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The Mesoamerican Abacus That Gives Modern Calculators a Run for Their Money

Ábaco mesoamericano. Captura de pantalla de video de YouTube.

Mesoamerican abacus. Screenshot of video posted on YouTube.

The nepohualtzintzin is a calculation device used in pre-Hispanic Mesoamerican cultures, including the Mayans, that is now making a comeback in several education programs, which are making use of this powerful tool to teach mathematics at an early age in a completely organic way.

The name nepohualtzintzin is formed by two words in the Mesoamerican Nahuatl language: nepohual, which means “counting,” and tzintzin, which means “the venerable or relevant.” Thus, the word nepohualtzintzin means “the relevant counting.”

There’s nothing magical about this ancient device, known also simply as nepo. It doesn’t require the use of paper or pencil, but instead makes its precise calculations using beads.

The Mayan numerical system was based on the number 20, unlike the decimal system used today. This vigesimal system included the number zero:

La notación en el sistema vigesimal es similar salvo que la base es 20. En este sistema se necesitan veinte cifras diferentes, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, y 19 que también se pueden representar como 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I y J.
[…]
Con el sistema numérico vigesimal, los mayas podían efectutar las operaciones matemáticas fundamentales por medio de tablas de sumar y de multiplicar y con la utilización de un ábaco constituido por una cuadrícula hecha con varillas, o dibujado directamente en el suelo, y se utilizaban piedrecillas o semillas para representar los números. Este ábaco recibía el nombre de Nepohualtzintzin.

The notation on the vigesimal system is similar, except that 20 is the base. This system needs 20 different figures, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19 that can also be represented as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I and J.
[…]
With the vigesimal numerical system, Mayans were able to carry out basic mathematical operations through addition and multiplication tables and using an abacus made out of a rod-based grid, or directly drawn on the floor, and they used pebbles or seeds to represent numbers. This abacus was known as nepohualtzintzin.

Due to the huge number of operations it allows to carry out, it could be said that the nepohualtzintzin is comparable to a modern computer. It's a set of 91 beads spread out in 13 rows of seven beads. Ninety-one is a fourth of 364, about the number of days in a year, so the total number of beads represents one season. Two times 91 is 182, the cycle of corn:

El sistema matemático del nepohualtzintzin surgió de la necesidad de sobrevivencia de nuestros antepasados; quienes, para cultivar la tierra, tenían que contar los días, los fenómenos de la naturaleza y sus ciclos y observar, por ejemplo, que el Sol, aparece día a día por el Oriente recorre el cielo hasta ocultarse por el Poniente.

The nepohualtzintzin mathematical system came out of the necessity that our forefathers had for survival; to till the land they had to count the days, natural phenomena and their cycles, and watch, for instance, that the sun appears every day in the east, goes across the sky and then sets in the west.

It's important to note that the Mayan civilization was the first in the Americas to figure out the number zero:

Las matemáticas mayas han dejado una huella en el tiempo; antes que cualquier otra civilización, los mayas originaron un concepto revolucionario: el cero.
El cero es un símbolo comúnmente utilizado para representar la nada; sin embargo, el concepto maya del cero no implica una ausencia ni una negación; para los mayas, el cero posee un sentido de plenitud. Por ejemplo, al escribir la cifra 20, el cero, puesto en el primer nivel, únicamente indica que la veintena está completa.

Mayan mathematics have left an imprint in time; before any other civilization, Mayans came up with a revolutionary concept: the number zero.
Zero is a symbol commonly used to represent nothing; however, the Mayan concept of zero doesn't imply an absence or a negation. For the Mayans, zero has a sense of fullness. For instance, when writing the figure 20, the zero, put on the first level, simply indicates that the score is complete.

Today, this pre Hispanic tool is being used to make teaching math easier, among other uses:

Su uso habitual fomenta la habilidad numérica, mejora la capacidad de concentración, de razonamiento lógico, la memoria, la agilidad mental, el procesamiento de información de forma ordenada y la atención visual. Se podría considerar que el uso del nepo es una excelente forma de ejercitar el cerebro, manteniéndolo activo y ágil a cualquier edad. El NEPO es uno de los pocos aparatos que estimula el mayor número de sinapsis (contactos neuronales) entre ambos lóbulos cerebrales simultáneamente, además de promueve en el niño el desarrollo de la motricidad fina.

Used frequently, it fosters numerical ability, improves the power of concentration, logical thinking, memory, mental agility, orderly information processing and visual attention. Using the nepo could be considered an excellent way of exercising the brain, as it keeps it active and flexible at any age. The nepo is one of few devices that stimulates a higher number of synapses (connections between neurons) between both brain lobes simultaneously, in addition to promoting children's development of their fine motor skills.

This website has an instruction manual of how to use a nepohualtzintzin. In the video below, professor Everardo Lara González shows how to do mathematical calculations with a nepo:

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