Showing posts with label The Mayan Calendar. Show all posts
Showing posts with label The Mayan Calendar. Show all posts

Friday, November 30, 2012

History Mystery: Mayans Number System!


I think this is the right time to discuss about the Mayan calendar and hence this post for your views. Before going to discuss the Mayan mathematics and numbers it is very important to know how we came to know all about them.

Here is a small briefing: Diego de Landa a Spanish Franciscan aged 17 landed in Yucatan peninsula and helped the Mayan people to resist the invasion of Herman Cotes of Spain. Remember that the people of the Yacatan peninsula were the descendants of the ancient Mayan civilization which was declined after 900 AD. Landa tried his best to protect the people from the Spanish masters and he visited all the ruins of the great Mayan cities of ancient civilization and learnt their customs and their history. Since he is a Franciscan a stunt follower of Christianity he abhorred their religious practice and sentiments he ordered for the Mayan idols and books should be destroyed. Later he has regretted for his action and he did mention in his book “Relación de las cosas de Yucatán” In that book he describes the hieroglyphics , Mayan customs, their temples and temple practices etc. Few Mayan documents which survived after Landa’s destruction were Dresden codex, Madrid Codex and Paris Codex. In the all above the Dresden Codex is believed to be copied from the original documents of Seventh century AD and it is a treatise of Astronomy. Knowledge of Mayan civilization has been greatly increased in the recent years due to the modern technology such as aerial photography, satellite imaging and high resolution radar imaging etc. The Mayan people constructed temples, palaces, shrines, thatched houses, terraced buildings causeways and huge dams to store rain water and the rulers were the high priests and possessed high knowledge in astronomy field. The farming was carried over in the raised fields with the help of the irrigation system.

 They were the highly cultured and civilized people who used calendar for their routine and religious life. Since they are masters in astronomy and calendar it is evident that they are masters in Mathematics too. The Mayan followed a very refined number system. It is assured that their mathematical system was the very advanced one of those times. Mayan number system is based on twenty (it is worth remember we are following number system based on ten). Most of the scholars give the following reason for their d vigesimal (twenty) system. Ancient people used both of their fingers and toes for calculation hence it is. Though it is of base twenty it has only three symbols for representing a particular number amazing isn’t it? They had the number zero and it was represented by a shell. Though the number system looks like positional, it is not actually so.

 The Mayan number mentions the unit numbers from one to nineteen in the first place and in the second place twenties up to nineteen and in the third place it denotes the numbers up to 360’s instead of 400’s after that the system reverts to the multiples of twenties ( i.e. 202 , 203 204 so on…)

 Let us see one example:

Consider one Mayan numeral: [9; 8; 9; 13; 7]

It actually represents the following number : + 13 × 20 + 9 × 18 × 20 + 8 × 18 × 202 + 9 × 18 × 203 =1357107

The above example was derived using the Dresden Codex. Some of the historian argued that they have followed different systems for astronomy, calendar and merchandizing but there is no written evidence for that.

 Let us discuss about the Mayan Calendars, they followed two calendars namely ritual calendar and civil calendar. The ritual calendar was known as the Tzolkin based on 260 days and it contained thirteen months of twenty days each. Each month was named after their gods and the days were numbered from zero to nineteen. The Haab, namely civil calendar consisted of 365 days and it had eighteen months of twenty days each and the remaining last five days were mentioned as wayem. According to Landa’s “Relación de las cosas de Yucatán” this last five days were considered as unlucky period for them and during those days they won’t wash comb and not even do any hard work. A satisfactory reason for why they followed two calendars could not be found. The years coincide after every 18980 days in other ward after every 52 civil years or 73 ritual years. Mayan astronomers accurately calculated the movements of Venus. Apart from these calendars the Mayans measured the time in another way also. It was an absolute time scale based on the creation date. 12th August 331 BC is taken as creation day but some historians differ from this Long count. The long count based on 360 days in a year is nothing but the count of days in Mayan number system hence it is more accurate than the other two calendars. Most of the inscriptions available from the Mayan towns are in terms of long count only.

Let us see one example for this:

 This [8; 14; 3; 1; 12] date is mentioned in a Plate found from the town Tikal.

 Let us calculate the year of inscription. 12 + 1 × 20 + 3 × 18 × 20 + 14 × 18 × 202 + 8 × 18 × 203 = 1253912 That is it was made 1253912 days after the creation date of 12th August 3113 BC. Hence the plate was carved in the year 320 AD.


The Mayans astronomical measurements are outstanding and more accurate. They don’t have any instruments other than sticks. They made a cross like shape with the help of two sticks both tied together at 90 degrees and through this they observed celestial bodies and their movements. Many of the historians believe that The Caracol building at Chichen Itza to be a Mayan observatory. Many of the windows in Caracol follow certain rules with respect the movement of moon and Sun. With their crude instrument namely with sticks the Mayans accurately calculated the length of a year as 365.242 days. Our modern scientific world recorded the same as 365.242198 days. In the similar manner Mayan accurately calculated the lunar month as 29.5302 days and latest findings displays it as 29.53059 days.

Thursday, January 20, 2011

History Mystery:Written in Stone

The mysterious Mayan writing used pictographs and phonetic symbols. The first sign to be understood were mathematical, and usually appear in the form of dates. The Maya used what is known as the Long Count system, in which each date was recorded as the number of days since an earlier, fixed date. Many archaeologists believe that this fixed date corresponds to August 13, 3114 BC- a day which precedes the earliest settlements of the Maya tribes by about 1000 years.
The date may relate to Maya legends about the origin of the world. The Maya believed that three worlds had been made and destroyed by the gods before their own world came into being. The first world contained men made from earth; the gods destroyed them because they were mindless. The men of the second world were made of wood; but they were soulless and unintelligent, and were drowned or devoured by demons. In the third world, the gods made the Maya ancestors from gruel of the scared plant, Maize. They were destroyed to make way for the present world- for men of flesh and blood.
Using 3114BC as a starting point simplifies the dating of the events of Maya history. At Tikal, all the engraved dates that have been found fall between AD292 and 869.
Maya mathematicians mainly counted in multiples of 20. Each Maya year, or tun, contained 18 months of 20 days each, and another five ’unlucky days’. Years were grouped into katun, or 20-years period; baktun, or 400 year periods; and so on up to the alautun, a period of more than 63 million modern years.
Until the deciphering of the stelae, the names and deeds of Tikal’s rulers were surrounded by uncertainty. A puzzling gap of more than a century in the erection of stelae at Tikal, falling between 557 and 682, has not been explained. In 562, Caracol a city subordinate to Tikal’s arch enemy, Calakmul- inflicted a defeat on Tikal. It was not until 672 that Tikal began to regain its former importance, and under the leadership of Hasaw Chan K’wail, Calakmul was eventually defeated in 695. Hasaw guided Tikal to the peak of its power.

Saturday, July 3, 2010

The Mayan Calendar

The calendar Imagery among the Maya is so prominent that some experts believe that they had an obsessive fascination with time rivaling that of present –day humans. They used two calendar systems, the Long Count Calendar and The Calendar round. The Long Count was perfected in Classical times that are AD 250-900, and its dates record the number of days that have elapsed since a mythological starting point corresponding to 3114 BC in our calendar. In fact the Maya believed that the world had been created and destroyed at least three times, the last creations having begun on August 13, 3114 BC, and the next being due on December 24, 2011.




Long count dates are precise counts of elapsed time based on the 360 -day year, which they called a tun, divided into 18 months of 20-day unials. The Mayan numbering system is based on 20, not ten, so a year was counted in groups of 20 tuns, termed a katun, and 20 katuns termed a baktun.
A Long Count date is made up of five numbers. The first figure records the baktun (400- year span).  The second is the katun (20-year span), the third a tun (360-day span, the fourth a uinal (20- day span0 and the last a kin, a single day.  The oldest recorded date is July 6, AD292, from Stela 29 at Tikal in northern Guatemala.
The Calendar Round simply names the day in two different calendars. The first is the sacred round of 260 days, the Tzolkin, composed of 20 day names and 13 numbers,  It is pictured as a set of interlocking cog wheels representing circular time: one with numbers from one to 13, the other with 20 named days,
Imix -
 Day one,
Ik   – Day two,
Akbak – Day three etc.
Supplementing this is the Haab (also called the Vague Year), a year of 365 days made up of 182 day months and then a five day period at the end of the year. It takes 18950 days, or 52 365 day years, for a combination of these two methods to repeat itself.