Lo «gnomone» di cui si parla in questo libro è un semplice strumento matematico: una figura geometrica, piana o solida, che aggiunta a un’altra ne genera una simile. Questa tecnica, ampiamente diffusa nell’antichità, risponde all’esigenza di ingrandire o rimpicciolire una forma conservandone l’aspetto. E ciò pone una delle più ardue questioni della matematica e del pensiero in genere: quella dell’invarianza nel mutamento. Questo principio è associato, in particolare nella tradizione vedica, a un patrimonio di norme rituali da cui potrebbe aver avuto origine la matematica stessa. Nei Greci scarseggiano i riferimenti rituali, ma non mancano legami con i problemi sollevati dall’etica, dalla cosmologia e dalla metafisica. Lo gnomone non aveva dunque importanza soltanto per la geometria. Dalla semplice operazione di correzione di una figura (come un quadrato) sono infatti dipesi la nozione di numero, la definizione di vari concetti dell’analisi e alcuni tra i principali algoritmi numerici e algebrici della matematica. Studiare lo «gnomone» permette così di riflettere sull’essenza del numero, cogliendolo in un vastissimo spettro di manifestazioni, dalle origini vediche alle speculazioni greche, cinesi e mesopotamiche, per attraversare poi la matematica araba e l’algebra moderna, e arrivare infine in quel grandioso progetto che, dalla metà del XX secolo, ha visto entrare in scena la macchina come protagonista del calcolo su larga scala. [Abstract translated by Google Translate: This is the abstract in English… The "gnomon" referred to in this book is a simple mathematical tool: a geometrical figure, flat or solid, which, when added to another, generates a similar one. This technique, widely used in antiquity, responds to the need to enlarge or reduce a shape while preserving its appearance. And this poses one of the most difficult questions of mathematics and of thought in general: that of invariance in change. This principle is associated, in particular in the Vedic tradition, with a patrimony of ritual norms from which mathematics could have originated. Ritual references are scarce in the Greeks, but there is no lack of links with the problems raised by ethics, cosmology and metaphysics. The gnomon was therefore not important only for geometry. The notion of number, the definition of various concepts of analysis and some of the main numerical and algebraic algorithms of mathematics have depended on the simple operation of correcting a figure (like a square). Studying the "gnomon" allows us to reflect on the essence of the number, catching it in a vast spectrum of manifestations, from Vedic origins to Greek, Chinese and Mesopotamian speculations, to then go through Arabic mathematics and modern algebra, and finally arrive in that grandiose project that, since the mid-twentieth century, saw the machine enter the scene as the protagonist of large-scale computing.]
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