2024
Volume 24, Number 3/4, pp. 124-129
The relationship between entropy and complexity quantitatively:
The case of throwing a fair die very many times
T. Modis
Growth Dynamics, Via Selva 8, 6900 Massagno, Lugano, Switzerland
A die thrown very many times will eventually undergo deformations, with its apices becoming progressively more rounded. Calculating the entropy for such a system as a function of time reveals an S-shaped trajectory. Doing so for complexity reveals that it first increases, goes over a maximum, and finally decreases towards zero as the shape of the die approaches that of a perfect sphere due to the wear and tear. The relationship of entropy to complexity in this system is similar to that of a mathematical function to its time derivative. The idea that complexity first increases and then decreases as entropy increases applied to our solar system suggests that we may be traversing the highest complexity and most interesting period of our world.
Keywords: complexity, entropy, fair dice, logistic function, time derivative