- CHINA 173
FIGURE 2. The Luo-shu.gestation is nine months. The problem is to determine the gender of the unborn
child. In what is apparently an echo of the / Ching method of divination, the
author begins with 49 (the number of yarrow stalks remaining after the first one
has been laid down to begin the divination process). He then says to add the
number of months of gestation, then subtract the woman's age. From the remainder
(difference?) one is then to subtract succesively 1 (heaven), 2 (Earth), 3 (man), 4
(seasons), 5 (phases), 6 (musical tones), 7 (stars in the Dipper), 8 (wind directions),
and 9 (provinces of China under the Emperor Yu) and then use the final difference
to determine the gender.^8
The nature of divisibility for integers is also studied in Chinese treatises, in
particular in the Sun Zi Suan Jing, which contains the essence of the result still
known today as the Chinese remainder theorem. It was mentioned above that
in general the Sun Zi Suan Jing is more elementary than the earlier Jiu Zhang
Suanshu, but this bit of number theory is introduced for the first time in the Sun
Zi Suan Jing. The problem asks for a number that leaves a remainder of 2 when
divided by 3, a remainder of 3 when divided by 5, and a remainder of 2 when
divided by 7. As in the case of Diophantus, the problem appears to be algebra, but
it also involves the notion of divisibility with specified remainders. The assertion
(^8) Although no explanation is given in the translation by Lam and Ang (1992, p. 182), and no
value is given for the final difference in this problem, the child is said by the author to be male.
Perhaps the subtracting of successive integers was meant to continue only until the number left
was smaller than the next number to be subtracted. In the present case, that number would be
1, resulting after 7 was subtracted. This interpretation seems to make sense; otherwise, the result
of the procedure would be determined entirely by the parity of the woman's age.