Version date 1998-08-02. Your comments and suggestions are welcome.

Seven Space Calendar

Contents

Short Characteristic
Desirable Qualities
Year and Day Lengths
Smaller Self-Similar Segments
Time and Date
Longer Periods
The Circalunar Period
Drawbacks
Start Date
Individual Calendar Switching
Possible Improvement During Transition
Number Curiosity

Tables (121 kB)
Correlation with Gregorian date
Loon Phases

Short Characteristic

The Seven Space calendar is an example of a fractal calendar: all periods are self-similar, because each is made of seven parts of equal length. The seven-day week is the central element of this calendar, although the week used here is about 6.5 % longer than a week on Earth.

Desirable Qualities

The Seven Space calendar is primarily inteded as a calendar to be used by people in space. Therefore people's body rhythms are the appropriate reference system. Since humans evolved on Earth, the relevant periods are much like those on Earth. The following qualities are desirable:

Year and Day Lengths

A space year (called "yea") should be as long as an Earth year, but have longer days. A yea is defined to have 343 space days (called "dayes", pronounced "da-ees") of about 25.5563 common (Earth) hours. This ensures the synchronization with the tropical year;
24 * 365.24219 = 25.55630484 * 343

There are no leap years like in the Gregorian calendar. Therefore, in three of four years, the yea starts on Earth' New Year's Eve (see below).

Smaller Self-Similar Segments

The self-similarity is based on the division of each period into seven parts of equal length. The period division applies on all scales. Here are the names of the most common periods:

The yea of 343 dayes divides into seven "monts" (space months) of 49 dayes, each with seven weeks of seven dayes. The monts are named Moon, Mars, Mercury, Jupiter, Venus, Saturn, and Sun, in similarity to the week.

Each daye is divided into seven "hours" (singular, size XL :-) of 3.65100 Earth hours (about 03:39:03 in common hours:minutes:seconds notation). Starting at midnight, this yields:

Each hours is divided into seven "hafs" of about 31 minutes and 17 seconds (pronounced "halfs", about half a common hour). Hafs are numbered one to seven.
Each haf has seven "septs" (pronounced "sets") of about 4 minutes and 28 seconds. Septs are numbered one to seven.
Each sept consists of seven "moves" of approximately 38 seconds. Moves are numbered one to seven.
Each move breaks into seven "breaths" of approximately 5 seconds. Breaths are numbered one to seven.
Each breath is made of seven "tiks" of approximately 0.8 seconds. Tiks are numbered one to seven.
Each tik is made of seven "moments" of approximately 0.1 seconds. Moments are numbered one to seven.

Time and Date

An appointment in the morning at 09:14:00 common hours might read
morning hours, 4th haf, 5th sept, 7th move
or alternatively
3.4.5.7.
It is easily seen that this time is in the middle (4th haf) of the morning hours, and in the late middle at that (just before the 6th sept).

Ship time runs from 1.1.1.1. to 7.7.7.7. (or 7.7.7.7.7.7.7. to be exact :-)

The smaller periods (septs, moves, breaths, tiks, moments) are only of value for purists of the seven. They will probably not be used, because the historic hour:minute:second system is ever-present in astronomical timekeeping. But the hours and hafs might prove useful for shift assignments, planning of activities, mealtimes etc since they tie in with the physiological rhythms of the human body. A typical attention span is about 3 hafs (movie length); two of those, together with two pauses of half a haf make an hours.

However, once people get to like to the seven-system, the next generation of space-borns might extend it to shorter time periods. Since computers can accommodate for every time-system this might not prove that inconvenient.

The Seven Space date consists of weekday, week number, and mont. The yea starts on Monday, 1 Moon and ends on Sunday, 49 Sun (see 121kB perpetual Seven Space calendar).

Dates can be written in long form or short form. For instance, the long date plus time "Tuesday, 3 Moon, morning hours, 4th haf, 5th sept, 7th move" is written in short form as #1#3#2, 3.4.5.7. Note the order reversal: mont, week, daye.

The yea may be written at the end of the long date, e.g. "Tuesday, 3 Moon, 503" in yea 503. Those who like to "show the seven" may also write ~1~3~1~6 for the yea 503 (= 1*7^3 + 3*7^2 + 1*7^1 + 6*7^0). In short form, this date can be written ~1~3~1~6#1#3#2

Longer Periods

Longer periods are the yea week of 2401 = 7^4 dayes or 7 yea(r)s
the yea mont of 16807 = 7^5 dayes, (49 yeas, currently about half a lifetime)
the yea-yea of 117649 = 7^6 dayes (343 yeas, something like a cultural epoch), and
the yea-yea week of 823543 = 7^7 dayes (2401 yeas, about the lifetime of a human culture).

The Circalunar Period

The circalunar period in the Seven Space calendar is called "loon". There are exactly twelve loons in a yea, so that the loon phases fall on the same daye each yea. A loonation has exactly
343 / 12 = 28.53333... dayes or
365.24219 / 12 = 30.4368... common days, within a day of 29.53 days, the lunar synodic month).

There are nice mnemonics for the daye and hours when the loon phases occur (see 121kB loonations table).

Drawbacks

These drawbacks will especially be felt by people who travel often between space and Earth. For the circadian rhythm, this is already the case today for intercontinental plane trips ("jet lag"). The circannual rhythm is conserved and the broken circalunar rhythm is deemed not that important. The biggest problem could be the different weekdays. At present, Earth's weekend behaviour (e.g. stop of stock trade, change in tv programmes) is significantly different from "normal" weekdays. If space is sufficiently colonized and gets important enough economically, this could result in the end of the "quiet weekend" - at least for those in space business.

Start Date

The start date of the Seven Space calendar will be on 00:00:00 of some January 1st. Yea 1 willl possibly be the lauch year of a space vehicle or some other significant year for space travel. Since the yea is exactly synchronized with the tropical year, an arbitrary year can be chosen in principle. I suggest to choose an Earth year that starts with a Sunday (or Monday), because this is the historical start day of the week. Suitable years are (start weekday) 2001(Monday), 2006(Sunday), 2007(Monday), 2012(Sunday) etc.

2001-01-01 is chosen for the 121kB perpetual Seven Space calendar; the yea starts on Monday, week 1. This is best because the current ISO norm has the week start on Monday and the yea count is Earth (Gregorian) year minus 2000 on most days.

Since 2001 is no leap year, yea 2 starts about 06:00 on 2002-01-01, yea 3 about 12:00 on 2003-01-01, and yea 4 about 18:00 on 2004-01-01. Yea 5 starts "correctly" at about 00:00 on 2005-01-01 , since 2004 is a leap year.

Individual Calendar Switching

People switching to the Seven Space calendar on the start date will not "lose a weekday", although weeks will diverge after that. People wishing to keep their personal week when switching to space count can only switch on certain dates.

Because 7 dayes are circa 7.4539222 days, the phase shift for the Earth week is 0.4539222 days per week. To switch from Earth week to space week one has to wait
6 / 0.4539222 = 13.218123 days at most.

Because 7 days are circa 6.573720 dayes, the phase shift for the space weekdaye is
7 - 6.573720 = 0.426280 dayes per daye. To switch from space week to Earth week one has to wait
6 / 0.426280 = 14.075266 dayes at most.

For possible switching day(e)s during the yea(r) see the (121kB !) perpetual Seven Space calendar

Possible Improvement During Transition

To keep Gregorian and Seven Space calendars synchronized, occasional leap seconds may eventually be necessary, because Seven Space is based on the current length of the tropical year.

Since the tropical year varies with time, it is useful to tie the yea and year fully together, so that New Year's Day always starts on the same second in both calendars. This would make the daye in leap years by a factor 366/365 longer than the daye in normal years.

The daye in leap years then has (366 / 343) * 24 = ca. 25.60933 Earth hours,
and in normal years (365 / 343) * 24 = ca. 25.539359 Earth hours; a difference of only 0.273973 %.

Probably this will be seen as too Earth-centered by the space dwellers and therefore be done away with as soon as Earth loses its dominance.

The astronomical time system with a year of 366.24219 mean sidereal days is useful for terrestrial astronomers but not for the Seven Space calendar.

Number Curiosity

By the way, the sum of the synodic periods of Jupiter (398.9 days) and Saturn (378.1 days) - the two most massive planets in the solar system - is 777.0 days.


Fractal Calendars

Other Calendrics at this site.

Essays on mathematical themes.


© Copyright 1998, Mario Hilgemeier, email: contact
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