Mathematics as Metaphor: Samuel Beckett and the Esthetics of Incompleteness

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When Samuel Beckett first visited France as an exchange lecturer from Trinity College to the Ecole Normale Superieure in Paris, he seized upon the opportunity to join the literary culture of Paris. His youth--he was but twenty-two years old--did not obscure his intelligence, for within the year he had met James Joyce and entered into the older Irishman's intellectual orbit. Beckett was some twenty-four years younger than Joyce, whose reputation was already secured: Mysses had been out for about six years, and fragments of Finnegans Wake were already appearing in transition. The subsequent history of their friendship is convoluted, but Beckett acted as translator, confidante, and polemicist for Joyce.(1) Joyce's decision to use his young friend's exegetical powers to voice the central critical tenets of Work in Progress demonstrates Beckett's immersion in both Joyce's coterie(2) and in the Modernist milieu.

Thus, in 1929, when he was only twenty-three years old, Beckett wrote "Dante ... Bruno . Vico . . Joyce," the principal essay of Our Exagmination Round his Factification for Incamination of Work in Progress. The work, however guided by Joyce's needs, is wholly Beckett's; it is here that I begin, for my interest is in how, out of his immersion in the intellectual life of Modernism, Beckett emerged as a highly problematic Post-Modern. His death at age eighty-three in December of 1989 truly signaled the remoteness of the Modern era, for while he has been our contemporary, his creative life began among the great Moderns, and with his death, the last link to that era suddenly seemed to break. In his aesthetic agenda we see both the residue of the earlier era and its reformulation, a reformulation through a strategy that relies upon the metapholic power of non-literary fields such as neurology, aphasiology, and mathematics to represent two related ideas: first, the descriptive (in)sufficiency of language, and second, the (in)ability of a formal system to comprehend itself.

Beckett's struggle with emergent ideas about descriptive sufficiency is idiosyncratic, but it also arises out of a cultural matrix that had problematized the question. Beckett was not alone in his concern about the adequacy and completeness of formal systems. As Douglas Hofstadter has shown, these concerns were at the heart of the mathematical debate that culminated in Godel's Undecidability Theorem. Beckett's interest in mathematics is as a metaphor for the art he will create, but the juxtaposition of the mathematics and the literature clarifies the persistence of Modernist questions about language into Post-Modern fiction.(3) But let us begin with the particular case:

Beckett's most recurrent mathematical allusion is to Hypasos the Akousmatic, a Pythagorean who, the narrator of Murphy tells us, "was drowned in a puddle . . . for having divulged the incommensurability of side and diagonal" (47). The allusion is to the following problem: the Pythagoreans supposed that any point on a line could be named as the ratio of two whole numbers. This mathematics was not abstract, but concrete; for example, numbers were portrayed by a series of dots (called Monads), and the complex ratios used to describe geometric figures served to demonstrate that reality is, at its most fundamental level, mathematical (Koestler, Guthrie). A quantity such as [square root]2 contradicts this fundamental belief because it is a quantity inexpressible as the ratio of whole numbers-hence its designation as an "irrational" number. The familiar formula for determining the length of the hypotenuse of a right triangle,

[A.sup.2] + [B.sup.2] = [C.sup.2] often yields such "irrational" numbers, numbers that exist in what mathematicians term a "surd" relationship. Hypasos's sin was to reveal that there are points on the number line that cannot be named as ratios of whole numbers, i.e., that the cherished connection between numbers and reality was in fact discontinuous. …