- Paperback: 416 pages
- Publisher: Princeton University Press; New edition (October 15, 2000)
- Language: English
- ISBN-10: 0691006598
- ISBN-13: 978-0691006598
- Product Dimensions: 5.5 x 1 x 8.2 inches
- Shipping Weight: 9.6 ounces
- Average Customer Review: 18 customer reviews
- Amazon Best Sellers Rank: #1,918,343 in Books (See Top 100 in Books)
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The Crest of the Peacock: Non-European Roots of Mathematics New Edition
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When we hear that mathematics is both the most noble endeavor of our species and that it was born in Europe, we naturally tend to be suspicious. Few writers could be as well-qualified to write about ancient math across the world as George Gheverghese Joseph, whose The Crest of the Peacock: Non-European Roots of Mathematics is a bright example of clear exposition and argument. Though the topic might intimidate those averse to mathematics, history, non-Western cultures, or some combination thereof, the book is essential for any reader who seeks a clearer understanding of any one of those. Joseph doesn't make things easy for nonmathematicians or nonhistorians, but the pleasure of meeting his challenge is robust. He explains ancient African, American, and Asian methods of counting and manipulating numbers with ease, paying particular attention to the historical development of and interrelationships between cultures. When discussing systems of mathematics as complex as those taught in ancient India and China, Joseph includes sample problems and discussions to help the interested student see numbers as past learners did. The revised edition includes a lengthy section, titled "Reflections," that updates and expands much of the material. Few readers will be able to match Joseph's grasp of both history and mathematics, but all will find The Crest of the Peacock as delightful and elegant as its subjects. --Rob Lightner
Enthralling. . . . After reading it, we cannot see the past in the same comforting haze of age-old stories, faithfully and uncritically retold from teacher to pupil down the years. . . . Invaluable for mathematics teachers at all levels. (New Scientist)
What is valuable here is the unified approach that Joseph brings . . . and the non-technical clarity that the attempt to reorder historical priorities and educate his readers out of their European prejudices requires. (The Times Literary Supplement)
A magnificent contribution. . . . The conventional wisdom being challenged is that there is one mathematics, largely invented by Europeans. Joseph demonstrates convincingly that the conventional wisdom is false. . . . A rich and fascinating canvas. (Race & Class)
If only this book had been available when I was a student!. . . This book will carry you to a deeper place: an appreciation of the many non-European roots of mathematics.---Jerry Lenz, Mathematics Teacher
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The colonial rationale to denigrate "Natives" no longer stands so the truth must be told. This is but the tip of an iceberg.
As you might have guessed, Joseph is vastly more biased and dogmatic than any of the traditional historians he is trying to criticise. His constant allegations that traditional scholarship suffers from “a deep-rooted historiographical bias” (3) are backed up by next to no evidence. Here is one typical rant:
“For some their Eurocentrism (or Graeco-centrism) is so deeply entrenched that they cannot bring themselves to face the idea of independent developments in early Indian mathematics, even as a remote possibility. A good illustration of this blinkered vision is provided by a widely respected historian of mathematics at the turn of the twentieth century, Paul Tannery. Confronted with the evidence from Islamic sources that the Indians were the first to use the sine function as we know it today, Tannery devoted himself to seeking ways in which the Indians could have acquired the concept from the Greeks. For Tannery, the very fact that the Indians knew and used sines in their astronomical calculations was suficient evidence that they must have had it from the Greeks. But why this tunnel vision?” (311)
Conveniently omitted from this diatribe is the pesky fact that Tannery was right, as Joseph himself discretely admits many pages later:
“There is some controversy as to the source of the Indian sine table. What seems likely is that … the Indian astronomers were indebted to an earlier source, possibly Hipparchus.” (399)
It is pretty clear who suffers from “tunnel vision” here. Evidently the fight for “anti-racist mathematics” (522) is too important to be checked by annoying details like the truth.
In one of his many inconsistencies, while Joseph condemns the methodology of Tannery et al., he also wants to use the exact same methodology himself, as he explicitly states. Joseph reasons that if Tannery et al. were allowed to conjecture Greek origins of non-Western mathematics, then he should be allowed to do the converse:
“If these conjectures [of non-western influences on European mathematics] are implausible, then so too must be the attribution of Greek or European origins to so many developments in mathematics and astronomy in other cultures.” (306) “A case for claiming the transmission of knowledge from Europe to places outside does not necessarily rest on direct documentary evidence. In certain circumstances, priority, communication routes, and similarities appear to establish transmission from West to East as more plausible, on the balance of probabilities, than independent discovery in the East. However, when it comes to East-to-West transmissions, there seems to be a complete change of orientation. The criterion for establishing transmission is no longer the comparative notion of ‘balance of probabilities’ but the absolute notion of ‘beyond all reasonable doubt’. This double standard makes it possible to sustain a case for Eurocentric histories” (438)
Joseph uses this logic to argue that 17th-century European proto-calculus was based on Indian Kerala mathematics (438), even though by his own admission there is zero direct evidence for this (443). The historiographic analogy between this and Tannery et al. is absurd. The source material for early Indian mathematics is very limited. Conjecture is unavoidable and the only way to say anything at all about this period. By contrast, for 17th-century Europe we have mountains of source material, often including not only hundreds of pages of published treatises from each leading mathematician but also copious personal correspondence and notes of many of them, in addition to endless contextual information. It is ridiculous to claim that these situations are historiographically analogous. It is not strange that a Greek influence is not explicitly recorded in a few succinct mathematical tracts from the early Indian period. But it baffles the mind how no evidence whatsoever of Indian influence, assuming there was any, has been found in the thousands upon thousands of pages of documentation of all kinds on the development of these ideas in 17th-century Europe. The racist European conspiracy to systematically steal Indian ideas and then erase any trace of this concerted effort must have been executed with extreme skill and diligence.
Ironically, Joseph’s twin goals—to prove for each non-Western culture that it was brilliantly modern and that it influenced the West—are often in direct conflict. Thus on the one hand he praises Chinese mathematicians for doing many things that were not developed in Europe until the 19th century (247, 302), yet at the same time he also wishes to argue that the possibility of “direct transmission of mathematical knowledge from China to the West” long before that “should not be dismissed out of hand, as many historians of mathematics are inclined to do” (305). In other words, Europeans both stole Chinese ideas and also remained ignorant of them at the same time.
Another inconsistency of a similar nature occurs when Joseph constantly flip-flops between characterising Europeans as on the one hand parochial bigots (which Joseph needs to “explain” why non-Western contributions have been neglected) but also at the same time as very open to absorbing ideas from other cultures (which Joseph needs to make hidden non-Western influences plausible). In the case of China for example, we are told that East-to-West transmission of mathematical ideas is plausible because, for example, “Leibniz (1646–1716), one of the founders of modern mathematics, … founded the Berlin Society of Science with the express purpose of ‘opening up China and the interchange of civilizations between China and Europe’.” (306) Some might take this kind of thing as evidence that Europeans were not a bunch of close-minded racists after all, but not Joseph. Apparently Joseph does not see any conflict between acknowledging this great Western openness on one page, and on the other claim that Europeans have dismissed the idea of Chinese contributions “because they find the idea unpalatable” (305).
The author constantly harps on Eurocentrism in mathematics history. This is wearing, and more than a little unfair. I image that the books he cites as having blinkered views of history probably do, but in my experience, this is not the general case. I took a math history course in a thoroughly American highschool back in 1986 or 87, and it covered most of the contents of this book as part of it, from Mesopotamian and Egyptian numerals and methods, to Indian works in permutations, trigonometry, and roots, to Arabic synthesis and improvements on Indian and Greek sources. I don't recall much on the order Chinese work in that history class, so perhaps Joseph has some point there.
The author wants desperately for there to be transmission and influence from different parts of the world to Greece and Europe, and has phrases like "The possibility of Zhu's work being transmitted to Europe should not be dismissed outright." This is peculiar in a book whose introduction asserts that finding connections is a valued activity, and, instead of making one wonder what interplay between societies occurred, makes one wonder why the author is so defensive about this particular idea. He allows that different mathematicians separated by a significant distance in a non-European culture can come up with the same idea independently, but then feels that the European mathematicians *must* have come up with ideas because of transmission from elsewhere. All of this feels hostile towards any chance that a Greek or European had an original idea, which just comes off as insecure and sad.
There are some points I wish were different -- Joseph translates historical sources into modern prose and notation much of the time, but leaves some of the earlier presented problems in a form closer to their original. I wish that he would have had the words in non-English languages in their native alphabet or characters as well as the anglified version. It seems a shame to refer to the Indus Valley Civilization by the term Harappa for where historians first discovered it.
It was pleasant to see some of the history of mathematics, though I wish it had been presented in a less frustrating way.