Writings on Reckoning

September 30, 2007 7:38 AM

The Suan shu shu (筭數書) is an ancient Chinese collection of writings on mathematics discovered together with other texts [Chinese, incl. image of bamboo slips from same excavation] when in 1983 archaeologists opened a tomb at Zhangjiashan in Hubei believed closed in 186 BCE. Main link includes a downloadable full translation with commentary of this earliest extant Chinese work on mathematics by noted China scholar Dr Christopher Cullen.
posted by Abiezer (9 comments total)

Oh awesome. I love ancient math/science stuff.

Oh crap, the PDF doesn't display for me. :(((((
posted by DU at 9:18 AM on September 30, 2007

Eek! It's opening fine for me here with Evince and xpdf under Ubuntu. Didn't think to check it under anything else.
You're missing out on such classic problems as

The fox goes through a customs-post
A fox, a wild-cat and a dog go through a customs-post; they are taxed 111 cash. The dog says to the wild-cat, and the wild-cat says to the fox ‘Your skin is worth twice mine; you should pay twice as much tax!’
Question : how much is paid out in each case? Result: the dog pays out 15 cash and 6/7 cash; the wild-cat pays out 31 cash and 5 parts; the fox pays out 63 cash and 3 parts.
Method: let them be double one another, and combine them [into] 7 to make the divisor; multiply each by the tax to make the dividends; obtain one for [each time] the dividend accommodates the divisor.

posted by Abiezer at 9:34 AM on September 30, 2007

I've always loved the story of how the 1600's mathematical genius Leibniz had invented the binary number system, then later studied a copy of the I Ching, written thousands of years earlier. He was shocked to discover each chapter headed with the a Hexagram: a number, written in binary.
posted by eye of newt at 10:08 AM on September 30, 2007 [1 favorite]

Some very cool stuff here. The PDF displays fine for me but I have Chinese fonts installed. Glad to see that people are continuing Needham's legacy.
posted by sudasana at 10:18 AM on September 30, 2007

Cool post Abiezer. "The Suan shu shu is the earliest known extensive Chinese writing on mathematics." wow.

Your mathematics link leads to an excellent history of math index.

I was fortunate in knowing a close friend and fellow scientist of Joseph Needham's, Professor Mansel Davies, who made the following, interesting statement:

"For forty years, Dr Joseph Needham of Cambridge has conducted a masterly survey into the history of science and technology, through the whole period of classical Chinese civilisation. Aided latterly by a small group of specialists, he has now published more than ten separate volumes entitled Science and Civilization in China. This monumental work has led to a number of observations in which aspects of Chinese achievements are compared with related activities in European science. These comments are concerned with what may be inadequacies in these comparisons. One of Needham's recurring problems is to explain why Chinese technology, ahead of that in Europe for more than two millenia, did not lead to the rational mathematico-logical science of the post-Galilean variety. Some of his assessments are criticised. It is suggested that a major feature in the West was Greek-Arabic mathematics with its logical structure and its enormous power in the analysis of physical systems. Needham, as a biologist, has a deep appreciation of the 'organic' world-view which is so strongly represented in Chinese writings: but there are dangers, to be avoided, in supporting a dichotomy between the biological and physical sciences. Is field theory essentially non-mechanistic only in that it cannot usefully be illustrated in terms of levers and pulleys? Some of Needham's claims for the significance of Chinese science are considered in relation in the science we call chemistry."
posted by nickyskye at 10:32 AM on September 30, 2007

I love this sort of stuff. (PDF displays fine for me on MacOSX, fwiw.)
posted by hattifattener at 11:27 AM on September 30, 2007

On XP/Firefox, the pdf file opened fine. The Chinese text is hard to follow, so the translation is really helpful.

A classical math problem 韩信点兵 is attributed to a general under Emperor Han Gao Zu (about A.D. 200): One version goes that the emperor asked the general how many soldiers did he have. The general answered: 每3人一列余1人、5人一列余2人、7人一列余4人、13人一列余6人... (If they line up 3 in a row, 1 person remains; 5 in a row, 2 remains; 7 in a row, 4 remains, 13 in a row, 6 remains...) Apparently the general solution of this type of problems is called Chinese Remainder Theorem.

Even more tangentially... In Jin Yong's famous Wu Xia novel, 射雕英雄传, one chapter features an enjoyable battle of wits/math between the heroine and a female recluse.
posted by of strange foe at 11:33 AM on September 30, 2007

errr....evince under Ubuntu is exactly what's failing for me. I assume it's a font problem.
posted by DU at 12:54 PM on September 30, 2007

I wish I could have found an accessible link in English on the textual contents of the tomb - the deceased seems to have been a minor scholar-official who was buried with a small library of works on law, philosophy and maths, as we have here. The bamboo slips pictured in the Chinese link in the FPP are a very early version of customs regulations, which the modern customs agency was having a modern copy made of.
The field of ancient Chinese is quite exciting these days, with a steady stream of new text discoveries, including quite different versions of well-known classics like the Dao De Jing.
posted by Abiezer at 6:48 PM on September 30, 2007