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Edice Hua
Maya Civilizations
6th
April, 2017
Mr. Cesar Ross
1. Introduction
2. Concepts of Mayan numeral
I. Significance of the number
13 and 9
II. Significance of the number
1 and 2
III. Significance of the number
4 and 7
• The Mayan numeric system
was developed in the Classic
Period 250-900 A.D) for
religious and mathematical
purposes.
• It was extremely significant
because it played a vital role
in making the Mayan
calendars.
• Maya numerical system is
quite different from the
number system we use today.
• According to some scholars, the 13
numbers with the idea that there were 13
heavens in the ancient Mayan
Otherworld. Others link this number to the
amount of joints we have in our body (13
in all: ankles, wrists, kneecap, elbows,
shoulder, hips, neck, etc) thus, the number
13 means humanity.
• To the Mayas, even numbers were often
notified as positive qualities into events
while odd numbers were seen as
challenging or intense.
• Unlike numbers of the contemporary
world, each numbers of the Maya numeral
hold great symbolism.
• In the Maya’s view of numbers, they
believed it flows in a wave-like
motion. Small numbers such as
0,1,2,3,4 and 5 are regarded as mild
and soft. However, the middle
numbers such as 6,7,8, and 9,
represents the days of balanced
energy and power.
• The final days such as 10, 11, 12 and
13 are too high, thus are potentially
dangerous and too powerful.
• Because of this, many rituals were
conducted on the balanced days at
the center of each trecena (13 day
period in the tonalpohualli [260
days] calendar).
• As previously mentioned, high numbers
were regarded as too powerful or very
intense.
• However, there are exceptions even to
this rule. On 13 days, it is said that the
spirit world is closer. Thus, a 13 day is
the best day upon which people
meditate, seek visions, and cultivate
psychic prophecies.
• The number 9 is an odd number, but
known to be an extremely positive one,
mostly used for ritual purposes.
Inscriptions surviving from the Classic
period suggests that 9 was the day
• The number 1, indicates a new start or
beginning, unity, the original energy of
creation. As a low number, it is powerful, for
it has to do with the energy of the new
trecena which is making its arrival.
• The number 2 is a symbol of duality. Maya
think in terms of cosmic polarities. This is
represented in their mythology: there are
two Hero Twins, two principal Lords of the
Underworld, as well as the two monkey
twins who represent the day-sign Chuen.
There is the eternal dichotomy of this world
and the Underworld, day and night,
darkness and light. These themes run like a
common thread in all of Mayan myth,
especially in the sacred book the Popol
Vuh.
• The number 4 symbolizes wholeness. It
could be linked to Ahau, the Sun God as
cosmic lord (the word ahau literally
means lord). Why is this a solar
number? The word for “day” (k’in in
Yucatec or q’ij in K’iche’) is the same as
the word for “sun”; a day is a complete
passage of the sun. The day has four
transitions: dawn, noon, sunset and
midnight. These four components of
each day, each “sun,” can be
conceptually expanded to include the
solstices and equinoxes; thus the year is
also a 4.
• There is evidence that the Classic Maya
divided the universe into four sections
marked by the two intersections of the
Milky Way with the ecliptic. Thus we live
in a fourfold universe. The Maya still lay
out their ritual altars in a fourfold pattern.
• As confusing as it sounds 7,
represents death, or at least “endings.”
The reason for this may not be readily
apparent. In order to explain this, take
a closer look at any tzolk’in diagram.
Interestingly, the sequence of numbers
in the top row will be:
• 1, 8, 2, 9, 3, 10, 4, 11, 5, 12, 6, 13, 7
• “Any day-sign sequence beginning
with 1 will end in a 7. This is why 7 is
so often considered a symbol of
endings. In the Popol Vuh, the Hero
Twins are named 1 Hunahpu and 7
Hunahpu, while the most important
Underworld Lords are named 1 Death
and 7 Death. When 1 and 7 are paired
together in such a fashion, it is as if we
were saying: “The beginning and end
of the Hero Twins archetype,” or “The
alpha and omega of the Death
archetype.”
Mayan Philosophy of Numbers: a
Mathematical Perspective
Kieran Samuels
Maya Civilizations in Belize
6th
April, 2017
Mr. Cesar Ross
• Mayan & other Mesoamerican cultures used the
vigesimal number system. Vigesimal system based on
base 20 and to some extent base 5.
• Theory suggest that it was develop from using the fingers
and toes.
• Dates back to the 4th
cent. Approximately 1,000 years
more advance than the Europeans
• Mayan number system consist of three symbol. A shell
that represent zero, a dot represent one, and a line
represent five. One could write up to 19 with the these
symbol. Mayans were one of the only civilization that
understood the concept of zero from 36 BCE.
• Mayans number system was used by merchants and in
speeches.
• Places values are arrange vertically.
• Numbers can be found on stelae and monuments.
• Mayan may have used a “ Abacus”
• Number system included Calendar dates. They used
head glyphs as numbers sign i.e. 1 is often depicted as a
young earth goddess, 2 represent the god of sacrifice. It
can be illustrated by face-to-face glyphs or pictures
• The concept of fraction was not included, however they
made accurate astronomical observational discoveries.
Main function was to keep tract of time.
• Mayan Calendar used base 18.
• Hoffman, Mary Ann. "Mayan Mathematics."In Thehistoryof the
Maya: usingcomputational skills inproblemsolving, 18- 24.
New York: PowerKids Press, 2005.
• Johnson, Kenneth. "The Mayan Philosophy of Numbers." The
Mayan Philosophy of Numbers |The Mayan CalendarPortal.
November22, 2009. Accessed April 05, 2017. http://www.maya-
portal.net/blog/ken/mayan_philosophy_of_numbers.
• Macdonald, Fiona. "Numbers of the Mayas." In TheAztec and
Mayanworlds, 47-49. New York: Rosen, 2009.
• O'Coner, J. J. (2000). Mayan mathematics. Retrieved from
http://www-history.mcs.st-
and.ac.uk/HistTopics/Mayan_mathematics.html
• David E. Smith and Jekuthiel Ginsburg. Numbers and Numerals. W.
D. Reeves, 1937
• Edkins, J. (2006). Mayan Numbers. Retrieved from
http://gwydir.demon.co.uk/jo/numbers/maya/

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Mayan Numeric System

  • 2. 1. Introduction 2. Concepts of Mayan numeral I. Significance of the number 13 and 9 II. Significance of the number 1 and 2 III. Significance of the number 4 and 7
  • 3. • The Mayan numeric system was developed in the Classic Period 250-900 A.D) for religious and mathematical purposes. • It was extremely significant because it played a vital role in making the Mayan calendars. • Maya numerical system is quite different from the number system we use today.
  • 4. • According to some scholars, the 13 numbers with the idea that there were 13 heavens in the ancient Mayan Otherworld. Others link this number to the amount of joints we have in our body (13 in all: ankles, wrists, kneecap, elbows, shoulder, hips, neck, etc) thus, the number 13 means humanity. • To the Mayas, even numbers were often notified as positive qualities into events while odd numbers were seen as challenging or intense. • Unlike numbers of the contemporary world, each numbers of the Maya numeral hold great symbolism.
  • 5. • In the Maya’s view of numbers, they believed it flows in a wave-like motion. Small numbers such as 0,1,2,3,4 and 5 are regarded as mild and soft. However, the middle numbers such as 6,7,8, and 9, represents the days of balanced energy and power. • The final days such as 10, 11, 12 and 13 are too high, thus are potentially dangerous and too powerful. • Because of this, many rituals were conducted on the balanced days at the center of each trecena (13 day period in the tonalpohualli [260 days] calendar).
  • 6. • As previously mentioned, high numbers were regarded as too powerful or very intense. • However, there are exceptions even to this rule. On 13 days, it is said that the spirit world is closer. Thus, a 13 day is the best day upon which people meditate, seek visions, and cultivate psychic prophecies. • The number 9 is an odd number, but known to be an extremely positive one, mostly used for ritual purposes. Inscriptions surviving from the Classic period suggests that 9 was the day
  • 7. • The number 1, indicates a new start or beginning, unity, the original energy of creation. As a low number, it is powerful, for it has to do with the energy of the new trecena which is making its arrival. • The number 2 is a symbol of duality. Maya think in terms of cosmic polarities. This is represented in their mythology: there are two Hero Twins, two principal Lords of the Underworld, as well as the two monkey twins who represent the day-sign Chuen. There is the eternal dichotomy of this world and the Underworld, day and night, darkness and light. These themes run like a common thread in all of Mayan myth, especially in the sacred book the Popol Vuh.
  • 8. • The number 4 symbolizes wholeness. It could be linked to Ahau, the Sun God as cosmic lord (the word ahau literally means lord). Why is this a solar number? The word for “day” (k’in in Yucatec or q’ij in K’iche’) is the same as the word for “sun”; a day is a complete passage of the sun. The day has four transitions: dawn, noon, sunset and midnight. These four components of each day, each “sun,” can be conceptually expanded to include the solstices and equinoxes; thus the year is also a 4. • There is evidence that the Classic Maya divided the universe into four sections marked by the two intersections of the Milky Way with the ecliptic. Thus we live in a fourfold universe. The Maya still lay out their ritual altars in a fourfold pattern.
  • 9. • As confusing as it sounds 7, represents death, or at least “endings.” The reason for this may not be readily apparent. In order to explain this, take a closer look at any tzolk’in diagram. Interestingly, the sequence of numbers in the top row will be: • 1, 8, 2, 9, 3, 10, 4, 11, 5, 12, 6, 13, 7 • “Any day-sign sequence beginning with 1 will end in a 7. This is why 7 is so often considered a symbol of endings. In the Popol Vuh, the Hero Twins are named 1 Hunahpu and 7 Hunahpu, while the most important Underworld Lords are named 1 Death and 7 Death. When 1 and 7 are paired together in such a fashion, it is as if we were saying: “The beginning and end of the Hero Twins archetype,” or “The alpha and omega of the Death archetype.”
  • 10. Mayan Philosophy of Numbers: a Mathematical Perspective Kieran Samuels Maya Civilizations in Belize 6th April, 2017 Mr. Cesar Ross
  • 11. • Mayan & other Mesoamerican cultures used the vigesimal number system. Vigesimal system based on base 20 and to some extent base 5. • Theory suggest that it was develop from using the fingers and toes. • Dates back to the 4th cent. Approximately 1,000 years more advance than the Europeans
  • 12. • Mayan number system consist of three symbol. A shell that represent zero, a dot represent one, and a line represent five. One could write up to 19 with the these symbol. Mayans were one of the only civilization that understood the concept of zero from 36 BCE.
  • 13. • Mayans number system was used by merchants and in speeches. • Places values are arrange vertically. • Numbers can be found on stelae and monuments. • Mayan may have used a “ Abacus”
  • 14. • Number system included Calendar dates. They used head glyphs as numbers sign i.e. 1 is often depicted as a young earth goddess, 2 represent the god of sacrifice. It can be illustrated by face-to-face glyphs or pictures
  • 15. • The concept of fraction was not included, however they made accurate astronomical observational discoveries. Main function was to keep tract of time.
  • 16. • Mayan Calendar used base 18.
  • 17. • Hoffman, Mary Ann. "Mayan Mathematics."In Thehistoryof the Maya: usingcomputational skills inproblemsolving, 18- 24. New York: PowerKids Press, 2005. • Johnson, Kenneth. "The Mayan Philosophy of Numbers." The Mayan Philosophy of Numbers |The Mayan CalendarPortal. November22, 2009. Accessed April 05, 2017. http://www.maya- portal.net/blog/ken/mayan_philosophy_of_numbers. • Macdonald, Fiona. "Numbers of the Mayas." In TheAztec and Mayanworlds, 47-49. New York: Rosen, 2009. • O'Coner, J. J. (2000). Mayan mathematics. Retrieved from http://www-history.mcs.st- and.ac.uk/HistTopics/Mayan_mathematics.html • David E. Smith and Jekuthiel Ginsburg. Numbers and Numerals. W. D. Reeves, 1937 • Edkins, J. (2006). Mayan Numbers. Retrieved from http://gwydir.demon.co.uk/jo/numbers/maya/