ABSTRACT
D'Arcy Thompson (1992) Natural scientists have long perceived and classified organisms primarily on the basis of their appearance and structure, otherwise known as their form. Beyond classification, students of biology study form in order to understand those processes that underlie variation in form, processes like disease, growth, and evolution. The true form of an object does not change whether an organism is moving across a surface (translation in mathematical terms) or spinning on an axis (rotation). Our perception of the organism may change when orientation changes, but perception is not our concern here. It follows that any quantitative representation of a form should not change if the coordinate system used to represent that form changes. Moreover, any comparison of forms should give us equivalent results regardless of whether the operations of translation and rotation are used in these comparisons. These simple observations underscore the importance of the principle of invariance in the study of form.
