¹ See W. Ross Ashby, An introduction to cybernetics (New York, 1956).

² In language, this type of selection is mostly brought about by sociocultural factors. Though from the sociocultural point of view these factors may not be random, they act in a random way on the linguistic system. Even from the linguistic point of view there may be constraints on the selective factors; see Edward Sapir, Language (New York, 1921), especially Chapter 7, Language as a Historical Product: Drift.

³ Holger Pedersen, Linguistic science in the nineteenth century 314 ff. (Cambridge, Mass., 1931), describes the development of this theory.

⁴ Charles F. Hockett, A course in modern linguistics 458 ff. (New York, 1958), gives a brief review of the comparative method.

⁵ Or A, B, and C are equidistant. Cf. Robert E. Longacre, Proto-Mixtecan 3 (Indiana University Research Center in Anthropology, Folklore and Linguistics, Publication 5; 1957): ‘Mixtec, Cuicatec and Trique reconstruct as a well-defined group with no obvious subgrouping of any two languages as opposed to the third.‘

⁶ For extremely divergent related languages, no perceptually identical particulars may be discoverable, but by definition there will always be systematically different particulars.

⁷ Sarah C. Gudschinsky, The ABC's of lexicostatistics (glottochronology), Word 12.175-210 (1958). Applications of glottochronology to the field of Romance have recently been discussed, with varying conclusions, by John A. Rea, Concerning the validity of lexicostatistics, IJAL 24.145-50 (1958); F. W. Householder Jr., review of Studies presented to Joshua Whatmough in Lg. 34.402 (1958); A. L. Kroeber, Romance history and glottochronology, Lg. 34.454-7 (1958); and Douglas Taylor, Concerning the validity of some translations, IJAL 25.70-1 (1959). It is premature to compare our results with those of glottochronology; we must first establish the validity of our methods.

⁸ The Romance materials are the work of Agard, and are to be published elsewhere (with D. F. Solá). For this paper, they are of interest only in quantified form; hence they are not given in detail. Their quantification and the conceptual scheme which underlies it, as well as the actual form of the paper, are the work of Grimes.

⁹ Other scales, for example, could be constructed by using instrumental values, or by using a Pan-Romance table of distinctive features and counting similarities and differences, as suggested by Sol Saporta, Frequency of consonant clusters, Lg. 31.25-30 (1955). No a-priori requirement weightier than plausibility has led to our choice of this scale, but trial and error may lead to the discovery of a more appropriate scale.

Mario A. Pei, A new methodology for Romance classification, Word 5.135-46 (1949), attempted to calculate the ‘relative degree of phonological change from the original Latin’ and the ‘degree of affinity with any other [Romance] language or dialect’ by totaling the values assigned to change of quality, diphthongization, or failure to follow a broad pattern of change in a specific environment, in the development of each of the Latin stressed vowels to each of the modern languages. Pei's calculations, however valid they may be for showing the amount of change from Latin, are not suitable for expressing degrees of affinity.

With regard to phonetic dimensions, see now also W. Haas, Relevance in phonetic analysis, Word 15.1-18 (1959): ‘General phonetics ... may be said to be the science of the dimensions of phonetic description. ‘

¹⁰ Kenneth L. Pike, Phonetics 129 ff. (Ann Arbor, 1943); Language in relation to a unified theory of the structure of human behavior 2.23-4 (Glendale, 1955).

¹¹ Calculating the degree of phonetic difference between 28 pairs of sounds in 169 sets of correspondences, at seven operations per comparison (six subtractions and one addition), requires 7 × 28 × 169 = 32,124 separate operations, all of a type suitable for calculation by machine. The differences between components are combined by simple summation on the basis of the observation by William M. Austin that ‘If the articulatory chart is visualized as a chessboard, sound-change can be thought of as following always the castle's move, never the bishop's’ (Criteria for phonetic similarity, Lg. 33.544 [1957]).

¹² An alternative way of calculating differences would be to find the difference in numerical value between each pair of components without summing the differences. Handling each component separately might show something about the relation of various components to each other in linguistic change. For this suggestion, based on experience in the fields of plant breeding and genetics, we are indebted to E. James Kennedy of Pueblo, Colorado.