On Growth and Form by Sir D’Arcy Thompson, first published in 1917, has become a classic study of the mathematics of biological form, and is indispensable for anyone exploring the relationships between biology and design.
The chapters in On Growth and Form include:
- On Magnitude
- The Forms of Cells
- The Forms of Tissues
- On Spicules and Spicular Skeletons
- The Equiangular Spiral
- The Shapes of Horns and of Teeth or Tusks
- On Form and Mechanical Efficiency
- On the Theory of Transformations, or the Comparison of Related Forms
The chapter on transformations is perhaps the most remarkable, with diagrams showing how differences in the forms of, say, species of fish can be construed in terms of distortions of the co-ordinate systems onto which they are mapped. A fish is drawn onto a squared grid which is then stretched or shifted in specific ways so that the image then can be identified as that of a related species.
Since the book deals with living things, there is more to this than mere form, as Thompson explains:
“we rise from the conception of form to an understanding of the forces which gave rise to it; and in the representation of form and in the comparison of kindred forms, we see in the one case a diagram of forces in equilibrium, and in the other case we discern the magnitude and the direction of the forces which have sufficed to convert the one form into the other.” (p.270)
The book is endlessly fascinating and is a triumph of scientific prose from an unusually gifted scholar, as Stephen Jay Gould’s foreword shows:
“D’Arcy Thompson, according to a legend that could have been true, was offered his choice of professorships in three apparently disparate disciplines: classics, mathematics, and zoology. The greatness of On Growth and Form lies in its genuine integration (not just ostentatious show) of these three foci.” (p.ix)