How communicatively optimal are exact numeral systems? Once more on lexicon size and morphosyntactic complexity
Authors: Chundra Cathcart, Arne Rubehn, Katja Bocklage, Luca Ciucci, Kellen Parker van Dam, Alžběta Kučerová, Jekaterina Mažara, Carlo Y. Meloni, David Snee, Johann-Mattis List
Organizations: Institute for the Interdisciplinary Study of Language Evolution University of Zurich, Zurich, Switzerland · Chair for Multilingual Computational Linguistics University of Passau, Passau, Germany
Recent research argues that exact recursive numeral systems optimize communicative efficiency by balancing a tradeoff between the size of the numeral lexicon and the average morphosyntactic complexity (roughly length in morphemes) of numeral terms. We argue that previous studies have not characterized the data in a fashion that accounts for the degree of complexity languages display. Using data from 52 genetically diverse languages and an annotation scheme distinguishing between predictable and unpredictable allomorphy (formal variation), we show that many of the world's languages are decisively less efficient than one would expect. We discuss the implications of our findings for the study of numeral systems and linguistic evolution more generally.
Figures & tables
Language
Concept
Source Form
Surface Form
Underlying Form
Morpheme Gloss
French
ten
dix
\IPA dis
\IPA /dis/
ten
French
sixteen
seize
\IPA sEz
\IPA /sEz/
sixteen
French
seventeen
dix-sept
\IPA disEt
\IPA /dis-sEt/
ten seven
French
eighteen
dix-huit
\IPA diz \textturnh it
\IPA /dis- \textturnh it/
ten eight
Balochi
ten
d \textschwa
\IPA d@
\IPA /d@/
ten
Balochi
sixteen
šãzd \textschwa [g]
\IPA Sãzd@
\IPA /Sãz-d@/
six 2 ten
Table 1: Selected examples of annotation scheme from French (stan1290; Doherty, 2016a ), Balochi (west2368; Barker & Mengal, 1969a ) and Dhivehi (dhiv1236; Gnanadesikan, 2017a ), slightly modified for increased clarity. Phonologically predictable allomorphs (e.g., French \IPA [di] before \IPA /s/ vs. \IPA [diz] before a voiced segment vs. \IPA [dis] elsewhere) are coded as underlyingly the same, whereas allomorphs with no clear phonological conditioning environment (e.g., Balochi \IPA [S@S:] vs. \IPA [Sãz] ‘6’, Dhivehi \IPA [Vihi] vs. \IPA [Vi:s] ‘20’) are coded as separate underlying morphemes. We exclude cognate codings, as cognacy is not relevant to the research question investigated here, which depends only on the synchronic configurations exhibited by languages.
Figure 1: Lexicon sizes plotted against morphosyntactic complexity values for languages in our sample, under broad and narrow data formats, with selected languages labeled. Colors represent posterior probabilities of component membership (lighter values indicate higher P(k=2) ). The solid line represents the Pareto frontier estimated by the evolutionary algorithm.
Institute for Artificial Intelligence, Peking University · School of Psychological and Cognitive Sciences, Peking University · Yuanpei College, Peking University +2