Noviembre 22-26
Tonantzintla - Puebla - México

Contact: iberamia2004@inaoep.mx

The Pre Hispanic Computer
[ Versión en Español --> ]

The logo of Iberamia 2004 is based on an image of a Nepohualtzintzin that serves as the capital letter. A detailed account of this prehispanic computer is given below.

A scientific development that emerges from the Mexican ancestral roots explains the magnitude of the knowledge that our native ancestors had, and how it was possible that they made so exact calculus of universal cosmogony. This development is the Nepohualtzintzin, that is a pre-Hispanic computer, whose conception includes not only mathematical calculations, but also astronomical and gestation interpretations. The Nepohualtzintzin is an instrument, similar to the abacus or soroban, that serves to make arithmetical and mathematical calculations. When the handling of these devices is known, it is possible to perform not only basic operations (addition, substraction, multiplication and division) but also complex operations like roots, powers and integral and differential calculus operations. The main difference between the devices is that the abacus is based on the decimal numerical system (base 10) and the Nepohualtzintzin in a vigesimal system (base 20).

The word Nepohualtzintzin comes from the Nahuatl and it is formed by the roots; Ne - personal -; pohual or pohualli - the account -; and tzintzin - small similar elements. And its complete meaning is taken like; counting with small similar elements by somebody. Its use was taught in the Kalmekak to the temalpouhkeh, who were students dedicated to take the accounts of skies, from childhood. Unfortunately the Nepohualtzintzin and its teaching were among the victims of the conquering destruction, when a diabolic origin was attributed to them after observing the tremendous properties of representation, precision and speed of calculations. The Nepohualtzintzin was one of the cultural victims of the evangelizing paranoia of the conquest. But now we know with certainty that not only it was not an instrument induced by the demon in the mind of our ancestors, but that is a concrete sample of the great scientific and technological development that the majority of the native cultures already had in those times.

As a support to illustrate that the Nepohualtzintzin was not a product of chance, in the first place it can be mentioned the use of the vigesimal system (base 20) as the basic numerical system. Its use was due to the fact that for our ancestors, the count of 20 in 20 was completely natural, since the use of huaraches (native sandals) allowed them to also use the toes for their calculations. In this way, the amount of 20 meant to them a complete human being. It can also be mentioned the ingenious arrangement given to this device, since it is divided in two separated main parts by a bar or intermediate cord. In the left part there are four beads, which in the first row have unitary values (1, 2, 3, and 4), and in the right side there are three beads with values of 5, 10, and 15 respectively. In order to know the value of the respective beads of the upper rows, it is enough to multiply by 20 (by each row), the value of the corresponding account in the first row.

And from here, the surprising part of the integral concept of the Nepohualtzintzin arises. Altogether, there are 13 rows with 7 beads in each one, which makes up 91 beads in each Nepohualtzintzin. This is a basic number to understand the close relation conceived between the exact accounts and the phenomena of life. This is so that one Nepohualtzintzin (91) represents the number of days that a season of the year lasts, two Nepohualtzitzin (182) is the number of days of the corn’s cycle, from its sowing to its harvest, three Nepohualtzintzin (273) is the number of days of a baby’s gestation, and four Nepohualtzintzin complete a cycle and form a year. It is worth to mention that in the Nepohualtzintzin, amounts in the rank from 10 to the 18 can be calculated, with floating point, which allows calculating stellar as well as infinitesimal amounts with absolute precision. This series of data allows us to infer the high scientific-mathematic level that managed to reach our ancestors to develop a device of this nature, many years before the arrival of the conquerors.

The rediscovering of the Nepohualtzintzin is due to the teacher David Esparza Hidalgo, who in his wandering by all Mexico has found diverse engravings and paintings of this instrument and has reconstructed several of them made in gold, jade, incrustations of shell, etc. There have been also found very old Nepohualtzintzin attributed to the Olmeca culture, and even some bracelets of Mayan origin, as well as a diversity of forms and materials in other cultures. This gives us an idea of the so early epochs in which our ancestors already had the sufficient knowledge to devise and to handle a device of such complexity, and the notion of the extension of its use in their daily activities.

It is necessary to mention that some essays and papers have been written emphasizing the importance that could have the teaching of the manipulation of the Nepohualtzintzin in the infantile education. This is due to the fact that its handling demands to take an active mental process, which stimulates not only the calculation, but also the memory and abstraction capacities, very different from that to memorize the multiplication tables,. In this respect, and as a reference, I want to emphasize the example of Japan where the use of the Soroban (abacus) is taught during six years in the primary schools, and forbids the use of computers and calculators during primary and the junior high school, in spite of being the greater producer of them. It is known that the Soroban is used daily in banks, commerce and all types of companies where accounting of high accuracy is demanded, in Japan, Russia and others Eastern countries. And there are some who attribute the great capacity of technological development of the Eastern people to the acquired mental abilities through the teaching of this type of mental tool. As a final point of reflection, I just want to emphasize that the Soroban was introduced to Japan by the Catholic missionaries who had learned its use in China, approximately 450 years ago, which is practically the same time we have of ignoring anything about the Nepohualtzintzin.