Indigenous Mathematic Systems
In Western culture it is often asserted that the "native brain" can't quantify. But a cursory examination of mathematics in the history of ancient Indigenous societies worldwide exposes this as a Eurocentric myth.
African Mathematics
By the 18th century, the African kingdom of Borno was the most important centre of learning of mathematics in the Central Sudan, attracting scholars from all over. They specialised in the science of Ilm al-Awfaq - magic squares. They had also developed advanced solar calendars and studied medicine, astrology, arithmetic, logic and astronomy. Not many people are aware that the famous scientist and mathematician, Ptolemy, was African, as he is usually portrayed as European.
Native American Mathematics
Native Americans developed highly sophisticated geometrical systems, although their texts recording these are usually dismissed as visual art in the West. They also developed advanced probability calculations used in gambling and meteorology, in accordance with Coyote religious texts. These algorithms were used to enhance genetic complexity in crops selectively bred for agriculture. They also developed highly sophisticated mathematical codes for smoke signal communication - codes so complex that they were used by the U.S. military in World War 2, the most famous being the Navajo Codes, which were far more advanced than their Western equivalents.
Australian Aboriginal Mathematics
In Australia, mathematical systems have been developed over tens of thousands of years to create intricate kinship systems ensuring genetic vigour. Similar systems were innovated millennia ago for species breeding and classification. Weight systems were based not on numbers, but on patterns on natural objects such as shells, conforming to what western scientists have only recently "discovered" and labelled as the Fibonacci sequence. Geometry was used in calculating time according to the angles and postion of the sun, moon and stars at different times, governing predictions about seasons and weather. This was also used for navigation.
Although in many Australian Indigenous cultures numbers had no names beyond three, large-scale quantifying was still used in records and calculations through patterns and diagrams on rocks, trees, bark and message sticks. Many language groups in New South Wales developed base five number systems. Calculators for this were developed based on one-to-one correspondence, using materials such as honky nuts (like a disposable abacus system), and served to perform calculations of addition, subtraction, multiplication and division.
Myth Of "Primitive Logic"
Sadly, in my country at least, a lot of the original Indigenous advanced mathematics has been lost through the process of colonisation. As a result, Indigenous students and workers are generally considered to be deficient in the field of numeracy, a problem that is too often attributed to genetic rather than social deficit. Shame prevents a lot of us from attempting to reclaim this ancient, sophisticated knowledge, which is dismissed as "primitive" by the dominant culture. Until the mainstream respects this knowledge, and supports our right to reclaim it, the remnants will continue to disappear, and this world will be the poorer for lack of it.
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