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On Growth and Form appeared in the summer of 1917, the second of four books D’Arcy Wentworth Thompson produced in a long career as scientist, author, translator, and editor. His only volume on a strictly scientific subject, On Growth and Form was conceived by the author around 1912 and had been promised to Cambridge University Press as a little book to cost no more than two or three shillings. In the course of distilling nearly three decades of observations on the forms of plants and animals, Thompson saw his book grow to more than eight hundred pages of text and illustrations; many delays in its preparation were caused by Thompson’s severe criticism of his own writing as well as by wartime conditions.
At the time of the book’s publication, Thompson’s career had already encompassed diverse scientific studies as well as digressions into mathematics, classical literature, poetry, and philosophy. On Growth and Form was by intention both a scientific work and an evocation of the seemingly boundless universe of organic and inorganic form which had been revealed by modern science. Thompson’s appreciation of poetry and classical literature played a significant part in its writing, and the enormous impression made by the book on its first appearance was based on its style perhaps as much as on its author’s scientific achievements.
By 1922 the first edition of On Growth and Form was sold out, but Thompson would not then agree to its reprinting. In the 1930’s and early 1940’s, he completed a revision of the book which appeared in 1942 and has been reprinted frequently. In 1961, an abridged edition was prepared in the light of a widespread recognition that the 1917 version was, in some ways, a better book than the 1942 edition, in which Thompson had expanded the original text by more than three hundred pages without giving attention to necessary revisions.
Thompson has been called one of the last of the “scientist-naturalists,” and a nature lover’s passion for observation is the mainspring of much of his work as an author. On Growth and Form has two related objectives: to describe the visible forms of plants and animals—including microscopic structures—and to reveal the mathematics that underlies the vast variety of organic form. Though it is for the most part comprehensible to the layman, the text of On Growth and Form is augmented with lengthy and detailed footnotes and contains many quoted passages in French, German, Latin, and Greek. Formulas requiring a significant background in mathematics for their full comprehension are included in the text, but they rarely impede its flow. Thompson is said to have been an outstanding lecturer, and the skills of an able and considerate public speaker are evident throughout the book, both in its structure and in its language. Particularly effective is the author’s provision of hundreds of drawings and diagrams to illustrate the issues raised in the text; in some cases, these become an almost autonomous source of interest.
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Introduction The character of life in 1914, while outwardly chaotic, was driven by what Dr. Alan Axelrod, author of The Complete Idiot’s Guide to 20th Century History, termed an ‘‘inner order, a logic all its own, a myriad of secret alliances that linked the fate of one nation to that of another.’’ It was a world on the verge of explosion.
Noise and Art Igor Stravinsky’s work was an expression of chaos out of logic. Stravinsky was a budding young Russian composer who created scores for the radical ballet The Rite of Spring in 1913. The music had a violent, sexual quality and...
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was quite primitive in feeling. The rhythms were intensely erratic, the music discordant. The work was a mirror of a man working from a primitive urge to create a modern, highly complex work in a way that no one had quite experienced. It was a deeper expression, a mirror of this tension of logical inner workings producing an outwardly chaotic sound and feel present in contemporary life. Parisian audiences were moved to tears or to riot—the music was viewed as either a modern triumph or the downfall of Western art and culture.
In New York, a new and different type of art was also raising eyebrows at the International Exhi- bition of Modern Art. It featured the works of the antiacademic artists, Paul Cezanne, Henri Matisse, Pablo Picasso, and Marcel Duchamp. The most controversial of the works, ‘‘Nude Descending a Staircase,’’ was not true to any conventional form and made no attempt at capturing reality as was traditional to art up to this time. The aim of Duchamp was to capture relative time and motion. His nude was portrayed from various perspectives as well as from different points in time, but simultaneously. The artist himself stated, according to Axel, ‘‘I have forced myself to contradict myself in order to avoid conforming to my own taste.’’ The same reviews prevailed—either audiences appreciated the work for its melding of art, physics, and psychology to amplify the relative nature of reality or they hated the work for such a dramatic departure from tradition.
Political Unrest in Europe In 1914, Germany and Austria had formed a political alliance, and France and Great Britain had formed another. These alliances were defensively formed in a clearly hostile atmosphere that characterized Europe at this time. The pacts amongst nations were vague, and the race for the accumulation of weapons was real. When Austria-Hungary seized Bosnia without Russian approval, Russia criticized the action, as did Britain and France. Germany, on the contrary, supported Austria, deepening the rift amongst countries. The assassinations of Austrian Archduke Francis Ferdinand and his wife Sophie by rebel Serbs, on June 28, 1914, would be the catalyst for a war occurring only months later.
World War I Europe was torn apart by the conflict, which involved the participation of thirty-six nations spanning Europe, colonial Asia, as well as Africa. Dr. Alan Axelrod characterizes World War I, claiming
The battle was among the most futile of a war that consisted of a seemingly endless chain of futile battles. Losses from enemy fire, as well as disease and thirst, were staggering, in excess of 200,000, and nothing had been gained by the time the allies were forced to withdraw.
Particularly for the British, the battle at Gallipoli was a tragedy for the British military. Axelrod claims that the lack of ability to plan and mobilize an attack successfully extended the war in addition to causing terrible loss of human life, particularly for the British. Axelrod also fittingly quotes BerO trand Russell, English mathematician and philosopher, in a Letter to the Nation:
And all of this madness, all this rage, all this flaming death of our civilization and our hopes, has been brought about because a set of official gentlemen, living luxurious lives, mostly stupid, and all without imagination or heart, have chosen that it should occur rather than that any one of them suffer under the infinitesimal rebuff to his country’s pride.
Before the War Perhaps the war influenced Thompson’s great passion for nature and, by extension, for life, as well as fueled the spirituality threading its way in and out of the text of his work with some frequency. Certainly, earlier in the decade, there were other pioneers who would serve to inspire him with their fantastic, if not revolutionary, discoveries.
Sigmund Freud, a Viennese physician, would also introduce his theories on sexuality, theories that would fundamentally change the approach to the study of human sexuality. In his theories, he expressed the belief that human sexuality was linked to the unconscious mind and was a drive that spanned a lifetime from infancy through childhood and far into adulthood. Although the reaction to Freud was initially one of outrage, he developed a following, his theories leaving a permanent impression on the study of the human psyche.
The theory of relativity was also revolutionary in 1905. Albert Einstein, a German scientist, discovered the theory of relativity, a theory that proposes a universe in which the only absolute is the speed of light and in which matter and energy are ultimately equivalent. He demonstrated that matter and energy are not two separate entities but are, in fact, readily convertible. Because of the theory, the views of theoretical reality changed, inspiring such achievements as the successful harnessing of atomic energy.
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Allusion Thompson draws on any number of familiar events, characters, or concepts to illustrate his ideas to make them clearer for the reader. In one particular instance, for example, the author makes reference to Jonathan Swift’s Gulliver’s Travels in his discussion of similitude. The principle of similitude, based on the idea that ‘‘in similar figures the surface increases as the square, and the volume as the cube, of the linear dimensions’’ is compared to an instance in Swift’s Lilliput:
His Majesty’s Ministers, finding that Gulliver’s stature exceeded theirs in the proportion of twelve to one, concluded from the similarity of their bodies that his must contain at least 1728 [or 12 to the third power] of theirs, and must needs be rationed accordingly.
In the footnotes following the passage, Thompson also cites that Gulliver had ‘‘a whole Lilliputian hogshead for his half-pint of wine: in the due proportion of 1728 half-pints, or 108 gallons, equal to one pipe or a double-hogshead.’’ Such passages draw on the practical or everyday, and in doing so help the reader make connections between the abstraction of mathematics and real world scenarios, thus providing clarity to otherwise challenging ideas.
Argument The principal driving Thompson’s work is a dramatic departure from traditional zoology because it makes a case for interpreting biological phenomena by way of mathematics and physics. The opening chapter of the work is written in defense of Thompson’s method of scientific study.
For example, the author does not refute the idea of final cause, man’s consistent pattern for explaining his world, which involves explanation of creation as being a function of purpose or design. Rather, Thompson demonstrates his desire to enhance such study by example. He draws on Aristotle’s parable in which ‘‘the house is there that men may live in it; but it is also there because the builders have laid one stone upon another.’’ Working from the passage, Thompson points out that ‘‘it is a mechanism, or a mechanical construction, that the physicist looks upon the world.’’
The assertion that traditional consideration of morphology, or growth and form, is enhanced by the introduction of mathematical and mechanical principles is demonstrated in the balance of the text. His defense is furthered by example, whether it be in regard to the hexagonal faces of a snow crystal or when comparing the conformation of a horse’s skull to that of a rabbit’s.
Classicism What makes Thompson’s message so powerful is precisely that he chooses to support his ideas by turning to ancient Greek and Roman literature, philosophy, and art. The text is loaded with such references. For example, in a discussion of the equiangular spiral, Thompson credits the earliest investigation, if not the discovery, of the spiral to Archimedes, a famous Greek mathematician and inventor who was known for his work in mechanics and hydrostatics. In speaking of the mathematical definition of form, he also mentions
We are brought by means of it in touch with Galileo’s aphorism (as old as Plato, as old as Pythagoras, as old perhaps as the wisdom of the Egyptians), that the book of nature is written in characters of Geometry.
Plato is a well-known Greek philosopher, who, with the help of Socrates and Aristotle, laid the foundations of Western culture. Greek scholar and mathematician Pythagoras was known for making great advances in both mathematics and astronomy.
Image Literal images are employed often throughout the work. They are concrete and involve little or no extension of the words used to express them; rather, their value is in description. Thompson’s images help to clarify the basis of his discussions and also give emphasis to the beauty and wonder of the subjects he is describing. ‘‘The large waxen honey cells are nearly spherical, nearly equal in size, and are aggregated into an irregular mass,’’ says Thompson of the bee’s honeycomb. He continues to describe their shape, stating that their spherical form is only visible from the outside of the mass of cells, ‘‘for inwardly, each cell is flattened into two, three or more flat surfaces, according as the cell adjoins two, three or more other cells.’’ Ultimately, these cells, he adds, when resting on other spheres of similar size, are the three surfaces ‘‘united into a pyramid.’’ This description is a ‘‘gross imitation of the three-sided pyramidal base of the cell of the beehive.’’
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1900s: In 1903, the Wright Brothers embark on the first flights ever in recorded history.
Today: ‘‘It’s time to say goodbye, station, and good luck, new crew,’’ says the outgoing station commander of the spacecraft Discovery, Russian Astronaut Yury Usachev, as he prepares to return to Earth.
1900s: In 1905, Sigmund Freud coins the term ‘‘psychoanalysis,’’ defined as self-examination into one’s inner thoughts and feelings.
Today: Internet service providers offer customers the opportunity to discuss their personal problems or field questions to experts in the field of psychology online.
1900s: In 1907, Albert Einstein expresses the relation between matter and energy in the formula e=mc2.
Today: Wolfgang Ketterle earns a Nobel Prize after demonstrating the first ‘‘atom laser’’ by producing a steady stream of drops of identical atoms from a sodium atom condensate.
1900s: In 1913, American geneticist A. H. Sturtevant develops gene mapping.
Today: After English embryologist Ian Wilmut at the Roslin Institute reports that a sheep named Dolly is the first mammal successfully cloned from adult tissue, ethical issues related to genetic engineering gain prominence.
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Sources Axelrod, Alan, The Complete Idiot’s Guide to 20th Century History, Alpha Books, 1999.
Clark, W. E. LeGros, and P. B. Medawar, eds., Essays on Growth and Form, Clarendon Press, 1945.
‘‘D’arcy Wenworth Thompson,’’ in Dictionary of National Biography, Oxford University Press, 1959. pp. 877–79.
Gould, Stephen Jay, Foreword to On Growth and Form, Cambridge University Press, 1961.
Kemp, Martin, ‘‘Doing What Comes Naturally: Morphogenesis and the Limits of Genetic Code,’’ in Art Journal, Vol. 55, No. 1, Spring 1996.
Medawar, P. B., ‘‘D’arcy Thompson and Growth and Form,’’ in D’arcy Wenworth Thompson: The Scholar-Naturalist, Oxford University Press, 1958.
Thompson, D’Arcy, On Growth and Form, Cambridge University Press, 1961.
Further Reading Clark, W. E. LeGros, and P. B. Medawar, ed., Essays on Growth and Form, Clarendon Press, 1945. Clark’s and Medawar’s collection of critical essays presents and examines the merits of On Growth and Form.
Gould, Stephen Jay, Foreword to On Growth and Form, Cambridge University Press, 1961. Gould offers insights into the nature of Thompson’s work.
Thompson, D’Arcy, A Glossary of Greek Birds, Clarendon Press, 1936. This work is the author’s study of medieval and modern ornithology, complete with classical references. This book is to be read as a companion to A Glossary of Greek Fishes.
———, A Glossary of Greek Fishes, Oxford University Press, 1947. This text by Thompson is a study of fish as they existed in classic Greek literature and in other ancient cultures. This book is to be read as a companion to A Glossary of Greek Birds.
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Bonner, John Tyler. Introduction to On Growth and Form, by D’Arcy Wentworth Thompson, 1961 (revised edition).
Hutchinson, G.E. “In Memoriam: D’Arcy Wentworth Thompson,” in American Scientist. XXXVI (October, 1948), pp. 577-606.
Le Gros Clark, W.E. Medawar, and P.B. Medawar, eds. Essays on Growth and Form Presented to D’Arcy Wentworth Thompson, 1945.
Thompson, Ruth D’Arcy. D’Arcy Wentworth Thompson: The Scholar-Naturalist, 1860-1948, 1958.
Whyte, Lancelot Law, ed. Aspects of Form: A Symposium on Form in Nature and Art, 1951.