In 1917, D'Arch Thompson suggested that one should study the change from one biological form to another by examining the unique mathematical object that maps between them in accord with biological homologies. Biorthogonal grids provide a particular coordinate system for visualizing such a map and lead to a quantitative syntax in which a change in shape is reduced to differential changes in size. Application of the method to hominid skull phylogeny has demonstrated three principal axes of evolutionary change anatomically homologous over a fossil sequence.