Samuel Beckett's use of mathematics to represent the discourse of fiction may at first seem ironic. Mathematics is a language of precision; it keeps undefined terms at a minimum; it makes common agreement about the meaning of certain terms (definitions) and the rules of its system (axioms). The discipline strives for both simplicity and for a well-defined domain where the rules operate without contradiction or ambiguity. However much a natural language and mathematical language each attempts to describe the world--and although neither language represents a closed system--the world mathematics describes is much smaller and less complex, albeit more precise, than the "buzzing, blooming confusion" that natural languages attempt to represent. This contrast between the limited but precise world of mathematics and the imprecise but unlimited world of natural language is seldom connected, but Beckett's Watt exploits the differences between these two languages and shows how attempts to apply mathematical precisio to a natural language fall short in descriptions of the self and the world.(1) This problem of mapping one language onto the other is embodied in Beckett's use of mathematical processes as artistic techniques. In Watt, he returns to exact notions about mathematics to understand language and to shape the techniques that will represent his understanding that language is a process of infinite approximation.
Beckett's specific knowledge of mathematics pervades Watt. For example, Beckett exposes his familiarity with the "tricks" of number theory in the bizarre scene with Nackybal and his committee.(2) His sophisticated knowledge of permutations, combinations, squaring, cubing, and rooting is evident, and these allusions reveal the extent of his knowledge and eventually their meaning, a meaning Rubin Rabinovitz suggests when he discusses the song Watt hears in the ditch on the way from the station: "For Beckett, the surds(3) become metaphors for the generations of humanity stretching through time" (Rabinovitz 153). While this is undoubtedly true, Beckett's intentions are surely more specific. The song reveals Beckett's recognition that the mapping of the world onto the language of mathematics is inadequate, a point critics have recognized since Jacqueline Hoeffer's study of Watt. Beckett's uses of such functions reflect a sophisticated knowledge of mathematical relationships: "The two figures are related...as the cute to its rube" (Watt 187). His distortion of the mathematical language ("cube" into "cute" and "root" into "rube") represents Beckett's general strategy with mathematics, i.e., to show the places where the map from mathematics onto language falls short, and to find in these differences a source of creative energy.
Aphasic Watt cannot represent his world with language. Watt's language assigns words that approach objects in the world but do not adequately describe them. Since natural language begins to fail Watt, Beckett turns to mathematical techniques to try to represent the self and the world to codify the formal relations and operations that language imposes on self and world. But Beckett does not use the language of mathematics; he uses mathematical techniques expressed in a natural language that demonstrate that this technical language is no more precise than mathematics. Both languages face the same problem of fitting themselves to an unruly reality. Mathematics and natural language always maintain a "hairbreadth departure" from each other, just as each maintains a hairbreadth departure from the world.
Beckett tries to describe the world mathematically by presenting all (or many) possible combinations or permutations of a situation. Watt's attempts to represent the world mathematically not only fail to describe it completely, they also lead to confusion. Using a natural language governed by mathematics, Beckett makes ambiguous statements that would be illegal in the language of mathematics because functions can only be defined in such a way that the operations on the domain do not yield any contradictions. …