A preliminary analysis of space-time structure of animal growth by the use of 4-dimensional vector

This study was designed to make a preliminary analysis of a space-time structure of animal growth by the use of 4-dimensional vector [G = (x₀, x₁, x₂ x₃)]. The magnitude of G (Gm) was regarded as the space-time structure of the growth of the individual animal. The analytic description of the animal growth was given by Gm and its partial differentiation, and the geometric description was given by Gm and the cosine component of G. Hypotheses (A)∼(E) were suggested. (A) The space-time dimensional inconsistency was hidden by an invariant that was given by analytic and geometric descriptions of the animal growth. (B) The animal growth was distributed among 4-dimensional space-time axes. (C) The increase in the growth along space axes caused the decrease in the growth along time axis, and vice versa. (D) There was a growth along time axis even when there was no growth along space axes. (E) The geometric description showed that the 4-dimensional information was projected onto 2-dimensional planes and that space and time were related on the complex plane that existed at every point of the space-time structure. This animal growth model suggested a hypothesis that the 4-dimensional space-time structure was related to a pseudo-relativ-istic growth mechanics and to the complex number world.