The Mayan Civilization

The fifteenth century was marked by the imposing of civilization onto the tribes in the Americas. Among those tribes, the Mayans are one of the most notable. Although not civilized by European standards, their cities were larger than some in Europe, and their calendar, science and mathematics surpassed any found in Europe at that time. (McLeish, pg. 128) The Mayans also kept "primitive" written records which were torched but their legacy and knowledge was not fully lost.

The Mayans inhabited the coastal plains of southern Mexico and northern Central America, between the years of 250 to 900 A.D. They were divided into about twenty different tribes, totaling over half a million people. The Mayans were mostly agricultural people. They developed a trade system based on barter and even established a system of credit. (Funk & Wagnalls Vol. 17, pg. 121) Despite their advancements in other areas such as architecture, writing, mathematics and the calendar however, they were a very religious people, with a great fear of death. (Morley, pg. 11) This combination of knowledge and fear contributed to the development of a complex number and calendar system, which are to be the focus of this paper.

The Mayans had two different types of written numbers: the normal forms, which resemble our roman numerals, and the those with head variants, which resemble our Arabic numbers. The most commonly used form however was the normal form. This form was used for trade and commerce and was even accessible to the uneducated. (Morley, pg. 87) The normal forms of numbers up to and including 19 were represented by combinations of dots ( ) and bars ( ). The Mayan dot represents a value of 1, whereas the bar represented a value of 5. (Morley, pg. 87) (It should be noted that since the vigesimal system was used, there was a special symbol or glyph for the number twenty.) When found in Mayan hieroglyphics, these symbols were often more elaborate and decorated, although their value remained unchanged. (Morley, pg. 88) They often had a glyph block to the right of them, as seen below. The Mayans also developed the concept of a place holder, and would place crescent shapes next to lone dots that were on a bar. (Morley, pg. 90) More important however is the fact that they used a zero, which is remarkable being that "most of the world’s civilizations had no concept of zero at that time." (http://www/cmcc.muse.digital.ca/membrs/civiliz/maya/mmc05eng.html) Their zero was represented with a specific drawing, which was also used as part of the number 20. ( Gilbert and Cotterell, pg. 27)

These are Mayan glyphs for the numbers: 1, 2, 6, 7, 11, 12, 16, and 17. (Morley, pg. 90)

Note the use of the crescent shapes as place holders.

In order to convert Mayan numerals to our Arabic numerals, it is necessary to note that the Mayans used the vigesimal, or base 20 system, rather than the decimal system. (McLeish, pg. 128) To demonstrate this method of conversion, the number 368, 667 will be converted below. First of all, Mayan numbers were written vertically, therefore they can be easily translated into our system by arranging them in that way. (McLeish, pg. 129) It is also important to start with the lowest denominations at the bottom, and to recall that the first five numbers in the vigesimal system utilized by the Mayans are 1, 20, 400, 8000 and 160,000.

Mayan Numeral

Place-Value

Decimal Value

2 times 160,000

320,000

6 times 8,000

48,000

1 times 400

400

13 times 20

260

7 times 1

7

 

 

The Concept of Time and the Mayan Calendar

Perhaps what the Mayans are most known for is their calendar, a lot of which is based on astronomy, being that they were great astronomers. (Gilbert and Cotterell, pg. 33) The fact is that they had two calendars, one for religious purposes and the other to regulate their everyday life. The reason the calendar was so developed, far in advance of any European calendar was that "Mayan intellectual life revolves round their calendar, astronomy and astrology." (McLeish, pg. 129) To the Mayans, time was a god and so each day or kin was associated with a particular god, each of whom had his/her own temperment. (McLeish, pg. 129) For this reason, priests were needed to determine the mood of the gods and counsel the people. The Mayans have 20 day names, each of which

were depicted by hieroglyphs, they are:

Imix- sea

dragon/water/wine

Cimi- death

Chuen- monkey

Cib- owl/ virtue

Ik- air/life

Manik- deer/grasp

Eb- broom

Caban- force/ earth

Akbal-night

Lamat- rabbit

Ben- reed

Eznab- flint/ knife

Kan-corn

Muluc- rain

Ix- jaguar

Cauac- storm

Chicchan-serpent

Oc- dog

Men- bird/ eagle/ wise one

Ahau- lord

(Gilbert and Cotterell, pg. 29)

Imix was the first and Ahau was the last and they would repeat in an endless cycle for all time. A day name alone was not sufficient to represent the day, therefore each day would have a number prefix ranging from 1 to 13, inclusive. The number 13 was used because it represented the total, original number of gods of the Mayan culture. (McLeish, pg. 132) Therefore to properly describe a day, a number prefix would be assigned to a particular day name. Consequently if Kan was selected as the starting point, it would be assigned the number 1, so then Chicchan would be assigned the number 2 and so forth.

Bearing this continuity in mind, one should realize that as the cycle continues, each day name will have a different number prefix assigned to it, and eventually everything will repeat. In fact, 260 days ( 13 * 20) will have to pass in order to have Kan be the number 1 again on the 261st day. This cycle or sacred calendar was referred to as the "count-of-day" or the tonalamatl, which meant "book of days". (McLeish, pg.132) In conjunction with this sacred calendar was the secular calendar, the Haab.

The Haab or Year of 365 Days

The second calendar used by the Mayans was the Haab or secular calendar, which is also known as the vague year calendar. This calendar was utilized in everyday affairs and denoted the seasons and agricultural periods. This implies that "it was based on the solar cycle, the time it takes for the Earth to go round the Sun." (McLeish, pg. 133) The Haab was divided into 18 months, each with 20 days ( due to the vigesimal system ), yielding a total of 360 days. The remaining five days, called the "xma kaba kin, or days without name" were grouped into a final month, during which bad luck was prevalent. (Morley, pg. 45) These extra five days resulted from the fact that the priests manipulated the number of days in one uinal to be 18 rather than 20, for religious purposes. Therefore time, in terms of days, is counted in the following way:

20 kins = 1 uinal

18 uinals = 1 tun (360, not 400 days)

20 tuns – 1 katun (7,200 days)

20 katuns – 1 baktun (144,000 days)

20 baktuns = 1 pictun (2,880,000 days)

(McLeish, pg. 135) This method of counting days is referred to as the long count and can be used to count up to 367,000,000 years. The long count was broken due to the work of Ernst Forstemann, and is what the Mayans used to record dates on monuments or documents. (Gilbert and Cotterell, pg. 33-34)

To start off, the first day of the Mayan year was always the first day of the month called Pop, which was noted by the Europeans to coincide with the 16th of July every year. The days in the Haab calendar were also counted, with the first day of the first month being 0 Pop. The reason behind this is that the Mayans did not consider a day to have elapsed until the next one started, therefore the second day of the month was 1 Pop. The rest of the months are classified in the same manner, the names of the months are below:

Pop

Tzec

Chen

Mac

Kayab

Uo

Xul

Yax

Kankin

Cumhu

Zip

Yaxkin

Zac

Muan

Uayeb- 5 days

Zotz

Mol

Ceh

Pax

 

(Morley, pg. 49)

From a combination of the two calendars then we have discerned the following: the number of differently named days, the names of the days, the order of the days, the number, names and length of the months into which a year is divided, and the order of the months. Now then it is possible to fully identify a single day in the Mayan calendar by giving the number, the tzolkin day, the number and the haab month. This combination of the two calendars is referred to as the Calendar Round or the round of days and the method by which they are combined is shown below.

(Morley, pg. 51)

The Calendar Round, included the 18,980 possible combinations of dates from the 260 days and 365 positions of the year. This meant that the same date would reoccur only once every 52 years or 73 tzolkins! (Morley, pg. 58) Time based on the Calendar Round was also divided into great cycles, each lasting 13 baktuns or 1,872,000 days. Once thirteen of these great cycles have been completed, the earth is supposed to end catastrophically according to Mayan legends. Therefore the present age will end on December 22, 2012 AD. (Gilbert and Cotterell, pg. 37, 296)

BIBLIOGRAPHY

Gilbert, Adrain and Cotterell, Maurice. The Mayan Prophecies: Unlocking the Secrets of

a Lost Civilization. New York: Barnes and Noble Books, 1996.

McLeish, John. The Story of Numbers. New York: Ballantine Books, 1991. 125-136.

Morley, Sylvanus G.. An Introduction to the Study of the Maya Hieroglyphs.

New York: Dover Publications, 1975.

"Maya". Funk & Wagnalls New Encyclopedia. Vol. 17. 1986 ed. (http://www/cmcc.muse.digital.ca/membrs/civiliz/maya/mmc05eng.html)