Humankind, should it not be thoroughly destroyed beforehand, will eventually take to the stars; and this poses fundamental issues for calendars as we know them. Ultimately, we either need to have a different calendar for each general area, or to have just one calendar for everything, or to have some mixture thereof; and we need to figure out how we will construct them.
Time's relativity seriously impacts the question of how to create a calendar or regular system of calendars that can support the whole universe. For example, Time passes more-slowly in areas of high gravitation than in areas without (Gravitational time dilation); so a person travelling between a planet that is near a black hole and a planet that is not, may find there to be years of difference between the two, even though both are using the same calendar.
Apart from how hard this would make it for these two planets to consistently communicate; this potentially means that a truly universal calendar may not be possible to meaningfully construct, since different places can literally be living at different points in time, even when starting with the same calendar at the same time. Differing local calendars don't really solve this "problem", but they do quite effectively hide it.
The total number of conversion algorithms needed to convert between multiple calendars can be represented as a graph with every vertex connected to every other vertex. That makes this mathematically identical to solving for the number of possible unique edges in a self-intersecting n-gon. The formula for this is
(n * (n - 1)) / 2, where
n is the number of calendars. This means that the total number of conversion algorithms needed increases exponentially as new calendars are added.
The solution to this is to have a reference calendar. New calendars can then convert to this reference calendar instead of to each other, reducing the many-to-many relation to a one-to-many relation; but also requiring twice as many calculations as would be required without the reference calendar. This reference calendar should be as simple as possible to reduce computational complexity. Since this will make the reference calendar unsuited to human use, a default calendar should additionally be created, to be used wherever a locality-specific calendar has not yet been adopted.
Every calendar needs an epoch -- the time it starts at. This is generally a fairly arbitrary choice. One regular way to decide on these, is to set them to the moment when a given locality was first continuously settled.
Over millennia, our biological clocks (or, "circadian rhythms") have evolved to match the modern Earth's 24-hour day. But humans living on non-24-hour planets in the future may genetically engineer themselves to have a different clock-length. More drastically: sentient aliens, when discovered, are no more likely to have a 24-hour clock than they are any other reasonable length of time. If humans and a given alien species have biological clocks that are too radically different, it may be impossible for both species to use the same day-length even while living on the same planet.
We can't simply set each planet's nominal day-length to its real day-length. Mercury and Venus, for example, both have *ridiculously* long days, meaning it's pointless to use real days there, since people would be biologically incapable of even genetically engineering themselves to match; so on such planets, it would seem best to keep a 24hr day. Yet, a 24hr day is not ideal on all planets; like Mars, for example, which has a very similar (but still different!) day-length to Earth; and it is important to remember that Earth itself is slowing its rotation over time, and will have 25hr-32hr days in 1 billion years' time. And planets orbiting a binary star system may have complex days not easily defined by a regular hourly cycle.
Years might also seem simple: just set them to each planet's year. But what if the planet in question has a year equal to 1000 Earth-years? How useful would a 'year', then, even be?
Months are similarly nonstandard: many planets don't even have moons, thus making true months impossible; and many others have many more than 1 moon, thus making true months confusing. And we can't universally base 'months' on seasons like some of the old Theodian calendars did, because some planets have none (like Venus), and others have theirs determined by where you are on the surface (Earth).
The cyclical considerations have implications for units of time -- since days can be different lengths on different planets, what units of time should we use?
One possibility is to have different lengths for hours, minutes, and seconds on each planet, with every planet's day being 24 "hours". This could be done; but could prove very confusing if people need to work across multiple planets.
We could just use the same units of time everywhere; but this would make math across days more-complicated, since on a
23.25 hour day, an hour from
0:45 o'clock, not
24:00 as the numbers would suggest.
One possibility is to use the same units everywhere, and just express each day in terms of percents. So instead of "2:24", we'd say "10%". This makes days always whole, round numbers; it keeps the actual time units the same everywhere; and both the units and the percents use the same math (ie, no looping after random numbers like 24). However, these percents are a kind of unit, themselves; which means we'd be left with a kind of dual-unit system -- potentially not much better than the 24-"hours"-per-planet situation. But, seeing as a universal unit is already going to be needed for places that do not conform to the human circadian rhythm; this seems an okay solution that may get the best of all worlds. Additionally, this frees up the base time unit to be derived from fundamental constants, rather than from the current length of an Earthling day; and it provides a more-useful metaphor (percentages) than the arbitrary divisors of 24.
Worldwide, the most-common week is, by far, the 7-day week. Non-7-day weeks have been tried many times before; but have almost always lost out to the 7-day week. The ancient Celts, Etruscans, and Romans all originally used an 8-day week; the Welsh and Balts used a 9-day week; the Classical Chinese and Revolutionary French used a 10-day week; and the Soviets used a 5-day period for work assignment. All of these eventually lost out to the 7-day week.
The reasons for why a 7-day week won out is not always clear, and it is not always the same. In Revolutionary France, the décade was abandoned due to a mixture of religious pressure and labourer dissent -- 1 day of rest after 9 days of work was a lot less than they got under the 7-day week. In the Soviet Union, the 5-day rotations included assigning every person a different day of rest in order to get continuous production. Unfortunately, the USSR assigned these roles at random, thus splitting apart people in the same family, including spouses. This, among other things, led to its temporary replacement with a 6-day week, before a final return to a 7-day. The 6-day week was never intended to be permanent, and the 7-day calendar was used throughout; so the return to a normal 7-day week was somewhat inevitable after the 5-day was abandoned.
The 7-day week, itself, originated in Babylon, and was adopted by the Jews and Persians, before spreading to the Hellenistic world, where it later became a part of Christianity, and thence spread throughout the rest of the world.
While the 7-day week has served societies very well for a long time, even surviving industrialization; it has a few issues. It is a prime number, so it cannot be evenly subdivided. Being an odd number additionally reduces the potential for internal symmetry. This has resulted in a week of 5 work days and 2 rest days, with schools often further subdividing those 5 days into every-other-day timeslots. Many of these could be made far-more-regular by switching to a rounder, more-divisible number. 7 is also difficult to fit evenly into other numbers, as it is a relatively large prime. This has resulted in months and weeks not lining up, thus causing additional complication for calendars.
A 6-day week solves these issues. It fits evenly into a 30-day month, it fits evenly into twelve (important for Theodia, which uses the duodecimal system), and it can be easily and evenly subdivided. 4 work-days and 2 rest days gets the 4-day work-week many are clamouring for, while only reducing the total percentage of time worked (relative to the 7-day, 40hr work-week) from 24% to 22%; the 7-day, 32hr work-week reduces time worked from 24% to 19%. 2-1-2-1 gets the same amount of work/rest hours, only over shorter stretches (something both Swena and CGP Grey prefer). It is also possible to work/rest every other day, albeit for a reduction in total hours worked. And schools that wish to do every-other-day slots for classes can evenly divide any of these work/rest ratios.
A 6-day week is also so close to a 7-day week that it shouldn't suffer from being too short. The main potential disadvantage is a lack of compatibility with religious traditionalists; but Theodia explicitly tries to avoid miring in path dependence, so this isn't a serious concern.
There is no real advantage to be had in placing one planet's moon into every calendar. However, months are still useful as an additional subdivision of a year; as any year of 60 weeks (as on Earth) is inevitably going to be divided somehow. Taking the 28-31 days per month in the Gregorian calendar as a indication of a good length for human months, each planet should have a month consisting of 4 to 6 weeks: 24, 30, or 36 days. 36 should be generally preferred, for mathematical regularity (as it is a perfect square); although 30 is more-familiar for those who use the decimal system; and 24 has the advantage of having its week total being within the human subitization range.
There should always be an even number of months (to support northern and southern hemispheres equally), and the days of the year should be divided as evenly as possible between them for the same reason. Calendars should use leap days to stay on-track. The 6-day week is easily adapted, so it is okay if a month's totals are not divisible by 6.
The breaks between months are useful places for entities to define their fiscal calendars. Months should be arranged so that two of them end around the solstices. Where relevant, moons' months should try to match or divide the time it takes them to orbit their host planet.
Years should be the approximate number of days it takes the locality (or its host) to orbit its host star(s). Localities with highly variable year-lengths, or which have years greater than 600twelve (768ten) average human circadian cycles (around 24 SI hours), should generally use the default year-length of 100twelve (144ten); but they can use a different year-length as-needed to better fit their environment.