197. Calendars and Astronomy
The earliest stage of anything like time reckoning in America was what might be called the descriptive moon series. The return of the seasons marked the year. Within the year, rude track was kept of the passage of time by following a series of “natural” months or lunations named after events, such as “heavy cold,” “flying geese,” “deer rutting,” or “falling leaves.” No one cared and perhaps no one knew how many days there were in a moon, let alone in a year. No one knew his age, nor, as a rule, how many years ago any event had taken place. It is a mark of pretty high civilization when people know how old they are.
From the point of view of accuracy, the moon series calendar left much to be desired, since there are something over twelve and considerably under thirteen visible lunations in a solar or seasonal year. Some tribes allowed twelve moons, others thirteen, in some different individuals disagreed. Whenever the geese actually flew, debates were settled: it was flying geese month, and every one went on with the series from there. If he had happened to get a moon ahead or behind, he accepted the event as a correction.
The moon series calendar was used by the majority of tribes in the United States and Canada.
Somewhat more advanced is the solstitial moon series. This takes one of the solstices, usually the one just before our Christmas, as the fixed beginning and end of the year. The days are noticeably shortest then. Some tribes went farther and employed landmarks to observe the place on the horizon of the sun’s rising. Until the solstice this place shifts daily southward, after it northward. Also, the noonday shadows fall longest at the winter solstice. Here then was a point in the year which was always the same, whereas the geese might fly or the leaves fall early one year and late the next. The definiteness thus obtained was followed up by numbering the moons instead of describing them, or by recognizing both solstices as a frame within which there fell two parallel groups of six moons, or of five moons and a slightly longer solstitial period.
This method also did not solve the really difficult problem of making twelve lunations and an irregular fraction fit automatically and permanently into the solar year; and provision for counting days and years was still wholly lacking. Yet the first beginnings of exact astronomical observations had been made and were utilized to give the year and its subdivisions a certain fixity.
The occurrence of the simple solstitial calendar in North America is significant. It occurs in the Southwest and Northwest: that is, in the area most directly influenced by the higher Mexican center, and the area which made most progress independently of Mexico.[29]
These two stages of the descriptive and the solstitial moon series were long ago passed through in southern Mexico and a need felt for a more precise time reckoning. No calendar can either serve accuracy or cover long periods which fails to concern itself with the exact arithmetical relation of its smaller units to its larger ones: the number of days in the month and year, for instance. This concern, would not be difficult if the relations were simple; but nature has put something over 29½ days into a lunation, something under 365¼ days and a little over 12⅓ lunations into the year. The first step ahead was undoubtedly a day count, as previously the numbering of the moons had marked an advance over their descriptive naming. The day count must have revealed the discrepancy between the actual numbers and those assumed for the larger units, such as 30 and 360. A great advance was therefore made when the natural lunation was wholly abandoned and artificial units substituted. The Mayas, or possibly some previous and forgotten people, invented a “month” of twenty days, probably because they counted by twenties instead of tens. Eighteen of these months, with five added leap days, made a 365-day year. Thirteen 20-day months made another and wholly arbitrary period of 260 days, which the Aztecs, who borrowed the system, called tonalamatl.[30] The tonalamatl had no basis in nature or astronomy and was a pure invention: a reckoning device. It ran its course concurrently with the year as two wheels of 260 and 365 cogs might engage. The same cogs would meet again at the end of 73 and 52 revolutions respectively, that is, 365 and 260 divided by 5, their highest common factor. At the end of each 52 years, therefore, the beginning of the year and of the tonalamatl again coincided, giving a “calendar round” of that duration. This 52-year period is the one by which the Aztecs dated.
The Mayas, however, did not content themselves with the 52-year period, but reckoned time by katuns of 20 and cycles of 400 years.[31] The dates on Maya inscriptions are mostly from their ninth cycle, with some from the end of the eighth and beginning of the tenth. This period corresponds approximately to the first six centuries of the Christian era. The beginning of the first cycle would fall more than 3,000 years before Christ. There is no reason to believe that this time reckoning began then. It is more likely that a little before the time of Christ the Mayas perfected this system of chronology and gave it dignity by imagining some seven or eight cycles to have passed between the beginning of the world, or some other mythological event, and the actual commencement of their record. From the close of their eighth cycle, however, the dates are apparently contemporary with the events to which they refer.
This system is so elaborate that it could scarcely have been devised and adopted all at once. There must have been a time lasting some centuries, perhaps over a thousand years, previous to the Christian era, during which the first day count was being elaborated and perfected into the classical calendar of the early post-Christian Maya monuments.
This calendar did not exhaust the astronomical and mathematical accomplishments of the Mayas. They ascertained that eight solar years correspond almost exactly with five “years” or apparent revolutions (584 days) of the planet Venus, and that 65 Venus years of a total of 37,960 days coincide with two calendar rounds of 52 solar years. They knew that their 365-day year was a fraction of a day short of the true year, determined the error rather exactly, and, while they did not interpolate any leap days, they computed the necessary correction at 25 days in 104 years or two calendar rounds. This is greater accuracy than has been attained by any calendar other than our modern Gregorian one. As regards the moon, they brought its revolutions into accord with their day count with an error of only one day in 300 years. These are high attainments, and for a people without astronomical instruments involved accurate and protracted observations as well as calculatory ability.
Much less is known of South American calendars; but, like the dwindling away from Maya to Aztec to Pueblo and finally to the rudiments of the descriptive moon series of the backward tribes in the northern continent, so there is discernible a retardation of progress as the Maya focus is left behind toward the south. The most developed calendar in South America was that of the Chibchan peoples of Colombia. Beyond them, the Inca, in their greater empire, got along with a system intermediate in its degree of development between the Aztec and the Pueblo ones. In the Tropical Forest and Patagonian areas there do not seem to have been more than moon name series comparable to those of peripheral North America.