Geocalendar: a system of date and time closer to nature

This essay describes a geocalendar, an Earth based lunisolar calendar with decimal time, designed to help being closer to nature.

1. Notation

Its units are the year, month, day, centiday, and dimiday. A date is represented by a series of two digits for each unit separated by colons:

YY:MM:DD:CC:BB (LAT, LON)

Every date should be accompanied by a set of geographic coordinates.

2. Example

84:03:03:71:59 (48.5136, -2.7653)

This example can be read as 84 years, 3 months, 3 days, 71 centidays, and 54 dimidays since the beginning of this calendar.

The notation can be split in two parts: this first one representing the date of a day, 14:03:03 in the example, and the second one, 71:51, the time.

3. Lunisolar calendar

This section describes the units representing the date of a day in the calendar.

3.1. Day

At the moment most human beings still live on the surface of Earth, the third planet orbiting the Sun.

In space, or any environments disconnected from the natural cycles of our planet, it could be easier to use only one unit of time. The Metric time, for example, uses only the second and its multiples like the kilosecond or the megasecond to measure longer stretches of time. But on Earth we can use a few simple astronomical observations, like the movement of the Sun, to help us mark the passage of time.

At any latitude outside of the polar circles, the Sun rises and sets periodically in the sky, alternating between a period of brightness when it is visible above the horizon and darkness otherwise. The Sun will reach its highest point in the sky at noon and its lowest point, usually below the horizon, at midnight. This phenomenon, caused by the rotation of the Earth on its axis, give us the day, the main unit of the geographic calendar.

Human beings, like many other animals, adapted to those conditions by sleeping during the period of darkness and by being more active during the day. This long resting time during the night give us the impression of starting a new cycle every morning when we wake up and regain consciousness. The change to a new day should therefor occurs at or before our awaking. But the moment we wake up is subject to variations, as is the sunrise, so a more regular time to mark the beginning of the day is midnight: when the Sun is at its lowest point below the horizon, or when our position on Earth is at the most opposite side from the Sun.

The mean solar day is defined by the yearly average interval of time between two midnights during one orbit of the Earth around the Sun, it is about 86,400 seconds.

In day to day observation, the apparent duration of a day may differ by as much as 30 seconds compared to the mean solar day because the orbit of the Earth is not exactly circular. But when this calendar refers to the duration of a day, it should be understood as a mean solar day.

It should also be noted that the start of a day is a local phenomenon, midnight is always related to the longitudinal position of the observer. Using time zones would mean introducing inaccuracies in the calendar, so every date should be accompanied by a set of geographical coordinates instead.

To perform time comparisons between different locations we should therefor revert to a universal time system.

3.2. Month

The Earth has a natural satellite orbiting 1.25 light seconds away, the Moon, that is almost a third of its size. Its apparent diameter in the sky varies slightly depending on its elliptic orbit, but it is, by coincidence, approximately the same as the Sun.

The Moon is tidally locked to Earth, so it always shows the same face in the sky, but its illumination varies during the course of its orbit around the Earth.

In the geographic calendar, a month starts on the day when the new moon takes place, that is when the Moon is closest to the Sun and the darkest in the sky.

A month can be further divided into four weeks.

The first week occurs during the waxing crescent until the right half of the satellite is illuminated by the Sun at the first quarter moon in the northern hemisphere. In the southern hemisphere it is the left half that will appear illuminated. At this time the Moon is visible during the afternoon.

The second week takes place during the waxing gibbous until the full moon is visible during the night.

It is followed by the waning gibbous during the third week until the last quarter moon, visible during the morning. This time it is the left side that is illuminated in the northern hemisphere, and the right side in the southern one.

Finally comes the fourth and last week during the waning crescent until the next new moon marking the beginning of the next month.

It takes 27.32 solar days for the Moon to orbit the Earth during a sidereal month. But because the Earth moves on its orbit around the Sun at the same time, the duration between two new moons, called a synodic month, is approximately equal to 29.53 days. Therefor some months, known as the full months, will be 30 days long, while others, the hollow months, will only last 29 days.

3.3. Year

A solar year is defined by the duration of one orbit of the Earth around the Sun, or about 365.24 days on average.

The Earth’s axe of rotation is tilted, which means that during half of the year the northern hemisphere will progressively get longer nights than the southern hemisphere, with more dramatic changes at higher latitudes near the north pole where the Sun never rises in the sky for a few months.

At temperate latitudes, the Sun reaches the highest elevation in the sky at the summer solstice and the lowest at the winter solstice. The day of the summer solstice is the longest day of the year, and the day of the winter solstice is the shortest day.

This variation in sunlight gives the Earth its seasons. This cycle is the reason why the geographic calendar is a lunisolar calendar instead of a simpler lunar calendar.

The number of months elapsed since the beginning of the calendar year is tracked by a counter reset to zero every new year.

A new calendar year begins on the day of the first new moon, which fall on or after the day of the winter solstice in the northern hemisphere.

There is a symmetry between the day starting at midnight and the year beginning on the darkest night of the new moon after the longest night of the winter solstice. Though this is true only in the northern hemisphere as it is summer during this time in the southern hemisphere.

One imperfection of this system is the absence of relations between the orbit of the Earth around the Sun and the Moon around the Earth. The solstice almost never occurs the day of a new moon, so an intercalary month is needed. Some calendar years will be 12 months long, while others with an intercalary month will be 13 months long.

This calendar is also less regular than some systems because it uses astronomical observations or computations to avoid the approximations of more regular calendars based on algorithms like the Metonic cycle of 19 years, which is a common multiple of the solar year and the synodic lunar month.

3.4. Century

One additional unit, the century or hectoyear, is available to keep the year on two digits. A century is 100 years. It can be omitted and deduced from context easily.

4. Decimal time

Shorter units than the day are required to mark the passage of time. This calendar uses decimal time represented by a fraction of the day to keep it as simple as possible.

4.1. Centiday

A hundredth of a day, or centiday, has been chosen over a ten or a thousandth of a day to provide enough discrete time intervals for precise precise time measurements while minimizing communication time. “Forty two centidays” is much faster to say than “four hundred and two millidays”. And it keeps all units in groups of two digits.

A centiday is an hundredth of a day, or one percent of a day. It is equivalent to the minute of the French Revolutionary Time and the Chinese unit “ke”.

In the metric system, a mean solar day is 86,400 seconds long, so the duration of a centiday is equal to 864 seconds or 14.4 minutes.

A clock in centidays will show the time elapsed since the beginning of the day. For example, it will show 50 at local noon because it occurs 50 centidays or half a day after midnight.

4.2. Dimiday

Shorter units of time would be useful for more precise measurements so we can divide the day again to get a hundredth of a centiday (8.64 seconds) or a even a thousandth (0.864 seconds).

Those short durations can be associated to physiological phenomenon of adult humans. The former is slightly lower than the normal respiration rate at rest, so this unit of time could be called a breath. And the latter, in the range of a normal heart at rest, could be called a beat.

The former is preferred to keep using two digits per units and because the latter would be competing with the second used in the universal metric system.

The primary name of this unit is the dimiday, an obsolete metric prefix equivalent to decimilliday (or centicentiday). It is known as “fen” in some Chinese calendars.

5. Epoch

The day 00:00:00 of this calendar corresponds to 1900-01-01 of the Gregorian calendar, because on that day occurred the first new moon since the previous solstice. The year is somewhat arbitrarily chosen to make conversion between both calendar more convenient.

Another good candidate for the year zero of this calendar would have been the day of the first new moon since the solstice of December 1969, which occurred one week into the year of 1970, used by modern computers to mark the passage of time by counting the number of seconds elapsed since that event known as Unix epoch.

For instance the date used in the previous example, 84:03:03:71:59, would be translated to 449947500 for a computer, which is almost 450 megaseconds since Unix epoch.

Unix epoch is also quite close to the date a human first walked on the surface of the Moon, symbolizing the beginning of both the Computer Age and the Space Age.

One last interesting date is the day of the first new moon since the solstice of December 2014, which occurred while this calendar was being conceived.

00:00:00:00:00:00 // 1900-01-01 00:03:40 UTC ~ Gregorian Epoch
00:70:00:00:00:00 // 1970-01-07 00:06:20 UTC ~ Unix Epoch
01:14:00:00:00:00 // 2014-01-01 00:03:40 UTC