Narrow Results

The golden ratio (GR) is an irrational number (close to 1.618) that repeatedly occurs in nature as well as in masterpieces of art. The GR has been considered a proportion perfectly representing beauty since ancient times, and it was investigated in several scientific fields but with conflicting results. This study aims at investigating if this proportion is associated with a judgment of beauty independently of the type of the stimulus, and the factors that may affect this aesthetic preference. In Experiment 1, an online psychophysical questionnaire was administered to 256 volunteers asked to choose among three possible proportions between the parts of the same stimulus (GR, 1.5, and 1.8). In Experiment 2, we recorded eye movements of 15 participants who had to express an aesthetic judgment on the same stimuli as Experiment 1. The results revealed a slight overall preference for GR (53%, p < 0.001), with higher preferences for stimuli representing humans, anthropomorphic sculptures, and paintings, regardless of the cultural level. In Experiment 2, a shorter dwell time was significantly associated with a better aesthetic judgment (p = 0.005), suggesting the possibility that GR could be associated with easier visual processing, and it could be hence considered as a visual affordance.

Chapter 9 addresses the foundational issues as they relate to the topological distinctions found in the Mereon Trefoil in particular and the Mereon geometry in general. Kauffman presents how the non-standard version of the trefoil knot seen tied by tracing the arcing angles of the Matrix is a higher energy version of the alternating weave of the 3,2 trefoil knot. Geospherical in nature, links are made to the pentagon, Petersen graph, the Five Elements. So too, connections are made to Fourier knots, and how the Mereon Trefoil form by connecting double helices. Connections are established between the pattern of DNA recombination, Spencer-Brown’s ‘Laws of Form’, and Shea Zellweger’s Logical Garnet. The assertion that the shape of the universe is dodecahedral is linked with how its construction might arise from the trefoil knot as the unfolding of a five-fold symmetry. It is presented how this would make the Mereon knot a complex but simple ‘cosmic loop’ around the whole universe, thus making knot theory universally applicable.