Calendars are Cool Part 0: Introduction and the Curse of a Calendar

Well, it's been two months instead of the three that I predicted.

Recently I've been experimenting with some calendar design as a part of my slow descent into worldbuilding and conlanging, and I think I'll make a few posts about my findings so that, if anything, I'll have made a coherent set of notes that I can refer back to.

For this post, I'll define some simple terminology that I'll use in the upcoming series. Please note that the list is not exhaustive and I may misuse some vocabulary that has a more technical meaning. Words that I'm pretty sure I'm using right will be bolded, and words that I made up or am not sure about will not be bolded.

A calendar at its core is a system to count and organize the passage of time on a large scale. Most calendars use the day as their fundamental unit, but there are various definitions for what a day can be. Below are some commonly used definitions.

1. The solar day is the amount of time in between the points where the sun is highest in the sky. This can vary since the Earth's orbit is elliptical, and is 24 hrs ± 8 seconds.
2. The sunset-sunset day is the amount of time that elapses from sunset to sunset, and it also changes throughout the year. This is typically 24 hrs ± a few minutes.
3. The sunrise-sunrise day is similar to the sunset-sunset day, only that days elapse from sunrise to sunrise.
4. The SI day is 86400 seconds. Not typically used in calendars.

With the advent of precise timekeeping, the Gregorian (meaning the Western) calendar uses SI days. However, the Hebrew calendar uses the sunset-sunset day, for example.

Once your calendar has a fundamental unit (not too hard), you then need to figure out what your calendar actually cares about (the fun part). Do you want to track the seasons? The phases of the moon? The rotation of the stars? The complex religious customs embedded in your society? There have been calendar which have tried to track one, more, or even all of these separate events. (Looking at you, Hindu Calendar.)

Some quick terminology about calendar types:

1. Solar calendars try to track the seasons and revolution of the Earth around the Sun.
2. Lunar calendars try to track the phases of the Moon.
3. Lunisolar calendars try to be both solar and lunar calendars.
4. Sidereal calendars try to track the rotation of the celestial sphere (the stars).
5. Religious calendars try to track events of cultural or religious significance.

Now, notice how I said try. The Gregorian calendar seems nice and dry with its months and years, although it does have that funny business with the leap year. But in reality, the nature of any calendar ever is to patch a sinking ship. If your calendar is nice and neat and has nothing complicated, then it's going to suck at tracking any celestial event you care about.

Allow me to explain with a visual that I stole from somewhere else but can't remember where from. (This is low-budget and a visual is not provided. Please use your imagination.) There is a truck driving around on a circular track. This is the Earth going around the Sun. On top of the truck, there is a ballerina pirouetting as evenly as she can. This is the rotation of the Earth. Flying around the ballerina is a parrot. This is the Moon circling the Earth.

In this example, it's pretty clear that you shouldn't expect there to be any relation between how long it takes the truck to go around once in the circle and how many times the ballerina completes a pirouette, or the same thing for the ballerina and parrot, or parrot and truck. In fact, you would expect the ballerina to pirouette a non-integer number of times (like 8.23 or 10.58) instead of a "nice" number (like 8 or 11) in the time it takes the truck to go around once.

It's the same exact deal with the Sun-Earth-Moon setup. The Earth spins ~365.2422 times in the time it takes to go around the Sun, and about 29.5 times in the time it takes for the Moon to go around the Earth. (As for why the Sun stat has 7 sig-figs and the Moon only 3, for some reason it's hard to find anything more specific for the Moon. 29.5 is just good enough for most calendars.)

This is the Curse of the Calendar: it's trying to represent non-integer relationships with integers. Months and years are made up of a whole number of days, and so it's inevitable that every calendar only approximates what they're trying to track.

The fun part is in seeing how well you can approximate it.