Connection between Growth/Development and Mathematical Function

Abstract

To investigate universal principles of growth and development, the author examined the questions of when mathematical functions can be applied to growth curves, what type of functions can be used, and, from a consideration of the historical background, the context for application and validity of such mathematical functions. Examinations of this issue have developed along two main lines: the establishment of logistic models as sigmoid curves showing the proliferation process of living organisms, and the establishment of polynomial systems (spline functions) that describe smoothing of the growth curve and fluctuations in the process. The conceptual prescriptions of fitting functions for the former are structural models, and those for the latter are nonstructural models. The fundamental thinking is that, similar to proliferation of organisms, growth phenomena can be described and explained with the use of differential equations. However, changes in aspects of growth curves are produced with differences in measurement intervals: waves are seen in growth phenomena as measurement intervals become shorter. Thus, a mathematical function is needed that can describe the changes in growth phenomena using a scaling concept on the time axis. To do this it is necessary to separate growth phenomena from biology and develop mathematical functions derived from an independent conceptual framework. In this context, the author has proposed unique wavelets. Herein, the author discusses the historical and theoretical backgrounds of mathematical fitting functions and their validity. The author also examine the interface of these functions with growth study, and its theoretical background.