Cambridge Ludic Proof Greek Mathematics And The Alexandrian by Reviel Netz

By Reviel Netz

This booklet represents a brand new departure in technological know-how reviews: an research of a systematic kind of writing, situating it in the context of the modern variety of literature. Its philosophical value is that it presents a singular manner of creating experience of the suggestion of a systematic kind. For the 1st time, the Hellenistic mathematical corpus - probably the most massive extant for the interval - is put centre-stage within the dialogue of Hellenistic tradition as an entire. Professor Netz argues that Hellenistic mathematical writings undertake a story technique according to shock, a compositional shape according to a mosaic of it seems that unrelated components, and a carnivalesque large quantity of aspect. He additional investigates how such stylistic personal tastes derive from, and throw mild on, the fashion of Hellenistic poetry. this crucial booklet might be welcomed through all students of Hellenistic civilization in addition to historians of historic technology and Western arithmetic.

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But even without any such assumptions concerning the author’s intentions, it is clear that the outcome of the proposition is indeed to leave the reader confused as to the precise structure of equalities and inequalities underlying Archimedes’ calculation. This is not merely a stylistic, but also a mathematical point. In order to calculate with inequalities, one needs to follow precise rules of algebra: from A>B and B>C, A>C may be deduced, but from A>B and B

Third, we notice the essentially open-ended nature of the exercise. Archimedes clearly intended his readers to see that the operations of bounding the circle could be extended ad infinitum, with the same type of calculations being extended. There is no inherent reason to stop with the -gon. Fourth, we notice that Archimedes’ final result is explicitly weaker than it needs to be. On both boundaries, Archimedes obtains a rather complex ratio which he then simplifies, at the price of getting a less precise ratio.

It may be that our appreciation of the beauty of texts is therefore always rooted, in some way, in such universals. And yet such universals cannot in themselves dictate the precise choice of aesthetics dominating a given text, for after all a basic fact of aesthetic value judgment is its historical and cultural variety. Beauty may be timeless, but different beautiful things are preferred in different times and places. When we look for Archimedes’ choices in the presentation of his works – that is, for his aesthetic preferences – we must then study the aesthetic preferences that were available to him in his culture and that he could assume among his readers.

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