All Tied in Knots

Abstract

In this note, I wish to critique a proposal put forward by Camps & Uriagereka (2006; C&U) and Balari et al. (2011; BEA) regarding the study of the evolution of language.In particular, I intend to cast doubt on the connection they draw between the computational properties of the language faculty and those involved in the conceptualization of a knot.In what follows, I will offer a rather negative commentary, in the sense that no alternative will be forthcoming.In fact, one of the main points of this paper will be that there is no phenomenon to explain at all; or at least it has not been properly formulated.The general idea underlying what C&U and BEA propose is clear enough.Considering that the language faculty is underlain by a computational system that generates sound/meaning pairs, it ought to be possible to outline some of its computational properties.Furthermore, it is at least a possibility for some other cognitive domain of the human mind to share some of these very computational properties.If that is the case, C&M claim, such a domain would constitute a "cognitive base" that can be said to be in a "causal correlation" with the linguistic capacity (p.35) ⎯ that is, the computational properties of such a 'base' would be parasitic on those of the language faculty.If this holds, the behaviors associated with this cognitive base could plausibly constitute indirect evidence for an "underlying linguistic prerequisite" (ibid.).I pretty much doubt that such an inference is in fact sound, but let it stand for the sake of the argument.The specific behavior that engages C&U and BEA relates to the ability to tie a knot, a skill that must have originated in modern man, given that evidence for it in the fossil record ⎯ such as in the binding of projectiles to their shafts (C&U: 58) ⎯ is only present in the archaeology of Homo Sapiens (p.45).Naturally, language and knot-tying are phenomena that at first sight appear to be completely unrelated, but C&U and BEA assure us that they may in fact share underlying properties.The overall argument is more or less as follows.According to mathematical linguistics, the expressive power of natural language is context-sensitive (or more accurately, mildly context-sensitive; Joshi et al. 1990); thus the computational system underlying language is of such power.Further, the mathematical structure of knots may be studied by employing the tools of Knot Theory, a subfield of mathematical topology.According to C&U, and citing a work from this literature (viz.Mount 1989), knots can only be created/ described by a context-sensitive system, a conclusion they take to be "not subject to rational debate" (p.63).In a related manner, BEA conclude, citing

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