Somnio, ergo sum


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Somnio, ergo sum

Donald Challenger

Zero

"I am in a sense," Descartes observes in the Discourse on Method, "something intermediate between God and nought." Trained in the emerging Jesuit tradition, Descartes almost reflexively recoiled from any conceptual scheme that formalized the void as a present absense rather than as the nullification of presence. As a mathematician, he disdained the concept of negative numbers, those less than zero; and he ridiculed the counter-intuitive notion of the square roots of negative numbers as "imaginary numbers," a dismissive term that nevertheless has become central to modern mathematics.

Less providentially, Descartes's seeming inability to account for voids and empty spaces within the natural order led him to reject any theoretical construct -- scientific or philosophical -- that was not grounded in some principle of extension, of material or quasi-material thread or connection. Descartes abhorred a vacuum. He sought, for example, to explain gravity and the movement of celestial bodies as the effects of etherial "vortices" acting upon matter through physical contact, a manifestation of extension that allowed him to ignore "occult properties" of mass postulated by Galileo -- whose work Descartes dismissed -- and later established by Newton.

The concept of zero itself, though, was essential to Descartes, however strong his metaphysical aversion to what might await on the far side of nullity. In two-dimensional space, (0,0) necessarily serves as the point of origin, the convergence of ordinate and abscissa to demarcate the field in which any point can be plotted with two (or in three-dimensional space, three) numbers. These numbers are now known as Cartesian coordinates. They were quite literally crucial -- the crossing point -- to Descartes's struggle toward a mathesis universalis, its reconstruction of algebra as geometric representation, and its extension as a mapping, a longitude and latitude, of human subjectivity and possibility. (32)

To operate "between God and nought" is in a sense to imagine oneself in a digital world, where each choice is a deceptively simple off/on, either/or; it is the only in the sheer accumulation of circuits that error is produced:

The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations had led me to imagine that all things to the knowledge of which man is competent are mutually connected in the same way. (33)

Zero -- the convergence of ordinate and abscissa -- is also the crossroads. Quod vitae sectabor iter? What road of life shall I follow?

"Every number arises from One, and this in turn from the Zero. In this lies a great and sacred mystery.... He creates all out of nothing, preserves and rules it: omnia ex nihilo creat, conservat et gubernat."

Salem Codex, by an anonymous twelfth-century monk