History of numeral systems - 1

   Even the ancient Egyptians and Babylonians, who later taught the Greeks, had special signs for writing down numbers. The Egyptian notation embodied the first of the fundamental principles of modern numeral system – its decimal basis, the Babylonian system – the second one, positionality. The ancient Egyptian system was decimal, but not positional, the Babylonian system – positional, but not decimal.

   Ancient Egyptians used special characters to denote units, tens, hundreds, etc., that is, degrees of ten (order units), but the placement of these symbols in a numeral did not matter at all. They only used to write down as much of them as there were units of a corresponding order in a given number. Writing a number in the ancient Babylonian system of numbering based on positionality. Namely, they invented a relatively simple way of writing down numbers from 0 to 59 – analogous to our unique numbers for 0 to 9 - and, besides, took into account the order (position) of these digits in the recorded number. The rule was that the first digit on the right denoted the number of units in this number (0 to 59), the second digit - the number of sixties (again - from 0 to 59), the third – sixties squared and so on. Thus, it was a sexagesimal positional number system. The tradition to divide an hour into 60 minutes, a minute into 60 seconds, and a degree into 60 minutes dates back to this system.

   The Greek and later the now well known Roman numbering systems are similar to the ancient Egyptian one. These systems were also decimal and non-positional. The slight improvement which took centuries concerned only symbols used for orders. Instead Egyptian hieroglyphs and their later stylized images now used this alphabet. Later this idea is embodied in the Ancient Rus numbering system.

   The invention of the now ubiquitous positional decimal numeral system took place in India about the VI century C. E. In the VIII century, this system was adopted by Arabs, who used to rule "all the world" at the time (it was already the time of the Arab Caliphate). Around the XII century,  through Arabs, the decimal positional numeral system became known in Europe. That is why it is often, but not quite correctly, called Arabic (it would be more accurate to call it the Hindu-Arabic system, as well as our Arabic numerals, which would also more accurately be called the Hindu-Arabic figures).

Next article: History of Numeral Systems - 2

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