A preprint of our paper: Bormashenko, E.; Shoval, S.; Frenkel, M.; Nosonovsky, M. Correlations between Symmetry and Frequency of Artificial and Natural Symbols. Preprints 2024, 2024071071. https://doi.org/10.20944/preprints202407.1071.v1 PDF file
We investigated correlations between letter frequency and symmetry in English and Russian languages. We found a positive correlation (i.e., more symmetric letters are more frequent) in both languages with the coefficients of determination of R^2=0.899 (English) and R^2=0.693 (Russian). We also studied the correlation between the symmetry of digits and first digit frequency for four different systems of numerals. Again, a positive correlation was observed with the coefficients of determination of R^2=0.740. The explanation of these trends may lie in the fact that more frequent symbols are simpler to optimize efforts needed to memorize them and to write them.
For comparison, we studied “symbol-like” 2D colloidal clusters. In such clusters, negative correlations between frequency and symmetry were observed, i.e., more symmetric letters are less frequent with the coefficients of determination of R^2=0.814 and R^2=0.994. This is explained by the fact that in natural systems more symmetric forms have lower mobility and there are fewer ways of building symmetric clusters than asymmetric ones.
The symmetry-frequency correlations in artificial systems reflect different causation. In human-made systems the frequency of using of a symbol is the driving force which leads to symbols simplification and symmetrizing. In natural system, symmetry leads to lower frequency of occurrence due to the prevalence of non-symmetric configurations over symmetric once.
Our results also indicate that there is a correlation between the symbol as a type and as a token. This is because symmetry is a property of a type, while frequency is a property of a token. We attribute this correlation to the inherent iconicity of symbols.
Every symbol combines two aspects: its form and its meaning. Iconicity is a similarity or analogy between symbols’ form and meaning. In the Chomskian generative linguistics, it was believed that the iconicity is not a significant factor that affects functioning of human language, in particular, that the rules of syntax are independent of semantics (“Autonomy of Syntax“) [22]. Contrary to that, Cognitive Linguistics establishes that there is influence of semantics upon syntax of language. Our study shows properties of a symbol as a type, such as symmetry of its form, and properties of a symbol as a token, such as frequency of use, correlate with each other.