Impotence Principle in Descriptive Morphology

Abstract

IT was recently proposed¹ that biological form should be specified by an expansion of the characteristic function of the form as a weighted sum of the elements of a complete set of orthonormal functions. The method was applied to two-dimensional forms, using Walsh functions². In the discussion it was suggested that each weight might be maximized with respect to all possible transformations of the form caused by any combination of displacements, rotations and uniform contractions or expansions. It was conjectured that this sequence of “maximal” weights constituted an unequivocal specification of the form, that is to say, two different forms would always be represented by different sequences. In the case of the Walsh functions, these weights would be real numbers lying in the interval − ½ to + ½, except for the first one which would lie in the interval 0 to 1.