The pattern of change in size and shape

Abstract

Abstract In introducing a discussion on the subject of growth, it is unnecessary to add to the many definitions of the word which previous writers have provided. It is, however, useful to try to define the particular theme of the present discussion, for as Weiss (1949) has put it, the term ‘growth’ has become a cover for a variety of diverse and complex phenomena. ‘It is not even’, he writes, ‘a scientific term with defined and constant meaning, but a popular label that varies with the accidental traditions, predilections, and purposes of the individual or school using it. It has come to connote all and any of these; reproduction, increase in dimensions, linear increase, gain in weight, gain in organic mass, cell multiplication, mitosis, cell migration, protein synthesis, and perhaps more.’ The present discussion has been designed to illuminate an aspect of the subject which is aptly described by Richards & Kavanagh’s (1945) definition of growth as ‘a fundamental attribute of living organisms, manifested by a change in size of the individual, or in the number of organisms in a unit of environment’, the change normally being an increase, with the possibility of negative growth or decrease in size under adverse conditions. Its main theme is the unfolding with time of a pattern of change in an organism—a pattern of change of size and of change of shape—and the methods by which the change can be defined. This was the aspect of the subject which dominated D’Arcy Thompson’s interest. ‘The study of form’, he wrote (1916, 1942), ‘may be descriptive merely, or it may become analytical. We begin by describing the shape of an object in the simple words of common speech: we end by defining it in the precise language of mathematics; and the one method tends to follow the other in strict scientific order and historical accuracy.’