More Thoughts on my New Calendar

I’ve grown quite enamored with my “new calendar” or “American Revolutionary Calendar”, inspired by the famous French Republican Calendar and Tolkien’s “Shire Reckoning”, for my science-fiction space-opera setting. I’ve already expressed a first set of thoughts on the subject of worldbuilding new calendars in a previous post, but since that time I’ve done some more thinking and research I’d like to present here.

Leaping Years

In particular, what to do with leap years? That has jumped out as a question in my mind. As far as accuracy with the vernal-equinox year is concerned, the Iranian (Solar Hijri) Calendar, whose new year begins on the vernal equinox, is by far the best; it’s not much more accurate than the Gregorian calendar over long time scales, but the timing of the equinox on the calendar varies by less than half as much over the course of a full leap-year cycle as it does in the Gregorian calendar.

This is because the Gregorian calendar, which ordinarily has a leap day every 4 years, omits leap day in years divisible by 100 (e.g. 1700, 1800, 1900), except in years divisible by 400 (e.g. 1600, 2000, 2400) which have leap day as usual. The Iranian calendar, by contrast, has a 33-year cycle, where every 4 years there’s a leap year, until year 32 comes around, in which case there isn’t a leap day until the following year, then the cycle repeats. Lengthening the interval between leap days from 4 years to 5 years every so often is a finer adjustment than omitting leap days entirely, which is why the Iranian calendar is less variable.

Misconceptions about the Iranian Calendar

All the information on the Internet one sees about the complex leap cycles of 2820 years is apparently a misconception, since first of all whether or not to extend or contract the 33-year cycle in the actually-existing Iranian calendar is based on observation rather than any mathematical rule proposed by 20th century reformers, which is where the 2820-year concept comes from.

Secondly, the whole 2820-year cycle concept makes the Iranian calendar less accurate than the simple 33-year cycle, because the Iranian calendar aims to track the interval between vernal equinoxes, not the “tropical year”, which due to (I think) precessional cycles are slightly different. Confusingly, before modern times the vernal-equinox year was referred to as the “tropical year”, likely the source of the misconception on the part of Iranian reformers.

It’s also sometimes said that the Iranian leap year rules are more complicated, but the 33-year cycle strikes me as at least as simple as the Gregorian leap year rules. Every year that is a multiple of 33 is a leap year, then every four years thereafter, until the year before a year that is a multiple of 33, in which case it is a common year, then the cycle repeats. There. That isn’t so hard, is it?

Simple Cycle, Accurate Results

This leads to 8 leap days in a period of 33 years, which adds 8/33 of a day to the average year, thus 365.2424… days is the average year. This is very close to the actual value of 365.242374 days, only 0.00005 days greater than the actual vernal-equinox year, an error of one day in 20,000 years. The Gregorian calendar, by contrast, has an error of one day in 7,700 years with respect to the vernal-equinox year, despite having a more complex leap-year cycle.

Keep in mind that over thousands of years these numbers change slightly, so what’s accurate now won’t be so accurate a few thousand years from now. Days on Earth are getting ever-so-slightly longer due to tidal effects, thus contracting the number of them in a year little by little, meaning there should be fewer leap years as the millennia go by.

Accounting for this, however, would mean subjecting everyone in the cosmos to far more complex leap year rules just in order to be totally accurate on one planet tens of thousands of years from now, and I doubt whether humanity would accept such a thing, especially considering the whole point of the cosmic standard calendar, as opposed to an Earth calendar, is to replicate the year as experienced by all mankind’s ancestors on Earth, which obviously (the space age began in the 1940s) would be very close to the numbers as of the year 2000, not the year as experienced by unfathomably-distant cousin Earthlings in the year 3000 or 20,000. So diverging from the contemporary Earth day or year may be a feature rather than a bug to people in my space opera’s far future.

33 Year Cycles: not so Superior for the Yule Year

A potentially more serious issue is that the beginning of the new year and the most important holiday (call it Yule, call it Kolyada, or call it Christmas) is the winter solstice. The winter-solstice year (or Yule year) in 2000 was 365.242740 days, 0.000316 days greater than the standard calendar’s 365.2424… days, an error of one day in 3,165 years, slightly worse than the Gregorian’s error of 0.00024 days, one day in 4,167 years. In the 4th millennium this isn’t a serious problem yet, but if the cosmic standard calendar is to be synchronized with the winter-solstice year then slightly more complex rules will be needed.

Adding more Leap Year Cycles: toward Perfection

Since the standard year is a bit too short, slightly more leap days will need to be added in over the long haul. Adding an additional leap day in years that are multiples of 3300 (every 100 cycles) leads to 801 leap days in 3300 years, an average year length of 365 and 801/3,300 days, or 365.242727… days.

This brings the deficit of days in the average year down to 0.000013 days, an error of one day in 76,923 years. Not bad. Even finer adjustments are possible. Adding on yet another leap day in years that are multiples of 82,500 (2,500 cycles of 33 years, 25 cycles of 3300 years) gives us an average year length of 365.24273939… days, an error of one day in 1,639,344 years.

20 cycles of 82,500 years is 1,650,000 years, near that value, so adding another leap day in years that are multiples of 1,650,000 is the obvious course. This yields an average year of 365.24270 days over this cycle, exactly the same as the value the best source I could find gives for the winter-solstice year: 365.24270 days. Who says there isn’t a perfectly accurate calendar?

A perfectly accurate Yule year Calendar?

I’m sure there is some remainder of time left after this and errors would accumulate, but even over multiple millions of years the mean deviation of this calendar from the true time of Yule (true if it, fictitiously, continued unchanged from “the time of the ancestors”) would be measured in minutes; the Gregorian calendar, by contrast, would accumulate an error of 240 days over the course of 1 million years, meaning the (fictitious, unchanged since 2000) winter solstice would move into the “spring” months and then through the “summer” months to fall on August 18 by that time.

Multiple Leaping

An interesting feature of this calendar is multiple layers of leap years that overlap, so that every 3300 years there is a leap year that has two leap days, every 82,500 years there is a leap year that has three leap days, and every 1,650,000 years there is a leap year that has four leap days, perhaps known as “double-leaping”, “triple-leaping”, and “quadruple-leaping” years, respectively, generically as “multiple-leaping” years.

I just got that by correcting the errors as they appeared until there was no remainder left over, but playing around with the fractions and divisions a lot today it seems like this multiple leaping behavior is necessary in order to get the requisite 400,521 leap days per 1,650,000 years. Spreading the additional leap days out more regularly over, say, every 3,167 years, would reduce short-term variability, but at the cost of having an unsightly remainder left over that would, ever so gradually, accumulate far more error than the negligible portion left over with the multiple-leaping solution.

That said, there’s no particular reason why the leap days should have to come in bunches. Instead of year 1,650,000 having four leap days, we could have years 1,649,997; 1,649,998; 1,649,999; and 1,650,000 all be leap years with one leap day each, but it’s so much more fun to treat whoever still adheres to the calendar to “quadruple-leaping”, right? Honestly, my view is that any calendar should reward those who give it such loyalty over so many centuries with something cool like that.

Far-sighted Vision in Calendar-Making: not just for Science Fiction!

Interestingly, such far-sighted vision has been found within our very own Gregorian calendar. Per Wikipedia:

In the 19th century, Sir John Herschel proposed a modification to the Gregorian calendar with 969 leap days every 4000 years, instead of 970 leap days that the Gregorian calendar would insert over the same period. This would reduce the average year to 365.24225 days. Herschel’s proposal would make the year 4000, and multiples thereof, common instead of leap. While this modification has often been proposed since, it has never been officially adopted.

Probably because basically nobody cares about the year 4000 as of today; I guess it’s much like how the creators of the Julian calendar knew at the time that the leaping every 4 years was overly aggressive, to the tune of an error of one day in 128 years, but since that was way off in the future and the primary objective was to eliminate the chaos the old Roman calendar had devolved to by that point, I suppose they decided to kick the can down the road. Pope Gregory XIII picked it back up and corrected it, though I wonder if Sosigenes and company ever expected it to take almost 1600 years for that to happen.

Anyway, I propose in my science-fiction history that the creators of this cosmic standard calendar are well aware of the possibility of some space colony going off into the unknown blackness and remaining isolated for thousands, maybe even millions, of years, and they plan out all the rules accordingly so no reform of the calendar will ever be needed for the purpose of hewing closer to the ancestral clock; it is already perfect.

Refining the Length of the Months

Another issue I’ve been thinking about is the length of the months. Since there are twelve months in my calendar, comporting with widespread ancient custom, each month averages 30.4368916666…. days in length. This is suggestive of mostly 30 and 31 day months, as in the Gregorian calendar.

Today’s months are most irregular, leading to such monstrosities as “Thirty days hath September” etc. etc. A much more elegant solution is to, once again, take a page from the Iranian calendar and put all the 30 day months in one chunk of the year and the 31 day months in another. The first half of the year, winter to summer solstice over spring, is slightly shorter than the second half of the year, summer to winter solstice over autumn, so the logical choice is to put the long months in the second half.

Thus the first seven months; Afteryule, Solmath, Rethe, Astron, Thrimidge, Forelithe, and Afterlithe could all be 30 days, adding up to 210 days. The last five months; Wedmath, Halimath, Winterfilth, Blotmath, and Foreyule could all be 31 days, adding up to 155 days, for a nice neat little total of 365 days.

Obviously some years will have leap days, so, once again taking a page from the Iranian playbook, leap day could be added onto the last month of the year, in this case Foreyule, turning it into a unique 32-day month during leap years. During rare multiple leap years it will be even longer, with its maximum length being 35 days every 1,650,000 years.

The Week: to change or not to change?

An alternative solution, often explored in the context of the Gregorian calendar, is to have 13 months of 28 days each, which conveniently add up to 364 days total; the final month in this case would be a unique 29 day month in common years, 30 days in leap years. However, if a calendar adopted it it would be impossible to have more than one solstice or equinox near the first of a month, since 13 doesn’t divide neatly into quarters or halves. There also are usually traditional names for 12 months, including in English, but not 13.

Speaking of traditional names, the 7-day week cycle remains unchanged in my calendar, retaining its status as a parallel day-counting system. One might think the revived pagan sensibility would threaten it, but the 7-day week long predates Christianity, and was even adopted more or less independently of Judaism and the Abrahamic tradition (with its unique insistence on never interrupting the 7-day cycle). This is the major reason why the names of the days of the week in many languages, including English, are to this day still pagan!

Week Names: why six Germanic Days and one Latin Day?

Monday is the moon’s day, Tuesday is Tiw’s day, Wednesday is Woden’s day, Thursday is Thunor’s day, Friday is Frigg’s day, Saturday is Saturn’s day, and Sunday is the sun’s day. All of these names, which were taken from the Roman week through a process of finding the equivalent Germanic god, are even Anglo-Saxon in origin to boot! All, that is, except Saturday, which irritatingly was the one day taken directly from the Roman pantheon, apparently because the Germanics had no equivalent to Saturn.

In German, however, Saturday is also referred to as S√ľnnavend or Sonnabend, which roughly corresponds to “Suneve”, but it still sticks out like a sore thumb in a sea of “Xdays”. The Norse were more consistent and called Saturday “laugardagr”, literally meaning (they think) “washing day”. “Laug” means “pool” and is cognate to the English “lye”, which has since diverged from its original meaning. Nevertheless the construction “Lyeday” suggests itself, and it fits in better between “Friday” and “Sunday” than “Saturday” does.

Out with Saturday, in with Sifday!

Saturn was a god of agriculture, so I might suggest the Norse god Gefjon as an equivalent, but what I’d really want to go for is Sif as an equivalent. Sif is famous for her long golden hair, which scholars have suggested is related to wheat, which is certainly agricultural. She also has associations with earth and fruitfulness. The golden color of the planet Saturn also correlates well, as does the beauty of the planet, far more than it does to the Greco-Roman god (not that the Romans knew that, being bereft of a telescope!). Even better, she was the wife of Thor, namesake of Thursday! Aside from all that, Sifsday or Sifday just sounds cool, certainly much more so than Lyeday. So since I’m in charge of my new calendar I’ll go with Sifday!

Out with Anno Domini, in with American Independence!

So with the months, weeks, and leap year rules duly changed, it might be worth noting that the epoch of my new calendar is also changed, from AD 1 (which is thought probably wasn’t even when Jesus was actually born…) to AD 1776, the year of American independence. In the Anno Domini spirit it might be denoted Anno Americae (or whatever the proper Latin term is), in any case being AA as opposed to AD. If an English abbreviation is desired YA, for year of America, might be employed, or even AA again, this time standing for “after America”. By analogy with BC (before Christ), BA for “before America” may be used. AE for “American Era” and BAE for “before American era” may also be used by analogy with CE and BCE.

The obvious year to begin the leap year cycle is AA 0 (AD 1776). The current year is AA 245, so the current 33-year leap-year cycle began in AA 231 (AD 2007), meaning this year, AA 245, is a common year; AA 243 (AD 2019), was a leap year, the next leap year being in AA 247 (AD 2023).

Stounds, Ticks, and Trices

As for intraday timekeeping, I’ve basically decided to incorporate stounds, ticks, and trices into my space-opera setting. Stounds correspond to the “centiday”, a hundredth of a day (14.4 minutes), ticks are a hundredth of a stound (8.64 seconds), and trices are a hundredth of a tick (0.0864 seconds). This decimalizes the day into convenient units; centidays were actually used by the Chinese in real life!

Analog clocks would be divided into a hundred units, most likely marked off in groups of five for convenience (e.g. 0, 5, 10, 15, etc.). The stound hand would of course complete a revolution in a day, half as fast as our hour hands do (unless you’re using a 24-hour clock, in which case it’s the same!). The tick hand completes a revolution in 14.4 minutes, meaning even 1 minute’s motion would be noticeable, something a bit lacking in the clocks we use today.

Conclusion

Well, that’s about all the thoughts I have on the new calendar I’m introducing into my worldbuilding. It’s quite a lot, but I hope it was illuminating for anyone who’s interested in it; writing this post certainly helped me refine my ideas a lot.

My far-future setting, which is the only place this calendar will appear in my stories, is over 1000 years into the future, which is AA 1200 or so and later. In “Warp Dawn” my characters mention the events of “Letters from the Airy Deep” occurring over a thousand years ago, and since I date that story rather firmly to around AD 2060, that places “Warp Dawn” at circa AD 3060 or later.

If it was AD 3060 it would be AA 1284, but after thinking about it for a while I like the idea of setting it in AA 1299 the best; 1299 just has a nice sound to it. It also corresponds to AD 2075, which is also a nice number. So I think I’ll date “Warp Dawn” to 1299, which corresponds to the century I tentatively set it in, the 31st century AD.

I still don’t have a date for the novel I’m working on currently, except for it taking place a century or perhaps two after “Warp Dawn”, which would place it in the 14th or 15th century AA (32nd or 33rd century AD).

So I think my calendar will be both useful and a real pleasure!

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