The Mayan civilization has always not been surprised by its advances in certain areas of science, its admirable pyramids, its extremely precise astronomical observations and more. Here we will know why it was one of the first civilizations to use the zero and also the Mayan numbers from 1 to 100.
Mayan numbers from 1 to 100
The numbering system used by the Mayans was a positional system that was based on the number twenty (vigesimal). This system that some call "long count" was used mainly for the calculation of calendars, in the daily life of the Mayans they used a non-positional additive system very similar to the number system used by the ancient Egyptians.
Mayan numeration uses a system similar to the positional system based on the number sixty (sexagesimal) used by the ancient Sumerians and the ancient positional system based on the number ten (decimal) used by the Chinese to count in the counting table (Abaco) .
The system of stripes and points that was used by the Mayans is their numbering and was already used in the ancient cultures of Mesoamerica from approximately the year one thousand before Christ. The dash-and-dot system and place value system probably developed in the Monte Albán culture and was used by the Olmec, among others.
It is estimated that the Mayans adopted this system in the Late Preclassic period and incorporated a symbol to represent zero that consisted of an empty shell. This representation of zero could be the earliest known appearance of the concept of explicit emptiness in the world, although it is possible that it may have been preceded by the Babylonian system.
The similarity of the design of the Mayan numbers with the ancient Egyptian, Roman and ancient Chinese numbers is due to the fact that initially the calculations were not carried out on paper. The numbers were placed on a flat surface with special rods. The Mayans also used an empty shell and, probably, stones or fruit pits.
Initially, zero was used as positional notation, which indicates the absence of a particular calendrical count, later it was developed as a number that could be used in calculations and was included in the glyphic annotations that were used for more than a thousand years. until the arrival of the Spaniards who put an end to its use.
In the Mayan numbering system during the Classic period several signs were used to indicate zero, from the Postclassic a shell (snail) was used, empty is its representation, the unit is represented by a point, thus two points, three points and four dots represent two, three and four respectively, the number five is represented by a horizontal line. Using the combination of these symbols, the Mayans represented all the numbers up to the number nineteen.
The exact value of a number is determined by the vertical position it occupies, going up a level the basic value of the unit is multiplied by twenty. Thus, the lowest symbol would represent the units in the base, the next symbol represented in the second position represents the multiplication of the unit by twenty, and a symbol represented in the third position would indicate a multiplication by four hundred, and so on.
History
The Mayan civilization was one of the few civilizations in the world that created a positional number system independently, apart from the Mayans only the Sumerians, Indians and Chinese managed to do this. Ancient Greek astronomers used the Babylonian, or rather Sumerian, positional system, thanks to which we still measure time and angles in the sexagesimal system. The Europeans mastered the Indian decimal positional system only in the Middle Ages with the help of the Arabs.
The Mayan civilization developed in a sedentary way in Mesoamerica and it was in Guatemala and southeastern Mexico where it reached its maximum splendor. The Mayans were one of the most developed and remarkable cultures before the arrival of the Europeans. Thanks to their territorial expansion they were able to build large cities throughout their region such as Calakmul, Tikal, Nakbé, Uxmal, Palenque, Uaxactún, Altún Ha, Chichén Itzá, El Mirador among others in which they built important monuments, the most impressive being their imposing pyramids.
These communities were governed politically, socially and economically as independent city-states, the basis of their economy being agriculture and commerce. Among the main products used in their trade were jade, cocoa, corn, salt and obsidian.
The writing system used by the Mayans was partly hieroglyphic because it used figures instead of letters, making a combination of phonetic symbols of syllables and ideograms. The deciphering of the Mayan hieroglyphs has been extremely complicated since by order of the Spanish priests all the codices were burned during the conquest with the exception of three of them: the Dresden codex, the Paris codex and the Madrid codex.
The Mayans were great astronomers and their observations were highly accurate. They equaled and even far surpassed other contemporary civilizations in the study of the movements of the moon and the planets and the most amazing thing is that their observations were made with the naked eye without using any type of apparatus.
The measurement of the length of the solar year used by the Maya and by other Mesoamerican civilizations were more precise than those used by Europe at the same time. In the Gregorian calendar used by Western civilizations every four years, leap years add a day, this difference was already considered by the Mayans in their conception of the year that they counted them in multiples of four years corresponding to the north, south, east and west.
For the Mayans, the year did not have a fixed start date, but they began at dawn, at noon, at dusk and at midnight of each year; therefore, the corresponding adjustment of one day plus each multiple of four was made.
position numbering
The objective of the numbering system created by the Mayans was to measure time and not to perform mathematical operations, which is why they are related to days, months and years and in the form of organization of the calendar. To represent the numbers from the number one to the number twenty, in addition to zero, the Mayans used three different modalities:
A system that represented numbers by dots and dashes; a cephalomorphic numeral system, each digit from one to nineteen is represented by a glyph in the form of a head; and a zoomorphic numeral system, which uses shapes of different animals to represent the digits.
The basic symbols for the representation of the digits in the Mayan numbering system are three: the point that has the value of one, the line, also called by scholars as the bar, with a value of five and the empty shell. , also called a snail or seed with a value of zero.
The amounts are grouped twenty by twenty in the Mayan numbering system, so that at any level the digits can be placed from zero to nineteen, to reach twenty a point is required in the next level. The first level is used to write the units, the next level is used to write the twenties (groups of twenty), the next level, the third is used for the groups of twenty by twenty and the fourth level is used for the groups of twenty. twenty times twenty times twenty.
This numbering system has five as an additional base despite being a vigesimal system. One is represented by a dot, two, three and four by two dots, three dots and four dots respectively, the number five is represented by a bar and dots are added horizontally over the bar to represent six, the seven the eight and the nine. To represent the number ten, two bars are used, one above the other horizontally.
To form the number fifteen, three bars are used and continue like this until reaching the number nineteen, three bars and four dots on top, which is the maximum number that can be represented at each level since it is a vigesimal system.
Mayan Numbering Rules
The point is not repeated more than four times. The number five, represented by a bar, is not repeated more than three times, if you want to represent the number twenty or a higher number, the higher level is used. To write a number equal to or greater than twenty, the same symbols are used, varying the value depending on the position and the level where they are.
In Mayan numeration, the numbers are written starting with the lowest level and ascending in order as the number increases. Units are written in lowest order, zero through nineteen. In the following order, each point is worth twenty units and each bar has a value of one hundred units.
For example, to write thirty-two, starting at the lowest level, two bars are written and above it two points (twelve), at the next level a single point is written (at this level the point is worth twenty). Twenty added to the twelve of the first level is thirty-two.
Another example, to write one hundred and sixty-six, write six in the first order, a bar (five) and a period above it; the number eight is written in the second order, a bar and three points above it, but being in the second order the bar is worth one hundred units and each point is worth twenty units (one hundred plus sixty) plus the six of the first order are one hundred and sixty six)
The third order of the Mayan numbering system has an irregularity, the value of the units varies depending on whether you want to represent dates or if it is for any other reason. In a use other than the calendar, each point is equivalent to four hundred units (twenty times twenty times one), but if it is for purposes related to the calendar, the unit is equivalent to three hundred sixty (eighteen times twenty times one).
This difference is due to the fact that the Mayan years are divided into three hundred and sixty days, which is the closest multiple to three hundred and sixty-five. For the Mayans, each level is related to the calendar, the first level is related to the days (kines), the second level is related to the months (uinals) and the third level is related to the years (tunes). To write very large amounts, the Mayan number system has four levels.
The Mayan Zero
It is estimated that in the year thirty-six before Christ the Mayans of the Preclassic period developed and adapted the use and concept of zero. The positional number system requires the use of zero to denote empty digits, since in this type of system each symbol has a value that varies according to its position.
In the Mayan numeral system, the symbol that is generally represented as zero is an empty shell (coffee seed, snail) but it could also be represented with a Maltese cross, a hand placed under a spiral or a face covered with a hand.
Representation of the Mayan Numbers from 1 to 100
To write the Mayan numbers from 1 to 100, it is necessary to be clear about the rules for writing Mayan numbers, the main ones are: the point is not repeated more than four times. The number five, represented by a bar, is not repeated more than three times, if you want to represent the number twenty or a higher number, the higher level is used. To write a number equal to or greater than twenty, the same symbols are used, varying the value depending on the position and the level where they are.
To begin the writing of the Mayan numbers from 1 to 100, one is represented with a point, two, three and four with two points, three points and four points respectively, the number five is represented with a bar and they go adding dots horizontally on the bar to represent six, seven, eight, and nine.
To represent the number ten, two bars are used, one above the other horizontally. To form the number fifteen, three bars are used and continue like this until reaching the number nineteen, three bars and four dots on top, which is the maximum number that can be represented at each level since it is a vigesimal system.
To represent the number twenty, the symbol representing zero is placed on the lower level, which some describe as an empty shell, a snail or a seed. In the second level, a point is placed that in this level is equal to twenty. To write the number twenty-one in Mayan numeration, at the first level, the lower level, a dot is placed which at this level has the value of one and at the next level another dot, which, unlike the previous one at this level, is equivalent to come, twenty plus one equals twenty-one.
The number twenty-five is represented by placing a horizontal bar on the lower level, which represents the value of five, a point is placed on the immediately higher level, this point is equal to twenty, plus the five of the lower level, twenty-five.
The number thirty is represented by two horizontal bars at the bottom level and a dot at the top level. To represent the number thirty-five, three horizontal bars are placed on the lower level, which would add up to fifteen, and one point on the upper level will result in thirty-five.
The number thirty-nine is written by placing three horizontal bars and four points above it at the lower level, which would add up to nineteen, at the level immediately above one point is placed, total thirty-nine. As the rule says, only three bars can be accumulated, so to write forty you put zero in the first level and two putos are placed in the upper level, which are worth twenty each, that is, forty.
And so on, bars, dots and shells are added to form the different figures, until being able to represent the Mayan numbers from 1 to 100. The number ninety-nine is represented by placing three horizontal bars with four dots on top, this is equivalent to nineteen on top. four points are placed, which have a value of twenty each, these eighty plus the nineteen of the lower level are ninety-nine.
As the rules say, you cannot accumulate more than three bars, therefore, to represent one hundred, the empty field that represents zero is placed at the lowest level and a horizontal bar is placed at the upper level, which at this level represents one hundred. (twenty times five) . This is how the Mayan numbers from 1 to 100 are represented.