The Decimal and Binary Systems
The decimal system is now universally used in mathematical calculations and the binary system plays a vital role in computer technology. These two systems were closely related to ancient Chinese explorations and innovations.
The decimal system, a positional numeral system employing 10 as the base and requiring 10 different numerals, looks quite simple and natural, but it took strenuous efforts for mankind to develop such a system. Counting of numerals appeared in China some 6,000 years ago in the late Neolithic period. At that time people counted numbers by making knots on a rope and cutting notches in wood. Numerals were found on pottery pieces unearthed at the Banpo site that dates back 6,000 years. On cultural relics dating from some 4,000 years ago that were unearthed in Shaanxi, Shandong and Shanghai, there were single digits and signs representing 10, 20 and 30, which means the decimal system was used at that time. Of the 13 characters used for counting from among the inscriptions on bones or tortoise shells of the Yin and Shang dynasties, nine were identified as single digits, and the rest four were symbols representing place values such as 10, 102 and 103. In the number system used in the inscriptions, numbers comprised the nine digits from one to nine and symbols of place values. Signs from the two groups were combined to represent certain place values, and groups of signs were then added together to represent numbers.
In an inscription dated from the 13th century BC, "547 days" was written as "five hundred plus four decades plus seven of days." And in Yi ling, (Book of Changes) was recorded the number of "eleven thousand five hundred and twenty." The way numbers were counted in the inscriptions on bones or tortoise shells has lasted all along to modern times. The Chinese numerals of zero and one to nine now in use were adopted before the Tang Dynasty, and the capital forms of the Chinese numerals were first used by people in the Tang Dynasty on formal occasions such as in official documents. After establishing the decimal system, ancient Chinese adopted fractions, decimal fractions and negative numbers, thus greatly expanding their understanding of numbers .
Ancient Chinese were the first to use the decimal system in the world. The Chinese likely created the decimal system because their language depended on characters (like pictures) instead of an alphabet. Historical records show ancient Babylonians used symbols similar to later Roman numerals in counting; ancient Egyptians and ancient Greeks also used special signs for such numbers as 20, 30, 40, which are multiples of 10. For instance, ancient people on the Greek Peninsula used 27 letters to record numbers, with nine letters for numerals from one to nine, another nine for 10 to 90, and the other nine for 100 to 900. Such clumsy special signs of place values were used till the eve of Renaissance in Europe. The Indians began using the decimal system in the 6th century. The first believed instance of the use of decimal system in Europe was in a Spanish manuscript dated around 976. The decimal system was a great, indelible contribution to mankind by ancient Chinese. Dr. Joseph Needham once said that without the decimal system, it would be almost unlikely to have the present-day unified world.
As the mathematical basis for computer technology, the invention of the binary system was attributed to German mathematician Gottfried Wilhelm Leibniz (1646-1716), a universal genius and an avid Sinophile. Leibniz's binary arithmetic was closely related to the bagua, or eight basic trigrams contained in the Chinese classic Book of Changes. The basic trigrams, said to be invented by one of the earliest legendary Chinese rulers Fu Xi, are formed by solid lines (representing yang) and broken lines (representing yin), and combinations of the eight trigrams again constitute the 64 hexagrams. Take the solid line as 1 and broken line as 0, the 64 hexagrams become natural numbers in the binary system in a descending order: 111111(63), 011111(62), 101111 (61)... 000000 (0).
Leibniz got the table of hexagrams from Joachim Bouvet (1656-1730), a French Jesuit scientist and missionary to China, which gave him great inspiration. In 1703 he published Explication de l'arithmetique binaire, avec des remarques sur son utilite, et sur ce qu'elle donne le sens des annciennes figures Chinoises de Fohy, in Memoires de l'Academic Royale des Science (An Explanation of Binary Arithmetic Using only the Characters 0 and 1, with Remarks about its Utility and the Meaning it Gives to the Ancient Chinese Figures of Fu Xi). Of binary numeration, he writes "it permits new discoveries in... arithmetic.., in geometry, because when the numbers are reduced to the simplest principles, like 0 and 1, a wonderful order appears everywhere..."
In China, philosopher Shao Yong (1011-1077) of the Northern Song Dynasty put forward a fairly complete binary system in his essays on Yi Jing (Book of Changes), but his discovery was not disseminated. |
