The Chinese Abacus. The abacus was first mentioned (possibly improved upon, but not invented) by the mathematician Xu Yueh (徐岳) at the end of Eastern Han Dynasty (25-220 A.D). The abacus is a tool for calculating numbers, and was widely used in ancient times up to the invention of the modern mechanical and electronic calculators. The abacus is similar to the modern calculator. It has a rectanglular wooden frame with beads in columns (nowadays you also can find abacus made with plastic or other materials rather than wood). There is a cross rod to divide beads into two parts, above the rod each bead represents quantities of five, while under the rod each bead represents quantities of one. The basic operations for which the abacus is helpful include arithmetic operations such as addition, subtraction, multiplication, and division. The computational methods using an abacus are called abacus calculations. Some people transform the abacus calculation operation’s principles for mental arithmetic (the mental abacus methods).

The mental abacus method rests upon a principle of visual imagination, as the mind recalls an abacus image and manipulates visual memory as imagined beads are moved around in the fantasized abacus. This is an interesting example of visual thinking (which is usually intuitive) performing abstract analytical thinking (mathematics). It is interesting to note that calculating prodigies often report that visual and intuitive methods lie behind their astonishing mathematical abilites, perhaps corresponding in some way to the mental abacus methods.

1. The Science Frontiers website has some interesting pages about calculating prodigies, which seems like a topic related to mental abacus.
2. This fascinating paper (actually, a book chapter) on Culture and Cognition (by Richard Nisbett and Ara Norenzayan) has, on page ten, a discussion of abacus users (pdf). If you’re ever interested in cultural differences in thought, look for the work of Richard Nisbett. He’s an expert in that field.
3. Here is a paper titled Change of Mental Representation with the Expertise of Mental Abacus (available in pdf) by Hidenari Negishi, Kazuhiro Ueda, Mitsugu Kuriyama, Masaharu Kato, Hideo Kawaguchi, and Hirokazu Atsumori.
4. Here is a Chinese language (traditional characters) website describing the history of the Chinese abacus, and mentioning Xu Yueh’s part in its history.
5. Another Chinese language article (traditional characters) about the abacus. This one says the Chinese abacus is one of the 101 most important inventions in human history.
6. This page from the Bookrags website gives a very thorough description of the history of the abacus, using descriptions from various reference sources on the Internet. Some sources claim an abacus was used in Babylon about 4,200 years ago, and many sources claim the abacus was not invented in China.
7. Finally, you can read page 32 from the Shorter Science and Civilisation in China: An Abridgement (of Joseph Needham's work by Colin A. Ronan) about the history of the abacus.

This work by Eric & Chun-Chih Hadley-Ives is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.