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06699_Field_TCUM T264.txt
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1996-04-10
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crisis in the history of our Western mathematics. Such a crisis
concerned the problems of determining the diagonal of a
square and the circumference of a circle: a clear case of
number, the tactile sense, trying to cope with visual and
pictorial space by reduction of the visual space to itself.
For the Renaissance, it was the infinitesimal calculus that
enabled arithmetic to take over mechanics, physics, and
geometry. The idea of an infinite but continuous and uniform
process, so basic to the Gutenberg technology of movable
types, gave rise to the calculus. Banish the infinite process and
mathematics, pure and applied, is reduced to the state known
to the pre-Pythagoreans. This is to say, banish the new
medium of print with its fragmented technology of uniform,
lineal repeatability, and modern mathematics disappears.
Apply, however, this infinite uniform process to finding the