Golden Ratio and Cybernetic Aesthetics for Hidden Patterns in Repetitive Human Movements: Golden-faux-sinus as a Two-Dimensional Optimization Model

Abstract: It is not easy to measure the amount of information within an object that is capable of leading to aesthetics-based feelings in a viewer, especially because of a subjective variability of human perception. Cybernetic aesthetics, for its part, might provide a rational way for understanding such a human phenomenon at least in special cases. Now, cyclic human movements — not only gait cycles, but also swimming strokes and tennis forehand strokes — were found, with their given internal sub-phases, to be characterized, from a temporal point of view, by the existence of coordinatively mechanized and self-similar harmonic fractal patterns. Such harmonic patterns were specifically found to be symmetrized in time so as to compose a generalized Fibonacci sequence and then implicitly dictated by the golden ratio, when it occurs as the ratio of the resulting sub-phases durations. The lowest amount of information for the movement temporal design (Shannon entropy minimization, SEM) makes one sub-phase duration of the movement temporally generate an entire sequence of sub-phase durations of the same movement. However, different spatial profiles can correspond to identical temporal partitions, suggesting the presence of an additional optimization principle that acts within the spatial domain. The original contribution of this paper consists of unveiling what is beyond the aforementioned temporal characterization, revealing the existence of a possible cyclic movement attractor, named golden faux sinus, which is based on a spatial smooth sewing of zero-jerk portions. This might suggest how the neuromuscular system organizes complex repetitive movements and how information processing is exploited into a sub-movement generation architecture. The resulting hidden patterns are the ones that might be caught by a viewer, who is able to concentrate separately on different categories of meaning. Experiments concerning young healthy walking subjects, as well as ATP-WTA top-level tennis players during some of the latest strongest moments of their career, illustrate the effectiveness of the presented derivations. Graphic Abstract: (Figure presented.)