The “handedness” of language: Directional symmetry breaking of sign usage in words
The normalized difference of the Gini indices ΔG = 2(GL − GR)/(GL + GR) (filled circles), which measures the relative heterogeneity between the occurrences of different signs in the terminal positions of words of a language, are shown for a number of different written languages (arranged in alphabetical order) that span a variety of possible writing systems—from alphabetic (e.g., English) and syllabic (e.g., Japanese kana) to logographic (Chinese) [see text for details]. All languages that are conventionally read from left to right (or rendered in that format in the databases used here) show a negative value for ΔG, while those read right to left exhibit positive values. The horizontal thick bars superposed on the circles represent the 95% bootstrap confidence interval for the estimated values of ΔG. To verify the significance of the empirical values, they are compared with corresponding ΔG (diamonds) calculated using an ensemble of 1000 randomized versions for each of the databases (obtained through multiple realizations of random permutations of the signs occurring in each word—see Materials and Methods for details), the ranges of fluctuations being indicated by error bars. Along with the set of known languages, ΔG measured for a corpus of undeciphered inscriptions from the Indus Valley Civilization (2600–1900 BCE) is also shown (bottom row).