Is there an english translation of Xu Yue's Shushu Jiyi? This is the work, around 190 CE, often described as containing the first description of the abacus. It is often associated with China's "Ten Computational Canons", but usually isn't listed as one of the 10 officially.

I understand that it describes 14 different computational mechanisms/strategies, one of which is the abacus. Even if there is no full translation, is there perhaps a paper or book chapter in english which describes each of the 14 techniques?

I am a mathematician, but I know basically nothing about ancient chinese mathematics, so maybe there are easy references that I'm not aware of. Thanks for any help!


1 Answer 1


I'm afraid that there no English translation. There is a Russian translation, see here, where it is also affirmed that

The secon part contains the descriptions of 13 [not 14] methods of representation of numbers with counting devices; one of them, the "computation with pearls", refers to a form of abacus similar to the Roman abacus. There is an additional part [...] concerning some particularities of operations with counting rods.

Here you can find the English translation of a short excerpt, more in the paper of Alexei Volkov Large Numbers and Counting Rods mainly devoted to the problem of the "finitess of numbers" raised in the first part of the Shushu Jiyi (with longer excerpts), while you are interested in the second part, devoted to the "counting devices", that Volkov briefly discuss in its eighth paragraph.


Yet this theoretical construction (whether we understood it properly or not) has one essential defect: it could not insure that there exists in reality something corresponding to very large numbers; a priori, one cannot be sure that in this world there is something corresponding to 104096 (the largest number in the superior system).

Xu Yue's descriptions are very brief, and the modern reconstructions are due to abundant commentaries of Zhen Luan who systematically interpreted each "method" as a real counting device (which probably does not correspond to the original meaning of these descriptions.) [emphasis added] For the most part the described "devices" have been organized as linear sequences of decimal positions; the techniques of representation of a digit in one position are diverse and some of them are based on the traditional connotations between colors, orientations, etc.

The first "device" in this list is that of the counting rods. They are not described as if they were well-known to the reader. [...]


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