On Growth and Form

Overview

D'Arcy Wentworth Thompson's most famous work, On Growth and Form was written in Dundee, mostly in 1915, but publication was put off until 1917 because of the delays of wartime and Thompson's many late alterations to the text. The central theme of the book is that biologists of its author's day overemphasized evolution as the fundamental determinant of the form and structure of living organisms, and underemphasized the roles of physical laws and mechanics. At a time when vitalism was still being considered as a biological theory, he advocated structuralism as an alternative to natural selection in governing the form of species, with the smallest hint of vitalism as the unseen driving force.

Thompson had previously criticized Darwinism in his paper Some Difficulties of Darwinism. On Growth and Form explained in detail why he believed Darwinism to be an inadequate explanation for the origin of new species. He did not reject natural selection, but regarded it as secondary to physical influences on biological form.

Using a mass of examples, Thompson pointed out correlations between biological forms and mechanical phenomena. He showed the similarity in the forms of jellyfish and the forms of drops of liquid falling into viscous fluid, and between the internal supporting structures in the hollow bones of birds and well-known engineering truss designs. He described phyllotaxis (numerical relationships between spiral structures in plants) and its relationship to the Fibonacci sequence.

Perhaps the most famous part of the book is Chapter 17, "The Comparison of Related Forms," where Thompson explored the degree to which differences in the forms of related animals could be described, in work inspired by the German engraver Albrecht Dürer (1471–1528), by mathematical transformations.

The book is descriptive rather than experimental science: Thompson did not articulate his insights in the form of hypotheses that can be tested. He was aware of this, saying that "This book of mine has little need of preface, for indeed it is 'all preface' from beginning to end."

Editions

The first edition appeared in 1917 with 793 pages, published by Cambridge University Press. The second, enlarged edition appeared in 1942, with 1116 pages; it extended many of the chapters somewhat but did not significantly change Thompson's thesis. Since then it has been reprinted and abridged many times, including in 1943, 1944, 1945, 1948, 1951, 1952, 1959, 1961, 1963, 1966, 1967, 1968, 1969, 1971, 1972, 1973, 1977, 1979, 1980, 1981, 1983, 1984, 1986, 1987, 1988, 1990, 1992, 1994, 1995, 1997, 1999, 2000, 2003, 2004, 2006, 2007, 2008, 2009, 2010, 2011 and 2014. It has thus been in print continuously since the Second World War. The book has been translated into German, Spanish, French, and Greek. The 1961 edition, skilfully abridged down to 346 pages by John Tyler Bonner, presents the essence of Thompson's argument.

Contents

The contents of the chapters in the first edition are summarized below. All but Chapter 11 have the same titles in the second edition, but many are longer, as indicated by the page numbering of the start of each chapter. Bonner's abridgment shortened all the chapters, and removed some completely, again as indicated at the start of each chapter's entry below.

1. Introductory

(1st edition p1 - 2nd edition p1 - Bonner p1)

2. On Magnitude

(1st p16 - 2nd p22 - Bonner p15)

3. The Rate of Growth

(1st p50 - 2nd p78 - Bonner removed)

4. On the Internal Form and Structure of the Cell

(1st p156 - 2nd p286 - Bonner removed)

5. The Forms of Cells

(1st p201 - 2nd p346 - Bonner p49)

6. A Note on Adsorption

(1st p277 - 2nd p444 - Bonner removed)

7. The Forms of Tissues, or Cell-aggregates

(1st p293 - 2nd p465 - Bonner p88)

8. The same (continued)

(1st p346 - 2nd p566 - Bonner merged with previous chapter)

9. On Concretions, Spicules, and Spicular Skeletons

(1st p411 - 2nd p645 - Bonner p132)

10. A Parenthetic Note on Geodetics

(1st p488 - 2nd p741 - Bonner removed)

11. The Logarithmic Spiral ['The Equiangular Spiral' in 2nd Ed.]

(1st p493 - 2nd p748 - Bonner p172)

12. The Spiral Shells of the Foraminifera

(1st p587 - 2nd p850 - Bonner merged with previous chapter)

13. The Shapes of Horns, and of Teeth or Tusks: with A Note on Torsion

(1st p612 - 2nd p874 - Bonner p202)

14. On Leaf-arrangement, or Phyllotaxis

(1st p635 - 2nd p912 - Bonner removed)

The numbers that result from such spiral arrangements are the Fibonacci sequence of ratios 1/2, 2/3, 3.5 ... converging on 0.61803..., the golden ratio which is

15. On the Shapes of Eggs, and of certain other Hollow Structures

(1st p652 - 2nd p934 - Bonner removed)

16. On Form and Mechanical Efficiency

(1st p670 - 2nd p958 - Bonner p221)

17. On the Theory of Transformations, or the Comparison of Related Forms

(1st p719 - 2nd p1026 - Bonner p268)

Epilogue

(1st p778 - 2nd p1093 - Bonner p326)

Contemporary

"J. P. McM[urrich]", reviewing the book in Science in 1917, wrote that "the book is one of the strongest documents in support of the mechanistic view of life that has yet been put forth", contrasting this with "vitalism". The reviewer was interested in the "discussion of the physical factors determining the size of organisms, especially interesting being the consideration of the conditions which may determine the minimum size".

J. W. Buchanan, reviewing the second edition in Physiological Zoology in 1943, described it as "an imposing extension of his earlier attempt to formulate a geometry of Growth and Form" and "beautifully written", but warned that "the reading will not be easy" and that "A vast store of literature has here been assembled and assimilated". Buchanan summarizes the book, and notes that Chapter 17 "seems to the reviewer to contain the essence of the long and more or less leisurely thesis... The chapter is devoted to comparison of related forms, largely by the method of co-ordinates. Fundamental differences in these forms are thus revealed", and Buchanan concludes that the large "gaps" indicate that Darwin's endless series of continuous variations is not substantiated. But he does have some criticisms: Thompson should have referenced the effects of hormones on growth; and the relation of molecular configuration and form; genetics is barely mentioned, and experimental embryology and regeneration [despite Thompson's analysis of the latter] are overlooked. The mathematics used consists of statistics and geometry, while thermodynamics is "largely absent".

Edmund Mayer, reviewing the second edition in The Anatomical Record in 1943, noted that the "scope of the book and the general approach to the problems dealt with have remained unchanged, but considerable additions have been made and large parts have been recast". He was impressed at the extent to which Thompson had kept up with developments in many sciences, though he thought the mentions of quantum theory and Heisenberg uncertainly unwise.

George C. Williams, reviewing the 1942 edition and Bonner's abridged edition for the Quarterly Review of Biology (of which he was the editor), writes that the book is "a work widely praised, but seldom used. It contains neither original insights that have formed a basis for later advances nor instructive fallacies that have stimulated fruitful attack. This seeming paradox is brilliantly discussed by P. B. Medawar [in] Pluto's Republic." Williams then attempts a "gross simplification" of Medawar's evaluation:

It was a compelling demonstration of how readily one can use physical and geometric principles in trying to understand biology. This was a major contribution in 1917 when vitalism was still being defended by prominent biologists. The battle was as won as it is ever likely to be by the time of the 1942 edition. The book was deficient because of Thompson's lack of understanding of evolution and antipathy for any concepts of historical causation."

Modern

The architects Philip Beesley and Sarah Bonnemaison write that Thompson's book at once became a classic "for its exploration of natural geometries in the dynamics of growth and physical processes." They note the "extraordinary optimism" in the book, its vision of the world as "a symphony of harmonious forces", and its huge range, including:

the laws governing the dimension of organisms and their growth, the statics and dynamics at work in cells and tissues including the phenomena of geometrical packing, membranes under tension, symmetries, and cell division; as well as the engineering and geodesics of skeletons in simple organisms.

Beesley and Bonnemaison observe that Thompson saw form "as a product of dynamic forces .. shaped by flows of energy and stages of growth." They praise his "eloquent writing and exquisite illustrations" which have provided inspiration for artists and architects as well as scientists.

The statistician Cosma Shalizi writes that the book "has haunted all discussion of these matters ever since."

Shalizi states that Thompson's goal is to show that biology follows inevitably from physics, and to a degree also from chemistry. He argues that when Thompson says "the form of an object is a 'diagram of forces,'", Thompson means that we can infer from an object the physical forces that act (or once acted) upon it. Shalizi calls Thompson's account of the physics of morphogenesis

ingenious, extremely elegant, very convincing and, significantly, aimed at very large features of the organism: the architecture of the skeleton, the curve of horns or shells, the outline of the organism as a whole.

Shalizi notes Thompson's simplicity, explaining the processes of life "using little that a second-year physics undergrad wouldn't know. (Thompson's anti-reductionist admirers seldom put it this way.)". He notes that Thompson deliberately avoided invoking natural selection as an explanation, and left history, whether of species or of an individual's life, out of his account. He quotes Thompson's "A snow-crystal is the same today as when the first snows fell": adding "so, too, the basic forces acting upon organisms", and comments that we have forgotten other early twentieth century scientists who scorned evolution. In contrast, he argues,

Thompson owes his continuing influence to the fact that his alternative doesn't beg questions at every turn. (Also, of course, he wrote beautifully, better than the poets of his day.)

The anthropologist Barry Bogin writes that Thompson's book

is a tour de force combining the classical approaches of natural philosophy and geometry with modern biology and mathematics to understand the growth, form, and evolution of plants and animals.

Bogin observes that Thompson originated the use of transformational grids to measure growth in two dimensions, but that without modern computers the method was tedious to apply and was not often used. Even so, the book stimulated and lent intellectual validity to the new field of growth and development research.

Peter Coates recalls that

Peter Medawar famously called On Growth and Form "beyond comparison the finest work of literature in all the annals of science that have been recorded in the English tongue."

Coates argues however that the book goes far beyond expressing knowledge elegantly and influentially, in a form "that can be read for pleasure by scientists and nonscientists"; it is in his view

one of the most peculiar and original works of modern science, advancing an idiosyncratic view of how organisms develop, a view that was deeply at odds with the intellectual climate of Thompson's time ... and a textbook on how to think in any field.

The science writer Philip Ball observes that

Like Newton's Principia, D’Arcy Thompson's On Growth and Form is a book more often cited than read."

Ball quotes the 2nd Edition's epigraph by the statistician Karl Pearson: "I believe the day must come when the biologist will—without being a mathematician—not hesitate to use mathematical analysis when he requires it." Ball argues that Thompson "presents mathematical principles as a shaping agency that may supersede natural selection, showing how the structures of the living world often echo those in inorganic nature", and notes his "frustration at the 'Just So' explanations of morphology offered by Darwinians." Instead, Ball argues, Thompson elaborates on how not heredity but physical forces govern biological form. Ball suggests that "The book's central motif is the logarithmic spiral", evidence in Thompson's eyes of the universality of form and the reduction of many phenomena to a few principles of mathematics.

The philosopher of biology Michael Ruse wrote that Thompson "had little time for natural selection." Instead, Thompson emphasised "the formal aspects of organisms", trying to make a case for self-organization through normal physical and chemical processes. Ruse notes that, following Aristotle, Thompson used as an example the morphology of jellyfish, which he explained entirely mechanically with the physics of a heavy liquid falling through a lighter liquid, avoiding natural selection as an explanation. Ruse is not sure whether Thompson believed he was actually breaking with "mechanism", in other words adopting a vitalist (ghost in the machine) view of the world. In Ruse's opinion, Thompson can be interpreted as arguing that "we can have completely mechanical explanations of the living world" – with the important proviso that Thompson apparently felt there was no need for natural selection. Ruse at once adds that "people like Darwin and Dawkins undoubtedly would disagree"; they would insist that

the adaptive complexity that we see in the living world simply cannot be explained by physics and chemistry. If D'Arcy Thompson thought otherwise, it can only be because in some way he was putting special direction into his physical models. He may not have been an explicit vitalist, but there is certainly the odor of spirit forces about what he claims.

Influence

For his revised On Growth and Form, Thompson was awarded the Daniel Giraud Elliot Medal from the United States National Academy of Sciences in 1942.

On Growth and Form has inspired thinkers including biologists Julian Huxley and Conrad Hal Waddington, mathematician Alan Turing and anthropologist Claude Lévi-Strauss. The book has powerfully influenced architecture and has long been a set text on architecture courses.

On Growth and Form has inspired artists including Richard Hamilton, Eduardo Paolozzi, and Ben Nicholson. In 2011 the University of Dundee was awarded a £100,000 grant by The Art Fund to build a collection of art inspired by his ideas and collections, much of which is displayed in the D'Arcy Thompson Zoology Museum in Dundee.

To celebrate the centenary of On Growth and Form numerous events are being staged around the world, including New York, Amsterdam, Singapore, London, Edinburgh, St Andrews and in Dundee where the book was written. The On Growth and Form 100 website was set up in late 2016 to map all of this activity.