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Author

Reviel Netz

Other affiliations: University of Cambridge
Bio: Reviel Netz is an academic researcher from Stanford University. The author has contributed to research in topics: Greek mathematics & Palimpsest. The author has an hindex of 17, co-authored 53 publications receiving 963 citations. Previous affiliations of Reviel Netz include University of Cambridge.


Papers
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Book ChapterDOI
Reviel Netz1
01 Jan 2005
TL;DR: In this paper, the authors focus on the Pythagoreanism of the late fifth and early fourth centuries, and the importance of Pythagoreans in the history of mathematics and the divine.
Abstract: This chapter focuses on the Pythagoreanism. The place of Pythagoras in the history of mathematics and the divine is well known. There are other people; “Pythagoreans,” were active in the late fifth and early fourth centuries. The most important of these were, apparently, Philolaus and Archytas. They did not suffer the fame of Pythagoras and thus the truth concerning them is somewhat easier to sift from the accretion of later legends. The historical significance of Pythagoreans lies precisely in this: that they were important for Plato and for Aristotle. It is clear that Plato and Aristotle opportunistically changed the meaning of the Pythagorean sources available to them. Plato and Aristotle perceived an affinity between a group of thinkers whom they associated with Pythagoras. They further saw in this group something useful for their own philosophy. To Plato, the usefulness was in the encouragement of a kindred spirit; to Aristotle, the usefulness was in the warning of a philosophical pitfall. The place of this comment is significant: in Aristotle's account, the Pythagoreans immediately preceded Plato, whose philosophy is explained through a mixture of influences from previous thinkers, mainly, that of the Pythagoreans.

5 citations

Journal ArticleDOI
TL;DR: The use of imagination in Greek mathematical writings has been studied in this article, focusing mainly on one key element, the use of the Greek verb noein, which is used to describe the ability to imagine a virtual presence as if it were on equal footing with the real.
Abstract: This essay is a study in the routine use of imagination in Greek mathematical writings. By "routine" is meant both that this use is indeed very common, and that it is ultimately mundane. No flights of fancy, no poetical-like imaginative licenses are at stake. The issue rather is the systematic use made of the ability to imagine a virtual presence, and to refer to this virtual presence as if it were on equal footing with the real. This process is not merely routine in Greek mathematics: it may well be considered one of its chief characteristics. In this essay, I describe some features of this practice in detail, and then briefly offer some interpretative comments on the history and philosophy of this practice. The emphasis, however, is on the description, and I concentrate mainly on one key element—the use of the Greek verb noein . Thus the structure of the essay is as follows: part 1 is an analysis of noein in Greek mathematical writings; part 2 is a less-detailed description of other practices of Greek mathematics that involve "imagination" or, in general, a "layered" reality; and part 3 is a tentative interpretation.

4 citations

Journal ArticleDOI
01 Jan 2003-Apeiron
TL;DR: In this article, the authors discuss the goal of Archimedes' Sand-Reckoner, which is related to a more general question in the history of the western exact sciences.
Abstract: Before discussing the goal of Archimedes' Sand-Reckoner, I should perhaps explain the goal of the article itself. The primary question, What is the goal of the Sand-Reckoner?, is related to a more general question in the history of the western exact sciences. It is often assumed that one major difference between ancient and modern science involves the latter's growing reliance on the numerical. Ancient mathematics frequently fails even to mention specific numbers; in modem mathematics everything, including geometrical objects, is considered through the prism of numerical values. This assumption is related to the thesis of Klein (1934-1936 /1968), where ancient mathematics is seen as more 'concrete' or first-order (and so typically related to the qualitative properties of geometrical objects) while modern mathematics is seen as more 'symbolic' or second-order (which in practice means the algebraic treatment of objects understood in terms of real numbers). More recently, it was argued in Fowler (1987, 2 ed. 1999) that Greek mathematics was non-arithmetized so that geometrical objects bore no numerical value of their size at all. It is also often noted that the modern exact sciences, much more than their ancient counterparts, are based on detailed calculation (modem calculation made possible, for instance, by the use of modem tools such as logarithms). Whether as a matter of concept or of practice, then, this standard — and, I believe, correct — picture contrasts a Greek mathematics based on geometrical figures with a modem mathematics based on the symbolic manipulation of numerical terms. Now, one major tool of this modern symbolic manipulation of numerical terms is the modem numerical system itself. Thus general histories of mathematics

4 citations

Journal ArticleDOI
01 Jan 2000-Apeiron
TL;DR: In a previous book, Mansfeld (1994), Mansfeld had covered a characteristically rich and varied literature, only to realize after the publication of the work that a significant body of literature (the mathematical one) had been neglected as discussed by the authors.
Abstract: This volume is the outcome of an unintended omission. In a previous book, Mansfeld (1994), Mansfeld had covered a characteristically rich and varied literature, only to realize after the publication of the work that a significant body of literature — the mathematical one — had been neglected. Mansfeld set out to correct this omission, and the result is this, extraordinarily useful, slim volume. It may be reassuring for us, Mansfeld's readers, to discover that he is capable of omissions, since he is one of the most meticulous and scholarly authors active today in the field of ancient philosophy. We tend to think, with hope and relief: if Mansfeld can commit oversights, discipline can be a bit relaxed! Clearly this is not Mansfeld's own view, and this volume displays the usual characteristics of Mansfeld's style: a thorough mastery of the literature, and an incisive power of judgement. Still under the impression of the tour de force of Mansfeld (1994), we the readers are left gasping, rather like a group of soldiers in basic training who, returning from a punishing day of exercise on the drilling grounds, are called again by their ever-energetic commander, to join him for yet another run around the barracks. There is a real moral to be learned from the circumstances leading to the writing of this book: that there is still far too little contact between scholars of ancient philosophy and scholars of ancient mathematics.

4 citations


Cited by
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01 Jan 2014
TL;DR: Thematiche [38].
Abstract: accademiche [38]. Ada [45]. Adrian [45]. African [56]. Age [39, 49, 61]. Al [23]. Al-Rawi [23]. Aldous [68]. Alex [15]. Allure [46]. America [60, 66]. American [49, 69, 61, 52]. ancienne [25]. Andreas [28]. Angela [42]. Animals [16]. Ann [26]. Anna [19, 47]. Annotated [46]. Annotations [28]. Anti [37]. Anti-Copernican [37]. Antibiotic [64]. Anxiety [51]. Apocalyptic [61]. Archaeology [26]. Ark [36]. Artisan [32]. Asylum [48]. Atri [54]. Audra [65]. Australia [41]. Authorship [15]. Axelle [29].

978 citations

Book
01 Aug 2003
TL;DR: The prehistory of science and technology studies can be traced back to the Kuhnian Revolution and the early 20th century as discussed by the authors, with a focus on the social construction of scientific and technical realities.
Abstract: Preface vii 1 The Prehistory of Science and Technology Studies 1 2 The Kuhnian Revolution 12 3 Questioning Functionalism in the Sociology of Science 23 4 Stratification and Discrimination 36 5 The Strong Programme and the Sociology of Knowledge 47 6 The Social Construction of Scientific and Technical Realities 57 7 Feminist Epistemologies of Science 72 8 Actor-Network Theory 81 9 Two Questions Concerning Technology 93 10 Studying Laboratories 106 11 Controversies 120 12 Standardization and Objectivity 136 13 Rhetoric and Discourse 148 14 The Unnaturalness of Science and Technology 157 15 The Public Understanding of Science 168 16 Expertise and Public Participation 180 17 Political Economies of Knowledge 189 References 205 Index 236

536 citations

Journal ArticleDOI
TL;DR: This essay explores the conceptual and semantic work required to render algorithmic information processing systems legible as forms of cultural decision making and represents an effort to add depth and dimension to the concept of “algorithmic culture.”
Abstract: How does algorithmic information processing affect the meaning of the word culture, and, by extension, cultural practice? We address this question by focusing on the Netflix Prize (2006–2009), a contest offering US$1m to the first individual or team to boost the accuracy of the company’s existing movie recommendation system by 10%. Although billed as a technical challenge intended for engineers, we argue that the Netflix Prize was equally an effort to reinterpret the meaning of culture in ways that overlapped with, but also diverged in important respects from, the three dominant senses of the term assayed by Raymond Williams. Thus, this essay explores the conceptual and semantic work required to render algorithmic information processing systems legible as forms of cultural decision making. It also then represents an effort to add depth and dimension to the concept of “algorithmic culture.”

346 citations

Journal ArticleDOI
TL;DR: Analyzing common visual communications reveals consistencies that illuminate how people think as well as guide design; the process can be brought into the laboratory and accelerated.
Abstract: Depictive expressions of thought predate written language by thousands of years. They have evolved in communities through a kind of informal user testing that has refined them. Analyzing common visual communications reveals consistencies that illuminate how people think as well as guide design; the process can be brought into the laboratory and accelerated. Like language, visual communications abstract and schematize; unlike language, they use properties of the page (e.g., proximity and place: center, horizontal/up-down, vertical/left-right) and the marks on it (e.g., dots, lines, arrows, boxes, blobs, likenesses, symbols) to convey meanings. The visual expressions of these meanings (e.g., individual, category, order, relation, correspondence, continuum, hierarchy) have analogs in language, gesture, and especially in the patterns that are created when people design the world around them, arranging things into piles and rows and hierarchies and arrays, spatial-abstraction-action interconnections termed spractions. The designed world is a diagram.

271 citations