Letters

42 Historically Speaking · May/June 2006 Letters Narrative and Popular History Writing a response to an essay becomes more of a challenge when the responder fundamentally agrees with it. Paul Jankowski's essay "Guilt byAssociation" {Historically Speaking, March/April 2006) is a first-rate discussion of narrative history. There is also a certain irony that Jankowski and I share, writing analytically in praise of narrative. Narrative and popular history are often linked. Many historians find popular history suspect. Look at another field, say, music, and this argument seems silly. The Beatles are the best-selling recording artists ever. They are also among the best. Being good and popular is hard, but why not try? Some first-rate historical works, such as those by James McPherson, sell very well. Good historical narrative is harder to write than narrowly focused analysis. Too many historians do not wish to make the effort to relate their little picture to the context provided by the ever-present big picture. Narrowness, too, is often a product of political correctness. Some historians consciously try to restore a balance by shedding light on groups ignored in the past. This is good. It is not good, however , when distortions creep in, perspective is lost, and narrow segments are inflated far past their real importance. Like it or not, for most of the past white guys were running things. Why pretend otherwise? Narrative, when taken to mean good storytelling , is the best way to get people interested in history. I am a writer, not an academic historian , and writers must use storylines to hook readers just as a carnival uses hucksters to attract customers. The best information, the greatest insights, the newest interpretations are useless unless disseminated. Bruce L. Brager Arlington, Virginia Goldstone and Ancient Mathematics Both Jack Goldstone and readers of Historically Speaking should be informed that at least one statement in his article "Knowledge—Not Capitalism" {Historically Speaking, March/April 2006) is very much Claudius Ptolemy, 1886 print. Library of Congress, Prints and Photographs Division [reproduction number , LC-USZ62-92884]. incorrect: he writes "Greek mathematics remained weak on arithmetic and never developed algebra (the study of solving equations with unknown quantities)" or (the next sentence implies) "trigonometry." The exact opposite is the case. The Greeks had developed algebra and advanced it as far as quadratic equations well before the time Diophantus wrote a practical textbook on the subject sometime before the 4th century A.D. (evidence that places him in the 3rd century is highly conjectural, but on no account did he write later than that). The Arabs didn't invent algebra. Arabic writers learned ofand commented and improved upon algebra from Greek sources like this. Goldstone's naive folk argument that the word "Algebra" being of Arabic derivation is evidence that Arabs invented algebra is as faulty as arguing that Ptolemy must have been an Arab because the title of his Almagest is Arabic. The Greeks also invented trigonometry. Some basic trigonometric ideas may have originated in India, but the first theoretical treatises in the field begin with Apollonius of Perga and Hipparchus, both in the 2nd centu- . ry B.C. Hipparchus composed the first known trigonometric tables and originated the modern system of degrees, minutes, and chords. Spherical trigonometry was then developed by Menelaus in the 1st century A.D. Hence, again, the Arabs didn't invent trigonometry. Arabic writers learned of and commented and improved upon trigonometry from Greek sources like this. On both facts, see "Diophantus," "Apollonius," "Hipparchus," and "Menelaus" in the Dictionary of Scientific Biography (including supplemental material in entries added in volume 15 ofthat work). For context see Serafina Cuomo, Ancient Mathematics (2001). In fact, I strongly urge all scholars and readers to make a more thorough effort to consult qualified sources on the actual achievements of ancient Greek mathematicians and scientists before issuing blanket statements about what they supposedly failed to do. Rodney Stark, for example, is thoroughly corrected on the subject ofHellenistic science by works like Lucio Russo's The Forgotten Revolution: How Science Was Born in 300 B.C. and Why It Had to Be Reborn (1996). Richard C. Carrier Columbia University Goldstone's Reply to Carrier Richard Carrier...