SYSTEM OF NUMERATION.
The manner in which the numbers were written was as simple as the system itself. A point or small circle indicated a unit, and these points sufficed for the numbers from one to nineteen. Twenty was indicated by a flag, four hundred by a feather, and eight thousand by a purse. One character placed above another indicated that the product was to be taken; for instance, 160,000 might be expressed either by twenty purses, or by a flag over a purse. To avoid the excessive use of the unit points in writing large and fractional numbers, each flag, feather, and purse was divided into four quarters, and only those quarters which were colored were to be counted. Thus five might be expressed by five points or by a flag with but one quarter colored; three hundred and fifty-six would be indicated by a feather with three quarters colored, two complete flags, three quarters of another flag, and one point.
We have seen that twenties were used, much as dozens are by us, as the foundation of all numeration, but strangely enough these twenties took different names in counting different classes of articles. The regular name, as given in the table, is pohualli; in counting sheets of paper, tortillas, small skins, and other thin objects capable of being packed one above another in small parcels, each twenty was called pilli; in counting cloths and other articles usually formed into large rolls, quimilli was the name applied to twenty; and in counting persons, lines, walls, and other things ranged in order, the term tecpantli was sometimes employed. In reckoning birds, eggs, fruits, seeds, and round or plump objects, generally tetl, 'a stone,' was affixed to each one of the numerals in the table; pantli was in the same way added for objects arranged in regular order, and also for surface measurements; tlamantli likewise was joined to the numerals for articles sold in pairs or sets, as shoes, dishes, etc.; while ears of corn, cacao in bunches, and other bulky articles required the termination olotl.
Among all the Nahua nations, so far as known, the arithmetical system was practically the same, and was essentially decimal. Nearly all gave great prominence to the number twenty; the Huastec language had simple names for the numbers from one to ten, twenty, and one thousand; the Otomí approached still nearer our modern system by making one hundred also one of its fundamental numbers with an uncompounded name as well as a compounded one.[616]
Astrology, soothsaying, the interpretation of dreams, and of auguries such as the flight or song of birds, the sudden meeting of wild animals, or the occurrence of other unlooked-for events, were regarded by the Nahuas as of the greatest importance, and the practice of such arts was entrusted to the tonalpouhqui, 'those who count by the sun,' a class of men held in high esteem, to whom was attributed a perfect knowledge of future events. We have seen that no undertaking, public or private, of any importance, could be engaged in except under a suitable and propitious sign, and to determine this sign the tonalpouhqui was appealed to. The science of astrology was written down in books kept with great secrecy and mystery, altogether unintelligible to the common crowd, whose good or bad fortune was therein supposed to be painted. The details of the methods employed in the mysterious rites of divination are nowhere recorded, and the continual mention of the seer's services throughout the chapters of this and the following volume render this paragraph on the subject sufficient here.
AUTHORITIES ON NAHUA ARTS.
In addition to the miscellaneous arts described in the preceding pages, separate chapters will be devoted to the Nahua calendar, hieroglyphics, architecture, and medicine.[617]
CHAPTER XVI.
THE AZTEC CALENDAR.
Astronomical Knowledge of the Aztecs—Contradictions of Authors respecting the Calendar—Value of the Researches of Various Writers—The First Regular Calendar—The Mexican Cycle—The Civil Year—The Aztec Months—Names of the Days and their Signification—The Commencement of the Aztec Year—The Ritual Calendar—Gama's Arrangement of the Months—The Calendar-Stone—The Four Destructions of the World—The Calendar of Michoacan—Reckoning of the Zapotecs.