By James Bailey
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Extra info for After Thought
This order is all composed of movement and change, and although it is life, not art, we may fancifully call it the art form of the city and liken it to the dance-not to a simpleminded precision dance with everyone kicking up at the same time, twirling in unison and bowing off en masse, but to an intricate ballet in which the individual dancers and ensembles all have distinctive parts which miraculously reinforce each other and compose an orderly whole. The ballet of the good city sidewalk never repeats itself from place to place, and in any one place is always replete with new improvisations.
It was, however, also the vehicle by which the ideas of "algebra," including the concept of an "unknown," entered Christian Europe. As is clear from the purely geometric work of Copernicus half a century later, the impact of the new algebraic technology was not immediate. It was integrated in halting and tentative steps. For example, at the time Regiomontanus was absorbing Diophantus, he was preparing his own treatise on triangles. Twice in this book, he departed from geometric orthodoxy. In an almost apologetic manner, he made Europe's first use of ars rei, or art of the thing, to do what he could not do with geometry.
Human minds seem to need something constant to hold on to. The mind of man doth wonderfully endeavor ... that it may light upon something fixt and immoveable ... 1l THE BOOK OF NATURE 27 The whole evolution of mathematical vocabulary, from geometry through algebra and now into adaptive intermaths, reflects the slow, grudging relaxation of the human need for constancy. " Both the figures in their astronomical diagrams and the motions around their circular orbits-what today we would call their programs and their data, respectively-were fixed for each planet.
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