Calendar Technology

I don’t know about you, but I don’t normally think of Calendars as a technological innovation; they’re just things to hang on walls and write appointments into. However, this is the time of year to replace our calendars, and a time of year that is replete with holidays, many of them determined by calendars that are not our usual day-to-day Gregorian calender, such as Hanukkah. As I unpacked calenders which were Christmas gifts, hanging them on my wall or placing them on my desk, it struck me that our common way of measuring days and time is an artificial technological structure, superimposed on the passage of time in order to measure and delineate it. I started to wonder how it is that we have decided to measure time, and what other alternate methods there might be to do this.


First of all, what do we mean by calender? A simple definition is an indexing system for large spans of time, which allows us to measure, order, predict, and compare events and smaller spans of time. There have been many such systems created throughout human history whose origins are rooted in history, commerce, religion, and even politics. However, if we examine the multitude of available calendar system, we can abstract common features and design choices made by the calendars’ authors.

Attributes of Calendar systems

Common Basics of calendar systems

Every Calendar system must have a few basic attributes to be able to measure the passage of time. These are:

Epoch: This is the beginning point of reference; zero on the scale. Calendar authors usually choose some significant, or easily remembered, event to start measuring time from, like Jan 1 1 Anno Domini, Sept 22 1792, or Jan 1 1970.

Unit: Every calendar measures time. Therefore there must be a basic unit of measurement. Most calendars use some measurable physical phenomenon, such astronomical cycles or atomic resonance frequencies.

Most calendar systems are based on the day, although this causes some difficulty: there is more than one kind of day. A solar day is the period between times where the sun occupies a given position in the sky, usually the meridian. However, the Earth’s daily movement through it’s orbit around the sun makes this different from the sidereal day, which is the time it takes the Earth to rotate once on its axis. Solar days tend to vary in length, periodically over a year, due to the inclination of the Earth’s axis, and the eccentricity of the Earth’s orbit. Sidereal days also change in length due to changes in the Earth’s rotational period as a result of gravitational interactions between the Earth and the Moon, although this is much more subtle and slow phenomenon (sidereal days lengthen by about 15 microseconds/year).

Means of measurement: This is an almost trivially obvious aspect, but some means of measuring the passage of time from the Epoch must be included in the system. In calendars based on days (of whichever type), a complex process called counting is used.

Calendar system “design choices”

In addition to these basic common requirements, a Calendar system can have many other features. Designers of a calendar system must make several “design choices” when authoring their calendar.

Complete v.s. Partial

While we are used to complete calendars that measure the whole span of time, this need not always be true. It is possible to have a partial calendar system where spans of time fall outside the system, and cannot be referenced with any accuracy by the calendar. The Romans, for example, are reputed to originally not had any internal calendar divisions for the winter period. This makes sense if one views the Roman calendar as an aid to the timing of agricultural (and possible military) activities; in the winter months agriculture (and military campaigning) was not possible, and thus there was no need to keep detailed track of time during winter. A more modern equivalent of a partial calendar would be the idea of a “school year”, in which the “summer holidays” and “term breaks” fall outside the measured and scheduled calendar system.

Observational v.s. Theoretical

Historically, most calendars have been observational, that is, they are based on the observation of periodic events. Usually these events are astronomical, such as the movement of the Sun (solar calendars), the Moon (lunar calendars), other astronomical bodies such as Venus (the Mayan calendar and some Ancient Egyptian calendars incorporated Venusian cycles into their calendar system), or even the combined cycles of more than one astronomical body (lunisolar calendars attempt to reconcile both solar and lunar cycles).

A theoretical, rules-based or arithmetical calendar is one in which the passage of time is accounted solely by the number of basic units passed i.e. the relation of smaller units to larger is fixed and unvarying. For example we might arbitrarily decide that 10 sidereal days make up a week, 3 weeks make up month, and 12 month make up a year, and ignore any natural cycles. This is a perfectly valid calendar system. While theoretical calendars might seem more “reasonable” approach to many, theoretical calendars tend to “drift” with regards to observable periodic natural phenomenon such as seasons and orbits which tend to have some natural variability.

A mixed calendar approach is one in which the basis of the calender is theoretical, but in which occasional intercalary units of time (leap day, leap week, leap second) are introduced into the calendar to realign it with an observable natural cycle.

Cyclical v.s. Linear

Since most Calendars are based on observable periodic natural phenomenon, most calendars incorporate periodic grouping elements of their basic units of time: weeks, months, seasons, years, decades, and even Regnal groupings.

Not all calendar systems do this however. Computational models of time, such as Unix time, are linear, simply keeping a count of the number of basic time units since their Epoch. The family of calender systems based on the Julian Day system, proposed in 1583, are also linear calendars.

Perpetual v.s. Multimorphic

A perpetual calendar is one in which the relation of the various internal divisions and cycles is constant with regards to one another, while a multimorphic (many forms) calendar can have variable internal structure. For example, a perpetual calendar that used months and weekdays might have January 1st always fall on a Sunday, while the day of the week for January 1st would change from year to year in a multimorphic calendar.

Obviously only calendars with subdivisions (years, months, weeks, days, etc.) can be multimorphic (linear calendars cannot be), and it is the fact that these internal subdivisions of calendars are often not regular (such as months, which can have a variable number of days in the Gregorian calendar), or not an integer fraction of a larger division (the cycle of weekdays is 7 days long. Neither the number of days in the year, nor the number of days in most months, is divisible by seven in the Gregorian calendar) that make a calendar multimorphic. However, perpetual calendars with cyclical internal subdivisions do exist.

The modern Gregorian Calendar

The calendar that most people are familiar with is the Gregorian calender. It is the modern de facto international standard calendar; most countries maintain dates in Gregorian, even if only in parallel with other regional calendars.

It is a refinement of the earlier Julian calendar, created by Aloysius Lilius in the 1580s, and was decreed by Pope Gregory XIII on February 24th, 1582.

So how does the modern Gregorian stack up when compared to all the basic attributes and design choices we’ve seen?

Epoch: January 1, 1 Anno Domini.
Unit: Solar Day.
Measurement: Count of days since Epoch.
Attributes: Complete; Mixed basis (theoretical with intercalary leap days to realign the year with seasonal variations); Linear over years, with cyclical subdivisions (weeks, months); Multimorphic, with 14 different forms.

Alternate Calendars

Despite the fact that the Gregorian is the unofficial international standard, there are a number of other calenders in use today, usually for religious purposes, but in some cases for political ones.

These include:

  • Indian national calendar: A variation on the Gregorian, which keeps pace with the Gregorian calendar, but which has a different Epoch and a different internal structure.
  • The Iranian, Persian, or Jala-li Calendar: An observational solar calendar based on astronomical observations made in Tehran and Kabul. It has different a different Epoch, basis, and internal structure than the Gregorian.
  • Hebrew calendar: a complex rules-based lunisolar calendar. It’s Epoch is October 7, 3761 BC. It’s structure is complex, vastly different from the Gregorian, and highly multimorphic. It introduces intercalary leap months seven of every 19 years, creating an overall repeating cycle of 235 lunar months. The Hebrew calendar is mostly maintained for Jewish religious purposes
  • Bahá’í calendar: a solar calendar with regular years of 365 days, and leap years of 366 days. Years are composed of 19 months of 19 days each, plus extra intercalary days (4 in regular and 5 in leap years). Years in the calendar begin at the vernal equinox, with 21 March, AD 1844 being the calendar’s Epoch.
  • Islamic calendar: a lunar calendar having 12 lunar months in a year of about 354 days. A lunar year is about 11 days shorter than the solar year, so Islamic dates usually shift 11 days earlier each successive year of the Gregorian calendar. It is used by Muslims to determine times of religious observances, and as the official calendar of many Muslim countries.
  • The traditional Chinese calendar, or the “agricultural calendar” (農曆 nónglì, 农历), is still maintained in the People’s Republic of China alongside the “Western calendar” (西曆 xīlì, 西历) which is Gregorian. The traditional calendar is an ancient traditional lunisolar calendar with a highly complex internal structure relating to Chinese mythology, metaphysics, and astrology. It is used mostly to determine the times of traditional Chinese festival days and for purposes of Chinese astrology.
  • The Fiscal Year: Lest you start thinking that all alternate calendars in use are ancient, or religious in nature, consider the fiscal calendar. Fiscal calendars, while based on the Gregorian, are not Gregorian. They have different starting and ending dates, and have an alternate system of internal divisions, and in some cases the length of the fiscal year is different than that of the calendar year. About 35% of corporations in the United States use an alternate fiscal calendar to regulate their business year.

Ancient calendars

Since most calendars are based on astronomical observation, and that such observations can be made with the naked eye, a civilization can keep observational records and thus create a calendar as soon as it creates a system of writing.

For this reason, many human cultures have created many calendar systems of varying accuracy and design, most of which are not used in any form today. Those with an interest in ancient civilizations, ancient astronomy, and ancient timekeeping, are encouraged to read more about some of the calendar systems listed below.

Calendar reform, and theoretical calendars

So all these alternate calendar systems are remnants from ancient cultures, and elements of religions, right? The Gregorian is the final word in caldendar systems and has finally been perfected. Everyone is happy with our modern calendar, right?

Well, no.

Calendar reforms are being proposed all the time, and a mutlitude of theoretical calendar systems exist (that is perfectly functional calendar systems someone has designed, but few – if any – people are using). Most alternate calendars have been proposed because the designers prefer different design choices from the list above than the creators of the Gregorian calendar did. A few created alternate calendars for political reasons, and some authors of science-fiction and fantasy literature have created fictional calendars for their fictional worlds.

Some of these proposed reformed calendars are:

Perpetual Calendar Variants

Lunisolar calendar variants

Fictional calendar systems

Politically motivated calendar variants

So, when you hang your calendars on your wall this year, try and be aware that the system you use isn’t the only one possible, nor the only one being used. Perhaps you might find it fun or interesting to keep more than one kind of calendar on the go.

As for me, I’m going to go check my appointment book and see if I have anything planned for February 34th.

Happy new year everyone – regardless of when that might be for you.

External Links / Further Reading

  • Calendar Converter: A javascript calculator to convert dates between a multitude of alternate calendar formats, including Mayan, Julian, Julian Day, Islamic, Persian, and many others.
  • List of calendars: A more comprehensive index of calendar systems at Wikipedia than are presented here.


One Response to Calendar Technology

  1. memorandumb says:

    If you’re interested in calendars, also check out, Calendar:: Humanity’s Epic Struggle To Determine A True And Accurate Year. Great book.

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