## Why Didn�t They . . . ?

**January 10, 2009**

Joseph Needham, right, with Chinese ambassador Hu Dingyi and Xie Heng. Photograph courtesy of the Society for Anglo�Chinese Understanding (http://www.sacu.org), which Needham co-founded in 1965.

**Book ReviewPhilip J. Davis**

**The Man Who Loved China.** *By Simon Winchester, HarperCollins, New York, 2008, 336 pages, $27.95. *

The Man in the title is Joseph Needham. Before Simon Winchester's book appeared, I knew the following about Needham. He was the author of the multi-volume *Science and Civilization in China* (Cambridge University Press), volumes of which began to appear in 1954 and are still appearing. Needham was a politically active and strong British Marxist. He was concerned with the question, If ancient China had been so far in advance of the West in science and technology, why did it lose this advantage? I had scanned very lightly Needham's 168 dense, footnote-laden pages on ancient Chinese mathematics in Volume 3 (1959), and the larger question, now dubbed the "Grand Needham Question," seemed to me to specialize to: If ancient Chinese mathematicians had been so great and fruitfully inventive, why didn't they invent mathematical proof in the sense of proof in Greek mathematics? I had the feeling that this lack must have rankled Needham, whose answer, it seemed to me, was that it was a consequence of a Taoist outlook. His article ends with 18 pages devoted to a comparison of Chinese and Western mathematics; I defer to the experts for their interpretation. More on the proof question later.

Joseph Needham (1900�1995) was a distinguished biochemist at Cambridge University. His *Chemical Embryology* (1931) is considered a masterpiece. In 1924 he married Dorothy Moyle, a biochemist in her own right, having contracted with her what was then called an "open" marriage. In 1936, a Chinese student, Lu Gwei-djen, appeared at his doorstep. She had begun a career in biochemistry and was hoping to learn from and collaborate with the Master. Additionally, she was greatly interested in the scientific traditions of her country. Needham fell in love with her, and from this association (which was life-long) and under her urging and tutelage, he learned Chinese and conceived a desire to know more about China, its history, and its culture. The opportunity came in 1942.

By 1942, the Japanese were in control of large portions of eastern China, Indonesia, Singapore, and other lands. The Chinese government moved its operations far to the west, to Chongqing. The British government, wanting to send a diplomatic/scientific mission of sorts to Chongqing, looked around for a qualified candidate and found one in Needham. After arriving in Chongqing---by no means an easy trip in wartime---Needham traveled extensively through the unoccupied portions of the country, meeting and talking with all sorts of people. He was amazed, entranced with what he saw and learned. He fell in love, Winchester writes, with everything Chinese: its history, accomplishments, people, food, landscape. Not least in significance, he met the future Communist leaders and politicians.

As early as 1948, Needham outlined a multi-volume study covering all aspects of Chinese science and technology, to which, without dropping biochemistry entirely, he was to devote the remainder of his life. There is no doubt that these volumes, written in collaboration with numerous scholars, have opened ancient Chinese science and technology to Western readers in a very substantial way. In these volumes, Needham seems to be saying that the ancient Chinese had it all, with little or no intrusion from the West. Or, to invert a quip of Disraeli: "Their ancestors were doing algebra when mine were painting their faces with woad."

Simon Winchester, a popular writer with a wide range of interests, has written numerous intriguing travel or travel-type books. It's no surprise, then, that the most engaging part of *The Man Who Loved China* is the description of Needham's travels in China (1942�46). The book cleverly avoids the word "science" in its title and claims eccentricity for its hero---probably a ploy of the publisher to secure a wide readership. Why did Winchester tackle Needham and the ancient Chinese? I conjecture that he had a sino-tropic epiphany similar to that of Needham. Strongly attracted by oddballs, Winchester is also the author of the earlier The Professor and the Madman, which tells the weird story of the creation of the *Oxford English Dictionary*. As concerns Needham's advertised eccentricity, his abrupt shift from biochemist to historian of science might be considered such, as might his early practice of nudism, but in devoting a half century to *Science and Civilization in China*, he showed no more eccentricity than a mathematician who has spent long years digging into a single arcane topic.

With Needham's vast and monumental accomplishment recognized and his reputation assured, it was inevitable that a later generation of scholars would begin to find fault with this and with that. Such is the nature of scholarship. Some said that Needham had applied a Western interpretation to what the Chinese had done, and that his philosophy of science admitted a single unitary science of nature. Others said that he had overemphasized the influence of Taoism and that he had downplayed the role of astrology, divination, and other such schemes in eliciting and applying mathematics.

Winchester lists 300 discoveries or advances in science and technology, from the 3rd millennium BCE to the 17th century CE, that Needham cited as pre-Western. Only a few of the 300 are mathematical accomplishments: the abacus, square and cube root algorithms, decimal place value, polar equatorial coordinates. I suspect that mathematics is not Winchester's long suit.

Needham was by no means the first to describe Chinese mathematical accomplishments to Western audiences. I was familiar, for example, with Yoshio Mikami's *The Development of Mathematics in China and Japan*, which first appeared in 1913, and I had seen Chinese accomplishments laid out in substantial measure in numerous pre-Needham Western histories.

Asserting that much more flowed out of than into China, Needham lists 14 mathematical ideas that, he says, emerged from China, went on thence to India, and thence to the Arabic/Western world: (1) decimal notation and zero as blank space, (2) computation of square and cube roots, (3) the rule of three, (4) vertical notation for fractions, (5) negative numbers, (6) visual proof of Pythagoras's theorem, (7) practical geometric problems, (8) area of a circular segment, (9) identity of certain algebraic and geometric relationships, (10) rule of double false position, (11) the Chinese remainder theorem, (12) equations with integer solutions, (13) numerical solution of cubic equations, (14) Pascal's triangle.

For criticisms of Needham specific to mathematics, I turn to *A History of Chinese Mathematics* by Jean-Claude Martzloff,* which, in my outsider's judgment, is currently the best general history of the subject; it places the mathematics strongly within the ancient Chinese cultural context.

Regarding Needham's claims for mathematics, Martzloff writes,

"This type of argumentation is controversial be-cause of its chronological and methodological imprecision. There is nothing to prove that concomitant developments could not have taken place."

Martzloff rebuts a few specific claims: The Chinese use of blank space as a zero is an unconfirmed hypothesis. The rule of three appeared in the Rhind Papyrus (1650 BCE). The negative numbers are not the same as those of the Indians. Roman land surveyors knew how to calculate the area of a circular segment, which is in the Heronian corpus (Alexandria, circa 50 CE). As regards Pascal's triangle, he points out that its uses in China, India, and the West differ. Even while asserting the glories of ancient Chinese mathematics and describing its own special flavor, Martzloff thus denies that the diffusion was largely one way:

"China was in contact with the outside world at different periods of its history, both over land and by sea."

I come now to the question of why the Chinese didn't have proofs in the Western sense. This very question irritates some historians of science, one of whom wrote to me:

"It is not very fruitful to ask why Chinese mathematicians did not do something. It is much more enlightening if one asks instead why some Greek mathematicians (but not all) became obsessed by foundational issues and searched for a means of compelling agreement to certain propositions."

Fair enough, but I consider the question both legitimate and interesting. Mathematics is a product of a culture. Recall: In one of the Sherlock Holmes stories, the answer to the question "Why didn't the dog bark?" was the principal clue. In my reading of history, the question of why the Greek mathematicians did what they did is as difficult to answer as the objectionable question.

Winchester, asserting that "Needham never fully worked out his answers to the Big Question," lists answers given by others: "They stopped trying." Why? Because there was never a mercantile class. Other answers include: Young people aspired to the bureaucracy. There was no intramural competition within a huge country. Totalitarian government, whether by an emperor or by communists, snuffs out creativity.

Specific to the lack of mathematical proof, J. Gernet writes (in a foreword to Martzloff's book):

"The Chinese have always preferred to make themselves understood without having to spell things out. . . . [They] have indulged their taste for conciseness and allusion, which is so in keeping with the spirit of their language, to the extent that they detest the heaviness of formal reasoning. This is not a case of innate capacity, since their reasoning is as good as ours, but a fundamental characteristic of a civilization. This loathing of discourse is accompanied by a predilection for the concrete."

Gernet provides a related explanation as well:

"For the Chinese, numbers and figures relate to objects rather than to abstract essences. This is in complete antithesis to the Greeks who rejected everything that might evoke sensory experience and runs counter to the Platonic concept of mathematics as . . . an objective science concerned with abstract notions that �enable the soul to pass from the ever-changing world to that of truth and essence.' "

If the ancient Chinese did not have proofs � la Euclid or proofs by contradiction (as in the Pythagorean proof of the irrationality of the square root of 2 or in Cantor's non-denumerability of the reals), what, then, were the hallmarks or the modalities of Chinese reasoning or argumentation? Martzloff points to the following: (a) progression from the particular to the general, (b) comparison, (c) analogy, (d) empirical methods, (e) heuristic methods, (f) non-linguistic means of communication.

The similarities between Chinese (Confucian) and Western principles of discovery and interpretation have received much scholarly attention recently, though admittedly these studies are vague concerning the question of intercultural diffusion. Each of these modes, the Chinese and the Western, is operative today as a method of mathematical discovery or invention, and even of exposition. Mathematics is a multi-semiotic enterprise; nonetheless, the pressures for "Western-style" justification via proof remain severe.

**Histoire des math�matiques chinoises*, Masson, 1987; English translation, Springer, 1997.

*Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at* [email protected].