The Enneagram - History of the Decimal System

One of the problems in determining the origins of the enneagram is that the sequence of the pattern of the internal lines is based on the decimal division of 1 by 7 yielding the repeating decimal 0.142857.


Shang Dynasty 1766-1122 BCE 
Decimal place system (14th century BCE) - 2300 years later in Western civilization

History of Chinese Invention - The Decimal System of Number Representation
Decimal number system, also called HINDU-ARABIC, or ARABIC, base 10 system, in mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and a dot (decimal point). 

A noteworthy characteristic of the Chinese system, and one that represented a substantial advantage over the Mediterranean systems, was its predilection for a decimal notation, as demonstrated by foot rulers dating back as far as the 6th century BC. An example of how the Chinese used the decimal system may be seen in an inscription from the thirteenth century BC, in which '547 days' is written 'Five hundred plus four decades plus seven of days'. The Chinese wrote with characters instead of an alphabet. When writing with a Western alphabet of more than nine letters, there is a temptation to go on with words like eleven. With Chinese characters, ten is ten-blank and eleven is ten-one (zero was left as a blank space: 405 is 'four blank five'), This was much easier than inventing a new character for each number (imagine having to memorize an enormous number of characters just to read the date!). Having a decimal system from the beginning was a big advantage in making mathematical advances. The first evidence of decimals in Europe is in a Spanish manuscript of 976 AD. 

The Genius of China
3,000 Years of Science, Discovery and Invention
written by Robert K.G. Temple and published by Simon and Schuster, 1986
Currently out-of-print

Encyclopedia Britannica, 1999


History of the Decimal System

The Arabic numeral system is considered one of the most significant developments in mathematics, and, ergo, several theories have been advanced about its origin. These theories include

  • the idea that it originated in China.
  • the idea that it was invented by Al-Khwarizmi.
  • the idea that it originated in the ancient Middle East and that the Arabic numeral system was simply an westward transmission of the Indian numeral system.

Although these theories contain varying amounts of truth, each is exaggerated in its thesis. Nevertheless, very few historians debate the Arabic numeral system was influenced by Indian mathematics.

Somewhat speculatively, the origin of a base-10 positional number system used in India can be traced to China. Because the Chinese Hua Ma system (see Chinese numerals) is also a positional base-10 system, Hau Ma numerals—or some numeral system similar to it—may have been the inspiration for the base-10 positional numeral system that evolved in India. This hypothesis is made stronger by the fact that years from 400 to 700, during which a positional base-10 system emerged in India, were also the period during which the number of Buddhist pilgrims traveling between China and India peaked. What is certain is that by the time of Bhasakara I (i.e., the seventh century AD) a base 10 numeral system with 9 glyphs was being used in India. This numeral system had reached the Middle East by 670. Significantly, however, this numeral system lacked a zero digit. Muslim mathematicians working in what is now Iraq were familiar with the Babylonian numeral system, which used the zero digit between nonzero digits (although not after nonzero digits). Furthermore, by 874, the latest Muslim mathematicians were using a base 10 positional numeral system, with the zero digit used both between and after nonzero digits. Mathematicians in India took the same step at essentially the same time (by 876 at the latest). The two groups apparently derived analogous numeral systems independently. In the early twelfth century AD, Arab mathematicians in North Africa extended the Arabic numeral system to include decimals.

Fibonacci, an Italian mathematician who had lived in North Africa, introduced the Arabic numeral system to Europe and promoted it with his book Liber Abaci, which was published in 1202. It should be noted that in the Muslim World—until modern times—the Arabic numeral system was used only by mathematicians. Muslim scientists used the Babylonian numeral system, and merchants used a numeral system similar to the Greek numeral system and the Hebrew numeral system. Therefore, it was not until Fibonacci that the Arabic numeral system was used by a large population.

This article is licensed under the GNU Free Documentation License
It uses material from the Wikipedia article Arabic Numerals


The Enneagram : A Lecture by Gurdjieff

(Note: A similar version of this lecture is presented in Chapter 14 of In Search of the Miraculous by P.D. Ouspensky.)


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