Swarthmore College Works History Faculty Works History 3-1-2002 Review Of "C. Wright Mills: Letters And Autobiographical Writings" Edited By K. Mills and P. Mills Robert C. Bannister Swarthmore College Follow this and additional works at: https://works.swarthmore.edu/fac-history Part of the History Commons Let us know how access to these works benefits ouy Recommended Citation Robert C. Bannister. (2002). "Review Of "C. Wright Mills: Letters And Autobiographical Writings" Edited By K. Mills and P. Mills". Isis. Volume 93, Issue 1. 155-157. DOI: 10.1086/343331 https://works.swarthmore.edu/fac-history/195 This work is brought to you for free by Swarthmore College Libraries' Works. It has been accepted for inclusion in History Faculty Works by an authorized administrator of Works. For more information, please contact [email protected]. C. Wright Mills: Letters and Autobiographical Writings Letters and Autobiographical Writings by C. Wright Mills; Kathryn Mills; Pamela Mills.; Dan Wakefield. Review by: rev. by Robert C. Bannister Isis, Vol. 93, No. 1 (March 2002), pp. 155-156 Published by: The University of Chicago Press on behalf of The History of Science Society Stable URL: http://www.jstor.org/stable/10.1086/343331 . Accessed: 11/06/2015 12:05 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press and The History of Science Society are collaborating with JSTOR to digitize, preserve and extend access to Isis. http://www.jstor.org This content downloaded from 130.58.65.13 on Thu, 11 Jun 2015 12:05:03 PM All use subject to JSTOR Terms and Conditions BOOK REVIEWS Ⅲ General ical texts and related to the division of the cubit into seven palms, each of four fingers. But the Roger Herz-Fischler. The Shape of the Great close relation between these two methods of -pp., figs., tables, apps., bibl., measurement in practical terms is clear, and ei 293 ם Pyramid. xii index. Waterloo, Ontario: Wilfried Laurier Uni- ther one could have been used with ease by an versity Press, 2000. $29.95 (paper). ancient builder. Herz-Fischler states that “there simply is no The existence of a mathematical theory deter- archaeological evidence for the above three rise mining the shape of the Great Pyramid is a long- over run based theories” (p. 168). Here he is too standing assumption, and speculation on the quick to dismiss the evidence presented by Flin- subject dates back to Herodotus. Roger Herz- ders Petrie from a mastaba at Meidum (pp. 41– Fischler’s study presents and discusses eleven 42, 168). Outside the corners of the structure are major theories and their proponents in the light walls with traces of horizontal lines at cubit in- of archaeological and philosophical considera- tervals and sloping lines marking the inclination tions. The historiographical aspect of the study of the faces. Herz-Fischler points to the lack of is very useful, as is the formulation and discus- marks to indicate how the slope was constructed, sion of some of the problems. A brief sociologi- but he fails to consider how an identical slope cal case study of the Pi-theory and the reasons was constructed eight times around the structure for its propagation and popularity in Britain is if such a horizontal measurement was not used. particularly interesting. But although this book Nor are the corners of the structure level; thus offers much that will be of interest to profes- the correct measurements must be calculated sional and amateur historians of mathematics relative to the depth. Mark Lehner, in his Com- and pyramid enthusiasts, it does not provide a plete Pyramids (Thames & Hudson, 1997), page definitive conclusion to the 2,500-year-old de- 220, offers evidence from Giza that the builders bate. constructed the corners by measuring in a certain Having dismissed all but three of the theories distance from reference points outside the sides. and unable to decide among them, Herz-Fischler The pyramid drawing from Meroe based on a reaches the rather extraordinary conclusion that rectangular grid (pp. 37–38) does not necessar- there may have been no true theoretical basis for ily conflict with a rise and run theory and cer- the angles of inclination that might have been tainly shows that a proportional system was used established “by eye” (p. 168). In settling for this relating side length to height. I find this archae- interpretation, however, he fails to consider how ological evidence for the use of rise over run the angle would have been replicated on the dif- theories convincing, if limited, and it strongly ferent sides of a pyramid or how angles of in- supports side-inclination based theories over clination would have been maintained or trans- those relating to the arris. ferred to other pyramids of different sizes: for The Meroe drawing cannot be taken as reli- example, Khufu’s three queens’ pyramids have able evidence that the seked theory was not used slopes virtually identical to those of the main in Fourth Dynasty structures (p. 38), as it dates pyramid (see V. Maragioglio and C. Rinaldi, to over 2,000 years after the Great Pyramid was L’architettura delle piramidi menfite IV [Centro constructed and lies outside Egypt. As for the per le Antichita` e la Storia dell’Arte del Vicino question of whether a seked-based system or in- Oriente-Roma, 1965], pp. 80, 86, 92). tegers were used to construct the angle of the The three theories among which Herz-Fischler sides, Herz-Fischler could have used the mea- cannot decide are all proportion-based theories, sured angles of sloping corridors and shafts in- two relating to the angle of inclination and one side the Great Pyramid that must have been con- to the angle of the arris (all theories involving structed using similar techniques. Further, he complex mathematics were those Herz-Fischler makes no attempt to apply these theories to the dismissed). This conclusion is significant in its slopes of other pyramids, although in some cases own right and relates to practical building con- he does consider examples presented by other siderations. Herz-Fischler is keen to distinguish authors. Applying these theories more broadly mathematically between integer proportional might lead to more decisive results. Before read- systems and the seked theory (see note on p. 28), ers undertake to do so themselves, however, they a system attested in ancient Egyptian mathemat- should be alerted that some of the measurements 83 This content downloaded from 130.58.65.13 on Thu, 11 Jun 2015 12:05:03 PM All use subject to JSTOR Terms and Conditions 84 BOOK REVIEWS—ISIS, 93 : 1 (2002) given in Appendix 2 are out of date. Corrected MS Istanbul, Aya Sofya 4832, fols. 66b–75b, figures are: Abu Rawash, c. 52Њ (Michel Vallo- which contains ibn Sina¯n’s treatise. gia, Au coeur d’une pyramid [Muse´e Romain de Hogendijk offers this reprint of Luckey’s the- Lausanne-Vidy, 2001], pp. 56–57); Bent Pyra- sis as “a tribute to the man and his work” (p. mid, 55Њ 00Ј 30Љ (lower section), 43Њ 01Ј 30Љ viii). This dedication reflects the opinion that, as (upper) (Josef Dorner, “Form und Ausmaße der Hogendijk says, Luckey was one of the foremost Knickpyramide,” MDAIK, 1986, 42:43–58); historians of Arabic-Islamic mathematics in the Red Pyramid, 44Њ 44Ј (Josef Dorner, “Neue Mes- twentieth century (p. vii). His thesis focused on sungen an der Roten Pyramid,” in H. Guksch and the mathematical and astronomical contents of D. Polz, eds., Stationen: Beitrage zur Kulturges- ibn Sina¯n’s treatise. Luckey embedded the tech- chichte A¨ gyptens Rainer Stadelmann gewidmet nical analysis of ibn Sina¯n’s particular work in [P. von Zabern, 1998], pp. 23–29). In this last brief surveys of the religious community ibn example considerable variation (up to 43Ј) was Sina¯n belonged to—that of the so-called Sa- noted in the inclination of different stretches of baeans—of the medieval scholar’s life and the same pyramid face, which suggests that an works, of his method of determining the area of angle of 45Њ was intended. This observed varia- the segment of a parabola, and of the theories of tion is very significant considering how little of sundials espoused by ancient and medieval (Ar- the casing of the next pyramid constructed—the abic) authors. Finally, he discusses two writings Great Pyramid—is preserved (as we can see in by al-Kindi and some aspects of a text by al- the photograph on the cover of the book). Mahani, both of whom lived in the ninth century. Although I find Herz-Fischler’s conclusions Luckey’s work is thus a good example of the rather weak and some of his treatments of ar- particular approach to the history of mathematics chaeological sources too dismissive, this volume that prevailed at the time he wrote. provides a useful introduction to the subject and His dissertation does, however, have a few pe- a clear formulation of the problems involved. It cularities. Luckey is concerned not only with is, then, a thought-provoking contribution to a mathematical progress and sources but also with long-standing debate. the intellectual excellence of individuals and KATE SPENCE groups (see, e.g., pp.