Combinatorial complexity is to “makes infinite use of finite means”, a description attributed to written language by Alexander von Humboldt. Indeed, with a finite set of elements, and some rules to combine them, we can produce quasi-infinite permutations. With four shirts and four pants, you have sixteen outfits, not four. When elements of a system compose, they multiply.
However, complexity simply as a product of composition does not entail additional information. After all, the most concise description of this system is still the set of elements and the rules, not an exhaustive list of all possible creations. Critically, there is a surplus that is produced in composition or, as elaborated in Gestalt psychology: the sum is greater than the sum of the parts.
It is from this essential fact that Georges Perec’s combinatorial experiments gain such potency. His bib⁄243 Postcards are a product of a simple generative system. When read in order, the repetitions are perceived as a rhythm, gesturing towards an underlying system. Nonetheless, the effect surpasses the union of the parts, as language’s referential capacity folds in layers of meaning outside of system. A similar effect is achieved in Invisible Cities by Italo Calvino, a friend of Perec. The mechanism behind this effect is precisely that natural language is not formal, as noted in Calvino’s memo on bib⁄Exactitude:
These are two different drives toward exactitude that will never attain complete fulfillment, one because “natural” languages always say something more than formalized languages can—natural languages always involve a certain amount of noise that impinges upon the essentiality of the information—and the other because, in representing the density and continuity of the world around us, language is revealed as defective and fragmentary, always saying something less with respect to the sum of what can be experienced.
As such, attempts at representation generate both a surplus within the structure, as well as surplus outside of the structure.