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 preHispanic 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 scientificmathematic
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.
