Motives for a dynamic calendar

Today, the calendar of main international use is the Gregorian calendar. Due to historical and religious reasons, this calendar is centered on the Western culture. The year numbering results from the estimate of Jesus Christ birth date; months names and lengths originate from the Roman Empire.

Moreover, it is a solar calendar, whereas many cultures attach importance to lunar cycles. One thinks of the Muslims (whose calendar is purely lunar), but this also holds for the Chinese (lunisolar calendar), and even the Christians (computus - i.e. calculation of the date of Easter).

The three main units of time which are year, month and day are not stable intervals, with their durations evolving in both the short-term (days do not have the same duration at the equinoxes and solstices) and the long-term (the Earth rotates more slowly on itself, but faster around the Sun, the Moon rotates slower around the Earth, etc).

Therefore, there is no reason for these durations to agree in "simple" proportions, such as a rational. The main calendars are doing their best to maintain a semblance of harmony between these three units (or between two of them in the case of the Gregorian calendar), sometimes with an amazing accuracy (e.g. the Persian calendar) but always with this same approach: rationalize irrational ratios.

Certainly we can do that well, it's even a very old and interesting problem whose optimal solutions are Diophantine approximations. But personally, in our context it makes me think of a brute desperately trying to fit a square inside a triangle in one of those kindergarten games.

The objective of this calendar was to see if it was possible to design a calendar correcting the above-mentioned defects, for fun.

Construction

Continuous time scale

International Epoch (or Époque Internationale, EI)

The epoch of our calendar is the 1977-01-01 00:00:00 TAI in the Gregorian calendar.

Why this choice ? For it is from this moment that the relativistic corrections were applied to realize the International Atomic Time (TAI), the same one that serves as an international reference for calculating the Coordinated Universal Time (UTC), from which are defined the legal hours in most countries (if not all?).

It is a technical event, decided by international bodies, whose consequences concerned all states, and therefore culturally neutral. Moreover, it has already been used by the International Astronomical Union (IAU) to define coordinate-time scales.

International Time (or Temps International, TI)

The international time (TI) is a coordinate-time scale realizing terrestrial time (TT) as defined by the IAU, but the zero is the international time.

To popularize, TI is the number of seconds (SI) that separate an event of the international epoch. Similar to what posix / unix time does but with a different epoch, and counting leap seconds.

Thereafter, the durations and the TI will be noted in kiloseconds (ks), unless otherwise specified. It will not use the minutes and hours, but we recall that one kiloseconde takes about fifteen minutes.

Astronomical time scales

Year

There is a change of year at each winter solstice. The exact moment of the year to change is the closest instant of the solstice where the TI takes an integer value (in kiloseconds).

Year 1 begins with the first winter solstice after EI.

Month

There is a change of month at every new moon. The exact moment of the month to change is the closest instant of the new moon where TI takes an integer value (in kiloseconds).

Month 1 begins with the first new moon after the change of year.

Day

A day is exactly the closest time of solar noon at the international reference meridian where TI takes an integer value (in hundreds of seconds).

Day 1 takes place at the first international solar noon reference meridian after the change of month.

Time zones

International date

An international date is a year-month-day triplet which conforms to the above-described rules.

Note that by definition, all people live all the time in the same month and year. The changes are simultaneous for everyone.

Note also that one day, unlike a month or a year, is not defined as a time interval, but as a precise moment. This is not a radical semantic change but just another way of presenting things, that will be more convenient to understand the following.

Thus, in our current Gregorian calendar, the 6th June 2016 can be understood as the time interval between the 2016-06-06 at 00:00:00 (UTC) included and the 2016-06-07 00:00:00 (UTC) excluded. Possibly for a legal interpretation, we can replace UTC by another time zone (for instance, UTC+1 is the legal time in the UK in the summer), but this does not change the perception of the day as the interval.

Another way to define the 6th June 2016 would be to see it as the precise moment 2016-06-06 00:00:00 (UTC). Therefore, the time (e.g. 13:00) is no longer seen as a position in the previous interval (13 / 24th), but as a distance of "13 hours from 2016-06-06 to 00 00: 00 (UTC)."

An international date therefore represents a subepoch from which we can count the seconds (or kiloseconds in our case).

DI time zone

Using our new point of view, one can reduce the time zone UTC at all times "midnight UTC", as expressing the time of an event in this time zone is equivalent to express the time between the said event and a "midnight UTC". The element "midnight UTC" selected is exactly the one represented by the date (year-month-day) in the Gregorian calendar.

It is by taking this idea that we will use DI to note a time zone (built on all days as defined above), and by extension DI+n for other time zones.

Attention: when writing UTC+n, n is an integer of hours; when writing DI+n, n is an integer of kiloseconds.

Legal time

From States decisions

Each sovereign state decides which time zone(s) DI+n will apply on its territory.

to individual decisions

In our current system, the party animal who folds a Saturday at 5 in the morning yet has the impression to bed late on a Friday night.

Conversely, the baker who gets up that Saturday at 4 to work has a good feeling to get up on a Saturday.

The perception of the current date is personal, because it depends on our lifestyles.

The objective of the dynamical calendar is to formalize this by allowing the use of a date (Friday, 2016-06-03 for example) or another (Saturday 2016-06-04). Going back to our example and using our current system, this would mean that the party animal can say that it went to bed on 2016-06-03 at 29:00, when our baker rose on 2016-06-04 at 04:00.

Though the above definitions do not impose a start and an end of validity to the use of a date, each State may decide otherwise for obvious practical reasons.

Use

Standard datetime format

A timestamp is written YYYY-MM-DD+TZ kk,k, where:

- YYYY is the year;

- MM is the month;

- DD the day;

- YYYY-MM-DD is an international date;

- + is a constant sign for all timestamps;

- TZ denotes the time zone;

- kk,k the number of kiloseconds that have elapsed since the subepoch YYYY-MM-DD+TZ.

One can notice this notation is very close to ISO 8601, which inspired it. The main difference being that the time zone is indicated after the date and not at the end, in order to fully define the subepoch before indicating the hour.

Whenever this is necessary (for years, time zones, hours, or even very rare day), we use the Q notation.

Birthdays

Age is an important quantity in most legal systems, used in particular to determine the rights and duties of an individual; hence the importance of determining birthdays.

The anniversary of a person is defined as the last day of the year for which the time:

TI(beginning of current year) + TI(birth of the subject) - TI(beginning of the subject birth year)

is written in positive time.