# If clock and calendar was reinvented with today's knowledge, what could they look like?

Our notion of recording and communicating time and date is based on very old concepts, many of them being built upon flawed assumptions (that the Sun should be at exact south at noon, that a year should have an integer number of days, etc.) and cultural heritage (7-day week, the arbitrary beginning of year a week and something after solstice, two months of 31 days in succession), and burdened by little fixes and exceptions trying to maintain as much of "backwards compatibility" as possible (time zones, leap years, leap seconds), not even mentioning atrocities like the daylight savings time. This all not only complicates the matter beyond necessity (the need to remember a lot of stuff for something that's just a unidirectionally flowing one-dimensional quantity) and creates a mild amount of unfairness (e.g., prices per calendar month, deadlines at the end of month but prior to weekends) but also gives computers, who use a completely regular (but not very human-friendly) internal format, a lot of work converting from and to our representation to communicate with us.

What if calendar and clock were designed in a society that knows what we do and our ancestors did not: that the Sun orbits Earth (relativistically speaking) continuously, that there's always noon somewhere, that seasons are the opposite on the opposite hemisphere and work completely different near the Equator, that the rotation of Earth is not synchronized with its orbit in any way? If the primary goals were simplicity and practicality of use for communication with both people in different places and with machines? Minuscule variations in the length of day and relativistic effects would presumably be neglected and the system should be rigid enough to allow such neglection without leaps.

I believe it should still be based on astronomical invariants like the equinoxes and noon to be physiologically relevant, not just blindly counting second after second like computers do. An agreed fixed reference like Year One is very reasonable. But I have a hard time coming with finer divisions of time instead of months and weeks that would make sense. Counting up all the way to 365-something is prone to errors, it would be good if at all levels of precision the data would remain reasonably bounded.

• calendar was invented to count days so I can imagine a modernized dynamic calendar would incorporate gravity map of the entire Solar system to account for the minuscular time dilation, that's not all it would also has to factor in chaos theory for the coriolis effect too. However expect diversity since every applications have different needs (resolution: microsecond). – user6760 Apr 1 '16 at 6:34
• You have to consider that the second is one of the 7 base SI units. How you express speed and energy, for instance, depends on the very definition of the second. Whatever you do with your calendar, you might want to keep that in mind. – AmiralPatate Apr 1 '16 at 8:33
• Another thing I will add is that the week isn't likely to go anywhere anytime soon. After all, it comes from the Bible/Torah, which are the religious texts of about a third of the world. – Xandar The Zenon Apr 2 '16 at 3:28
• An interesting element of the French Revolution was the attempt to rationalize the calendar. Days were divided into 10 hours, hours into 100 minutes, minutes into 100 seconds. This Wikipedia article covers the whole system: en.wikipedia.org/wiki/French_Republican_Calendar – Howard Miller Apr 2 '16 at 20:01
• Even with today's knowledge, scientists cant agree on a calendar. There are to many variables. – Keltari Jul 2 '16 at 2:55

The current date/time system is based on applying arbitrary numbers to important physical constructs: day, moon-th, and year. Month is the odd one, because you cannot divide a year into moon cycles evenly, which is why we get the arbitrary number of days in a month.

Moon cycles mean a lot less to modern humans, so we can theoretically dispense with that. However, days are still vitally important to us, as are years. Given those as fixed constructs, let's see what can be done.

## Summary

• 5-day Weeks.
• Years divided into 4 Quarters of 18 weeks each. The remaining days are arbitrarily assigned between quarters, and are given unique names.
• Leap days are added as special days between quarters, just like the remainder above.
• Quarters divided into 3 6-week Periods.
• Days are divided into 24-Hours
• Hours are divided into 1000 "seconds" or some other such name.
• For sub-seconds, go metric. And for large counts of seconds, go metric.

## Details

### Year Divisions

Well, the number of days per solar year is not a whole number. So as much as we don't like it, leap years, leap centuries, and the like are still going to have to be around. So whatever divisions we make here need to recognize that.

The basic year will need to be 365 days long, with adjustments made as needed for leap years and the like. That number does not divide evenly by very many numbers. Basically, just 5. So if we need a "week" division, the least painful would be 5, which leaves us with 73 weeks in a year.

Well, 73 is prime, so that poses a division problem. We need larger subdivisions of a year. And ideally, 4 such subdivisions would be reasonable (which matches with the useful, physically observable concept of "seasons"). So consider this.

There would be 5 days in a week, with 18 weeks per season. That covers only 72 weeks per-year. We take the extra 5 days and put them between the seasons as special days, which are not considered part of any particular week. You'd have to double-up on one of them.

So you get 18 weeks, followed by a special day, followed by another 18 weeks, then two special days, and so forth.

When it comes time for a leap year, you just add another special day. Presumably opposite the double special day that already exists on the calendar.

Such quarter year divisions are large enough that we can do things like build commerce around them (much as we do at present). And special days would be useful for arbitrary holidays and such.

However, 18 weeks, 90 days, is a long period of time to talk about. So it would be useful to divide them into shorter stretches of time. Perhaps 6-week periods (30 days) within a quarter. So you would have "first-quarter, second period."

What would a date look like? Using US dating schemes, "3.1-27-2016" would be the 3rd quarter, first-period, 27th day of the year 2016. Special days would be numbered as a fourth period of the quarter preceding them: "3.4-1-2016". That's the first special day after the 3rd quarter.

Note that this is not too dissimilar to what we have now. It's more regular, in that each period has a fixed number of days. But the division of a year into 12 sections makes the groupings of days reasonably bite-sized for human consumption. You're not required to count past 30 or anything.

### Day Divisions

Say what you will about hours, 24 is a very impressive number. It can be evenly divided by 2, 3, 4, and 6. And that's very important for many human uses of sub-day divisions.

If you went to a 25 hour day, you can't even talk about half of a day without having to use fractions, let along 1/3rd of a day. Consider medicine that you take 3 times a day. How many hours is it between the times you take the medicine? With a 24-hour day, it's 8. With 25? Or 20? It's a fraction, and people generally don't want to deal with fractions in those cases.

And however much decimalization has happened, people generally do not want to deal in fractions. 100 is useful in decimalization because you can divide it by 2, 4, and 5, and can even get a decent approximation of 3. However, having 100 divisions in a day leads to "hours" that are just too short to be meaningful.

So you have several points of tension in this choice. You need a number that can be evenly divided by quite a few numbers. It needs to be big enough that an hour is not a large quantity of time. But it also needs to be small enough that an hour is not too short of a quantity of time.

I would say that such tension will inevitably lead you back to 24. It turns out that people in the past weren't stupid.

Beneath the 24-hour daily cycle however, things can get more arbitrary. As such, subdividing an hour via the metric system makes sense. Centi-hours, milli-hours, and the like.

However, technology becomes an issue. Why? Because lots of technology already currently works on the order of milli-seconds, micro-seconds, and nano-seconds. And there are already 3600 seconds in an hour. So now you'd be required to talk about pico-hours and femto-hours. That's rather cumbersome.

So it wouldn't be unreasonable to have a specific name for milli-hours.

• @Brythan: I never said that you could do any of those things; indeed, I was very specific about months not being a single moon cycle in length. And non-terrestrial dating and calendar systems were very much not on-topic for this question. – Nicol Bolas Apr 3 '16 at 3:27
• You said, "Month is the odd one, because you cannot divide a year into moon cycles evenly". I'm pointing out that it's not just months. Days and years have the same problem. There's 365.24 days in a year. And this was explicitly mentioned in the question while non-terrestrial times aren't. I'm pointing out that we know about non-terrestrial references -- why would we pick a time system that only works on Earth? The only reason is that you are starting with our current system. If someone really started fresh, they wouldn't do that. – Brythan Apr 3 '16 at 3:34
• @Brythan: "why would we pick a time system that only works on Earth?" Because we live there, rely on days and years a very great deal in our daily lives, and this will continue for 99.99% of humanity for the immediate and forseeable future? Also, because that's what the question asked for. The question very clearly focused on terrestrial concepts like years and the divisions thereof. So extra-terrestrial issues would be irrelevant. – Nicol Bolas Apr 3 '16 at 4:12
• @XandarTheZenon: "You made the same mistake metric makes by not using the decimeter" ... Decimeters are a real thing in the metric system. I have no idea what you're talking about or what decimeters have to do with minutes. Are you suggesting that there needs to be some specific named measurement between 1000ths of an hour and 1 hour? – Nicol Bolas Apr 3 '16 at 4:13
• From the Q: “What if calendar and clock were designed in a society that knows what we do …?” I’m not sure about much, but that society would certainly not be using “US dating schemes”, but either big or little endian order of parts. – Crissov Jul 1 '16 at 15:01

There have been a lot of proposed calendars with a variety of different features.

The ideal calendar is simply one that makes is easy for humans to describe reference time. Humans like the clock/calendar roughly corresponding to the local day and night cycle. 25 time zones world-wide would be suitable - but please let the time zones be named zone 0 thru zone 24 or such like.

100,000 seconds in day seems like a nice modern method. Kiloseconds would nicely approximate quarter hour intervals - no need to have hours and minutes. No AM/PM and please God no daylight saving time.

A weekly cycle is nice because weekends and workdays, though not essential. 5 day weeks would be ok, with 73 weeks per year (5*73 = 365). Leap days still needed to sync with a solar year, I would make the leap day not part of any day of the week, so you just have an extra holiday after the last regular day of the year. With this system 1st day of month is always 1st day of the week, etc., so calendars are easier to plan. With 6 5 day week in a month (another convenient division for some purposes), but the final month would have 7 weeks plus occasional leap days.

No matter which calendar you use, people will still invent other calendars and timekeeping to corresponding to something convenient for them, just as Julian calendars supplement Gregorian calendars today.

While we are at it, maybe we could replace the 360 degree circle with perhaps either 100 or 400 (grads), so angles in radians or metric degrees of some form.

Of course, we would also be better off by discarding decimal and moving to a base 16 number system so that computers and people would share a common numerical view of the natural numbering system. We should have started with this change of course.

• 25 time zones? Why? – AmiralPatate Apr 1 '16 at 8:22
• We already have gradians or gon, 400 to a circle. You are free to use them if you want to, but don't expect everyone to be familiar with them. Also see some discussion on why 360. – a CVn Apr 1 '16 at 8:26
• Unless we can grow additional fingers, it would be more natural to use decimal and change computers than vice versa. – RedGrittyBrick Apr 1 '16 at 8:44
• @RedGrittyBrick Computers use base 2. It's how they physically work. Hexadecimal is essentially a compact form of binary that is slightly easier to read for humans, e.g. compare FF and 11111111. Not that FF is easier to read than 255. – AmiralPatate Apr 1 '16 at 11:10
• @AmiralPatate: At the outset of my IT career, we learned octal. Still useful for *nix permissions. 377. – RedGrittyBrick Apr 1 '16 at 11:16

### There is no time

With relativity, we know that nothing can happen simultaneously unless at the same point. So instead of talking about times, we should be talking about spacetime positions. We might say home dawn, office dawn, and home sunset. Home and office are positions in space while dawn and sunset are times.

When trying to synchronize times across two positions, we'd have to pick one as the source and make the other refer to it. The communication time would become part of the conversion process. Much as a seller will specify a free-on-board point (the place where you can pick up the item without paying a delivery fee), a time keeper will specify a synchronization point (the place where communication is expected to originate). The synchronization point will take the place of a time zone in our system.

### Intervals

A truly excellent way of measuring intervals might use meters. That would make time intervals work like distance intervals. Unfortunately, I don't have a good way of expressing time as meters. Perhaps it's not possible. In a spacetime system, space and time make up a complex number. That may be systemic. Or simply beyond our current understanding to express. Time may be an illusion, but it's a convenient one. So let's stick to separate measures of time and distance.

A lot of people are suggesting that we use solar days as the basis of a time unit. However, over time, the solar day changes in length. We already know that, which is why we don't define seconds as an 86,400th of a day. Also, I don't think it's the most basic unit about which we care. Rather than pick a time period based on a changing value, let's pick something more arbitrary and therefore enduring.

### Actual unit

The basic unit of time could be a work-period. For example, that could be roughly eight hours (our time). So from dawn of one day to the next would be about three periods. A milliperiod would then be around twenty-nine seconds (28.8). That's shorter than our minute but not ridiculously so. A kiloperiod would be shorter than our year, but also not ridiculously so. A hectoperiod would be similar in length to a month. A decaperiod is a few days (a bit less than half a week, although more than three days). A deciperiod would be forty-eight minutes; again, shorter than an hour but not by a lot. A centiperiod (4.8 minutes) would be a useful interval that doesn't correspond with anything in our system.

A side effect of this is that days wouldn't be an even length. In fact, if we go dawn to dawn, they wouldn't even be a constant length. So we might drop the twenty-four hour day as a concept entirely. We could just track intervals as periods and work from dawn. Dawn makes more sense than noon, as it really is a noticeable change in the day/night cycle. Dawn makes more sense than sunset because we would probably prefer the end of our day to vary rather than the beginning.

• Thanks for taking time to answer my question, great points! I like the proper use of special relativity that actually remains practical. Your last paragraph reminded me of a curiosity I've heard. It may sound surprising that in medieval ages people actually counted days from sunset to sunset in certain parts of Europe, see "Italian time" or "old Czech time", en.wikipedia.org/wiki/Hour#Counting_from_sunset. Part of the reason is that one can more easily wait for sun to set (and one can do some reasonable work until then) than to wake up before sunrise and catch the moment it rises. – The Vee May 2 '16 at 21:54

Every society has its culture with all its arbitrary traditions, so you can never have a totally objective reform or introduction of date and time measurement. Even if, for instance, humanity vanished and an alien species would colonize Earth, they wouldn’t completely abandon their previous customs.

In designing the best calendar for humans on Earth, one has to take natural cycles into account. Some of them are obvious, others could be found empirically.

Research with isolation studies has found out that evolution tuned our bodily functions quite well to the daily cycle. Without natural light sources, clocks and contact to the outside world, most subjects acquired a routine spanning 24 to 25 hours, if I remember correctly. That means, one should absolutely keep the solar day as a base for the calendar.

The menstrual cycle is in the magnitude of one month. A pregnancy lasts about ten such cycles, but roughly nine months. Neither are bound to seasons or lunar phases, i.e. every day, about the same number of babies are born and about the same number of women bleed. There are cultural effects on the distribution of birth dates, though, e.g. because there are rarely planned C-sections on weekends and some occasions lead to statistically significant more unprotected sex within a population. In short, it may be nice to have a regular n-week, m-day, 1/p-year or 1-lunation period, but it’s no necessity.

Astronomic, astrologic and meteorolgical seasons differ by region, hemisphere, culture and time. There are places with a single season throughout the year, others have 4 seasons of very similar, but slightly different length, others have just 3 or maybe 6 per year. That means, they cannot be defined globally and long-term. As I said above, they’re also not innate to the human reproduction cycle (unlike with many other species). So any time unit between a month and a year would and could be rather arbitrary and specific to a culture, but it could also contribute to defining a culture (e.g. fiscal quarters). They’re certainly not strictly necessary for a good calendar design. Almost anywhere, however, some cycles of nature repeat annually, i.e. approximately each solar year with a possible error margin of several days, so let’s try to keep the year, but let’s worry more about long-term accuracy of the mean year than short-term differences from the astronomical ideals. It may be preferable to align the year start with either of the two solstices or equinoxes – or the middle date between two of these.

The week of 7 days – and there have been others, e.g. market weeks, even different ones running concurrently and synchronized with each other, e.g. Balinese pawukon – are almost entirely a cultural convention, although it’s close to the duration of a phase of our moon. I’m not aware of any research having been conducted that tried to find a natural short-term day-based work–rest cycle. I would assume it depends a lot on the kind of work one does. However, 5 work days of ca. 8 hours each followed by 2 full days of recreation seem to be good enough for quite a lot of people (although some are forced on different plans), but maybe 7+3 or 3+1 would work even better. Assuming that a culturally humane week length could be determined, it would make sense to make it an integral divisor of larger calendrical entities (month, season, year). That means, among other things, that 1 to 5 days outside the week cycle and a leap day are probably a worse choice than a leap week. If nothing else, the leap cycle should contain a whole number of weeks like the Gregorian 400 years do, but the Julian 4 years and revised 450 or 900 years do not.

Finally, there’s the matter of efficiant and readable notation. Since we want to keep a year of three-hundred-something days, we need at least 3 decimal digits to address any annual date, e.g. simple ordinal DDD (single number). Humans aren’t good at dealing with and remembering chunks larger than 7 and numbers larger than they have unique words for (twelve). We currently most commonly use 4 digits for 2 numbers: MMDD (or DDMM), but existing weeks would support 3:2 WWD, whereas 4:3 MMWD has no major advantage. With quarters and current conventions, we’re back to 4 with 4:3 QMDD or QWWD (a good dozen of weeks) and 4:4 QMWD, except for 3:2 QDD, but 90ish days is psychologically hardly better than hundreds of days. There are other combinations that make good use of 3 places with decimal digits, e.g. between 7×7×7 = 343 and 7×7×8 = 392 (see Cal7 or Octalendar). It may be a minor point, but certainly an objective advantage to be not more verbose than necessary. The decimal system is of course also a rather arbitrary choice, but one that humanity almost agrees upon nowadays.

Assuming the existence of decimal prefixes as in the SI, which make absolute sense with decimal numbers, and the retaining of the day as a fundamental, because natural/humane unit of timekeeping, it would make sense to employ a 10−n fraction of the day, e.g. its nominal 100’000th part (a bit shorter than our second), as base absolute unit of time in physics – alternatively one could use an integer base-ten multiple of Planck units and also make other natural constants (e.g. Avogadro’s number) simple fixed values. It would make sense to divide the day into sections of simple multiples of this period.

Many people are used to eat their three major daily meals about a quarter day (6 hours) apart. (Adults sleep about a third of each day at night if they can.) I’m not sure how much of this is cultural habit or human nature, but 4 major equal divisions of the day make sense for another reason: On a radial clock face without markings, we can easily distinguish top, right, bottom and left – 4 values. It’s also simple to estimate the middle between two such points (which makes 8 values), but dividing each quarter into thirds and each of these into fifths is asking too much of the brain without the help of explicit markers. Despite the great divisibility of 12, 24 and 60, only some of the possibilities have developed into cultural conventions: ½- and ¼-hours, but 5- and 10-, sometimes 20-minute intervals (not ⅓-hours or 1/5-hours for instance). I would therefore argue that these are possible humane approximations:

• second equivalent: 1/100’000 day (10 µd) =: 1 part = 0.864 s
• minute equivalent: 1/1’000 day (1 md) = 1 hpart = 1.44 min
• 5-min equivalent: 1/200 day = 5 hpart = 7.2 min
or                         1/250 day = 4 hpart = 5.76 min
• 10-min equivalent: 1/100 day (1 cd) = 1 kpart = 14.4 min = 0.24 h
• ¼-hour equivalent: 1/80 day = 1¼ kpart = 18 min = 0.3 h
• hour equivalent: 1/16 day = 6¼ kpart = 1.5 h = 90 min
or                       1/20 day = 5 kpart = 1.2 h = 72 min
• meal-to-meal equivalent: ¼ day = 25 kpart = 6 h
• midnight to noon: ½ day = 50 kpart = 12 h

Let's start with the physical pieces that limit what time is attempting to measure and regulate: the orbit of the earth around the sun, the rotation of the earth, and the cycle of the moon from new to full and back.

None of these things line up; a lunar month is 29.53 days, a solar cycle is 365.25636 days, and a solar day is 24 hours. Worse, these numbers change over time; the day used to be longer, and even today, the length of a day changes almost at random. Not that it would have mattered even 100 years ago; a leap year is all you really need to keep track of time if you're using the sun.

## Time Increments

Let's start with the largest useful increment of time: the year. It's a full growing season, shorter than a lifetime but long enough that a lifetime is less than 100 years (generally). Of all the measurements of time, the year has lasted the longest.

The next most useful increment of time is the day; a day and night cycle to mark time passing in a meaningful way. As long as we're on Earth, the year and the day will be immutable. Trying to survive on, say, a strict 25 hour day, will simply not work; the human body is built around the day/night cycle.

Years and days have a fairly solid relationship by the stars, too, so they are easy to keep track of over time.

Between the two are months and weeks:

## Weeks

Weeks are best for delineating work schedules, and organizing days into manageable chunks. These days, the majority of people have a 5-day work week, followed by a two-day break. Soviet Russia tried a 5, 6, and 10 day week, to little success, though that probably has more to do with a rolling calendar than actual number of days worked. There have been a few other experiments with work-week lengths, but as far as I can find, nothing conclusive.

But, what is optimal today with our low-impact and low-energy work wouldn't be best for 100 or 1000 years ago. A 7-day week makes sense for hard, manual work; working sunup to sundown, six days in a row, then taking a seventh day off to rest pushes the body to the limit, but not beyond. That means if you want a week with a different number of days, it should be between 5 and 7 days, but for a long-term solution, 7 days to a week makes decent sense. It allows for the maximum amount of work, without over-stressing the body.

## Months

There are three ways to handle months - lunar months, equal months, or no months. Lunar months are designed to line up with the lunar phase; so, each month should be about 29.5 days long, or 29 days on odd months and 30 days on even months. 12 lunar months last 354 days, which means there are 11 or so extra days in a year - and months start sliding around, which means January is in winter one year, but ten years later it's late spring. That's really confusing - don't do that. If you want that system, months shouldn't have names; treat it like we treat weeks today: month 1 is the month at the beginning of the year (and may begin in the middle of a week), through month 13 or 14.

The second option is equal months, not lined up with lunar months. To make a year line up exactly (except for leap years), there should be 5 months of 73 days each. To make weeks line up exactly, there should be 13 months of 28 days each, with 1 day extra (2, for leap years). In a world I created, there are still 12 months, with 8 months having 28 days, and 4 (those with a solstice or equinox) having 35; I eliminated the extra days, but they could well be special holidays or such. A 12-month year is a little easier to divide than a 13-month year. If you want a different-length week, you can divide your months to match.

The third option is to ignore months all together. They don't make a lot of sense if they aren't tethered to the moon, so they aren't much use - just use numbered weeks instead.

## Timezones

You won't be able to avoid time zones. The sun was the best way to measure time until clocks came along, and according to a sundial, noon happens when the sun is high in the sky - and a different time all over the world.

However, time is on your side! Ancient cultures didn't care about time zones; if it took two days to walk from City A to City B, who cares if they are an hour apart, or even six? It wasn't until clocks and high-speed, long-distance travel travel were invented that time zones even mattered at all.

## End Result

Find a common origin for a year - and to cut down on complaining, make it Year 0. Then, find the number of days in a week: 6 or 7. Then, pick months; I like rolling numbered months, as moon phases matter to many cultures, and it can help delineate time without confusing people too much.

Smaller increments of time honestly don't matter. There's nothing that takes an hour, or a minute, or a second, so go ahead and divide the day into pieces as you want: 24 hours in a day, 60 minutes in an hour, 60 seconds in a minute if you like what we've got; 10 hours in a day, 100 minutes in an hour, and 10 seconds in a minute if you're one of those decimal people; or, 16 hours in a day, 64 minutes in an hour, and 64 seconds in a minute if you like binary.

One option would be to start with the day as a basic unit. Then define units like

• Hectoday (approx. three months) or Kiloday (approx. three years) as the basis for celebrating anniversaries, long-term leases or work contracts, ...
• Decaday (approx. 1.4 old-style weeks), suitable for recurring timetables. Would there be two or three days off per decaday?
• Deciday (2.4 old-style hours), could be the length of a lesson in school, even if it is a bit long. Probably the rest break would be taken out of the deciday.
• Centiday (14.4 old-style minutes), that's what you use when you decide when to have dinner today.

This would be better for a planetside civilization than seconds, kiloseconds, and megaseconds.

• I beg to differ. Both the real day and year have very solid foundation in everyday life and thus significance. A Kiloday is not going to replace a year (not to mention that a certain part of the world cannot handle the metric system as it is). – Ghanima Apr 1 '16 at 11:42
• Hello @Ghanima, I kept the day for just this reason, it is more important than they year. When it comes to the inability to handle metric, there are good reasons to go to base-12 mathematics, but few people are seriously proposing it. As long as we use base-10 numbers, people should learn the principles. – o.m. Apr 1 '16 at 13:26
• I also beg to differ. Because I agree with Ghanima. The metric system is too arbitrary from my point of view. If we had eight fingers it would all be in base 8. The customary system sprang to being because those were the kind of measurements people used, i.e. cups, tablespoons, etc. – Xandar The Zenon Apr 1 '16 at 13:56
• @XandarTheZenon, we are using the decimal system. As long as we do that, the system of measurements should be a compatible one. So there are two sane options, go metric or go duodecimal. Sexagesimal has to many different symbols to be practical. – o.m. Apr 1 '16 at 14:16
• My main point here is that instead of arbitrarily dividing up the day, try to choose some numbers that make sense for people, and that are convenient measures. For example, I don't want to have to say "two centidays and seven milidays from now, I want to say, "forty minutes". – Xandar The Zenon Apr 2 '16 at 3:22

At once, they would include notions of day (period of Earth's rotation, see also Solar time and Sidereal time) and year (period of Earth's translation, see also Axial precession).

Unfortunately for most of us humans, order-oriented which we are, a year isn't an exact multiple of a day, thus defined. Worse, these periods vary, even if slightly, with time.

So, any time system will need to have arbitrary/ad-hoc adjusting of its structure to approximate the actual periods of day and year - exactly what happens nowadays.

More at Calendar reform and Time standard.

I think that the real useless complication of our system are months, especially the fact that months all have different length So, imho, you have 3 ways.

1. You divide the basic time component (length of a day, length of a year) in its smallest component (e.g. the greatest x such that nx=average day and mx=average year for some natural n and m) and use this unit as the base unit of the new system, but I think that this unit will be too small to be meaningful and it won't be perfectly accurate.

2. take the day (average day) as your unit and count from that. You can divide the day in any smallest unit you want (actual hours, deciday?) and 365 days make a year. I'd divide the year in four season (but no months) between equinoxes end solstices (chosen in an arbitrary time zone)

3. Make the sun meaningless. Depending on your setting, you may have a civilization that can control when it's day or night ( think of a human space station near Neptune) this way you can choose an arbitrary time system and align life in the station to it.

• How many recurring payment systems are based on 1 per month per month interval? I would argue that a month is clearly a convenience as is fits a natural duration. Too long and the amounts get too large, Too small and the frequent payments and processing are their own form of inconvenience. If you say, just make the payments due every x days or weeks, you lose the convenient trigger of remembering which week or day is the payment due. If payment is due on the 1st, every months has a 1st. Not saying months actually needed, but that they are still useful in some contexts. – Gary Walker Apr 5 '16 at 8:24
• You are right. As you'll get approximately 90 days season you can put payments every 30 days to get a system similar to our own. In the end from this question we can learn that our system isn't qs bad as it seems – karmalu Apr 5 '16 at 9:01

What about using years, months, and days with metric prefixes? When combined, the terms with larger units (not the units themselves) would be rounded to the nearest multiple of the smallest unit.

FWIW, here are exact definitions of the units (C is the center, P is a point on the surface):

• Year: cycle of $$m\angle C_\text{earth}C_\text{sun}P_\text{sun}$$ (the position of the earth relative to the sun)
• Month: cycle of $$m\angle C_\text{moon}C_\text{earth}P_\text{earth}$$ (the position of the moon relative to the earth)
• Day: cycle of $$m\angle C_\text{sun}C_\text{earth}P_\text{earth}$$ (the position of the sun relative to the earth)
• Welcome to Worldbuilding, Solomon Ucko! If you have a moment, please take the tour and visit the help center to learn more about the site. You may also find Worldbuilding Meta and The Sandbox useful. Here is a meta post on the culture and style of Worldbuilding.SE, just to help you understand our scope and methods, and how we do things here. Have fun! – Gryphon - Reinstate Monica Jan 19 at 20:36