A Calendar Design by Peter Kokh 

This document supersedes the earlier version splityear_cal.htm which is no longer online.

first posted November 14, 1999 - last modified April 1, 2004

1999-200Lunar Reclamation Society


History
I did my first "Mars Calendar" in my youth. It called for 24 months of (4) 7-day weeks each, plus leap year arrangements.

When I became aware of Mars' Eccentric Seasonal Patterns, 192-180-146-150 days or sols, however, I became intrigued.

Could you devise a calendar that would reflect that, yet be rational?

It seemed to be a very difficult task.

 Feb 1994

[I do not know the roots of the discrepancy between these season lengths and those stated in the paragraph above.

 

I was very interested in the Shape that the Culture of the Mars Frontier would take.

The weather, climate, seasons would certainly be a major shaper of that culture, along with days just longer enough to induce constant mild jet lag, and the very much longer years; as would the thinness of the air, the dust storms, the one-sided color palette, the lack of open bodies of water and the seamless, shoreless land surface.

A calendar is not just a mathematical tool. It is a cultural institution, a bit of cultural infrastructure if you will.

I came to think that a calendar that did not just "note" the seasons, but "featured" them, even being organized around them, would be optimized to serve as a cornerstone of this fresh new human culture.

Then in 1993, when Bob Zubrin published his new Mars Calendar which threw month length regularity to the winds, and assigned three months to each of the widely differing seasons, I found his calendar radical yet extremely appealing as the sort of cultural mainstay I had envisioned. Zubrin's zodiacal months range in length from 46 to 66 days. In the summer of 1999, I published a series of friendly amendments (no longer online) that would go a long ways to address common objections to his calendar's various features.

Could there be another way, a way that paid homage both to the seasons and to the documented psychological preference for months of more nearly equal lengths?

Introducing a Hemisphere-neutral Season Name terminology:

The Seasons are introduced by Equinoxes (the Sun crosses the celestial equator and the days and nights are equal in length) and Solstices (the Sun reaches its northernmost, or southernmost position in the sky so that the difference in length between the days and nights is at its maximum.)

  • "Vernal" Equinox introduces Spring
  • "Autumnal" Equinox introduces Fall or Autumn)
  • "Summer" and "Winter" Solstices introduce those seasons.

The problem is that we traditionally name the equinoxes and solstices by the season that they introduce in the northern hemisphere. To people in the southern hemisphere, these chauvinisms makes no sense. Nor, for all its many-centuries long ingrained tradition, is it necessary.

Instead, we urge the adoption of new names for the equinoxes and solstices, and for the planet wide seasons that they introduce. It is time, as we set out to settle a brand new world, to leave these unnecessary chauvinisms behind.

  • Northward Equinox - introducing Spring (Latin Vernes) in the North, Autumn in the South - so we can call this planet wide season Vertum
  • Northern Solstice - introducing Summer in the North, Winter in the South - so we can call this planet wide season Sumwin
  • Southward Equinox - introducing Autumn in the North, Spring (Vernes) in the South - so we can call this planet wide season Tumver
  • Southern Solstice - introducing Winter in the North, Summer in the South - so we can call this planet wide season Winsum

Twenty four months, or twenty two?

Recently I came across Richard Weidner's calendar. He had noticed that the two shorter seasons approximated 5/22nds of a Mars year each, while the two longer seasons approximated 6/22nds of a Mars year each. By allowing the month lengths to range from 29 to 32 days, the same variation we have on Earth (28-31), he was able to produce a calendar in which the equinoxes and solstices introducing the various seasons always fell on the first of the first month assigned to the season in question. In other words, instead of giving each season its Earth-traditional quota of 3 months, he assigned five months to two of them, six to the other two, and came out with months very much more similar in length than Zubrin's, and very close in length to what we are familiar with on Earth. A year with twenty-two months? It does not seem the obvious choice at first. Ours has twelve; twice that is 24 with the same friendly multiply divisible feature. Yet Mars' year IS about 22 Earth months long!

Splitting the Mars Year into Halves, each 334 dates or sols long

I found that if we did not require all the equinoxes and solstices to fall on the first day of each "calendar season", but just one of them, e.g. the northward (vernal) equinox serving as an anchor, that you could cut the month length range from 4 to 3 (29, 30, 31, 32 to 29, 30, 31) and end up with two equal half years, allowing twice-a-year celebration of various religious litanies of observances, even personal birthdays and wedding anniversaries, if and as one so chose. Those who point out that their 16-month or 24-month calendars can also be cut in half, miss the point. I wanted two equal split years that put the seasons on front center stage, not just footnoted when they each started and ended.

Then in trying to see what would happen if you wanted to regularize further to 30 days, I came up with the concept of the "I-period", an "I"ntercallary "I"ntermission "I"nsert period that would bundle up all the leftover days outside of both the month sequence and the day of the week sequence. I found the idea intriguing.

The mantra of "perpetuality"

Finally, the discussion of perpetual calendars came up. A perpetual calendar is one in which any given date always falls on the same day of the week year after year. Some of our discussion group wanted to go for broke, and have the date/day match more frequent than yearly. Some wanted monthly "perpetuality". That takes a procrustean approach to calendar making. Procrustes was a mythological Greek king. The beds in his palace guest rooms were say five feet long. If the feet of his guests hung over the end of the bed, he had the overlapping portions summarily cut off. A "Procrustean Approach" has always been a pejorative expression, and it is in that spirit that I use it here. On the altar of this sudden new standard of exaggerated perpetuality, all other calendar features must suddenly pass the test of be sacrificed. If you wanted 22 months of 30 days, then you must have 10-day weeks, etc.

Well, maybe in your world.

But I decided to see what would happen if you compromised and had each calendar season, rather than each month, be an integral number of weeks. In the long ago proposed World Calendar (for Earth), each quarter had months of 31, 30, 30 days which comes out as 13 weeks on the money (that left one leftover day, two in leap years, to be handled as intercalary inserts between the regular sequence of the days of the week). In that system, you could reduce the calendar to 4 pages, 3 months each, and they all repeat in perpetuity.

The calendar outlined here is the happy result of this long brainstorming journey. The "calendar seasons" very closely fit the astronomical seasons off by no more than two days at end. Each calendar season has its five or six months total an integral number of weeks (21 or 26), plus the "I" Period in the longest season, Northern Vernes (Spring), Southern Autumnis, or in planet wide terms (free of northern hemisphere chauvinism), VerTum.

This calendar meets all my design goals and is presumptively my final effort (subject to details such as month names, I-Period day names/designations, etc.) Everyone has different perspectives, and many will think that it is sufficient for a calendar to "note" the seasons, that "featuring" them, giving them "top billing", is overdoing it, especially if it means compromising a march to the most mathematically simple and regular a division and subdivision of Mars 686.6 annual days as possible.

Those less interested in the cultural implications of a calendar, and more interested in unembellished utilitarian service, will not agree with my design goal priorities and dislike this calendar. That is their prerogative. But I hope that this will be one of the calendar options presented to the pro-Mars community. It is the culmination of an on and off effort spanning four decades.

 

Versions - This Calendar has 3 versions:

  • For each version a permanent physical calendar could be produced with four invariable pages, each one holding all the dates and days for a whole season.
  • The first version, immediately below, starts at Northern Solstice
  • The other two start 2 days before Southern Solstice
  • In all three versions, the start day is back-calculated from the Northward (Vernal) equinox which is, by design criterion, on the first day of the northern spring, southern autumn (VerTum) calendar page
  • The First Month of each Season Page starts on the first day of the week
  • The Last Month of each Season Page ends on the last day of the week

     


 

Key to these Graphics

  • The months are accurately 29, 30, 31 pixels wide, respectively
    • The darker gray line indicates the 1st day of each month
    • The number of days in each Season Page is given at the right, with the number in parentheses being the actual length of the Season represented.
  • The weeks are accurately 7 pixels wide
    • The darker blue line indicates the 1st day of each week
  • The I-Period (I for "Insert" or "Intermission") is neither a month nor a week
    • As indicated by the vertical match to both the month bar and week bar of VerTum
    • The vertical red line indicates the placement of the leap year day (#669)
    • The days of the I-Period would have their own names - they are an "insertion into" or an "intermission from" the weekday sequence, and the month sequence, both.
    • The I-Period is the Mechanic of the Perpetual Season Page Split Year Calendar by carrying the giant share of the burden of irregularity. The I-Period both takes up the difference in length between VerTum and Sumver and resets the sequence of the days of the week so that the calendar as a whole is perpetual.

 

About Our Design Goals:

  • Keeping pace with Mars' unequal Seasons - Our top priority
  • The seven-day week is preserved as the basis of work/rest rhythms
  • A neat split into two half years of a length more in tune with human experience of time. Such a requires less adjustment than one twice as long for religious and personal and other observances that we are used to having on a 365 day rhythm. These can now be celebrated twice a 668/9 Mars year, instead of just once.
  • Annual date/day of the week repetition - A Calendar with annual repetition as a minimum, more frequent repetition if possible. A calendar that repeats the date/day of the week lineup month after month would have require either (24) 28-day months or (19) 35 day months neither of which could be optimized to fit the flow of the seasons.
  • Seasonal Calendar Pages is an idea we have instead borrowed the idea of from the proposed World (Earth) Calendar. In that proposal, each "page", containing three months of 31, 30, and 30 days respectively, equaling 13 weeks exactly, is alike. There would be 2 intercalary days outside the weekday sequence to reset the calendar to repeat the following year.
    • In our plan, we have four different calendar page date/day of week lineups
    • These could be smoothed into just two identical sequences (VerTum & SumTer - the two longer 6 month pages; TumVer & WinSum - the two shorter 5 month pages), if we observed the same sequence of month lengths in each of both pairs.
    • There would seem to be no mnemonic benefit in doing this - unless we had as month names, simply Vertum I, Vertum II, Vertum III etc. - actually not a bad idea. Then the date/day of the week match would be identical for Vertum I-VI and SumTer I -VI, and they would similarly be the same for TumVer I-V and WinSum I-V, meaning only two seasonal date/day of the week sequences (one 182 days or 26 weeks long, the other 147 days or 21 weeks long) would need to be remembered
    • Using same direction month length sequences would muddy up the way the suggested month length sequence reflects Mars relative distance from the Sun in its eccentric orbit - of some real educational benefit, in our opinion.
    • We are presently inclined not to make this tradeoff.

 

Fit of calendar "Season Pages" to Equinoxes & Solstices

  • Northward Equinox occurs on the first day of VerTum (ideal)
  • Northern Solstice occurs on the first day of SumWin (ideal)
  • Southward Equinox occurs 2 days before the 1st of TumVer (off 2 days)
  • Southern Solstice occurs on the 2 days after the 1st of WinSum (off 2 days)
  • Average error 1 day - The reason for the slight discrepancy is our decision to make each Season Page an integral number of weeks long (I-Period excluded). The Season Pages "feature" or "showcase" the Seasons, rather than defining them.

 

Month Length in Days Varies Slightly and on Cue

  • 31 31 30 30 30 30 | 30 30 29 29 29 | | 29 29 29 30 30 | 30 30 30 30 31 31 = 22
    • This variation reflects Mars' distance from the Sun
    • 31 day months nearer aphelion
    • 29 day months nearer perihelion
  • Pattern: 2 of 31, 6 of 30, 6 of 29, 6 of 30, 2 of 31 = 22
  • Month length Summary: 4 a of 31, 12 of 30, 6 0f 29 = 22

 

Half Year Fit

  • SumWin & TumVer = 47 weeks exactly = 329 days
  • WinSum & VerTum = 47 weeks exactly = 329
    • That is, not counting the 10-11 day I-Week

 

Could we start at the Northward Equinox instead?
  • Not if you want to keep conveniently equal half year periods (one of our personal design goals)
    • You would end up with one "half" being, 364 days (not counting the I-Period), the other just 294 days)
  • But you could start with one season earlier than Northward Equinox, 2 days before Southern Solstice
    • i.e. with the WinSum Page
    • If you keep the I-period at the end of VerTum (near the onset of N Summer, S Winter) it would fall between the 2 half year periods. Plus, in this position, Mars is just coming off aphelion, its furthest distance from the Sun. To be closer to aphelion, it could be put between the 5th and 6th months of VerTum.

If you move the I-period to the start of VerTum (onset of N Spring, S Autumn), you still have 2 equal half years as the "I-period" is an "intermission" in the day count, as suggested.


 

INDEPENDENT ISSUES - not an integral part of the "Mars Pulse" Calendar

The following suggestions are not take-it-or-leave it parts of the above Calendar Schemes. Any of the above schemes can be adopted without adopting any of our suggestions below - and vice versa!

 

Week Day Names
  • The suffix "-day", is commonly replaced by "-sol" referring to the Sun has the problem that the "sol" is the generic name for the rotations of all bodies in the solar system. If we do not want to use -day because we reserve it for the Earth period, then we ought not to use the generic -sol for the Mars rotational period, as that would rob it of its useful generic currency. What we are trying to name is the period from local midnight to local midnight centered around sunrise-noon-sunset. So I suggest we use "-noon" as the suffix. It's familiar and instantly significant. (And it has that "Barsoomian" sound to it!)
  • Using our Sunday-Saturday names is inappropriate and awkward because their coordination with those days on Earth slips by a sizable fraction of an hour per day, "lapping" behind a day every 37 days. You can come up with other names based on celestial objects or any other set of seven names as you like. But
  • The seven notes of the diatonic musical scale, recycling on the octave, are an ideal model: do, re, mi, fa, so[l], la, ti, (do). Our Weekday names are then:
  • Donoon - Minoon - Renoon - Fanoon - Sonoon - Lanoon - Tinoon.
    The sequence is instantly clear and transparent and so easy to remember that you can sing it. The initial vowels keep their familiar Latin - Italian sonorous value (doh, ray, mee, fah, soh, lah, tee).

 

I-Period dates & day names
  • This period does several useful things
    • It smoothes out the irregularities of the seasons
    • It resets the weekday sequence
    • It absorbs the leap year day
    • It makes easier a pair of equal half-years for twice a long year celebrations.
  • As an "intermission" in the month and week sequence, it is prime cultural location for special planetwide holidays and as a time for retreat-rethinking-renewal-rededication.
  • The I-period is neither a week nor a month.
  • Thus it is not appropriate to have a distinction between dates and day names within this period
  • The period varies in length between 10 days and 11 days (leap years)
  • I have not prepared a date/day proposal.
  • This is a calendar innovation which might best be left to the pioneers to flesh out.

 

Month Name Options
  • 1. Simplest Idea: The Name of the Planetwide Season plus sequence place
    • VerTum I, II, III, IV, V, VI (Roman numerals)
    • SumWin I, II, III, IV, V, VI
    • TumVer I, II, III, IV, V
    • WinSum I, II, III, IV, V
    • You could substitute 1-6 (Arabic numerals) or A-F (letters)
    • This simple system has an advantage IF you decide not to sequence the variable month lengths to reflect Mars distance from the Sun (shorter 29 day months near perihelion, longer 31 day months near aphelion)
  • 2. Two Half Year sets of Eleven Months based on mnemonic A-K sequence plus root "-ber"
    • A'ber 1 - B'ber 1 - C'ber 1 - D'ber 1 - E'ber 1 - F'ber 1 - G'ber 1 -H'ber 1 - I'ber 1 - J'ber 1 - K' ber 1
    • A'ber 2 - B'ber 2 - C'ber 2 - D'ber 2 - E'ber 2 - F'ber 2 - G'ber 2 -H'ber 2 - I'ber 2 - J'ber 2 - K' ber 2
    • The day of the month would be given prior, European style; 12 D'ber 1, 23 B'ber 2 etc.
  • 3. Mirror Image Half Year sets - this proposal is more elaborate, with each month name beginning and ending with the opposite letters (A-K + K-A): i.e. AK, BJ, CI, DH, EG, FF, GE, HD, IC, JB, KA.
    • The names of the outbound leg half year are distinguished from those of the inbound leg by reversing the consonants of the root ber, the vowel e omitted: br and rb. This works well because r is a liquid, so the combination br and rb are pronounce with equal ease, there being a vowel both before and after. The choice of the first vowel is dictated by the sequence a-e-i-o-u being followed as far as it can restarting with the vowel of each month beginning with a vowel. Thus
      AK,
      Bej, CiI, DoH, EG, FiF, GoE, HuD, IC, JoB, KuA.
    • [As luck would have it, we have is following C which makes it soft and distinguishable phonetically from K. And also by luck we have o following G which makes it hard, as soft G would be pronounced like J.]
    • Next we add the root br (for the first set, rb for the second) and the opposite sequence of vowels. The result is two sets of month names. Those of the alternating set turn out to be exact mirror images of the first step in reverse order.
    • The sequence of names below would be the same regardless of the season with which we choose to start the year.

 

"br" series - outbound

"rb" series - inbound

Abruk

Arbuk

Bebroj

Berboj

Cibri

Cirbi

Dobrah

Dorbah

Ebrog

Erbog

Fibrif

Firbif

Gobre

Gorbe

Hubrod

Hurbod

Ibric

Irbic

Jobreb

Jorbeb

Kubra

Kurba

 

  • Note that the first letter is A to K in sequence, while the last letter is K to A in sequence
  • The first vowel sequence is AeioEiouIou, where the last letter sequence is uoiuoieoiea, the exact reverse order.
  • The first month outbound, Arbuk, is the phonetic opposite of the last month inbound, Kurba and so on.
  • The first name proposal (A'ber) is simpler and easier to remember, but needs a qualifying halfyear number.
  • The second name proposal (Arbuk) is more elegant and logical in that the names mirror one another in reverse sequence suggesting equivalent inbound and outbound positions as well as 1-11 sequence, and also by incorporating the distinction between outbound and inbound months in the labial/liquid [br] - liquid/labial [rb] reverse consonant root combinations. It will be harder to learn initially, but has these two advantages:
    • The names follow immediately from a few principles with no arbitrary additions, unlike Frans Blok's Rotterdam name set.
    • The names have an unearthly yet easily pronounceable ring to them, something that will lend them well to a distinctively Martian ambiance. The only consonant combinations include a liquid [l, m, n, r, y].

A totally different, Celestial-based, month name option

  • A set of names put together using names of 22 stars along Mars' Celestial Equator (to get away from Zodiac Constellations with all their irrational baggage) overhead near midnight during the various months. There is some fudging in this list, as named stars are not placed at similar intervals for our convenience. The sequence depends on the Season with which we start the year. Like colors for the pair of seasons in each alternate "half year" - which half year we run first makes no intrinsic difference. These star names, like most others, are time-honored corruptions of the original Arabic.
    • WinSum - five months Northern Winter, Southern Summer
      1 Deneb Kaitos (Beta Ceti)
      2 Baten Kaitos (Zeta Ceti)
      3 Mira (Omicron Ceti)
      4 Menkar (Alpha Ceti)
      5 Aldebaran (Alpha Tauri)
    • VerTum - six months Northern Spring, Southern Autumn
      (with the "I-Period either before Nath or after Alula
      (1) 6 Nath (Beta Tauri) - Northward Equinox
      (2) 7 Mebsuta ( Epsilon Geminorum)
      (3) 8 Castor (Alpha Geminorum)
      (4) 9 Talitha (Iota Ursae Majoris)
      (5) 10 Tania* (Mu & Lambda Ursae Majoris)
      (6) 11 Alula* (Nu & Xi Ursae Majoris)
    • SumTer - six months Northern Summer, Southern Winter
      1 Denebola (Beta Leonis) - Northern Solstice
      2 Diadem (Alpha Comae Berenices)
      3 Arcturus (Alpha Bootes)
      4 Cor Serpentis (Alpha Serpentis)
      5 Yed* (Delta & Epsilon Ophiuchi)
      6 Sabik (Eta Ophiuchi)
    • TumVer - five months Northern Autumn, Southern Spring
      (1) 7 Kaus* (Delta, Epsilon, & lambda Sagittarii)
      (2) 8 Ascella (Zeta Sagittarii)
      (3) 9 Nunki (Sigma Sagittarii)
      (4) 10 Alnir (Alpha Grus)
      (5) 11 Fomalhaut (Alpha Pisces Australis)

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