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Amplification

I patterned my behavior on that of travelers who, finding themselves lost in a forest, must not wander about, now turning this way, now that, and still less should remain in one place, but should go as straight as they can in the direction they first select and not change the direction except for the strongest reasons. By this method, even if the direction was chosen at random, they will presumably arrive at some destination, not perhaps where they would like to be, but at least where they will be better off than in the middle of the forest. (30)

Descartes is first and finally a disciple of the line. The unbroken path permeates his thought from the beginning. Mathematically, the line is for Descartes the expression of a proportional magnitude that can be represented spatially as well as through the language of numerals and symbols. But the line is not merely a figure of geometrical purity; it is also a philosophical imperative and a metaphor of personal comportment. As early as March 1619, he writes in a letter to his mentor Isaac Beeckman that he hopes soon to demonstrate that certain classes of mathematical problems "can be solved with straight lines and circles alone, or "with curves ... which can be generated by a single [continuous] motion." This claim quickly metamorphoses into another order of magnitude: "I do not believe one can imagine anything which could not be solved along similiar lines."

Within what is probably weeks, Descartes's claim has solidified into a model of geometrical alchemy. He now conceives of a mathesis universalis -- "a general science that explains everything that can be raised concerning order and measure irrespective of the subject matter." Just as important, Descartes does not claim to discover this universal mathematics -- which he pointedly relates etymologically to the Greek for "learning" or "alertness," wrenching it in a single gesture from its numerical and "scientific" constraints -- but to rediscover it. A number of ancient mathematicians, he claims, show vestiges in their work of this "true mathematics," but seem to have suppressed and encrypted it in their writings "with a kind of pernicious cunning," reducing it to "the barbarous name of algebra." (31)

There emerges, then, through Descartes's early adulthood -- the period, in fact, bracketing the dreams of Nov. 10, 1619 -- a preoccupation with the line that merges with a second discourse, sporadic and muted, of history as an encryption, a verbal labyrinth or forest. A figure of clarity, hierarchy, and sequence plays against, but also arises within, a figure of disorientation and the "occult" -- the concealed and darkened. The binary, however, is perhaps not so neat as it appears; like the forest or the dreamstreets of a city, the figures themselves constitute a third trope -- a trope of possible maps, a tension of geometry and geography given body in the ordinate and abscissa of Cartesian coordinates.