## The Lost Calendars of Mars## Copyright © 1988 by Thomas Gangale
## Introduction
In "Martian Standard Time" ## The Lovelock-Allaby Calendar
I happened to come across Although they noted the correct length of the Martian solar day as 24 hours 39 minutes 35 seconds and intended that their Martian calendar be based on the Martian solar year, they made the mistake of having 687 days in their calendar when this is in fact the number of Terran solar days in a Martian solar year. It was as obvious to Lovelock and Allaby as it was to me that the cycles of Phobos and Deimos are entirely unsuitable as the bases for units of time. But, whereas I chose to adopt an artificial chronometric unit based on the cycle of the Moon, there are no months at all in the Lovelock-Allaby calendar:
Recognising the sociological necessity of the seven-day week, Lovelock and Allaby adopted this unit of time that has no astronomical analogue either on Earth or Mars. Their calendar thus consists of days, weeks, and years. They retained the same names of the days of the week that are used on Earth, and the weeks themselves were numbered from the beginning to the end of the year. As their fictional character explains:
Although Lovelock and Allaby were not explicit on this point, the above passage implies that they intended each year and each week to begin on Sunday. If we assume a year of 687 days as Lovelock and Allaby did, we find that seven divides this number 98 times with a remainder of one day. This last day of the year would in effect be an intercalary day, for in their system the dates of the last two days of the year and the first day of the following year would be 7.98 (a Saturday), 1.99 (a Sunday), and 1.01 (another Sunday). But if we correct their error and consider years consisting of 668 and 669 days, we find that the 96th and final week would be only three or four days long, and of course Lovelock and Allaby did not confront the social desynchronisation that might result from this. The Egyptians, for instance, who had five intercalary days at the end of their solar calendar, did not try to resolve this anomalous period into something resembling a regular work week, but rather dealt with it by instituting a festival of five days in celebration of the rising of Sirius above the morning horizon and the rising level of the Nile. The Darian calendar avoids this issue by having a six-day week at regular intervals throughout the year. It is not so much that I am against having a big blowout at the end of the year; I just prefer to have as symmetric a calendar as possible. Lovelock and Allaby chose to begin their Martian chronology with the establishment of the first human outpost on Mars. They were unclear as to whether they intended the anniversary of this event to be New Year's Day on their calendar. In any case, since the beginning of their chronology is defined by an event that has yet to come about, their calendar cannot be referenced to the Gregorian calendar. ## The Aitken CalendarBefore either man or machine ventured into space, before the first transistor and the first digital computer, the astronomer Robert G. Aitken envisioned a human civilisation on Mars and foresaw the need for a calendar based on the diurnal and annual cycles of that world. Aitken beat Lovelock, Allaby, and me to the punch by over three decades, but by the 1980's, when the subject of human expeditions to Mars and the colonisation of that world at last began to be given wide and serious consideration, his Martian calendar had been forgotten. The Aitken calendar is truly a lost calendar of Mars. It would have been easy to leave it buried, and certainly safer for the Darian calendar not to call attention to a potential rival, but regardless of whatever calendar the Martians eventually choose to adopt, the Aitken calendar is part of their heritage, and it would have been less than honest of me to conceal what I unearthed. Of course, only time will tell if my own work is in turn forgotten.
Odd-Numbered Years
Even-Numbered Years
It was in a 38-year-old book about Mars that I chanced across a passing reference to a Martian calendar, which attributed the invention to the astronomer Robert S. Richardson. Eventually, I tracked down Richardson's 1954 book, Richardson led up to his discussion of the Aitken calendar by entertaining various methods of dealing with the fractional portion of the 668.599-day year. The first scheme had common years of 669 days and every fifth year consisted of 667 days. In the second method, common years would be 668 days and every fifth year would contain 671 days. Aitken's solution was to have the years run alternately 668 and 669 days and insert an extra day in every year whose number was divisible by ten. This is strikingly similar to the Darian calendar, except that Aitken had his odd-numbered years 668 days long and his even-numbered years 669 days long, and therefore every tenth year had 670 days. In contrast, all odd-numbered years have 669 (an odd number) days in the Darian calendar, and except for those years divisible by ten but not 1,000, which also have 669 days, all even-numbered years have 668 (an even number) days. Thus the Aitken calendar had years of three different lengths, while in the Darian calendar years come in only two varieties. Lacking the 1,000-year correction factor, the Aitken calendar is still accurate to a day over that period of time. Aitken also dispensed with months as Lovelock and Allaby did, and like them he retained both the seven-day week and the terrestrial names of the days of the week. But while the Lovelock-Allaby calendar divided the year into units no larger than the week, Aitken devised two intermediate periods of time. He first divided the year into equal quarters of approximately 167 days, which he called 'seasons' and named Spring, Summer, Autumn and Winter. Each 'season' he quartered in turn so that each sixteenth of a year contained about 42 days, or six weeks. These sub-divisions of the 'seasons' Aitken called 'quarters,' although this term usually connotes a quarter of a year. Indeed, while he chose not to call them months, in order to keep the terminology in this article consistent, one can think of them as such. Now, owing to the fact that the naturally-occurring seasons of Mars are quite asymmetric, there would be a very poor correlation between these and Aitken's symmetric 'seasons.' Assuming that Aitken's calendar began with the vernal equinox, he would have his first day of Summer 27 days before the summer solstice, his first day of Autumn 37 days before the autumnal equinox, and his first day of Winter 12 days before the winter solstice.
[The 12th, 18th, and 24th months ware later changed from Vrisha, Asleha, and Ali to Rishabha, Simha, and Vrishika, respectively. The above table has been updated to reflect this. --TG] Rather than having a six-day week at the end of each quarter as needed and thereby enabling each quarter to invariably begin on the first day of the week as in the Darian calendar, Aitken allowed the days of the week to regress through his calendar over a two year period. His odd-numbered years began on Sunday, and since each 'season' was 167 days--one day short of being evenly divisible by seven, his Summer began on Saturday, Autumn on Friday, and Winter on Thursday. In even numbered years, Spring began on Wednesday, Summer on Tuesday, Autumn on Monday, and Winter on Sunday. Since even numbered years contained 669 days, this last 'season' was a day longer than normal; 168 being divisible by seven, the following Spring also began on Sunday to begin the two year cycle again. A nice feature of the Aitken calendar was that within each of the 'seasons,' all of the six-week periods began on the same day of the week. Aitken treated the extra day that he inserted every tenth year as an intercalary day--having no day of the week--so as not to upset his biennial cycle. The leap day occurred at the end of Summer--halfway through the year--so Aitken called it Mid-Year Day and declared it a Holiday. Aitken did not specify a starting year for his calendar, and so like the Lovelock-Allaby calendar, his cannot be correlated with the Gregorian calendar. ## The Levitt Calendar and The Levitt-Mentzer Clock
While searching for the details of what at the time I believed to be Richardson's calendar, I discovered evidence of yet another lost Martian calendar--and the first construction of a Martian clock--invented by his contemporary I. M. Levitt. I also subsequently found that in addition to describing the Aitken calendar, Richardson mentioned the Martian calendar devised by Levitt in a footnote of
Levitt published his idea of a Martian calendar in the May 1954 issue of Since the cycles of Phobos and Deimos are quite useless in connection with a calendar, and the lunar cycle has nothing at all to do with Mars, it was quite reasonable for Aitken, Lovelock and Allaby to do away with months on their Martian calendars. From a social scientist's point of view, however, would it not be important to retain a chronometric concept that has been a part of most human cultures for centuries and even millennia? I believe that a major advantage of the Darian calendar over these two competitors is that it demonstrates that months need not be abandoned on Mars, and that in fact months fit very neatly into the 668.5990-day Martian year. Levitt also saw that the month was a desirable unit of time to transplant to Mars; however, whereas I based my Martian months on the original model--the period of the Moon's orbit around the Earth and arrived at a total of 24 months of approximately 28 days each, Levitt proceeded along a different line of reasoning and instead divided the Martian year into 12 months as do most calendars on Earth. Levitt's months are thus half as many and twice as long as mine, averaging just slightly less than 56 days each. Compared with the four Martian solar calendars discussed so far--the Aitken, the Levitt, the Lovelock-Allaby, and the Darian--Levitt's is the most conservative. He retained the same names of the 12 months of the year that date back to ancient Rome. Like the other four Martian calendars, the Levitt calendar inherited the seven-day week from the Gregorian calendar, and like the Aitken and Lovelock-Allaby calendars, he preserved the Anglicised names of the seven days of the week. In my view, the similarity in nomenclature of any Martian calendar to the Gregorian calendar is an invitation to great confusion, and I have purposely avoided this in the Darian calendar. I have exported to Mars the concepts embodied in the Gregorian calendar where possible, improved upon them where I saw the opportunity, but I have changed the names of the months and the days to give the Darian calendar a distinctive Martian flavour and eliminate any possible ambiguity. For all that, the architecture of the Levitt calendar is nearly identical to that of the Darian calendar. His calendar, like mine and Aitken's, divides the year into equal quarters of 167 days, except in the case of the last quarter of a 669-day year, which is 168 days, But as opposed to Aitken, who employed unvarying seven-day weeks throughout his calendar so that the days of the week slid backward from quarter to quarter, Levitt contrived a six-day week to end each 167-day quarter. Thus, just as in the Darian calendar a six-day week ends with Dies Veneris and is followed by Dies Solis, Levitt's six-day week ends with Friday and is immediately followed by Sunday. As a result, every month on the Levitt calendar begins with a Sunday, just as on the Darian calendar each month begins on Dies Solis. In fact, ignoring the differences in the names of the months of the year and the days of the week, if one were to bisect each month of the Levitt calendar, the resulting structure would be indistinguishable from the Darian calendar.
I chose to begin the Darian calendar with an historic Martian event and a Martian astronomical event: the vernal equinox prior to the landing of
So while the Aitken and the Lovelock-Allaby calendars cannot be referenced to the Gregorian calendar, the Levitt calendar, like the Darian calendar, can be. Also like the Darian calendar, Levitt began his with the year 0 rather than 1. Thus January 1, 4713 BC on the Julian calendar was also January 1, 0 MY (Martian Year) on the Levitt calendar. Although Levitt did not furnish an exact correlation between his calendar and a modern date on the Gregorian calendar in his 1954 One of the most important aspects of a calendar is its relationship to the seasons, yet Levitt failed to mention whether his New Year's Day is in the Martian spring, summer, autumn or winter. It is possible to calculate the dates on which the equinoxes and solstices fall on the Levitt calendar and thus make it a bit more complete. Also, by so doing, we can establish a correlation between the Levitt calendar and the Darian calendar. Sagittarius 1, 0 ME on the Darian calendar corresponds to JD 2,442,771.657. Dividing this number by 1.0274913 yields 2,377,413.4, the number of Martian solar days that have elapsed since January 1, 0 MY on the Levitt calendar. If we divide further by 668.599, the integer portion of the quotient--3555--is the corresponding year on the Levitt calendar, and the remainder plus one--545--is the numerical day of the year. Since the structure of the Levitt calendar is so similar to that of the Darian calendar, Table 2 can be used to convert this numerical value to the corresponding Levitt calendar date if for the Sanskrit months we add 28, and for Sagittarius and Dhanasu we read instead January, February for Capricornus and Makara, et cetera. Thus Day 545 on the Levitt calendar, the date of the vernal equinox in the northern hemisphere, is October 44, and so December 26,1975 AD, Sagittarius 1, 0 ME, and October 44, 3555 MY are all equivalent dates. Further calculations of this nature show that January 1 on the Levitt calendar occurs in the late spring, with the summer solstice taking place on February 14. Similarly, May 24 marks the autumnal equinox and July 27 is the date of the winter solstice.
Now there is a serious discrepancy between the correlation of Levitt and Gregorian dates that Levitt himself reported and the result that I have reached here. How could January 1, 1954 AD be in the year 3641 MY if December 26, 1975 AD corresponds to October 44, 3555 MY? Levitt obtained his result by taking the Julian Day of January 1, 1954 AD and dividing this figure by the number of Martian solar Days in a Martian solar year. Levitt's error was in not also dividing by the ratio of Terran solar days to Martian solar days, or alternatively he could have divided the Julian Day by the number of Terran solar days in Martian solar year to obtain the correct Martian Year of his calendar. It turns out that January 1, 1954 AD on the Gregorian calendar actually corresponded to December 39, 3544 MY on the Levitt calendar.
Hopefully, this error appeared only in Levitt's
And it was not only electronic computers that were in their infancy in 1954 when Richardson discussed Aitken's calendar in ## The Moore CalendarHaving now found three Martian solar calendars, I resolved to make a general search; how many more were out there, I wondered?
The Viking landings on Mars inspired an invasion of the bookstands by a host of books about Mars. One of them was Patrick Moore's 1977 ## ConclusionAlthough I had read many books and magazine articles about Mars before I began my work on Martian time, I was somehow unlucky enough never to have come across even one of these other Martian calendars. Or perhaps this was good fortune, for had I known in advance of a Martian chronometric system that pre-dated mine, I might have been daunted from plunging into the task with such zest as I have done in my happy ignorance. What I had assumed was a brand new field I have since come to see is already a rather crowded one, and there may be still other Martian calendars out there somewhere. But of all the ones that I have found, none can claim all of the features that are incorporated into my own Darian calendar: A seven-day week. An integral number of weeks per month, enabling each month to begin on the first day of the week. A 28-day month that approximates the familiar lunar cycle. A year that begins on the vernal equinox, symbolic of the beginning of life. The simplest possible intercalation sequence, requiring calendar years of only two different lengths. An accuracy on the order of one day in 20,000 Martian years. A date and time reference to the Roman calendar based on a Martian historical event, enabling any occurrence to be expressed in either system. A computer program that prints calendars and generates monitor displays correlating Martian and Terran dates and times. A distinctive nomenclature that precludes any possibility of confusion between the Martian and Terran chronometric systems.
And with these proud strokes of the word processor keys I thought I was finished writing this article. I had looked through every astronomy book about Mars I could find, but could uncover no more calendars. The next morning, in the last REM period before waking, I dreamt of a calendar in Robert A. Heinlein's 1949 Except for references to days of the week, named the same as the ones we know on Earth, Heinlein made no further mention of a Martian calendar, but the above passage proves that my invention of a 24 month Martian year, like many of the features in the Darian calendar, is not a new one under the Martian Sun. ## Bibliography
Heinlein, Robert A.,
Levitt, I. M., "Mars Clock and Calendar,"
Lovelock, J., and Allaby, M.,
Moore, Patrick,
Richardson, Robert S., New York Times, "Mars Clock in Debut," February 15, 1954. |