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Measure units are concepts with which we cannot understand our world; be litres, parsecs, carats, metres, arshins, inches, grains or nanoseconds, without patterns and these multiples them we will have difficulties even with petty tasks. In order to bring things into measure and proportion we must have absolute references.
Indeed, patent and patron offices around the world strive to give us the most precise measure of a metre or a carat. What started as measures taken from naturally repeatable references, such as the seeds that gave birth to the carat as a weight measure for small and delicate things, like gems, precious stones and jewels, then evolved into concepts defined by technology as it advances. But one of the characteristics of humanity is that with our capability for reasoning we can create different ways to solve similar problems and even understand and value the existence of solutions different to ours even if we don't understand them wholly. Take for example, a book written in Chinese. Most people around the world would be unable to read it but almost everybody would value it as a book; the symbols contained therein certainly express ideas, perhaps similar ones to those found in a book written in a language and alphabet understandable to us. Perhaps the Chinese book tells a story that we have already enjoyed in a "readable" book format.So the fact is that even despite being useless for us, the Chinese book doesn't cease to be valuable as a book, and very few people would dare use it to light on a barbecue.
The native cultures in America have a common origin. It is important to stress that I speak about one America and not various because in reality it is one unit much like there are no two Europes or Asias; - understanding it as both North, Central and South America as a whole, more correctly in my opinion than saying "The Americas" for historic and geographic reasons, as well as anthropological: The Mapuches of Patagonia have exactly the same ethnic origin as the Sirionos of Bolivia, the Apaches and Inuits. And thus, they share common views and concepts that are different to what is found in the Indo-European origins of Western culture, but no less valid. Certain absolute concepts for us are not so absolute for Indians: For example, many groups didn't have written language yet they were far more advanced than Indo-Europeans at the time they didn't have them either.
Some Indian groups didn't have a clue about what a war is, or a God, but they lived perfectly well without them. Some Indian groups had more than thirty thousand words in heir languages, and Indians were capable of articulating about fifteen times more words as they spoke than most scholars of the time of the conquest of the New World that landed on the beaches of the continent in order to "civilise" the "surely" primitive Indians. This is not to say that Indians were free from faults and mistakes, but there are a lot of things that have been since discarded about their universal perspective, and that's a pity.As the ancestors of the modern Indians entered into America by the Bering strait, they began developing their own values and ideas. Units of measure are inherently necessary but for people still in a nomadic stage of things absolutes are never absolute, so at the most basic level, units of measure as we know them were a conceptual impossibility form these, the original settlers of the continent.
Over time, civilisations sprouted; some of them in North, Central and South America reached a level of development that was second to none. Incas, Mayans and Aztecs are prime examples. Each one of these cultures evolved, in turn, their own cultural aspects but one, which is very interesting was the perspective on measures that the Mayans conceived. Mayan culture was indeed violent; they developed warfare to a great extent but also they did the same with science and technology at large. The Mayan calendar is, by all means, more efficient and precise than ours, and you cannot achieve that without being excellent in many disciplines. However, being excellent as they were, Mayans didn't have one single clue about what an absolute reference is. Something like an ounce or a pound didn't have any value or meaning because they did not established concepts by measuring them against immutable references, but by seeing proportions between and into things. Indeed, Mayans developed their whole science and technology, including architecture and engineering based on there elation of natural forms. Their units of measure were two fundamental geometrical shapes: The circle and the square. For them, everything could be understood by combinations of these two shapes and perfection was achieved by making the fit between them as tight as possible.
An analogy could be established between the dichotomy of the Mayan versus our view of magnitudes and proportions and the way in which the two main types of computer graphics are generated: On one hand we have bitmaps, which are based on dots or pixels and would correspond to our magnitude-based outlook, and the other is the vector-based type, which is intrinsically related to proportions. We should only remember that their buildings have lasted until our days, and that should serve as a testimony of the correctness of their views and standards.
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