The great incas technology is still the subject of many studies.The Incas achieved great knowledge because they achieved objective truth through accurate and reasoned knowledge of things or facts, that is, by their own methods. The sciences that were cultivated in the empire mostly in the Yachayhuasi and some in the Acllahuasi: they were Philosophy, Cosmology, Astronomy, the latter in relation to Mathematics and Geometry. They also treated History, Geography, Medicine and Law.
The Incas knew perfectly the components of the natural environment, its various processes and phenomena of the biosphere as a whole and the ecological systems that compose it, which is demonstrated by the successful use of agricultural and climatic technologies, well applied in their time.
For centuries the men of the Andean societies progressively subdued nature, which means that they knew how to take advantage of accidental discoveries and planned achievements, to enrich the accumulation of knowledge they had about their natural environment, taking advantage of it for their benefit, with which already at the time of Tahuantinsuyo it meant the highest degree of development in scientific, technological and cultural aspects, such as:
• There is a count of thousands of useful, edible, medicinal, poisonous plants, as well as those necessary for construction, elaboration of domestic and ornamental objects.
• Exploitation and classification of animals, fish and insects: edible, dangerous or poisonous; wild, domesticable and working.
• Domain of astronomy, weather phenomena, seasons and their changes for the development of solar and lunar calendars; astrological charts and their application to agricultural cycles, forestry, navigation, etc.
• They generated units of measurement to quantify data, areas, objects, distances, volumes, weights, dimensions, time, etc., and that have evolved into abstract, mathematical and philosophical concepts, as well as equipment for calculating and archiving data. obtained: yupanas and quipus.
• Manufacture of utensils and instruments to increase the potential of human strength, resulting in increased productivity with less effort and in new relationships with the environment.
Everything said above was used in practical and specialized application: platforms, canals, aqueducts, suspension bridges, great palaces, fortresses and even cities built with the use of carved and polished stone, among others, show the extraordinary capacity, ingenuity and mental and physical strength of the Inca people until the arrival of the Spanish.
The history of the Inca empire is magnified if we consider that, in general, the instruments used in science and technology were natural: stones, metals, vegetable fibers, etc., but their techniques were of complex knowledge for their time, giving as result, great achievements in various decisive fields of scientific, technological and ecological production. This is the first premise to measure the origin and meaning of the material production of the Incas.
When speaking of the mathematical knowledge of the Inca culture, reference is generally made to its decimal administrative organization and its famous quipus, yupanas and quipucamayocs, leaving aside other important aspects of its ethnomathematical knowledge, which had great practical and practical use. Currently they are little known due to the lack of explanation and adequate disclosure. We identify that the Incas, collecting all the experience and knowledge of the cultures they conquered, reached important technological achievements which we can see in their architecture, ceramics, textiles, agriculture and other cultural manifestations.
They used these ideas to model their palaces, temples, fortresses, inns, and other buildings (doors, windows, niches, and walls).
They applied these notions to design the plan of their cities and plan their growth in an orderly manner.
CERAMICS AND GOLDWORKS
In modeling their ceramics (keros, huacos, aríbalos, ceremonial vessels, plates, pots) they used bodies of revolution, truncated cones, cylinders
They used these notions for the design of their drawings, prints and engravings. So that the finish is aesthetic, harmonious and elegant.
The Incas used both 2D and 3D scale figures to reproduce crop fields, irrigation canals, scale models, etc.
But let’s focus on the mathematics of the Inca people. Their number system was, as for many other peoples who used their hands to begin to develop the concept of number and its arithmetic, decimal. Furthermore, it was a positional system, like our Hindu-Arabic numeral system, with the special feature that the numbers were represented, as we shall see, by means of the quipus’ strings.
The decimal system was not only used to represent numbers, but was used as part of the social organization of the empire. At the base of the social structure were the puric, who were the working Indians, who were also the ones who paid taxes (peasants, ranchers, artisans and soldiers). The purics were organized in groups of ten (10), a court, which were under the command of a cancha-camayo. In turn, every ten cancha-camayos were supervised by a foreman, or pachaca-curaca, who had under his command, through the 10 cancha-camayos, 100 workers, a pachaca.
Climbing a little higher in the pyramid were the supervisors, guaranca-curacas, of a dozen (10) pachaca-curacas, a hundred (100) cancha-camayos, and a thousand (1,000) tributary Indians, known as a waranka. And the hierarchy followed, each person in charge in control of ten people of a lower rank than his own, with the Huno-Kuraka or chief of the tribe, with a total of 10,000 purics, what was known as a Hun, in charge of the.
The Incas used a device with ropes, the quipu (a word that in Quechua means “knot”), to represent numbers. But the quipu was more than a numerical writing system, it was an instrument to record information, such as statistical data related to census data, tax accounting, economic and production records, and similar numerical information related to the Inca empire and its government, which made it possible to conserve said numerical information in a lasting way.
The Quipus could also record other types of information, such as historical information, poems and songs, genealogies, times, or even function as a calendar. Each village, province, region had its own quipucamayos. The rulers used this information for the government of villages, provinces, regions or the entire Inca empire. As the chronicler Poma de Ayala writes “with the strings they governed the whole kingdom”.
The quipus were ropes, normally made of cotton or camelid fiber (obtained from llamas and alpacas), which used to consist of a main rope, which was the backbone of the quipu, from which they hung, knotted to the main rope, a series of hanging ropes on which the knots that represented the numbers were made. From these hanging ropes other secondary hanging ropes could in turn hang or there could even be superior ropes.
There were three types of knots, simple knots, long knots and figure eight knots. Even today, the Indians of Bolivia and Peru continue to use a system for recording numbers related to the quipu, whose name is the chimpu. Each number is represented in a bunch of strings, the knots tied on a single string are the units, the knots tied on two strings are the tens, on three strings the hundreds, on four the thousands, and so on up to the power of 10 that is needed for each number. In the following example, which represents the number 5,477, the 7 knots (or long knot of degree 7) that are below, and that are on a single rope, represent the units, the next 7 knots, which join two ropes, are the tens, then come the hundreds, which are 4 knots tied on three strings and, finally, 5 knots tied on the four strings the thousands.
Currently around a thousand copies of quipus are preserved all over the world. This word means “knot” in the Quechua language and is the name used to refer to the knots that the Incas wove in ropes knotted together.
The making of the quipus was not within the reach of the entire population, they could only be made by the quipucamayoc, the elite that administered the Inca empire, in other words, the wisest. An enormous variety of quipus have been found, but all with the same structure: a rope to which other cords are tied, either cotton or wool, made from llama or alpaca hair.
The main rope was called the main or transversal rope, and other colored ropes with knots of different shapes and sizes hung from it.
The key was in the knots
It is said that writing was born in Mesopotamia as a way to satisfy the accounting need, with it you could list merchandise, animals, what was stored and what was transported. Fictional narrative would come much later.
Some time ago, a team of researchers from Harvard University (United States) discovered that quipus were documents used to share accounting information. It was a communication code that allowed registering and transmitting numerical data related to finances, military figures or censuses.
The knots of the quipus kept truly complex information, which not only depended on the position they occupied, but also on the direction of the twist or the type of knot. All this makes some scholars suppose that the quipu was, in a way, a writing system.
Yupana, the abacus of the Incas
When more complex mathematical calculations were needed, the Incas used the yupana, a kind of abacus. Its name derives etymologically from Yupay, which in Quechua means to count.
This instrument was basically made up of a wooden frame with a table with five rows -two, three and five in the central cells, plus individual holes of larger upper and lower size- and four columns, which corresponded to the units, tens, hundreds and thousands units.
It seems that the officials used small stones and grains of corn that were displaced by the quadrants. If they were black, they were used to count what was owed, while if they were white, they recorded what had been paid.