The series of units of time thus composed is that employed by the Maya of Yucatan, as recovered from the early Spanish records and the codices. In this region the katun was the historical unit of prime significance, for both Landa and Cogolludo note the fact that at the end of every katun a graven stone was erected or laid in the walls of an edifice to record the event. Study of the sculptured stelae of the capitals and cities of the Old Empire of the south has convinced archaeologists that these stelae are similarly, in great part, monuments erected not primarily to honor men or commemorate events but to mark the passage of time. The units, however, as recorded from readings of the dates, are not primarily katuns (of 7200 days), but halves and quarters of the katun. Morley,[93] to whom belongs credit of the demonstration of the system, gives to these lesser periods the names hotun ("five tuns," or 1800 days) and lahuntun ("ten tuns," or 3600 days). The amazing monumental wealth, therefore, of the old Maya cities turns out to be chiefly due to the importance which the Maya peoples attached to the idea of time itself and to the recording of its passage.
Such an idea could only have reference to religious or mythico-religious beliefs, of the nature of which something is to be inferred from the monumental and codical indications of the cycles and the Great Cycle which entered into Maya computations. The cycle is clearly a conception induced by the necessities of vigesimal notation, with, no doubt, mythic associations suggested by its pictographic notation; it is a period of twenty katuns, just as the katun is twenty tuns. But the duration of the Great Cycle is matter of dispute. Bowditch and Goodman, basing their judgment on the fact that the cycles in the inscriptions are numbered 1 ... 13, and again upon the fact that the two known starting-points, or eras, of Maya monumental chronology are just thirteen cycles apart, regard the Great Cycle as composed of thirteen cycles; Morley, chiefly from evidence in the codices, believes that it was composed of twenty cycles. It is possible, of course, that the conception of the Great Cycle changed from the time of the Old Empire to that of the New, perhaps influenced by the change in the period of erecting monumental records; but in any case the immense numbers of days embraced in the Maya reckonings excite our wonder. Such calculations could have been made possible only by the use of a highly developed arithmetical system, and this the Maya possessed; for they had developed a positional notation, employing a sign for zero, a system of dots and bars for the integers 1 ... 19, while the conception of positive and negative was achieved through the use of these elements recorded vertically—units above zero, twenties above the units, tuns in the third position upward, and so on. The tun (= 360) is an obvious calendric number, and this makes clear that the Maya certainly developed the higher possibilities of their mode of computation in connexion with the needs of their reckoning of time. The perfection of their achievement is indicated by the fact that through its use they were enabled to distinguish any date within the range of a Great Cycle from any other, thus creating a numbered time-scheme which in our own system would be measured by millenia.
To complete its historical value only one element need be added, the selection of an era from which to reckon dates. Two such eras are known, one bearing the name 4 Ahau 8 Cumhu, and the other (found in only two inscriptions) that of 4 Ahau 8 Zotz, this falling thirteen cycles earlier than the other. The former, from which nearly all the monumental inscriptions are reckoned, is some three thousand years anterior to the period of the inscriptions themselves and probably, therefore, refers to an event in the third millennium b. c., assuming that the monuments belong to the first thousand years of our era. It is altogether unlikely that a date so remote can represent any but a mythical event, such, we may suppose, as the end of a preceding "Sun," or Age of the World, and the beginning of that in which we live; for the Maya, like the Nahua, possessed the myth of ages of this type. Cogolludo mentions two of these ages as terminated by annihilation of the human race through epidemic, and a third as ended by storm and flood; while Landa's account of the calamities following the destruction of Mayapan seems clearly to be intermingled with a myth of world catastrophes. The Popul Vuh shows that the character of the Quiché legend was not essentially unlike that of the Aztec, who may, indeed, have received from the Maya their cosmogony along with their calendric system, of which it is doubtless in some degree a product.
Astronomical data must have entered into the calculation of these great epochs. Förstemann and other students have discovered in the codices, particularly in the Dresden Codex, evidences of the reckoning of the period not only of Venus (five hundred and eighty-four days), but also of lunar revolutions, of the period of Mars (seven hundred and eighty days), and possibly of the cycles Jupiter, Saturn, and Mercury as well. Such periods, for astrological and divinatory purposes, were recorded in the books of the priests; and, as elsewhere in the world, the synodic revolutions of the planets, and the recurrences of their stations with respect to the day-signs, gave the material for the formation of huge cycles of time which their mathematical system enabled them to compute. Thus it is that Förstemann finds near the end of the Dresden Codex vast numbers—designated as "Serpent Numbers" because of the occurrence of the serpent-symbol in connexion with them—which correspond to such cyclic recombinations of signs and events.
"In the so-called 'serpent numbers,'" writes Morley,[94] "a grand total of nearly twelve and a half million days (about thirty-four thousand years) is recorded again and again. In these well-nigh inconceivable periods all the smaller units may be regarded as coming at last to a more or less exact close. What matter a few score years one way or the other in this virtual eternity? Finally, on the last page of the manuscript, is depicted the Destruction of the World, for which the highest numbers have paved the way. Here we see the rain serpent, stretching across the sky, belching forth torrents of water. Great streams of water gush from the sun and moon. The old goddess, she of the tiger claws and forbidding aspect, the malevolent patroness of floods and cloudbursts, overturns the bowl of the heavenly waters. The crossbones, dread emblem of death, decorate her skirt, and a writhing snake crowns her head. Below with downward-pointed spears, symbolic of the universal destruction, the black god stalks abroad, a screeching owl raging on his fearsome head. Here, indeed, is portrayed with graphic touch the final all-engulfing cataclysm."
PLATE XXII.
Final page from the Codex Dresdensis showing "Serpent Numbers" and typifying the cataclysms destroying the world. See pages [151-2] for description, and compare Plates [XII], [XIII], [XIV].
In their sculpture the Maya far surpassed the artistic expression of all other Americans, attaining not only decorative power, but such idealization of the human countenance as is possible only among people whose aesthetic sensibilities have an intellectual background and guidance. No more convincing evidence of this mental power could be forthcoming than is shown in their mathematical and astronomical learning, at once a testimony to the antiquity of their culture and to the force of their native genius.