Cambridge Ludic Proof Greek Mathematics And The Alexandrian by Reviel Netz

By Reviel Netz

This ebook represents a brand new departure in technology stories: an research of a systematic form of writing, situating it in the context of the modern type of literature. Its philosophical value is that it offers a singular approach of constructing feel of the idea of a systematic type. For the 1st time, the Hellenistic mathematical corpus - the most big extant for the interval - is positioned centre-stage within the dialogue of Hellenistic tradition as an entire. Professor Netz argues that Hellenistic mathematical writings undertake a story process in accordance with shock, a compositional shape in line with a mosaic of it seems that unrelated parts, and a carnivalesque great quantity of aspect. He additional investigates how such stylistic personal tastes derive from, and throw gentle on, the fashion of Hellenistic poetry. this significant publication can be welcomed via all students of Hellenistic civilization in addition to historians of old technological know-how and Western arithmetic.

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See Appendix to this chapter, pp. –.  The carnival of calculation The treatise, brief as it is, displays the mosaic structure we are familiar with. It begins – there is no extant introduction – with a strictly geometrical proposition, showing that the circle is equal to a right-angled triangle one of whose sides is equal to the perimeter of the circle, the other – to its radius. This is a strong result, rather simply obtained, and at first sight it appears to constitute already a squaring of the circle – though a moment’s reflection (not made explicit in the treatise as we have it) reveals that we are not quite there as, after all, we still need to measure the perimeter of the circle.

Now, it is logically possible to have a deductively sound treatise without adhering to the principle that results required by proposition n are all proved in propositions n– or less. In fact any permutation of propositional order within a deductively sound treatise still remains deductively sound: deductive soundness depends not on the sequence of presentation (at heart, a stylistic concern), but on the absence of circular paths of demonstration. The Measurement of the Circle as it stands is therefore deductively sound.

This task will bring us, I shall argue, to the poetry of Alexandria. Now this, in itself, is not a foregone conclusion of what was said above. When I say that a scientific text must be written with a view to the aesthetics of its era, I do not necessarily mean that its aesthetic structure must copy that of contemporary poetry. Not at all: one may well have cultures where the dominant aesthetics of science and of poetry diverge, so that science, among other things, marks itself by being non-poetical while poetry, among other things, marks itself by being non-scientific.

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