Transformation of shape

Abstract

We are lucky to be able to discuss to-day so simple a concept as that of ‘growth’. Growth means change of size, and the size of an organism is something definite, unambiguous and measurable. It has been more than once suggested that ‘growth’ is an all but impenetrably obscure concept because it relates to a very heterogeneous process, i. e. because a great number of diverse factors contribute to change of size. One might equally well argue that the respiratory quotient was an ill-defined ratio because of the complexity of the respiratory process. The diversity of the causes of change of size does not imply that change of size is an obscure idea. As biological concepts go, it is an uncommonly clear one. It can, of course, be made as obscure as we wish by arbitrary subdivisions of its terms of reference. One may distinguish, for example, between a ‘true’ sort of growth and a ‘mere’ sort of growth ; molecular replication is ‘true’, and the intussusception of water is ‘mere’. This sort of distinction is a surviving remnant of the habit of mind that distinguishes between the protoplasm of the animal, which is truly alive, and the rest of it, which is dead. There are, indeed, profound differences between the processes that severally contribute to change of size, but they are not differences of which terms like ‘true’ and ‘mere’ can usefully be applied. A description of growth must necessarily precede an investigation of growth processes, just as an analysis of the mechanism of nerve regeneration or skin healing cannot be begun unless we know what is actually going on, in an anatomical sense, when nerves regenerate and skin heals. The recording of growth is thus primarily an exercise in anatomy or descriptive embryology. Because size is measured numerically, the description of growth is necessarily mathematical in the everyday sense, but this is not inconsistent with its being anatomical as well. An anatomist who says that one organism is ever so much larger than another, or is longer and thinner than another, is making statements which in a general sense are mathematical. They are mathematical statements and they are mathematically imprecise. There are some purposes for which documentary information about growth is best presented in the form of parallel columns of figures for sizes and ages, or weights and heights, as it is in some weighing machines on railway platforms. A person who weighs himself is interested in his own weight and may be interested in the mean weight of other people of his own age or height. One pair of entries among a double column of figures can provide him with this information instantly, and it would be unkind to expect him to extract it from a growth equation intended to be applicable to all ages. But for most purposes the con­struction of growth equations is very well worth while: they expedite the analysis of growth rates; they allow comparison between the modes of growth of related organisms; and, most important, they make it possible to frame inductive ‘laws' of growth after an investigation of the general analytic properties which the growth equations of different organisms share in common (Medawar 1945).