Pseudo-relativistic vector analysis of animal growth in four-dimensional space-time - Preliminary report with problem of dimensional inconsistency between space and time -

This study investigated the space-time relationship in the growth analysis of an individual animal by introducing a pseudo-relativistic vector, under the problem of dimensional inconsistency between space and time. Space and time were treated equally and growth vector inclining to space-time axes was introduced. The growth vector (G) of the animal was described using a pseudo-relativistic vector in four-dimensional space-time, G = (x, y, z, t). The magnitude of G (Gm) was regarded as an index of the four-dimensional growth of the animal. The results obtained were as follows, (i) If G inclined greatly to z-axis compared with the other three axes (x, y, i), then this was a result of the fact that the animal became taller by the efficient utilization of the height direction in space, (ii) If G inclined greatly to i-axis compared with space axes (x, y, 2), then this was a result of the fact that the animal showed a smellier growth because of the inefficient utilization of time, iii An invariant connecting geometric and analytic representations of growth was proposed to make an inclusive comparison of veirious cases of animal growth. It was suggested that space and time were related in a pseudo-relativistic vector analysis of animal growth, under geometric and analytic representations.