Reflections on Chinese Numeration Systems: What If?

Frank J. Swetz (The Pennsylvania State University)

If a bundle of sticks had such a prolonged and productive involvement with mathematics, then where do we see evidence of their existence today? The traditional written characters used to express some numbers in China and Japan bear vestiges of their heritage in counting rods. Specifically, Ei ,er, and san, the first three counting numbers, provide evidence of rod origins:

Chinese characters for the numbers 1, 2, 3.
Figure 11. Characters for the numbers \(1\), \(2\), and \(3\). Figure drawn by the author.

Further, and perhaps more interesting, is the conjecture by historians of mathematics such as Wang Ling, Joseph Needham, and Lam Lay Yong and Ang Tian Se that our contemporary numeral system is derived from rod placements [Xu 2005]. They suggest that, as rod numerals were recorded and copied over centuries, scribes became complacent and hastened their writing process, gradually slipping into more cursive forms as illustrated below.

The author's conjecture for the evolution of numeration systems.
Figure 12. A conjectured evolution of numeration systems. Figure drawn by the author.

What do you think? Perhaps our numeral system could more correctly be designated as the ‘Sino–Hindu–Arabic’ numeral system. Such a title might be more encompassing and historically revealing.