Months, What Are They Good For?

Let's Adopt a Calendar for a New Era

This week begins autumn. Isn't it strange that we have 12 months, which are divisible by 4, and the equinox doesn't fall exactly on the quarterly boundary? Shouldn't October 1st be the autumnal equinox? And shouldn't it be called December since it's the 10th month?

Why do we even need months? Why not specify dates by the week number or day of year number? Today is Monday of the 39th week of 2023. Or I had this genius thought on 268/2023 to eliminate months.

Maybe even write that as 2023+268 because now it's a mathematical statement which evaluates to the number of days since the beginning of the Common Era... (2,023 years * 365.242199 days/year) + 268 days = 739,153 days since 0000+001 (ie. January 1st, 0000 -- abandoning the Gregorian Calendar conception of CE beginning at year 1).

It's been over 450 years since a major calendar update. Months aren't equal length, but have rules/mnemonics for determining length, aren't connected to lunar phases, and serve no real use. The unequal months also create unequal quarters meaning balance sheets aren't comparable from quarter to quarter because of differing numbers of days. And, as pointed out earlier, solstices and equinoxes don't fall on monthly boundaries either. And they’re not even named appropriately.

Let's instead have the year start on the winter solstice. Perfectly divided 13 week quarters align with the seasons. Week 13 begins with the spring equinox. Week 26 begins with the summer solstice. Week 39 starts with the autumnal equinox. The first half of the year is 26 weeks and the second half is 26 weeks.

Just one problem — 52 weeks is 364 days and the Sun rises and sets 365 times in each orbit of the Earth around the Sun, bringing us to the same relative point in space and restarting the same seasonal cycle (i.e. a tropical year). Perhaps we can make it a “leap” day at the very end of the year? But strictly speaking, that messes up the perfect division. Clearly the periodicity of the Earth’s spin and orbit were not “designed” very well or they’d have aligned better. Furthermore, the exact time of the solstice isn’t clearly on a daily boundary either, but falls sometime within the day.

Summer solstice this year (assuming the year started at midnight following the last winter solstice) is Wed, 2023+182, 14:58 UTC, i.e. a first half period of 182 days, 14 hours, and 58 minutes. Winter solstice this year is Thu, 2023+366, 03:28 UTC. That’s a second half period of 183 days, 12 hours, 30 minutes. So the second half of the year is a day longer than the first half? Almost. We assigned an extra 2 hours and 12 minutes to the prior year by starting at midnight when really the new year started Wed, 2022+365, 21:48 UTC. Giving those additional 132 minutes to 2023 makes the first half 182 days, 17 hours, and 10 minutes, which is still shy of the second half by 19 hours and 20 minutes. Why the discrepancy?

Well it turns out that when Earth is closer to the Sun (perihelion) during it’s elliptical orbit, the star’s gravitational pull is stronger, speeding up the orbital time approximately two weeks after the winter solstice.  Conversely, the orbital time is slowed around the farthest point (aphelion), which is about two weeks after the summer solstice. Thus the first half is slightly shorter than the second half because the winter quarter is sped up and summer quarter is slowed down. Ergo, we can’t actually get a perfect calendar division by solstices and equinoxes after all. At least not anymore — the solstices and apsides lined up about 800 years ago, but have since gone out of sync.

That being said, maybe we should simply adjust the New Year to the perihelion point, which was on January 4, 2023 at 16:17 UTC, so 2023+01 would begin at the following midnight. Aphelion is then 2023+181 at 20:07 UTC, or 182 days, 3 hours, and 50 minutes later. The next perihelion is 2023+363 at 00:39 UTC, or 181 days, 4 hours, and 32 minutes later. But wait a second, even if you add back the 2022 time (7 hours and 43 minutes) between perihelion and midnight, that adds up to only 363 days, 16 hours, and 5 minutes in a year! What’s going on? Shouldn’t half a year from perihelion to aphelion and half a year from aphelion to perihelion add up to one whole year?

Unfortunately, no, the dates of perihelion and aphelion change over time due to precession and other orbital factors. These cyclical patterns are known as Milankovitch cycles. In the short term, perihelion and aphelion dates can vary by up to 2 days from one year to another. So once again, our proposed calendar based on the very components of what we consider to be a year cannot be evenly divided. There’s no way to exactly line up the seasons or Earth’s orbital characteristics into neatly discrete quarters, halves, or months.

Maybe a “leap” day every year would make sense after all. It can be our day (and a quarter) of winter celebration. But wait a second, even the seasons themselves are changing over time due to the precession of the equinoxes. The tropical year, measuring the cycle of the seasons, is 20 min and 24.5 seconds shorter than the sidereal year, which is measured by the Sun's apparent position relative to the stars. Thus, every year, the seasons shift by this amount of time. After about 12,886 years (although the rate of change is not constant, so this is an estimate), the seasons are completely flipped. So if we set aside a “leap” day every year, it would not continue to line up with a particular seasonal celebration. This is why they actually came up with the Julian Calendar and Gregorian Calendar in the first place!

There’s probably no perfect formula as you will always have to balance the desire for uniformity and symmetry with the desire to align time to the constantly changing solar and other cycles. On the extreme latter end, we could just use computers to calculate variable length days every single day based on the sunrise, sunset, orbital characteristics, etc. But then you couldn’t compare even one day to another. How many hours should you work or sleep? Maybe seconds or fractions of a second difference from day to day wouldn’t really impact things greatly though. You’re not likely to be late for a meeting or appointment simply because the length of the day changed by a second or two. It won’t likely throw off sales figures for the quarter either. But it may keep us better aligned with the natural cycles if, for example, the solstices and equinoxes occurred predictably on the same day and same time each year.

Perhaps keeping track of the time will be yet another function of AI moving forward.