[Speaking of which, parts of this post may be “dated” because I began writing it about 3 years ago (in early 2019) and then set it aside awaiting further research, which I have never quite completed. So, now (early 2022) I will publish a slightly revised and updated version to reflect what I now know (and don’t know) about calendar math and related topics. Comments in italics — except the quotations — are things I have added to the original draft.]
For as long as I can remember, I’ve been intrigued by the passage of time. Perhaps everyone is. I have many snippets of memory that involve time. I remember learning to tell time, for example, in Mrs. Heather’s nursery school (yes, in the days before digital clocks!). And then there was the day my father turned 40 — I was astounded that he was still able to walk; 40 just seemed incredibly old to me. As a teenager, I was a voracious reader of science fiction, and a fan of The Twilight Zone; in those fantasy worlds, time travel was a frequent theme.
It probably didn’t hurt that my grandmother Wilcox was an historian. I was enthralled by her tales of days long ago. She was such a good storyteller that I could picture being in the places she described. My favorites involved the Stockbridge Indians or her grandfather, who served as a surgeon in the Civil War.
My sense of the span of time evolved for me early in life as a result of being immersed in these stories, as well as ones my mother would tell about her growing up. She told me about the trolley that used to run down our street [Park Street in Stockbridge], but was long gone by the time we lived there. She pointed out a place where the trolley line crossed the Housatonic in Glendale; the bridge stanchions are still there. In her youth (in the 1920s), she told me, for local transport there were more people using a horse-and-buggy than an automobile.
Although I fully understood that the Stockbridge Indians had been forced out of town long before the Civil War, and even longer before my mother was born, I couldn’t resist teasing her about her being old. Because she was old, to me. My parents were married for several years before I (their eldest) was born, because my father was away, serving in the Army Air Corps in Africa and Italy during WW II. I am among the first of the Baby Boomers, having been born nine months after that war ended. My parents were several years older than the parents of many of my classmates. Sometimes I would remind my mother of her ancient status by saying, in the presence of my siblings, “Mom, tell us again how it was when you were young, living among the Indians!”
Learning about the hours of the day, the points of the compass, and left from right, all seemed logical to me. But the calendar violated my sense of order. Why did the months have different numbers of days? And what was this leap-year thing? And why did not the calendar line up with the seasons? Why not begin the year on December 21, if that was the shortest day of the year? And why did Easter come on a different day each year?
People experience time as both linear and circular. On the one hand, it marches remorselessly from birth to death, a vector with fixed endpoints and a constant velocity. On the other hand, time is cyclical, with the wheel of the seasons endlessly spinning, and no clear end or beginning. Calendars are records of a culture’s attempt to weight and reconcile these different versions.
from Appendix D “Calendar Math” in 1491 by Charles C. Mann
Calendars of one sort or another have existed since time immemorial. In fact, one of their purposes was to memorialize time. Other functions of calendars had to do with religion or agriculture. Many ancient cultures evidenced a supreme grasp of mathematical and astronomical concepts. Such ideas were necessary to create accurate (and therefore useful) calendars. These same skills were needed to practice the art of navigation.
My friend John Robison has written an essay, Were the Timekeepers of the Ancient World Autistic? speculating on the role that certain autistic people might have played in ancient times in developing calendars and mathematics. John later wrote a related essay on navigation in the South Pacific.
While researching local history for my upcoming OLLI class, I came to realize the importance of dating. Not in the romantic sense, although that may be important, too. There are (at least) two different problems in establishing exactly when historical events took place.
(1) Transposing Dates from One Calendar System to Another
The most commonly-used calendar in today’s world is the Gregorian calendar, a reform introduced in 1582 by Pope Gregory XIII. It was at first used only in Catholic jurisdictions, and then gradually adopted throughout the Western world. It was not until 1752 that the Gregorian calendar was adopted by the British Empire, including its 13 colonies along the eastern seaboard of North America that were to become the United States of America.
So, for a period of 170 years, including much of the early history of European involvement with the Americas, there were two different calendar systems in use by the colonizers. All of this can lead to great confusion when interpreting dates that were recorded during the overlap with the older (Julian) calendar system.
In addition, there were (and in some cases, still are) different calendar systems used throughout the world. In the Americas, the two systems that I know the most about are
- The Turtle Calendar
- The Mesoamerican (Mayan) calendar
More on these in a moment.
(2) How long ago did certain things occur?
It can be very difficult to pinpoint dates that were not recorded with precision, or are part of an oral tradition, or are inferred from other dating methods.
Astronomical Measures of Time
Originally the month was the interval between one new moon and the next…
The modern English word “month” is of Germanic origin, and was (in Old English) the same (or a closely similar word) that was used for “moon.” As I understand it, this equivalency is also true in many modern languages. In Old English, it was mōnath (month) or, mōna (moon) and in German it is Monat or Mond. In Dutch it is maand or maan; but the name of Henry Hudson’s ship was De Halve Maen, so the word must have evolved since then.
In Latin, there were two different words for moon (I’m not sure what distinguished one from the other): luna and mēnsis (the prefix mens- indicates measured, and the root of both words seems to mean measure). From luna comes the English words lunar and lunatic. From mēnsis comes the Latin mēnstruus (happening monthly), hence the English menstrual and related words.
In all of this, a monthly cycle was taken to be ~28 days. Actually, the moon rotates around the earth and on its own axis once every 27.322 days; known as the sidereal month, from the Latin sidus, “star” — but that rotation does not coincide with the phases of the moon, since our planet is also moving through space. As a result, by the time our moon completes a single rotation, although it has returned to its previous location relative to the stars, it is no longer in the same place relative to the sun. And since the new moon is observed when the sun is on the exact opposite side of the earth from the moon, new moons are ~29.53 days apart.
The interval between new moons is known as the synodic month, a word related to “synod” which is a meeting, or “getting together” and indicates the meeting of the sun and the moon in the same place relative to the earth. This is also called the lunar month.
Unfortunately for early time-keepers and calendar-makers, the sideral (solar) year does not correspond to an even number of lunar months. A new moon occurs ~12.37 times for every rotation of the earth around the sun.
In the interval since I drafted the above comments, I have begun to study the Western Abenaki dialect of the Algonkian language. I posted a query on Facebook, and received several helpful responses. One was a link to a lunar calculator, and another was a post about the Western Abenaki lunar calendar. (The Abenaki word for moon [kizos] — in the sense of month — is explained in that post.)
I’ve also added a link (above) to the Cherokee story of the Turtle Calendar. In that origin story is contained an explanation of the thirteen 28-day months of that calendar, with an extra day added in the summer to make it come out to a year of 365 days. But that would mean that, unlike the Abenaki calendar, the months would not be tied to the lunar synodic cycle. I’ve not yet investigated whether the Cherokee’s relatives, the Haudenosaunee, have a similar calendar.
I’m going to leave it at that. I’m still puzzled by (among other things) how the Abenaki calendar was adjusted to the solar year. I’m also not going to address the Mayan calendar, which was much more complex (and more accurate) than any other calendar I’ve come across. The appendix in 1491, mentioned above, has a good description, and my interest at the moment is more in the indigenous peoples of the Northeast.