“Entropy Trade-Offs in Artistic Design: A Case Study of Tamil kolam, N.-Han Tran, Timothy Waring, Silke Atmaca, Bret A. Beheim2021-03-01 (, , ; similar)⁠:

From an evolutionary perspective, art presents many puzzles. Humans invest substantial effort in generating apparently useless displays that include artworks. These vary greatly from ordinary to intricate. From the perspective of signaling theory, these investments in highly complex artistic designs can reflect information about individuals and their social standing.

Using a large corpus of kolam art from South India (n = 3,139 kolam from 192 women), we test a number of hypotheses about the ways in which social stratification and individual differences affect the complexity of artistic designs.

Consistent with evolutionary signaling theories of constrained optimization, we find that kolam art tends to occupy a ‘sweet spot’ at which artistic complexity, as measured by Shannon information entropy, remains relatively constant from small to large drawings. This stability is maintained through an observable, apparently unconscious trade-off between 2 standard information-theoretic measures: richness and evenness.

Although these drawings arise in a highly stratified, caste-based society, we do not find strong evidence that artistic complexity is influenced by the caste boundaries of Indian society. Rather, the trade-off is likely due to individual-level esthetic preferences and differences in skill, dedication and time, as well as the fundamental constraints of human cognition and memory.

[Keywords: art, signaling, entropy, skill, material culture, Bayesian inference]

Kolam drawings are geometric art practised by women in the Kodaikanal region of Tamil Nadu, southern India (Layard1937). A kolam consists of one or more loops drawn around a grid of dots (in Tamil called pulli). On a typical morning, a Tamil woman will prepare a grid of dots on the threshold of her home, and then draw a kolam with rice powder or chalk. During the day the drawing weathers away, and a new kolam is created the next day. Kolam drawings are historically traditions of matrilines, but more recently are also a topic of cultural education in Tamil schools. Girls in Tamil Nadu begin practising kolam-making from an early age, and competency in this art is considered necessary for the transition into womanhood (Nagarajan2018, Feeding a thousand souls: Women, ritual, and ecology in India—An exploration of the kolam). Although the primary medium is the threshold of the home, women practice kolam-making in notebooks, and it is common for artists to share, copy and embellish each other’s kolam designs. Such unrestrained artistic exchange is fostered by the fact that kolam designs are not considered to belong to any one person, but rather to be a type of community knowledge (Nagarajan2018). However, the ability to successfully draw esthetically pleasing (ie. diverse, complex, large) kolam drawings is said to reflect certain qualities of a woman (eg. her degree of traditionalness or patience), and as such her capacity to run a household and become a good wife and mother (Laine2013; Nagarajan2018).

…Here we study the ner pulli nelevu or sikku kolam family because of its unique form. Because sikku kolam drawings represent an unusually strict system of artistic expression, kolam drawings can be mapped onto a small identifiable set of gestures and are therefore well suited to systematic, quantitative analyses as a naturalistic model system of cultural evolution. A given kolam’s gesture sequence can be characterised by a number of informative summary statistics which capture aspects of kolam itself: the sequence length (ie. the total number of gestures), the discrete canvas size (measured by the grid of dots, or pulli), the gesture density per unit canvas area and gesture diversity as measured by evenness (here, the Gini index), richness and Shannon information entropy.

Figure 3: Trade-off between evenness and richness. The grey lines measure maximum entropy isoclines. The raw kolam data are jittered and illustrated in blue (light blue = low density, dark blue = high density). The (90, 75, 50%) kernel density of the average richness and evenness for each canvas size of the data are depicted in the orange area (light orange to dark orange).