THE SEXAGESIMAL SYSTEM

CASE 5:  Popular Belief in Ancient China

In ancient China, at least since the Shang Dynasty, people used a sexagesimal system to calculate dates. “Sexagesimal” is an adjective that means proceeding by sixties. In particular, it refers to or concerns a system of measurement or numerical notation that either uses sixty as a base or is based on a division into sixty equal parts. For instance, an hour is divided into sixty equal minutes and a minute into sixty equal seconds.

In the sexagesimal system found in the Daybook, every day is tagged with a combination two characters. The first character comes from a series of ten “heavenly stems,” which are jia 甲, yi 乙, bing 丙, ding 丁, wu 戊, ji 己, geng 庚, xin 辛, ren 壬, and gui 癸. The second character belongs to a series of twelve “earthly branches,” which are zi 子, chou 丑, yin 寅, mao 卯, chen 辰, si 巳, wu 午, wei 未, shen 申, you 酉, xu 戌, and hai 亥.

The first day combines the first characters of both series (jia zi 甲子), and the second day comprises the second characters of both series (yi chou 乙丑) and so on until the tenth day which is gui you 癸酉. Since the “heavenly stems” only number ten, the first character of the eleventh day rotates back to the first “heavenly stem,” jia 甲. However, since the “earthly branches” number twelve, the second character of the eleventh day is the eleventh “earthly branch,” xu 戌. Thus, the eleventh day is jia xu 甲戌, and the twelfth day is yi hai 乙亥. Yi 乙 is the second of the ten “heavenly stems” and hai 亥 is the twelfth and last in the “earthly branches” series. In turn, the first character of the thirteenth day is the third of the “heavenly stems,” bing 丙; and its second character rotates back to the first of the “earthly branches,” zi 子. The thirteenth day is bing zi 丙子. Following this sequence, the sixtieth day is gui hai 癸亥. Given that qui 癸 is the tenth and last “heavenly stem,” while hai 亥 is the twelfth and last of the earthly branches, the sixty-first day would form a repetition of the first day, jia zi 甲子.

Since the combinations of ten “heavenly stems” and twelve “earthly branches” form sixty different permutations, beginning with jia zi 甲子 and ending with gui hai 癸亥,the cycle of sixty became the basis of the calculations of years and days. The Chinese lunar calendar, which is still used today in conjunction with the solar calendar, uses the sexagesimal system to name the years. For example, the year 1895, when Taiwan was ceded to Japan after China’s defeat by Japan, is the year of jia wu 甲午. Therefore, that particular war between China and Japan was called named “The War of Jia Wu,” which is a famous date in Chinese history. The next year of jia wu, sixty years later, was 1955. For an example of the use of the sexagesimal system in date notation, see the translated text on CHILDBIRTH in the Daybook.

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