloud, was December 25th chosen because it was the halfway point between the logical (but pagan-associated) solstice and the incorrect but well-established Roman new year?

So to start the year I will deal with some unfinished business. I’ve been promising to return to the topic of calendar reform since… January, gawd. As you’ll no doubt remember, I reached the conclusion that it would be nice if we could have one that keeps time with both the sun and the moon. The obvious problem here is that in reality, the periods of day, month and year just don’t divide into one another evenly. Why should they, after all? They’re just rocks spinning around in space.

The trick then is to find approximated versions of these periods that fit together neatly enough. Many civilisations have tried only to give up. Islam settled on a fully lunar calendar, which is why it is about 11 days shorter than the solar Christian one. That itself still has a vestigial lunar element; its months were originally in time with the moon, but various reforms have broken this almost beyond recognition.

Not though, beyond repair. They managed to square the solar cycle by adding an extra day every four years; we just need a similar idea to fix the months, so that the waxing and waning of one moon fits precisely into each. Because that would be cool. I put a lot of work into this, and figured out that it could be done quite easily. The real month is very close to being 29.5 days long, so we could simply have alternating calendar months of 29 and 30 days. No problem!

OK, months of that length don’t fit evenly into a year. There will be twelve and a bit between every winter solstice. But that’s the whole point – there aren’t an even twelve months in a real year, and trying to make it be that way has wrought a world where we all have to memorize a stupid rhyme. We just need to accept that and then we can move on.

But what we do want is for the months to stay, at least approximately, at the same time of the year; April will always be Spring, September Autumn, and so on. And as it turns out, just two “leap months” in every five years is sufficient to keep them aligned with better than 98% accuracy. Add a couple of minor rules and the cycles can be kept in time for thousands of years. I checked this out thoroughly, even using spreadsheets to painstakingly project the cycles centuries into the future. Incredibly, it stays in time. It seems almost too simple. Why had no one thought of this before?

Well of course, someone had – quite some time ago. After several days of calculations, I realised I’d basically just reinvented the Jewish calendar. It’s a fine piece of astronomical workmanship with roots going back to the very beginnings of civilization, and has been successfully keeping sun and moon in harmony for a very, very long time. Why don’t we use it, or something like it? I strongly suspect, simply because it is Jewish.

We should though.