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08824_Field_TCGG T589.txt
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supernatural powers. . . . even the enlightened Greeks never
completely freed themselves from this mysticism of number
and form.” (pp. 25­6)
It is easy to see with Dantzig how the first crisis in
mathematics arose with the Greek attempt to apply arithmetic
to geometry, to translate one kind of space into another before
printing had given the means of homogeneity: “This confusion
of tongues persists to this day. Around infinity have grown up
all the paradoxes of mathematics: from the arguments of Zeno
to the antinomies of Kant and Cantor.” (p. 65) It is difficult for
us in the twentieth century to realize why our predecessors
should have had such trouble in recognizing the various
languages and assumptions of visual as opposed to audile-
tactile spaces. It was precisely the habit of being with one kind
of space that made all other spaces seem so opaque and