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2 Sir Isaac Newton developed a theory of the moon, which "till then never submitted to the bridle of calculations, nor was ever broke by any Astronomer. "J The mythology of a sequence of sole-practitioner scientists is an important element of Western culture. When Newton professed that if he had seen further, it was by standing upon the shoulders of giants, he was not talking about the view from the mosh pit. He was imagining something more like a totem pole. The new intermaths assert that such formulations can well up out of a computational mosh pit, not just be added atop the totem pole or spring full grown from the head of Zeus.

One of the great opportunities I think for the next few decades is the development of a mathematics which is suitable to social systems, which the sort of eighteenth-century mathematics which we mostly use is not. The world is topological rather than numerical. We need non-Cartesian algebra as we need non-Euclidean geometry, where minus minus is not always plus, and where the bottom line is often an illusion. 12 Technology itself was critical in the transition from Part One to Part Two, and it is critical again today.

5 Galileo saw himself as part of this tradition, carrying on a dialogue with nature in its very own language of geometry. In fact, science, and the mathematical language for expressing it, were both changing dramatically during his lifetime. Once indifferent to time, Europe had finally obtained the technology with which to measure it. " Part Two of the Book of Nature changed the focus from place to pace. Physics replaced astronomy as the central science. Today, computa- THE BOOK OF NATURE 25 tional scientists routinely predict the rate at which fuel will burn in various parts of an engine cylinder or the rate at which vortices will shed off a helicopter blade.

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