History of the Conquest of Mexico (Vol. 1-4). William Hickling Prescott
None of the Aztec compositions have survived, but we can form some estimate of the general state of poetic culture from the odes which have come down to us from the royal house of Tezcuco.[174] Sahagun has furnished us with translations of their more elaborate prose, consisting of prayers and public discourses, which give a favorable idea of their eloquence, and show that they paid much attention to rhetorical effect. They are said to have had, also, something like theatrical exhibitions, of a pantomimic sort, in which the faces of the performers were covered with masks, and the figures of birds or animals were frequently represented; an imitation to which they may have been led by the familiar delineation of such objects in their hieroglyphics.[175] In all this we see the dawning of a literary culture, surpassed, however, by their attainments in the severer walks of mathematical science.
They devised a system of notation in their arithmetic sufficiently simple. The first twenty numbers were expressed by a corresponding number of dots. The first five had specific names; after which they were represented by combining the fifth with one of the four preceding; as five and one for six, five and two for seven, and so on. Ten and fifteen had each a separate name, which was also combined with the first four, to express a higher quantity. These four, therefore, were the radical characters of their oral arithmetic, in the same manner as they were of the written with the ancient Romans; a more simple arrangement, probably, than any existing among Europeans.[176] Twenty was expressed by a separate hieroglyphic,—a flag. Larger sums were reckoned by twenties, and, in writing, by repeating the number of flags. The square of twenty, four hundred, had a separate sign, that of a plume, and so had the cube of twenty, or eight thousand, which was denoted by a purse, or sack. This was the whole arithmetical apparatus of the Mexicans, by the combination of which they were enabled to indicate any quantity. For greater expedition, they used to denote fractions of the larger sums by drawing only a part of the object. Thus, half or three-fourths of a plume, or of a purse, represented that proportion of their respective sums, and so on.[177] With all this, the machinery will appear very awkward to us, who perform our operations with so much ease by means of the Arabic or, rather, Indian ciphers. It is not much more awkward, however, than the system pursued by the great mathematicians of antiquity, unacquainted with the brilliant invention, which has given a new aspect to mathematical science, of determining the value, in a great measure, by the relative position of the figures.
In the measurement of time, the Aztecs adjusted their civil year by the solar. They divided it into eighteen months of twenty days each. Both months and days were expressed by peculiar hieroglyphics,—those of the former often intimating the season of the year, like the French months at the period of the Revolution. Five complementary days, as in Egypt,[178] were added, to make up the full number of three hundred and sixty-five. They belonged to no month, and were regarded as peculiarly unlucky. A month was divided into four weeks, of five days each, on the last of which was the public fair, or market-day.[179] This arrangement, differing from that of the nations of the Old Continent, whether of Europe or Asia,[180] has the advantage of giving an equal number of days to each month, and of comprehending entire weeks, without a fraction, both in the months and in the year.[181]
As the year is composed of nearly six hours more than three hundred and sixty-five days, there still remained an excess, which, like other nations who have framed a calendar, they provided for by intercalation; not, indeed, every fourth year, as the Europeans,[182] but at longer intervals, like some of the Asiatics.[183] They waited till the expiration of fifty-two vague years, when they interposed thirteen days, or rather twelve and a half, this being the number which had fallen in arrear. Had they inserted thirteen, it would have been too much, since the annual excess over three hundred and sixty-five is about eleven minutes less than six hours. But, as their calendar at the time of the Conquest was found to correspond with the European (making allowance for the subsequent Gregorian reform), they would seem to have adopted the shorter period of twelve days and a half,[184] which brought them, within an almost inappreciable fraction, to the exact length of the tropical year, as established by the most accurate observations.[185] Indeed, the intercalation of twenty-five days in every hundred and four years shows a nicer adjustment of civil to solar time than is presented by any European calendar; since more than five centuries must elapse before the loss of an entire day.[186] Such was the astonishing precision displayed by the Aztecs, or, perhaps, by their more polished Toltec predecessors, in these computations, so difficult as to have baffled, till a comparatively recent period, the most enlightened nations of Christendom![187]
The chronological system of the Mexicans, by which they determined the date of any particular event, was also very remarkable. The epoch from which they reckoned corresponded with the year 1091 of the Christian era. It was the period of the reform of their calendar, soon after their migration from Aztlan. They threw the years, as already noticed, into great cycles, of fifty-two each, which they called “sheafs,” or “bundles,” and represented by a quantity of reeds bound together by a string. As often as this hieroglyphic occurs in their maps, it shows the number of half-centuries. To enable them to specify any particular year, they divided the great cycle into four smaller cycles, or indictions, of thirteen years each. They then adopted two periodical series of signs, one consisting of their numerical dots, up to thirteen, the other, of four hieroglyphics of the years.[188] These latter they repeated in regular succession, setting against each one a number of the corresponding series of dots, continued also in regular succession up to thirteen. The same system was pursued through the four indictions, which thus, it will be observed, began always with a different hieroglyphic of the year from the preceding; and in this way each of the hieroglyphics was made to combine successively with each of the numerical signs, but never twice with the same; since four, and thirteen, the factors of fifty-two,—the number of years in the cycle,—must admit of just as many combinations as are equal to their product. Thus every year had its appropriate symbol, by which it was at once recognized. And this symbol, preceded by the proper number of “bundles” indicating the half-centuries, showed the precise time which had elapsed since the national epoch of 1091.[189] The ingenious contrivance of a periodical series, in place of the cumbrous system of hieroglyphical notation, is not peculiar to the Aztecs, and is to be found among various nations on the Asiatic continent,—the same in principle, though varying materially in arrangement.[190]
The solar calendar above described might have answered all the purposes of the people; but the priests chose to construct another for themselves. This was called a “lunar reckoning,” though nowise accommodated to the revolutions of the moon.[191] It was formed, also, of two periodical series, one of them consisting of thirteen numerical signs, or dots, the other, of the twenty hieroglyphics of the days. But, as the product of these combinations would be only 260, and as some confusion might arise from the repetition of the same terms for the remaining 105 days of the year, they invented a third series, consisting of nine additional hieroglyphics, which, alternating with the two preceding series, rendered it impossible that the three should coincide twice in the same year, or indeed in less than 2340 days; since 20 × 13 × 9 = 2340.