Abstract
This paper argues that there are rather unexpected fundamental connections to be made between the principles of language and the laws governing the inorganic world. After summarizing the major development of economy principles in physics and the basic results of discrete optimization problems in combinatorial mathematics, I will argue that the economy principles which theoretical linguists are currently trying to discover in the theory of language are something comparable to the Principle of Least Action in physics. This provides us with a concrete interpretation of the point Chomsky has repeatedly made (Chomsky, 1991a,b, passim), i.e., language, despite its biological nature, shares the fundamental property of the inorganic world; it is designed for “elegance,” not for efficient use. I will then discuss the nature of two types of economy principles of language proposed in the literature, “economy of derivation” and “economy of representation,” from the point of view of the theory of computational complexity, and claim that the two economy principles exhibit quite different properties with respect to their computational complexities: economy of representation is efficiently solvable and therefore seems to be in the complexity class P in the sense of the theory of computational complexity, whereas economy of derivation is fundamentally computationally intractable and appears to belong to the class NP-P. How, then, can language be ever used, if its fundamental property (economy of derivation) poses an intractable optimization problem? I will suggest that language is equipped with certain mechanisms, the real-world counterparts of the “heuristic algorithms” studied in the theory of optimization, that facilitate its efficient use. Thus, to the extent that these mechanisms are available, language becomes usable, despite its fundamental computational intractability.
