“The only reason for time is so that everything doesn’t happen at once.”
— Albert Einstein
In one very real sense, time doesn't exist. What we think of as "time" can really be viewed as just an abstraction which we've assigned to our awareness of change.
It is almost certain that all living organisms are conscious (whatever that word means) of change; even bacteria "know" when their energy reserves are depleted and it's "time" to eat. However, it may be impossible to determine at what level of complexity living things become aware of abstract "time". It may be that a type of memory called "episodic memory" is what allows us humans to have a relationship with the abstraction of "time".
For our purposes, it’s more important to explore how time is perceived, measured, and recorded by humans. At some point in human development, simply being aware that night followed day and was, in turn, followed by day again—or that the Moon looks differently from day today, but always cycles among a very specific set of shapes—led to a need or a desire to track those kinds of changes, and then to record them. And this development leads to the ability to anticipate events which have not yet occurred, but which can be expected with more-or-less certainty or regularity to occur at some future "time".
The earliest remnants yet discovered of recognizable calendar systems date back to 3300 BCE in the Ancient Near East, China, South Asia, and northern Europe. They were based on an awareness of various kinds of changes and cycles: things such as the Sun rising in the same place on the horizon periodically; the Moon changing its shape on a regular basis; the weather being cold and snowy at some times and hot and sunny at others.
This (along with the ability first to count and then to do rudimentary arithmetic) led to "time" being measured out and tracked in various units, ranging from larger to smaller:
- The year: related to both changes in weather and in the locations of the Sun relative to landmarks;
- The seasons: related to cyclical changes in the local climate and weather;
- The month: related (most often) to the regular, cyclic changes in the appearance of the Moon;
- The week: measured either as fractions of a month, or multiples of a day; and,
- The day: measured by periods of daylight and nighttime.
Let's look at these in more detail starting with the day and working up to the year. For the sake of brevity and simplicity, let us examine the situation for Earth, and later we can do some thought experiments with other possible worlds.
Terran Time Periods
The Week: The week is the only unit that doesn't seem to arise from an Earthly or astronomical cycle. It is an arbitrary collection of a number of days, sometimes simply a fraction of a month.
The Month: A single, large Moon orbits the Earth once every ~29.5 days, and changes its appearance on a regular basis, transforming from a disk to not-visible-at-all and back again. Because of its distance from the Earth, the Moon is visible at some point during each month from every point on the surface of the Earth. Indeed, the word for "month" in many languages is based on or related to the name of the Moon.
The Seasons: The Sun appears in the morning at some point on the horizon, moves higher into the sky until midday, when it reaches its highest point, the zenith (the position of which changes throughout the year), and then descending toward nighttime, all on a regular schedule. At some times, it is higher in the sky at midday than at other times; at some times it rises behind a particular mountain peak, and beyond a certain valley at other times. The same is true of its setting—now in this location, later in another. But always, it returns to where it has been at some time before.
The changes in irradiance due to these (apparent) motions leads to warming and cooling trends that create the cycle of the seasons. This oscillation and the seasons associated with it occur on a cycle of ~365¼ days. In addition, the obliquity of the Earth and its orbital path causes the stars which are visible in the night sky to change on a regular schedule, also comprising a cycle of ~365¼ days.
The Year: Broadly speaking, a year is the time it takes a planet to orbit its star(s) once. While this is certainly as significant a measure of time passage as is the rotational period of the planet (its day), the two time periods are in no way physically related nor dependent upon one another, and the fact that it is the planet which is moving and not the star(s) was a matter of heated debate in Europe for a very long time—a debate which could, and often did, turn deadly. So, the "year" as we think of it—in terms of one revolution of the Earth around the Sun—is actually something of a modern idea, at least in the West.
Mathematical and periodical relationships may be found between all these cycles, but neither the period of Earth's rotation, nor the duration of Moon phases, nor the span of the revolution of Earth around the Sun is in any way determined by any of the other cycles. They are, in a word incommensurable: which means that there is no integer number which will evenly divide into all of them. A day is one day long, but as soon as you try to subdivide a day into smaller parts, you find that there is always a fractional part "left over". Similarly, a "month" cannot be evenly divided by a "day": they cannot be measured using the same units and have an integer number of units be the result.
- Subtle seasonal changes due to differing apsidal distances, especially for planets with high orbital eccentricities; and,
- The stars in the sky of the night-side of the planet would gradually shift across the sky as the planet completed each orbital cycle. Noting this cycle could lead to an awareness of the planet’s year.
On Earth, the “day” can be—and has been—measured by any of several intervals:
- Sunset to sunset: referenced in the Jewish Torah  and the Christian Bible;
- Sunrise to sunrise: traditional in the Classical Roman period ;
- Crossing of the local meridian (the zenith);
- Crossing of the local anti-meridian (the nadir; the point at which the Sun is directly on the opposite side of the Earth from the local zenith.); used in modern astronomy.
The reason all of these week lengths "work" is related to the fact that the week is an arbitrary division of the month or the year. Rounding the number of days in a year to 365 means that there are only 3 numbers which divide the year into an integer quotient: 5, 73, and 365 itself—in fact, 5 ⨉ 73 = 365. Well, a week of 365 days hardly makes sense—by definition, 365 days makes a year! And, a week of 73 days seems excessive, so a week of 5 days, repeated 73 times will add up to 365 days in the year. (Of course, in the modern world, we know that the year isn't exactly 365 days long—it is 365 and a fraction—so there is no number which will divide the length of the year (measured in days) into an integer quotient).
Interestingly, there doesn't seem to have been a single ancient culture that settled on a 5-day week. The fact that the month (discussed next), is more-or-less evenly divisible by 7, and that there are just over 52 of these 7-day periods in a 365-day year is probably why the 7-day week was finally settled on, and is the definition of the week in the modern world.
So, rather than a collection of days or weeks, the month probably began as a standard, basic time unit based on the duration of the period between one new moon and the next, and which then gave rise to weeks as a result of being evenly divisible by certain whole numbers of days. The fact that the Jewish —and the related Islamic —religious calendars are lunar is a strong indication of the lunation as the ancient basic time-marker, not to mention the evidence found in other ancient calendrical systems .
However, a lunation is not a whole number; its duration is 29.530587981 days  (29ᵈ 12ʰ 44ᵐ 2.8016ˢ). This is, however, the “month” on which most modern calendars are based, known as the synodic month. To further complicate matters, the eccentricity of the orbits of the Moon and Earth make the synodic month variable by up to 7 hours.
So, the number of days in a month is not exactly equal to a lunation: if you measure the time between one full moon and the next, you will count 29 days, 12 hours, 44 minutes, and 2.8016 seconds, or 29.530587981 days, which is not an integer number of days. That is why the phases of the Moon don’t fall on the same day every month.
We’ll revisit the month when we discuss the year, below.
The seasons are related to four cardinal points in the Earth’s orbital journey around the Sun. The solstices are those days when the Sun is directly overhead at noon at the tropical latitudes and the hours of daylight are maximal. The equinoxes are those days when the Sun is directly overhead at noon on the equator and the number of daylight hours is equal to the number of nighttime hours (hence, equi- "equal" + nox "night").
Note that the vernal equinox (denoting the beginning of springtime) in the northern hemisphere is the autumnal equinox (denoting the beginning of autumn) in the southern hemisphere. Similarly, the summer (aestival) solstice in the north is the winter (hibernal) solstice in the south. So, wherever this document refers to the vernal or autumnal equinoxes or the summer or winter solstices, it is not important to specify which hemisphere. (See “Lengths Of The Seasons”, below, for a discussion of when the hemisphere in question does matter.)
Spring is astronomically defined as the period between the vernal equinox and the summer solstice; to wit, that period between the day when the Sun is directly overhead at noon on the equator and the day when it is directly overhead at noon at the tropic latitude. It is characterized by the Sun reaching higher in the sky at noon each day until the solstice and a there is a general warming trend in the local climate due to the increasing sun angle of the local solar irradiance.
The summer solstice is in many places the official beginning of the summer season, which is the period (astronomically) between the summer solstice and the autumnal equinox. This season has the warmest days and the sun angle and solar irradiance, leading to less warming and thus progressively cooler temperatures. In the polar regions, the Sun never descends below the horizon on the day of the solstice and the daily light cycle oscillates between full noon and civil twilight during the rest of the season.
Autumn covers the period between the autumnal equinox and the winter solstice. At the autumnal equinox, the Sun is once again directly overhead at noon on the equator, and from then on its midday point in the sky is lower by the day until the winter solstice. In the temperate regions, this is the time of year when the leaves of deciduous trees change color and eventually fall to the ground (hence the epithet “Fall”). Some animals prepare themselves for hibernation (from the Latin word hībernātus, past participle of hībernāre "to spend the winter") and some plants (perennials) go into dormancy (from the Latin dormīre "to sleep").
Winter is the span between the autumnal equinox and the winter solstice (which marks the official first day of winter in many locales). On the winter solstice, the Sun at noon is the lowest it reaches during the year, after which time it begins to climb again as the vernal equinox once again approaches. This is the time of the coolest temperatures. Latitudes closer to the polar regions get the least amount of sunlight during this season and precipitation is usually in the form of snow. Within the polar regions, the Sun does not ascend above the horizon at all on the day of the winter solstice, and the nocturnal cycle oscillates between civil twilight and full darkness the rest of the season.
THE CROSS-QUARTER DAYS
Some cultures and/or spiritual practices (in particular Wicca), also make note of, and sometimes have celebrations on, the days which fall midway between a solstice and an equinox. Since the solstices and equinoxes comprise the "quarters" of the year, these midpoint days are known as "cross-quarter" days.
In most Wiccan practices, the quarter and cross-quarter days are:
- Ostara: the vernal equinox (which ultimate gave its name to Easter);
- Betaine: halfway between the vernal equinox and the summer solstice;
- Litha: the summer solstice (also known simply as Midsummer);
- Lammas or Lughnasadh: halfway between the summer solstice and the autumnal equinox;
- Mabon: the autumnal equinox;
- Samhain: halfway between the autumnal equinox and the winter solstice;
- Yule: the winter solstice; and,
- Imbolc: halfway between the winter solstice and the vernal equinox.
Of these (there than Ostara/Easter), Samhain and Yule are most familiar to non-Wiccans, Samhain occurs on-or-about November 1 (the Christian observance of All Hallow's Day, and is, therefore, related to Halloween. Yule falls on-or-about December 22, and is closely associated with the Christian observance of Christmas. Most people have heard of or participated in decorating a yule log.
It is reasonable to suppose that inhabitants of other worlds would note and perhaps mark with observances or celebrations similar hallmark "days" of their "year" (more on this in the next blog).
THE WET AND DRY SEASONS
In the tropics, the dry season is that period of the year when there is minimal rainfall, due to a number of factors, but mostly as a result of the migration of the tropical rain belt. A massively oversimplified description is that when the Sun is directly overhead north of the equator, it prompts more evaporation, which results in more precipitation. When the rain belt migrates south of the equator, there is less evaporation in the northern tropics, and therefore less precipitation. The reverse situation happens just south of the equator.
The time when the rain belt is active in a given hemisphere results in the wet (or monsoon) season. In some parts of the world, monsoon season can be quite harrowing; on July 15-16, 1995, Cherrapunji, India received 98.15 inches (8 feet, 2.15 inches) of rainfall in a 48-hour period.
THE MILD SEASON
In areas that straddle the equator, there can be a three-season division of the year; winds from the north and south hemispheres collide and interact in what is called the Inter-Tropical Convergence Zone (ITCZ), which, like the tropical rain band, migrates north and south of the equator throughout the year. In those areas covered by the ITCZ, the cool and dry season (the mild season), is when the ITCZ is in the opposite hemisphere; as the ITCZ approaches and crosses the equator, the region experiences its hot and dry season; and, once the ITCZ has fully migrated, the region will have its hot and wet season.
On a planet with a higher obliquity than Earth, these zones would be wider, and traverse a larger span of latitudes throughout the local year.
LENGTHS OF THE SEASONS
It would seem obvious on the surface of it that if there are 4 seasons per year, each season would be exactly one-fourth of the year long, or ~91⁵/₁₆ days each. They’re close, but they’re not precisely the same length, due to the eccentricity of the Earth’s orbit and Kepler’s Second Law, which states that planets travel at different speeds in their orbits at different times—faster when closer to the star, slower when farther away .
It might seem counter-intuitive to those living in the northern hemisphere that the Earth is closest to the Sun during winter in the northern hemisphere; it gets mighty cold in Europe, Asia, and North America! But remember, the difference in the distance from the Earth to the Sun (~3%; 5 million km) is negligible in determining the character of the seasons; it is the obliquity (the axial tilt) that is the primary driver of seasonal variations. Perihelion and aphelion only contribute to the length of the seasons.
The seasons in the southern hemisphere (particularly winter—except in the Antarctic) do tend to be milder, but not because of the distance from the Sun; it is because there is much less exposed land in the southern hemisphere, and the water of the South Atlantic, South Pacific, and Southern Ocean heats up and cools down more slowly than land does, so during the winter months, it re-radiates its stored heat into the atmosphere .
AN ALTERNATIVE METHOD OF GENERATING "SEASONS"
One other way a planet might experience "seasons" would be if its orbit carried it into and out of its star's habitable zone for a time at perihelion or aphelion, or both. A planet with an orbit of high enough eccentricity could find itself migrating into the friozone and/or the calorozone for part of its year.
In the first, the planet's orbit carries it beyond the outer habitable zone limit at apastron and within the inner habitable zone limit at periastron. This planet would experience extreme warming at periastron and extreme cooling at apastron.
In the second case, the planet remains within the habitable zone at periastron, but at apastron it is beyond the outer limit of the habitable zone. In this case, the planet would experience deep cooling at apastron, but remain "seasonably" cool at periastron.
Finally, the planet passes inside the habitable zone at periastron, but at apastron, it remains within the outer habitable zone limit, and so would have mostly moderate winters, but exceedingly hot summers at periastron.
Another possibility would be a planet that does have an axial tilt, but is on a very distant, highly eccentric orbit around a particularly bright star. If its orbit were that of the second illustration above, then for a time before and after apastron, it might experience extreme cooling ("Winter Is Coming", perhaps?)
Alternatively, a planet on an orbit such as the third illustration would experience intense heating for a time around periastron. In this case, it might be preferable for the planet to have a fairly close, rapid orbit, so that the heating period is long enough to be challenging, but not of such a duration that it results in mass extinctions.
These planets would have orbital eccentricities in excess of 0.40, which is highly eccentric. (In the Solar System, Mercury's orbit has the highest eccentricity, at 0.2056). So, in this planet's system, there might be only this planet and a massive outer planet (or brown dwarf, or companion star) which distorts the planet's orbit into such an extreme ellipse. This would likely also cause a more rapid apsidal precession of the planet's orbit.
Another effect would be that the size of the star in the sky would change markedly between perihelion and aphelion.
The most obvious solar cycle as seen from Earth is the solar (or tropical) year, which is ~20 minutes shorter than the sidereal year, at 365.2421897 days (or 365ᵈ 5ʰ 48ᵐ 45.14ˢ), and is the basis for the civil year or calendar year in the much of the world .
In this Gregorian calendar—named for the pope (Gregory XIII) who in 1582 CE decreed its usage in all countries adhering to Catholicism—and which is used by much of the world today for secular and financial record-keeping, the year is defined as precisely 365 days (a common year) or 366 days (a leap year). The leap years help to account for the odd 0.256363004 days "left over" at the end of the calendar year, to keep the calendar synchronized with the seasons.
As mentioned above, the lengths of days, weeks, months, and years are collectively incommensurate, which is to say that there is no way to relate them such that all of their relationships all work out to be whole numbers.
A year of 365 days can only be divided evenly by 5 into 73 weeks, but 73—being a prime number—isn’t evenly divisible by anything but itself. Weeks of 5 days would allow 30-day months of 6 weeks, but there would be 12 months of 30 days, with 5 days “left over.”
As stated earlier, 7 days per week and 4 weeks per month gives 28 days per month, which, multiplied by 13 yields 364 days, but the length of a lunation is closer to 30 days than to 28, so such months don’t neatly line up with Moon phase cycles. (Throw all this back at the next "Intelligent Design" proponent who corners you!)
Two solutions have been implemented by various cultures in the past to handle this time-keeping incommensurability: intercalary periods (of days/weeks/months) and epagomenal periods (of days/weeks/months).
Intercalary periods are spans added to existing periods in the calendar to make the civil calendar remain synchronized with the seasons. In the Gregorian calendar, the 29th day of February in leap years is an intercalary day, because it is affixed to an existing month and considered to be fully part of that month for that year.
The Hebrew calendar, being luni-solar and consisting of 12 months alternating between 29 and 30 days, has to intercalate an additional lunar month periodically to remain synchronized.
Similar to the Gregorian calendar, the Islamic calendar intercalates a day on the last month of the year periodically.
Epagomenal periods are spans of time observed in order to synchronize the civil calendar with the seasons, but which are not considered to be added to any pre-existing period or grouping. The intercalary leap day in the Gregorian and Islamic calendars is not epagomenal because it is considered in both systems to be a part of the month to which it is attached. Likewise, the intercalary month added in the Hebrew calendar is not epagomenal because it is considered to be a fundamental part of the year to which it is attached.
Epagomenal periods, then, are defined as standing apart from any other defined timespan. The ancient Egyptians, as mentioned above, had 12 months of 30 days each, as well as 5 epagomenal days, which were not part of any month or year, but were seen as a timespan completely independent of the year or any month. Epagomenal periods also have the distinction of occurring regularly, not intermittently as intercalary periods do. These may seem like trivial distinctions, but the subtle implications for social custom are intriguing: perhaps those born during intercalary or epagomenal periods are seen as somehow gifted? Or, perhaps, cursed?
Subdivisions Of The Day
It was in Sumeria that the circle was first divided into 360 equal parts, because they, like the Egyptians, used a 360-day year comprising 12 months of 30 days each (they also counted in sexagesimal, or base-60). Also, the Earth turns through one complete circle each day, and if that circle is divided into 30 equal parts, there are 24 of those parts, which corresponds to the round-number of hours in a day. (Here, again, they could have divided those 360 degrees into 36 equal parts, of which there would be 20, but they didn't....)
It was probably in Babylonia, where they had borrowed the sexagesimal (base-60) counting system of the Sumerians, that the hour was further divided into 60 minutes and each minute further divided into 60 seconds .
- The Metonic Cycle
- The Calippic Cycle
- The Hipparchic Cycle
The Metonic Cycle
In 432 BCE Meton of Athens revealed that he had discovered that 19 tropical years equate to very nearly 235 lunar months. Mathematically:
In the Metonic cycle, an extra month is added in years 3, 6, 8, 11, 14, 17, and 19 of the cycle, and this cycle was used in the European Middle Ages in the computation of the correct date of Easter.
The Calippic Cycle
Calippus, in 330 BCE, 102 years after Meton, proposed a modification to the cycle to make it more accurate. He computed that 76 tropical years is quite close to 940 lunations (lunar months), with the result that Calippus' year is precisely 365.25 days long. This cycle, named for him, has an error of 1 day per 553 years, so it is actually less accurate than Meton's cycle.
The Hipparchic Cycle
Hipparchus, some time around 141 BCE, proposed a correction to the Calippic Cycle by making a 1-day correction every 4 Calippic Cycles, which makes:
It is also the case that 11 tropical years are approximately equal to 136 lunations, and through appropriate combininations of 11-year and 19-year cycles, more and more accurate cycles can be generated. For instance:
Keep these kinds of harmonies in mind. In the next blog, I will discuss possible ways that intelligent beings on other planets might mark and record time, and these kinds of harmonic cycles are likely to appear for Worldbuilt worlds, depending on whether those worlds have a moon (or moons), are part of a double-planet system or a Lagrangian-pair or -triple, etc.
5. en.wikipedia.org/wiki/Maya_calendar - Tzolk.27in
6. en.wikipedia.org/wiki/Week - History
8. There may also have been some relationship to human menstruation cycles. This does not have to have been a scientific relationship; for human culture, a perceived relationship is all that is necessary for complex social rituals to come into being. See https://www.athenainstitute.com/lunarmpl.html
12. en.wikipedia.org/wiki/Month - Types_of_months_in_astronomy
13. en.wikipedia.org/wiki/Month - Types_of_months_in_astronomy
16. en.wikipedia.org/wiki/Southern_Hemisphere - Climate
17. en.wikipedia.org/wiki/Tropical_year - Time_scales