Pythagoras was right

Months are an attempt to divide the year (one trip around the Sun) into Moon cycles. But our orbit around the Sun just doesn’t divide evenly into Moons. It takes us just slightly more than 13 Moons to get around the Sun—and that’s not even an integer. When you round it down to 13… Look, 13 is a pretty terrible number. It’s prime so it’s not evenly divisible by anything. And people literally die when you use 13 too much. It’s like dividing by zero.

So instead of dividing a year into 13-point-whatever Moon cycles, we ought to continue to divide the year into an even 12 months. Pythagoras was right: 12 is nice. It divides into 2, 3, 4, and 6 evenly. (And sounds lovely.) It’s pretty great to be able to say “we divorced half a year ago” or “I’ll finish that report next quarter, get off my back, Doug” and have that mean an actual even number of months instead of some annoying fractional nonsense.

Days per month

But here’s where we can make some progress. Let’s restrict the number of days in a month to either 30 or 31. Period. None of this 28 days. (Don’t even come at me with 29 days.) A month has either 30 days or 31 days and that’s final. And this should alternate. If last month had 30 days, this one has 31, and vice versa. That means 6 months of the year have 30 days and the other 6 months have 31 days—that gives us a full 366 days per orbit around the sun:

I hope I didn’t lose you with some simple arithmetic there, because we’re about to up the nerd factor. Since we’ve declared that the first month of the year will have 30 days, then the next will have 31, then 30, and so on—we know that every odd month has an even number of days, and every even month has an odd number of days. We can codify that idea with this equation which uses a modulo operator:

Let’s flesh that out with an example. We’ll start with the first month. Its month number is 1, obviously. If you’re familiar with modular arithmetic, you’ll know that 1 modulo 2 equals 1. How many days does the first month have? It has 30, and 30 modulo 2 equals 0. When we add these two outcomes, 1 plus 0 equals 1, so the above equation checks out.

Similarly, if we take the 6th month, its month number is 6, and 6 modulo 2 equals 0. Meanwhile, the 6th month has 31 days, and 31 modulo 2 equals 1. We add 0 plus 1 and that of course equals 1, so our equation continues to hold true. Things are going rather well so far. (Perhaps it’s time to add a complication?)

Leap Day

You probably noticed that 366 days is not 365 days. (Smart ass.) But that’s fine, it just means that we’ve got Leap Year covered already. On a Leap Year, the final month will have 31 days and our whole system follows the above rules beautifully and we all get the warm fuzzies in our hearts. On non-Leap Years, the final month will have only 30 days. I know that’s not perfect—forgive me—but this method places the exception to the pattern at the end of the year instead of randomly shoving it elsewhere. (I mean... February? Really?!)

Month names

I think it’s a bit awkward and even embarrassing to just invent magical new names for things. But this current mess we put up with has got to stop. For example, the prefix “oct” in “October” of course means “eight” as October was originally the 8th month of the year prior to the insertion of January and February. September, November, and December suffer the same discontinuity. Their names are decoupled from their original numeric meaning and now at best serve as false cognates. Gross!

Additionally the alphabetical sorting of month names as we know them also has no relationship to their sequential order. It’s a small but recurring annoyance that when you open a folder on your computer that has files named by month they don’t just alphabetically fall into their intended chronological order. I mean really… Here’s what it looks like when you alpha-sort the months: April, August, December, February, January, July… Who needs that hassle?

To resolve these issues let’s draw some inspiration from the Greek alphabet. These (admittedly ridiculous) new month names simultaneously sort themselves chronologically and alphabetically. Bonus: Names beginning with vowels evenly divide the year into thirds and all have exactly six letters, while names beginning with consonants all have exactly seven letters. Just observing the length of the names in an alphabetical listing already yields a clean division of the year into integers of months. I think we’re getting somewhere.

Ok, so let’s see what that looks like all put together into a 12 month calendar. Notice the week-ends actually come at the end of the week like the Europeans do. It just makes more sense. (As does universal healthcare.)

Below we can see an emphasis on the cadence of sounds. Again, the year is naturally divided into thirds by month names beginning with vowels. Months in the first row end with —lamen, the second row with —damen, and the final row with —namen. These sounds signal what time of year we’re in. And it’s got flow:
Alamen, Belamen, Calamen, Delamen.
Edamen, Fedamen, Gadamen, Hedamen.
Inamen, Jenamen, Kanamen, Lenamen.

We can also see below how the use of vowel sounds propagate downward through columns. The first column of months uses unique vowels for each row (A, E, and I). The second column uses E. The third uses A. Then back to E in the final column.

Weekday names

Can we apply some of that to days of the week too? Yes. It makes sense for weeks to remain the same; to be truer to the Moon than the Sun, right? So each week is still composed of 7 days, allowing 4 weeks to roughly fit into the moon’s 29.5-ish day cycle. Sure, it doesn’t fit evenly into months, but we already put up with that noise anyway so we’re not worse off.

Although it was tempting to create a system where the first day of each month was always the first day of the week (called an Invariable Calendar), this leads to some impractical results. For example, the Hanke-Henry model, which takes the unusual tack of adding an extra week every 5 or 6 years, breaks our aim-for-tidy assertion that the length of months should always be as equal as possible. That model’s reshuffle would have created only 240 weekdays of 366 (66%) versus the current calendar which yields 261 (71%) thus decreasing regulated human productivity severely. (Wait—are you reading this at work right now? Getting work done, are we?)

That’s all I have the heart for right now. (Should a year begin on the spring equinox? Should our epoch begin with the Trinity Test? Who knows!) After kicking these ideas around for a while, I originally published this essay on the twelfth day of the twelfth month of 2012. I’ve grown and changed a lot since then. But fixing months still feels like a positive move.
To be continued some day . . .