Just as biologists are cleaning up the confetti from last year's big double anniversary of Charles Darwin and his Origin of Species, it's time to celebrate again. This year marks the 150th birthday of D'Arcy Wentworth Thompson, the Scottish polymath (a natural historian, linguist, classicist, physicist, mathematician...) whose most famous book, On Growth and Form (Google Books preview of the 1961 abridgement by J.T. Bonner, with an introduction by Stephen Jay Gould), pioneered the study of biomechanics and biomathematics.
On Growth and Form is a rich book that can be repeatedly savored with profit. In many ways, it is a product of its times (it was first published during WWI, and the revised edition came out during WWII): Thompson wrote hopefully about bioelectric fields and their application to the study of cell division (drawing a parallel, as many did at the time, between the arrangement of spindle fibres, which had only just been discovered, and the field lines of an electric dipole). Those chapters and sections now seem arcane and outdated, even though they have value as a historical and literary document. On the other hand, his ruminations on the geometrical and mathematical patterns inherent in natural forms, such as the spirals of shells and the Fibonacci sequence in leafy shoots, could still very well be a subject for the latest issue of Scientific American.
It is his application of mathematics and geometry to the science of morphology that has been his most lasting legacy. Morphology prior to Thompson was very much a descriptive field. What he did was to suggest that abstract principles underlay natural forms, and that these principles could be accounted for, and perhaps even predicted, on the basis of mathematics and physics. The great question for morphologists of his day was that of homology - how to detect it and to explain it in evolutionary terms. The most famous illustrations from his book, those depicting species differences as geometric transformations, intimated to the reader the promise of his new morphology: the ability to predict gross form in a quantitative way. In his 'theory of transformations', so it seemed, lay the key to homology. Could one gain some special insight from the formula to transform a bird's wing to a lizard's forelimb?
Thompson's transformations turned out to be of limited use to the science of development (see Wallace Arthur on the transformation theory) as it itself evolved from its origins in descriptive embryology. The experimental approach to embryology, and later the genetic one, took center stage and eclipsed the physicalist approach. Embryologists were not inclined to treat the developing embryo as the equivalent of a deformed rubber tube, as Thompson illustrated, though modern developmental biologists are revisiting the mechanical origins of form, with more sophisticated tools and concepts.
Where Growth and Form might have really caught on, oddly enough, was in paleontology, where genes and physiology are long disappeared and form is all that remains. The morphospace concept (review) has been popularized by the work of David Raup, as applied to gastropod shells (which can be mathematically described as the product of a limited number of 'coiling parameters'), and Karl Niklas, with the vascular plants. Their work shows the difficulties facing any earnest application of Thompson's mechanistic paradigm. Their work has been hugely fruitful in getting people to accept and understand the concept of a morphospace. However, they have remained largely proofs-of-principle, and did not spawn frutiful research programs in the same way that, say, genetic screens did in developmental biology. The idea itself is seductively simple - natural forms can be explained solely by mechanical and physical forces that shape them - but difficult to work out in practice, except in the most abstract way (both Raup and Niklas made pioneering use of computer simulations), because we still do not fully understand the physics of living materials. Their fine-scale complexity has made both analysis and modeling prohibitively difficult without introducing simplifications that may turn out to be oversimplifications. Why then were they so attractive and enchanting to biologists in the first half of the 20th century? The answer requires historical context. That period saw vitalism, the idea that living matter, or protoplasm (when we use that term in intro biology as a synonym for cytoplasm we are usually oblivious to the historical baggage that it carries) has a special 'life force' that makes it fundamentally different from inanimate matter, become upended and discredited once and for all. A purely mechanistic and mathematical morphology, as Thompson suggestively alluded to, was about as far as one could get from the Romantics.
All that said, even if we remove the outdated 'fields of force' or nebulous 'theory of transformations', there is still a substantial book left behind. The revised edition (still published cheaply by Dover) is almost 1500 pages octavo. He presents with alacrity topics such as the statics and dynamics of limbs and skeletons, that remain the bread-and-butter issues of biomechanics today. One of his examples, the correspondence between the lines of force and the skeletal elements in the spongy bone of a femur head, is still repeated in almost every textbook of biomechanics that I've seen. He romps through the aerodynamics of flight (citing an early paper by James Clerk Maxwell on the best design for a paper plane), the shapes of bubbles and the shapes of cells, the relation between an ox and a suspension bridge... and all of it in lyrical prose so enthusiastic that I am citing all these examples from memory having last read the book years ago. D'Arcy Thompson is the eccentric professor with the sparkling mind that we all wished we could have had. Through Growth and Form we can still savor the fruits of his broad learning. May it long continue to enthrall new generations of biologists!