1. How the Maya distinguished 1 day from the 259 others in the tonalamatl;

1. How the Maya distinguished 1 day from the 259 others in the tonalamatl;

2. How they distinguished the position of 1 day from the 364 others in the haab, or year; and, finally,

3. How by combining (1) and (2) they distinguished 1 day from the other 18,979 of the Calendar Round.

It remains to explain how the Maya insured absolute accuracy in fixing a day within a period of 374,400 years, as stated above, or how they distinguished 1 day from 136,655,999 others.

The Calendar Round, as we have seen, determined the position of a given day within a period of only 52 years. Consequently, in order to prevent confusion of days of the same name in successive Calendar Rounds or, in other words, to secure absolute accuracy in dating events, it was necessary to use additional data in the description of any date.

In nearly all systems of chronology that presume to deal with really long periods the reckoning of years proceeds from fixed starting points. Thus in Christian chronology the starting point is the Birth of Christ, and our years are reckoned as B. C. or A. D. according as they precede or follow this event. The Greeks reckoned time from the earliest Olympic Festival of which the winner's name was known, that is, the games held in 776 B. C., which were won by a certain Coroebus. The Romans took as their starting point the supposed date of the foundation of Rome, 753 B. C. The Babylonians counted time as beginning with the Era of Nabonassar, 747 B. C. The death of Alexander the Great, in 325 B. C., ushered in the Era of Alexander. With the occupation of Babylon in 311 B. C. by Seleucus Nicator began the so-called Era of Seleucidæ. The conquest of Spain by Augustus Cæsar in 38 B. C. marked the beginning of a chronology which endured for more than fourteen centuries. The Mohammedans selected as their starting point the flight of their prophet Mohammed from Mecca in 622 A. D., and events in this chronology are described as having occurred so many years after the Hegira (The Flight). The Persian Era began with the date 632 A. D., in which year Yezdegird III ascended the throne of Persia.

It will be noted that each of the above-named systems of chronology has for its starting point some actual historic event, the occurrence, if not the date of which, is indubitable. Some chronologies, however, commence with an event of an altogether different character, the date of which from its very nature must always remain hypothetical. In this class should be mentioned such chronologies as reckon time from the Creation of the World. For example, the Era of Constantinople, the chronological system used in the Greek Church, {61} commences with that event, supposed to have occurred in 5509 B. C. The Jews reckoned the same event as having taken place in 3761 B. C. and begin the counting of time from this point. A more familiar chronology, having for its starting point the Creation of the World, is that of Archbishop Usher, in the Old Testament, which assigns this event to the year 4004 B. C.

In common with these other civilized peoples of antiquity the ancient Maya had realized in the development of their chronological system the need for a fixed starting point, from which all subsequent events could be reckoned, and for this purpose they selected one of the dates of their Calendar Round. This was a certain date, 4 Ahau 8 Cumhu,[36] that is, a day named 4 Ahau, which occupied the 9th position in the month Cumhu, the next to last division of the Maya year (see Table III).

While the nature of the event which took place on this date[37] is unknown, its selection as the point from which time was subsequently reckoned alone indicates that it must have been of exceedingly great importance to the native mind. In attempting to approximate its real character, however, we are not without some assistance from the codices and the inscriptions. For instance, it is clear that all Maya dates which it is possible to regard as contemporaneous[38] refer to a time fully 3,000 years later than the starting point (4 Ahau 8 Cumhu) from which each is reckoned. In other words, Maya history is a blank for more than 3,000 years after the initial date of the Maya chronological system, during which time no events were recorded.

This interesting condition strongly suggests that the starting point of Maya chronology was not an actual historical event, as the founding of Rome, the death of Alexander, the birth of Christ, or the flight of Mohammed from Mecca, but that on the contrary it was a purely hypothetical occurrence, as the Creation of the World or the birth of the gods; and further, that the date 4 Ahau 8 Cumhu was not chosen as the starting point until long after the time it designates. This, or some similar assumption, is necessary to account satisfactorily for the observed facts:

1. That, as stated, after the starting point of Maya chronology there is a silence of more than 3,000 years, unbroken by a single contemporaneous record, and {62}

2. That after this long period had elapsed all the dated monuments[39] had their origin in the comparatively short period of four centuries.

Consequently, it is safe to conclude that no matter what the Maya may have believed took place on this date 4 Ahau 8 Cumhu, in reality when this day was present time they had not developed their distinctive civilization or even achieved a social organization.

It is clear from the foregoing that in addition to the Calendar Round, the Maya made use of a fixed starting point in describing their dates. The next question is, Did they record the lapse of more than 3,000 years simply by using so unwieldy a unit as the 52-year period or its multiples? A numerical system based on 52 as its primary unit immediately gives rise to exceedingly awkward numbers for its higher terms; that is, 52, 104, 156, 208, 260, 312, etc. Indeed, the expression of really large numbers in terms of 52 involves the use of comparatively large multipliers and hence of more or less intricate multiplications, since the unit of progression is not decimal or even a multiple thereof. The Maya were far too clever mathematicians to have been satisfied with a numerical system which employed units so inconvenient as 52 or its multiples, and which involved processes so clumsy, and we may therefore dismiss the possibility of its use without further consideration.

In order to keep an accurate account of the large numbers used in recording dates more than 3,000 years distant from the starting point, a numerical system was necessary whose terms could be easily handled, like the units, tens, hundreds, and thousands of our own decimal system. Whether the desire to measure accurately the passage of time actually gave rise to their numerical system, or vice versa, is not known, but the fact remains that the several periods of Maya chronology (except the tonalamatl, haab, and Calendar Round, previously discussed) are the exact terms of a vigesimal system of numeration, with but a single exception. (See Table VIII.)

TABLE VIII. THE MAYA TIME-PERIODS

1 kin = 1 day 20 kins = 1 uinal = 20 days 18 uinals = 1 tun = 360 days 20 tuns = 1 katun = 7,200 days 20 katuns = 1 cycle = 144,000 days 20[40] cycles = 1 great cycle = 2,880,000 days

Table VIII shows the several periods of Maya chronology by means of which the passage of time was measured. All are the exact terms of a vigesimal system of numeration, except in the 2d place (uinals), {63} in which 18 units instead of 20 make 1 unit of the 3d place, or order next higher (tuns). The break in the regularity of the vigesimal progression in the 3d place was due probably to the desire to bring the unit of this order (the tun) into agreement with the solar year of 365 days, the number 360 being much closer to 365 than 400, the third term of a constant vigesimal progression. We have seen on page 45 that the 18 uinals of the haab were equivalent to 360 days or kins, precisely the number contained in the third term of the above table, the tun. The fact that the haab, or solar year, was composed of 5 days more than the tun, thus causing a discrepancy of 5 days as compared with the third place of the chronological system, may have given to these 5 closing days of the haab--that is, the xma kaba kin--the unlucky character they were reputed to possess.

The periods were numbered from 0 to 19, inclusive, 20 units of any order (except the 2d) always appearing as 1 unit of the order next higher. For example, a number involving the use of 20 kins was written 1 uinal instead.

We are now in possession of all the different factors which the Maya utilized in recording their dates and in counting time:

1. The names of their dates, of which there could be only 18,980 (the number of dates in the Calendar Round).

2. The date, or starting point, 4 Ahau 8 Cumhu, from which time was reckoned.