Today speakers of Chinese use three written numeric systems namely the Arabic numerals used worldwide and two indigenous systems. The most familiar indigenous one is based on Chinese characters that correspond to numerals in the spoken language. The second indigenous system is the Su(1)zhou(1) or hua(1)ma(3) – literally meaning picture number which is based on the rod system (see later). Today the hua(1)ma(3) system is only used for showing prices in Chinese markets or on traditional invoices.
Chinese people are fascinated by numbers and wherever you go in the country there are numbers everywhere and not just in phone directories, calendars and clock faces. In fact its numerologist’s paradise and numbers are deeply embedded in the Chinese language and culture. For example when entering the Forbidden City you will be informed amongst other things that there are 980 buildings and 8,704 rooms.
This short article will attempt to introduce you to this interesting topic. It is a vast subject and I only hope I can do justice to it. Chinese mathematics was, like their language, very concise and precise.
As in many other countries calculations were first carried out using the fingers hence the importance of the number ten. As business and commerce activity increased other techniques were introduced in other countries including the use of knots in strings, counters in the form of pebbles, bones or sea shells. China however introduced a method of counting using rods as the counters. Five rods were used in various combinations as shown below. The five bamboo rods representing numbers one to nine are shown below – first row for positive and second row for negative numbers.
As can be seen the rods are laid horizontally and vertically depending on the number to be shown.
Ten was represented by I –, while 100 was I– — and 1000 was 千.
As time progressed the rods were replaced by the abacus – a counting frame. That topic is for another article.
As in other cultures some numbers can bring good fortune whilst others bad luck and calamities. However in China it is more extensive. In fact ancient Chinese books were written in chapters that reflected the principles of numerology and important events that are held on dates that will bring good fortune as I will describe later.
The current numbers used in China are shown below with the numbers one to twelve. The first column shows the character and the second column the name in pinjin:
Higher numbers up to 99 are combinations of the above numbers. For example twenty is expressed as two-ten namely: er(4)shi(2) and ninety nine as nine-ten-nine namely: jiu(3)shi(2)jiu(3).
Higher numbers are expressed in units so 100 is -百: yi(1)bai(3), 1,000 is – 千: yi(1)qian(1) and 10,000 is -万: yi(1)wan(4).
The numbers in China like in other countries are considered lucky or unlucky as well as having other meanings. In Britain seven is considered lucky whilst thirteen unlucky but in China there are many more as described below and are deeply embedded in Chinese culture and language.
In recent times the number one has come to represent the state of being single. The number two is generally regarded to be a good number if not particularly lucky. The number three indicates many and in Confucianism and Taoism three represents Heaven, Earth and mankind. Four is considered a very unlucky number because it sounds like death si(3) some buildings omit all floors with 4 in them and some cinemas and theatres omit rows with 4 in them. Five is associated with the five elements and the Emperor of China. That is why there are five archways at the Tiananmen Gate (built in 1651). Remember the five elements are Water, Fire, Wood, Metal and Earth. Six is another lucky number especially for business and commerce. Seven is associated with traditional religions and with relationships and symbolises togetherness. For example it is said that 7×7 (49) is the number of days that a dead person’s spirit remains among the living. Eight is a lucky number as it sounds like prosperity and good fortune. A recent example of its use as a lucky omen was the 2008 Olympics started at 8pm on 8th August 2008 – 8/8/2008! People will pay a great deal of money to get 8’s on their car registration plates. Nine is considered auspicious as it was associated with the Emperor and dragons. The nine dragons were often displayed on the Emperor’s robes. Ten is the symbol of totally in the Chinese culture.
Numbers also figure when indicating days of the week and the months of the year. Monday is xing(1)qi(1)yi(1) literally meaning week one and this is continued up to Saturday as xing(1)qi(1) or week six the only exception is Sunday which is referred to as xing(1)qi(1)tian(1) meaning ‘week heaven’ or ‘week of the heaven’ and Sunday is also referred to as xing(1))ri(4)meaning the ‘the day of the sun’.
The months of the year are again easy to memorise and involve numbers for example January is yi(1)yue(4) namely first month whilst December is shi(2)yue(4) namely twelfth month. Yue (4) means the moon or month as the traditional Chinese calendar was based on the lunar cycle so the character also means the moon.
Number also figures significantly in the language e.g. in every day speech, idioms, proverbs and other sayings. A few examples are ‘to be agitated’ literally is seven up eight down – qi(1)shang(3)ba(1)xia(3), read ten thousand books and walk ten thousand miles, it takes ten years to grow a tree, but a hundred to bring up a generation of good men and it is as impossible to find a perfect man as it is to find 100% pure gold.
Ordinal numbers are formed by adding di(4) before the number e.g. di(4)yi(1) the first number di(4)shi(2) the tenth number.
One consequence of China’s fascination with numbers is they are very numerate and outperform people in Western countries. Some commentators suggest that Chinese speakers can memorise more numbers than English speakers in the same amount of time. Chinese students can memorise numbers faster because of the way they sound as the words for the numbers one to ten are all short and concise very similar to bullet points for example yi(1), er(4), san(1) and ba(1) on average take about one quarter of a second to say compared with about a third of a second for the English equivalents.
The history of Chinese Mathematics is truly amazing. They developed branches of the subject many centuries before the West although the West has been reluctant to acknowledge these achievements. The West prefers to celebrate and extoll the achievements of Greece and Egypt. However as recent research and archaeological findings confirm, China was in the forefront of mathematics and very much a pioneer of the subject.
Martzloff, Jean-Claude. ‘A History of Chinese Mathematics.’ Springer- Verlag. ISBN 3-540-54749-5. 1997. (An excellent text of the topic of Chinese Mathematics).
Submitted November 2018