The Nothing that Is by Kaplan Robert

Author:Kaplan, Robert [Kaplan, Robert]
Language: eng
Format: epub
Publisher: Oxford University Press
Published: 1999-10-27T16:00:00+00:00

The triumph of the Arabic numerals

Yet Adam Riese was right: people skilled in arithmetic on an abacus, or with their fingers, calculate much more quickly than do those who conquered them (excepting the rare John Palegraves) with the quill. What then is the significance of their victory? It is the question we asked long ago about the divergence of body and mind. Wordless manipulation will carry you with dash and glory to the outermost edges of arithmetic – but it will leave you stranded once you cross the border into algebra, and all the lands of mathematics that lie beyond. There thought travels by signs laced into a language that can speak even about itself; that lifts forms away from the substances they restrained, becoming abstractly substantial too. It is a language that lets us dwell on relations, playing a cool light over our wordless doings and so picking out their permanence.

This language came into its own when zero entered it as the sign for an operation: the operation of changing a digit’s value by shifting its place. This opened the door to granting equal status to the signs for quantities and for the operations on them, all subject now to yet more abstract operations in turn, and those to others, endlessly, each bearing the peculiar, defining mark of this language: that no matter where in its hierarchy an operation or relation stood, it was expressed by a sign of like standing with the rest, in the matrix of their common grammar. These signs could be read as pointing beyond themselves to the language of which they were the parts.

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