Oracle Bone Numerals

**c. 14th - 11th centuries BC**

In 1899, a Chinese scholar-official by the name Wang Yirong (王懿榮 wáng yì róng, 1845–1900) discovered a set of bones with unusual markings from an apothecary. The bones, referred to as "dragon bones" (龍骨 lóng gǔ) by the apothecary, were used for treating his malaria. Under closer inspection, Wang Yirong noticed the markings resembled Chinese characters and concluded that the fragments contained inscriptions written in an archaic form of Chinese writing. Not long after, the spread of Wang Yirong's discovery piqued the interest among antiquarians. This led to a boom of excavations over several decades. Thousands of inscribed cattle bones and tortoise plastrons were excavated in Xiaotun, a village near Anyang in Henan province. This excavation sites were the remains of the last capital of the Shang dynasty (商朝 shāng cháo, 17th - l lth centuries BC), now called Yinxu (殷墟 yīn xū).

Throughout the 20th century, many archaologists, historians, and epigraphers have studied these inscriptions in detail. The scholars concluded that the collection largely comprised of records and divinations.

Some of these writings include numerical information: the number of people, animals, shells, days, months, sacrifices, and war expeditions.

The Shang scribes employed two systems of counting. The first system was a sexagenary cycle used for tracking time (originally for marking the days). The sexagenary is comprised of two components: the ten Heavenly Stems (天干 tiān gān) and the twelve Earthly Branches (地支 dì zhī).

Tuses a combination of two elementary series of symbols, one consisting of ten elements (the ten celestial trunks, tiangan) and the other of twelve elements (the twelve terrestrial branches dizhi). Associated in pairs, these symbols give rise to a series of 60 doublet^.^ This series is usually called "the sexagesimal cycle" since it is used to number units of time in blocks of sixty units. Originally, the Chinese counted the days in groups of sixty, later the lunar months and, still later, from the second century BC, the years in the same way. This last system is still in operation today. However, 60 does not correspond to any natural astronomical cycle and this system has never been used for arithmetical calculations. The second system is decimal and comprises the following 14 symbols8 consisting of thirteen signs for numbers and an additive conjunction corresponding to "and" :

Thus, a simple horizontal stroke is used to represent 1, while repetition of this one-stroke as many times as necessary specifies the numbers 2, 3 and 4 in a highly concrete way. The Sumerians, the Babylonians, the Egyptians, the Mayas and the Romans all used the same procedure to denote small numbers. The other symbols are much more difficult to interpret. In his Shuowen jiezi (a famous dictionary), Xu Shen (ca. 100 AD) explains the small numbers using magic correlations of the yinyang and the "five phases" (wuxing). Under the Tang dynasty, the philologist and exegete of the classics, Yan Shigu (581- 645) remained on analogous ground in his attempt to explain that the Chinese symbols for numbers came from the trigrams of the Y~jin~.~ These explanations are not really convincing, but they at least have the merit of reminding us that in China, numerous scholars believed that numbers and divination often went hand in hand. More recently, palaeographic study of the jiaguwen has led to the formulation of hypotheses of a different order. For Chen Mengjia,l0 the symbols representing 5, 6, 7, 8, 9, 100, 1000 and 10 000 are all "false borrowings" jiajiezi (in traditional Chinese philology, this is the name given to any written character

which is conventionally used in a new sense which it did not have originally; this is one of the six ways of forming Chinese characters). There is certainly some truth in this notion, because, for example, the symbol, which stands for the myriad is simply the pictogram of the scorpion. As Sakai Hiroshi explains," the swarm of colonies of new-born scorpions sticking together along the back of the females of this arachnid is an appropriate evocation of an immense number. In the same vein, we note that the jiaguwen uses a single symbol to represent one thousand and a man. To explain this curious telescoping, we may assume that in ancient China, the word "man" was pronounced in the same way as the word "thousand." We may also suppose that there was a link between certain parts of the human body and the symbol for a thousand. For example, just as the number ten may be explained using the fingers of two hands, a thousand could be derived from the ten toes of two feet, if it were true that each toe counted as a hundred. It seems that this was actually the case, since the pictogram for a hundred is precisely the same as that for the toe @ .l2 Of course, these are not the only possible hypotheses. Like Zhang Bingquan, we may also suppose, for example, that the symbols for certain numbers simply translated gestures of the hands or arms associated with these numbers.13 In any case, it is now important to analyse the way in which these symbols are combined to form numbers. As far as the notation for tens is concerned, we first note that the numbers 20, 30 and 40 are denoted by repetitive addition of the sign for ten. After 40, the following tens are denoted using a multiplicative principle; the same is true for hundreds, thousands and myriads. More precisely, in each case, the elements composing the pairs of symbols which are used to denote tens, hundreds etc. are written either on or above one another (the symbols may then be separate but they may also touch as though one were placed on top of the other)1

Intermediate numbers are written using both the additive and the multiplicative principles. For example15:

The largest number discovered in this system17 is 30 000. Could the Chinese of the Shang have denoted arbitrarily large numbers had the need arisen? Strictly speaking, we cannot answer this question, since we do not know if they asked themselves it. If we assume that they could only have done so within the conceptual framework of their system of numerals, we are however forced to conclude that to do so they would probably have had to invent indefinitely many new symbols to denote successive powers of ten.