## History of Numeral Systems - 3

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- Published: Thursday, 04 August 2016 10:09

Well-known is a fairly plausible hypothesis of one of the researchers of the ancient culture, the American mathematician Otto Neugebauer, on the origin of the Babylonian numeral system. The gist of it is that after the ancient inhabitants of Mesopotamia - Sumerian tribes – were conquered by Acadians, there was a natural unification of the "money-weighting" systems. It turned out that the Sumerian mina was balanced by about 60 Acadian shekels (in the absence of coins, the calculation was conducted based on the weight of materials adopted for the calculations). This ratio between two powers in the monetary system could have spread to other values.

In addition to the advantages related to ease of addition and multiplication tables, there was another, much more important factor which determined the predominant spread of the decimal numeral system. It was its "consistency" with the very first and very effective method of calculation: counting on one’s fingers. The same reason obviously made some peoples use quinary (Chinese, Japanese) and vigesimal (Celts, Maya tribes in pre-Columbian Central America) numeral systems. Even the use of the duodecimal system can also be explained the anatomic features of the human hand. Namely, four fingers of one hand have exactly 12 joints. The origin of the word "dozen", often used as a synonym for the numeral "twelve", is related to the duodecimal system.

In the depth of the past centuries, we can recognize traces of the use of numerical systems with some other bases. Notable among them is the binary system, which is well known to everybody through counting by twos. And one of the greatest mathematicians of all time Gottfried Wilhelm Leibniz (1646 - 1716) developed the theoretical foundations of arithmetic in binary numeral system, noting its particular simplicity and, seemingly, sensing intuitively the greatest suitability of this system for computing through digital computing machines.

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