Simulation of Word-Meaning Stochastic Processes

provided the first quantitative comparison of related languages based on a well-defined model of language change. The stochastic nature of this model was poorly understood by linguists, in the main, and many have rejected the theory in the course of a protracted and confused controversy. Meanwhile field linguists, especially those working with language groups of unknown history, have accepted lexicestatisties and have found it to he an efficient, valid and reliable tec huique. The Swadesh thee .r~ There are serious oversimplifications of reality implicit in lexicostatistics, and it is these, rather than the stochastic aspects, which are limitations of the theory. Swadesh hypothesized, in effect, that (i) it is possible to discover a set of basic, universal and non-cultural meanings, and he constructed a list of about 200 such meanings; (ii) in every natural language, at a given tl ~e, there is a unique lexical representation (word)corresponding to each of these meanings; but (iii) over short time intervals, the word representing any meaning runs a small but constant risk of being replaced by a different (non-cognate) word; and (iv) the replacement, or non-replacement, of the lexical representation of a meaning occurs independently of that of any other meaning, and independently over different periods of time. To formalize (i) and (ii), we must postulate the existence, for each natural language, at all points t in time, of a lexico_..___~n, represented by a finite abstract set Lt. A well-defined equivalence relation corresponding to cognation partitions the elements of ~TLt (T a real interval) into equivalence classes. If k6Ls, I~L t (t,s6T) are cognate, we write ~(k,l) = i. Otherwise ~(k,1) = O. Further, we must postulate the existence of a finite abstract set M (corresponding to the universal set of meanings), and a procedure for defining, for any t, and any Lt, a unique map from M into Lt. This map, written M ~Lt, specifies that for each t m~M there is a i~ L t such that m~l (i mean., ss m). Hypotheses (iii) and (iv) imply that the changes over time in the image of the map M-~*-t Lt have a certain stochastic aspect. This can be modelled by the probability statement P[~(k,l) = 1] = i-X(t-s) ÷ h , a universal constant, t>s, and ~t-s-~ 0 as t-~s; and two independence conditions ; let This model has a number of immediate properties which form the central thesis of the …