knows objects separately, one after another, and unlike the eye 
it has no way of getting a practically simultaneous view or 
acquaintance with a group of objects as a single awareness. 
Unlike the eye, the unaided hand is unable to discover whether 
three or more objects are on a line.”

     But what concerns us about the first crisis in 
mathematics is the evident fictions which must be resorted to 
in order to translate the visual into the tactile. But the greater 
fictions lay ahead in the infinitesimal calculus.

     As we shall see, with regard to the sixteenth century, 
number and visuality, or tactility and retinal experience, split 
quite asunder and went their divergent ways to set up the rival 
empires of Art and Science. This divergence, so strikingly 
initiated in the Greek world, was held in relative abeyance until