Editing On Growth and Form

{{Short description|Book by the Scottish D'Arcy Wentworth Thompson 1917}}
{{good article}}
{{Use dmy dates|date=November 2014}}
{{Use British English|date=November 2014}}
{{Infobox book
<!-- |italic title = (see above) -->
| name             = ''On Growth and Form''
| image            = On Growth and Form 1st Edition 1917 title page.jpg 
| caption          = Title page of first edition
| author           = [[D'Arcy Wentworth Thompson]]
| illustrator      = Thompson
| country          = United Kingdom
| subject          = [[Mathematical biology]]
| genre            = Descriptive science
| publisher        = Cambridge University Press
| pub_date         = 1917
| pages            = 793<br>1942 edition, 1116
| awards           = [[Daniel Giraud Elliot Medal]] 
| oclc             = 
| dewey            = 
| congress         = 
| wikisource       =
}}

'''''On Growth and Form''''' is a book by the Scottish [[mathematical biology|mathematical biologist]] [[D'Arcy Wentworth Thompson]] (1860–1948). The book is long – 793 pages in the first edition of 1917, 1116 pages in the second edition of 1942.

The book covers many topics including the effects of scale on the shape of animals and plants, large ones necessarily being relatively thick in shape; the effects of surface tension in shaping soap films and similar structures such as cells; the [[logarithmic spiral]] as seen in mollusc shells and ruminant horns; the arrangement of leaves and other plant parts ([[phyllotaxis]]); and Thompson's own method of transformations, showing the changes in shape of animal skulls and other structures on a [[Cartesian coordinate system|Cartesian grid]].

The work is widely admired by biologists, anthropologists and architects among others, but is often not read by people who cite it.<ref name=Ball/> [[Peter Medawar]] explains this as being because it clearly pioneered the use of [[Mathematical biology|mathematics in biology]], and helped to defeat mystical ideas of [[vitalism]]; but that the book is weakened by Thompson's failure to understand the role of [[evolution]] and evolutionary history in shaping living structures. [[Philip Ball]] and [[Michael Ruse]], on the other hand, suspect that while Thompson argued for physical mechanisms, his rejection of [[natural selection]] bordered on vitalism.

==Overview==

[[File:D'Arcy Wentworth Thompson 1860-1948.jpeg|thumb|upright|Thompson with a bird skeleton. He studied the structures of organisms, seeking explanations for their forms.]]

[[D'Arcy Wentworth Thompson]] was a Scottish biologist and pioneer of mathematical biology. His 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.<ref>{{cite journal |last=Jarron |first=Matthew |title=Sketching the Universe: the Artistic Influence of D'Arcy Thompson |journal=Scottish Society for Art History Newsletter | date=2010 |issue=Summer 2010 |volume=34 |page=9 |url=http://ssah.org.uk/files/2012/05/SSAHnewsletter08-10.pdf}}</ref> 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 [[physics|physical laws]] and [[classical mechanics|mechanics]]. At a time when [[vitalism]] was still being considered as a biological theory, he advocated [[structuralism (biology)|structuralism]] as an alternative to [[natural selection]] in governing the form of species, with the smallest hint of vitalism as the unseen driving force.<ref name=Ruse>{{cite book |last=Ruse |first=Michael |author-link=Michael Ruse |editor1-last=Henning |editor1-first=Brian G. |editor2-last=Scarfe |editor2-first=Adam |title=Beyond Mechanism: Putting Life Back Into Biology |date=2013 |publisher=Lexington Books |page=419 |chapter-url=https://books.google.com/books?id=3VtosxAtq-EC|chapter=17. From Organicism to Mechanism-and Halfway Back?|isbn=9780739174371 }}</ref>

Thompson had previously criticized [[Darwinism]] in his paper ''Some Difficulties of Darwinism''.<ref>{{cite journal |last=Thompson |first=D'Arcy Wentworth |title=Some Difficulties of Darwinism |journal=Nature |date=1894 |volume=50 |issue=1296 |pages=433–436|doi=10.1038/050433b0|doi-access=free }}</ref> ''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 [[Morphology (biology)|biological form]].<ref>{{cite book | author=Boden, Margaret A. | author-link = Margaret A. Boden | date=2008 | title=Mind as Machine: A History of Cognitive Science | publisher=Oxford University Press | page=1255 | isbn=978-0199543168}}</ref>

[[File:Haeckel Phaeodaria 1.jpg|thumb|upright|Thompson analyses the polyhedral forms of [[Radiolaria]] from the [[Challenger expedition]] drawn by [[Ernst Haeckel]], 1904.]]

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 [[viscosity|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 number|Fibonacci sequence]].<ref>{{cite journal | author=Richards, Oscar W. | title= D'Arcy W. Thompson's mathematical transformation and the analysis of growth | journal=Annals of the New York Academy of Sciences | volume=63 | issue=4 | doi=10.1111/j.1749-6632.1955.tb32103.x | pages=456–473 | year=1955| bibcode= 1955NYASA..63..456R | s2cid= 83483483 }}</ref>

Perhaps the most famous part of the book is Chapter 17, "The Comparison of Related Forms," where Thompson explored the degree to which [[allometry|differences in the forms of related animals]] could be described, in work inspired by the German [[engraving|engraver]] [[Albrecht Dürer]] (1471–1528), by [[Transformation (mathematics)|mathematical transformations]].<ref>{{cite web | author=Milnor, John | author-link=John Milnor | title=Geometry of Growth and Form: Commentary on D'Arcy Thompson | url=http://video.ias.edu/milnor-80th | work=video | date=October 2010 | publisher=[[Institute for Advanced Study]] | access-date=31 March 2012}}</ref>

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."<ref>Thompson, 1917. 'Prefatory Note', first paragraph.</ref>

==Editions==

The first edition appeared in 1917 in a single volume of 793 pages published by Cambridge University Press.  A second edition, enlarged to 1116 pages, was published in two volumes in 1942. Thompson wrote in the preface to the 1942 edition that he had written "this book in wartime, and its revision has employed me during another war. It gave me solace and occupation, when service was debarred me by my years. Few are left of the friends who helped me write it." An edition of 346 pages was abridged<!--the changes are indicated in the next section--> by [[John Tyler Bonner]], and is widely published under the same title.<ref>{{cite web |last1=Ulett |first1=Mark A. |title=On Growth and Form, by Sir D'Arcy Thompson |url=http://embryo.asu.edu/pages/growth-and-form-sir-darcy-thompson |website=The Embryo Project Encyclopedia | publisher=Arizona State University |access-date=13 November 2014 |date=25 September 2013}}</ref> The book, often in the abridged edition, has been reprinted more than 40 times,<ref name=WorldCat/> and has been translated into Chinese, French, German, Greek, Italian, and Spanish.<ref name=WorldCat>{{cite book | title=All editions for 'On Growth and Form'| publisher=Worldcat | oclc=1610840}}</ref>

==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 p. 1 – 2nd edition p. 1 – Bonner p. 1)
:: Thompson names the progress of [[chemistry]] towards [[Kant]]'s goal of a mathematical science able to explain reactions by molecular mechanics, and points out that zoology has been slow to look to mathematics. He agrees that zoologists rightly seek for  reasons in animals' [[adaptation]]s, and reminds readers of the related but far older philosophical search for [[teleology]], explanation by some [[Aristotle|Aristotelian]] final cause. His analysis of "growth and form" will try to show how these can be explained with ordinary [[physical laws]].

=== 2. On Magnitude ===
[[Image:Boat models by William Froude.JPG|thumb|right|Models used (by [[William Froude]]) to show that the [[Froude number|drag on a hull varies with square root of waterline length]]<ref>{{Cite book | last=Newman | first=John Nicholas | author-link=John Nicholas Newman | title=Marine hydrodynamics | url=https://archive.org/details/marinehydrodynam00newm | url-access=limited | year=1977 | publisher=[[MIT Press]] | location=Cambridge, Massachusetts  | isbn=978-0-262-14026-3 | page=[https://archive.org/details/marinehydrodynam00newm/page/n43 28]}}</ref>]]

(1st p. 16 – 2nd p. 22 – Bonner p. 15)
:: Thompson begins by showing that an [[Surface-area-to-volume ratio|animal's surface and volume (or weight) increase with the square and cube of its length]], respectively, and deducing simple rules for how bodies will change with size. He shows in a few short equations that the [[Froude number|speed of a fish or ship rises with the square root of its length]]. He then derives the slightly more complex scaling laws for birds or aircraft in flight. He shows that an organism thousands of times smaller than a bacterium is essentially impossible.

===3. The Rate of Growth ===

(1st p. 50 – 2nd p. 78 – Bonner removed)
:: Thompson points out that all changes of form are phenomena of growth. He analyses growth curves for man, noting rapid growth before birth and again in the teens; and then curves for other animals. In plants, growth is often in pulses, as in ''[[Spirogyra]]'', peaks at a specific temperature, and below that value roughly doubles every 10 degrees Celsius. [[Dendrochronology|Tree growth]] varies cyclically with season (less strongly in evergreens), preserving a record of historic climates. Tadpole tails [[Regeneration (biology)|regenerate]] rapidly at first, slowing exponentially.

===4. On the Internal Form and Structure of the Cell===

(1st p. 156 – 2nd p. 286 – Bonner removed)
::Thompson argues for the need to study cells with physical methods, as morphology alone had little explanatory value. He notes that in [[mitosis]] the dividing cells look like iron filings between the poles of a magnet, in other words like a [[force field (physics)|force field]].

===5. The Forms of Cells===
[[File:Vorticella campanula.jpg|thumb|''[[Vorticella campanula]]'' (stalked cup shaped organisms) attached to a green plant]]

(1st p. 201 – 2nd p. 346 – Bonner p. 49)
::He considers the forces such as [[surface tension]] acting on cells, and [[Plateau's laws|Plateau's experiments]] on [[soap film]]s. He illustrates the way a splash breaks into droplets and compares this to the shapes of [[Campanularia]]n zoophytes ([[Hydrozoa]]). He looks at the flask-like shapes of [[protista|single-celled organisms]] such as species of ''[[Vorticella]]'', considering teleological and physical explanations of their having [[minimal area]]s; and at the hanging drop shapes of some [[Foraminifera]] such as ''[[Lagena (foraminifera)|Lagena]]''. He argues that the cells of [[trypanosomatid|trypanosomes]] are similarly shaped by surface tension.

===6. A Note on Adsorption===

(1st p. 277 – 2nd p. 444 – Bonner removed)
::Thompson notes that surface tension in living cells is reduced by substances resembling oils and soaps; where the concentrations of these vary locally, the shapes of cells are affected. In the green alga ''[[Mesocarpus|Pleurocarpus]]'' ([[Zygnematales]]), potassium is concentrated near growing points in the cell.

===7. The Forms of Tissues, or Cell-aggregates===

(1st p. 293 – 2nd p. 465 – Bonner p. 88)
::Thompson observes that in multicellular organisms, cells influence each other's shapes with [[triangle of forces|triangles of forces]]. He analyses [[parenchyma]] and the cells in a [[embryogenesis|frog's egg]] as soap films, and considers the [[symmetry|symmetries]] bubbles meeting at points and edges. He compares the shapes of living and fossil [[corals]] such as ''[[Cyathophyllum]]'' and  ''[[Comoseris]]'', and the hexagonal structure of [[honeycomb]], to such soap bubble structures.

===8. The same (continued)===
(1st p. 346 – 2nd p. 566 – Bonner merged with previous chapter)
::Thompson considers the laws governing the shapes of cells, at least in simple cases such as the fine hairs (a cell thick) in the rhizoids of [[moss]]es. He analyses the geometry of cells in a frog's egg when it has divided into 4, 8 and even 64 cells. He shows that uniform growth can lead to unequal cell sizes, and argues that the way cells divide is driven by the shape of the dividing structure (and not vice versa).

===9. On Concretions, Spicules, and Spicular Skeletons===
[[File:Demospongiae spicule diversity.png|thumb|upright=1.2<!--size for low image-->|A selection of [[spicule (sponge)|spicules]] in the [[Demospongiae]]]]

(1st p. 411 – 2nd p. 645 – Bonner p. 132)
::Thompson considers the skeletal structures of [[diatom]]s, [[radiolarians]], foraminifera and [[sponge]]s, many of which contain hard [[spicule (sponge)|spicules]] with geometric shapes. He notes that these structures form outside living cells, so that physical forces must be involved.

===10. A Parenthetic Note on Geodetics===
(1st p. 488 – 2nd p. 741 – Bonner removed)
::Thompson applies the use of the [[geodesy|geodetic]] line, "the shortest distance between two points on the surface of a solid of revolution", to the spiral thickening of plant cell walls and other cases.

===11. The Logarithmic Spiral ['The Equiangular Spiral' in 2nd Ed.]===
[[Image:NautilusCutawayLogarithmicSpiral.jpg|thumb|Halved shell of ''[[Nautilus]]'' showing the chambers (camerae) in a [[logarithmic spiral]]]]

(1st p. 493 – 2nd p. 748 – Bonner p. 172)
::Thompson observes that there are many [[patterns in nature|spirals in nature]], from the horns of ruminants to the shells of molluscs; other spirals are found among the florets of the sunflower. He notes that the mathematics of these are similar but the biology differs. He describes the [[spiral of Archimedes]] before moving on to the [[logarithmic spiral]], which has the property of never changing its shape: it is equiangular and is continually [[self-similar]]. Shells as diverse as ''[[Haliotis]]'', ''[[Triton (gastropod)|Triton]]'', ''[[Terebra]]'' and ''[[Nautilus]]'' (illustrated with a halved shell and a [[radiograph]]) have this property; different shapes are generated by sweeping out curves (or arbitrary shapes) by rotation, and if desired also by moving downwards. Thompson analyses both living molluscs and fossils such as [[ammonite]]s.

===12. The Spiral Shells of the Foraminifera===
(1st p. 587 – 2nd p. 850 – Bonner merged with previous chapter)
::Thompson analyses diverse forms of minute spiral shells of the [[foraminifera]], many of which are logarithmic, others irregular, in a manner similar to the previous chapter.

===13. The Shapes of Horns, and of Teeth or Tusks: with A Note on Torsion===
[[File:Big Horn Sheep 2.jpg|thumb|The spiral horns of the male bighorn sheep, ''[[Ovis canadensis]]'']]
(1st p. 612 – 2nd p. 874 – Bonner p. 202)
::Thompson considers the three types of horn that occur in quadrupeds: the [[keratin]] horn of the [[rhinoceros]]; the paired horns of sheep or goats; and the bony [[antlers]] of deer.
:: In a note on torsion, Thompson mentions [[Charles Darwin]]'s treatment of climbing plants which often spiral around a support, noting that Darwin also observed that the spiralling stems were themselves twisted. Thompson disagrees with Darwin's [[teleological argument|teleological explanation]], that the twisting makes the stems stiffer in the same way as the twisting of a rope; Thompson's view is that the mechanical adhesion of the climbing stem to the support sets up a system of forces which act as a 'couple' offset from the centre of the stem, making it twist.

===14. On Leaf-arrangement, or Phyllotaxis===
<!--[[File:Cones14062008.jpg|thumb|upright|[[Phyllotaxis]] of cones of ''[[Abies koreana]]'']]-->
[[File:SunFlower Closeup Hungary.jpg|thumb|[[Phyllotaxis]] of [[sunflower]] florets]]

(1st p. 635 – 2nd p. 912 – Bonner removed)
::Thompson analyses [[phyllotaxis]], the arrangement of plant parts around an axis. He notes that such parts include leaves around a stem; fir cones made of scales; sunflower florets forming an elaborate crisscrossing [[patterns in nature|pattern]] of different spirals (parastichies). He recognises their beauty but dismisses any mystical notions; instead he remarks that

::{{quote|When the bricklayer builds a factory chimney, he lays his bricks in a certain steady, orderly way, with no thought of the spiral patterns to which this orderly sequence inevitably leads, and which spiral patterns are by no means "subjective".|Thompson, 1917, page 641}}

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

::{{quote|beloved of the circle-squarer, and of all those who seek to find, and then to penetrate, the secrets of the Great Pyramid. It is deep-set in [[Pythagoreanism|Pythagorean]] as well as in [[Euclidean geometry]].|Thompson, 1917, page 649}}

===15. On the Shapes of Eggs, and of certain other Hollow Structures===
(1st p. 652 – 2nd p. 934 – Bonner removed)
::Eggs are what Thompson calls simple solids of revolution, varying from the nearly spherical eggs of [[owl]]s through more typical ovoid eggs like chickens, to the markedly pointed eggs of cliff-nesting birds like the [[guillemot]]. He shows that the shape of the egg favours its movement along the oviduct, a gentle pressure on the trailing end sufficing to push it forwards. Similarly, [[sea urchin]] shells have teardrop shapes, such as would be taken up by a flexible bag of liquid.

===16. On Form and Mechanical Efficiency===
<!--[[File:Gray250.png|thumb|Lines of stress calculated for a human femur]]-->
[[File:Forth Rail & Road Bridge 2.jpg|thumb|300px|Thompson compared a dinosaur's spine to the [[Forth Railway Bridge]] (right).]]

(1st p. 670 – 2nd p. 958 – Bonner p. 221)
::Thompson criticizes talk of [[adaptation]] by [[animal coloration|coloration in animals]] for presumed purposes of [[crypsis]], [[warning coloration|warning]] and [[mimicry]] (referring readers to [[E. B. Poulton]]'s ''[[The Colours of Animals]]'', and more sceptically to [[Abbott Thayer]]'s ''[[Concealing-coloration in the Animal Kingdom]]''). He considers the mechanical engineering of bone to be a far more definite case. He compares the strength of bone and wood to materials such as steel and cast iron; illustrates the "cancellous" structure of the bone of the human [[femur]] with thin trabeculae which formed "nothing more nor less than a diagram of the lines of stress ... in the loaded structure", and compares the femur to the head of a building crane. He similarly compares the [[cantilever]]ed backbone of a quadruped or dinosaur to the [[girder]] structure of the [[Forth Railway Bridge]].

===17. On the Theory of Transformations, or the Comparison of Related Forms===
[[File:Durer face transforms.jpg|thumb|upright|[[Albrecht Dürer]]'s face transforms (1528) were among Thompson's inspirations]]

(1st p. 719 – 2nd p. 1026 – Bonner p. 268)
::Inspired by the work of [[Albrecht Dürer]], Thompson explores how the forms of organisms and their parts, whether leaves, the bones of the foot, human faces or the body shapes of [[copepod]]s, crabs or fish, can be explained by geometrical transformations. For example:

[[File:Transformation of Argyropelecus olfersi into Sternoptyx diaphana.jpg|thumb|upright=1.3<!--size for low image-->|Thompson illustrated the [[Transformation (geometry)|transformation]] of ''[[Argyropelecus|Argyropelecus olfersi]]'' into ''[[Sternoptyx|Sternoptyx diaphana]]'' by applying a [[shear mapping]].]]

::{{quote|Among the fishes we discover a great variety of deformations, some of them of a very simple kind, while others are more striking and more unexpected. A comparatively simple case, involving a simple shear, is illustrated by Figs. 373 and 374. Fig. 373 represents, within Cartesian co-ordinates, a certain little oceanic fish known as ''Argyropelecus olfersi''. Fig. 374 represents precisely the same outline, transferred to a system of oblique co-ordinates whose axes are inclined at an angle of 70°; but this is now (as far as can be seen on the scale of the drawing) a very good figure of an allied fish, assigned to a different genus, under the name of ''Sternoptyx diaphana''. Thompson 1917, pages 748–749}}

::In similar style he transforms the shape of the carapace of the crab ''[[Geryon trispinosus|Geryon]]'' variously to that of ''[[Corystes]]'' by a simple [[shear mapping]], and to ''[[Rochinia|Scyramathia]]'', ''[[Paralomis]]'', ''[[Lupa (crab)|Lupa]]'', and ''[[Chorinus]]'' ([[Pisinae]]) by stretching the top or bottom of the grid sideways. The same process changes ''[[Crocodylus porosus|Crocodilus porosus]]'' to  ''[[Crocodylus acutus|Crocodilus americanus]]'' and  ''[[Notosuchus terrestris]]''; relates the hip-bones of fossil reptiles and birds such as ''[[Archaeopteryx]]'' and ''[[Apatornis]]''; the skulls of various fossil horses, and even the skulls of a horse and a rabbit. A human skull is stretched into those of the chimpanzee and baboon, and with "the mode of deformation .. on different lines" (page 773), of a dog.

===Epilogue===
(1st p. 778 – 2nd p. 1093 – Bonner p. 326)

::In the brief epilogue, Thompson writes that he will have succeeded "if I have been able to shew [the morphologist] that a certain mathematical aspect of morphology ... is ... complementary to his descriptive task, and helpful, nay essential, to his proper study and comprehension of Form."  More lyrically, he writes that "For the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty" and quotes [[Isaiah]] 40:12 on measuring out the waters and heavens and the dust of the earth. He ends with a paragraph praising the French [[entomologist]] [[Jean-Henri Fabre]]<ref>{{cite web | last1=Russel | first1=Alfred | title=Decoding D'Arcy Thompson – Part 1 | url=http://www.uncommondescent.com/intelligent-design/decoding-darcy-thompson-part-1/ | access-date=13 November 2014}}</ref> who "being of the same blood and marrow with [[Plato]] and [[Pythagoras]], saw in Number 'la clef de voute' [the key to the vault (of the universe)] and found in it 'le comment et le pourquoi des choses' [the how and the why of things]".

==Reception==

=== Contemporary <!--this means "in Thompson's time"--> ===

"J. P. McM[urrich]", reviewing the book in ''[[Science (magazine)|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".<ref>{{cite journal |last1=McM___ |first1=J. P. |author-link=J. P. McMurrich |title=Book Review: On Growth and Form |journal=Science |date=23 November 1917 |pages=513–514 |doi=10.1126/science.46.1195.513 |volume=46|issue=1195 |url=https://zenodo.org/record/1448201 }}</ref>

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".<ref>{{cite journal |last1=Buchanan |first1=J. W. |title=On Growth and Form by D'Arcy Wentworth Thompson |journal=Physiological Zoology |date=January 1943 |volume=16 |issue=1 |pages=135–137 |jstor=30151680|doi=10.1086/physzool.16.1.30151680 }}</ref>

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 uncertainty unwise.<ref>{{cite journal |last1=Mayer|first1=Edmund |title=On growth and form. By D'Arcy Wentworth Thompson |journal=The Anatomical Record |date=January 1943 |volume=85 |issue=1 |pages=111–116 |doi=10.1002/ar.1090850108 }}</ref>

[[George C. Williams (biologist)|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''."<ref name=Williams/><ref name=Medawar>{{cite book |last1=Medawar |first1=Peter |author-link=Peter Medawar |title=Pluto's Republic |url=https://archive.org/details/plutosrepublic00meda |url-access=registration |date=1982 |publisher=Oxford University Press |pages=[https://archive.org/details/plutosrepublic00meda/page/228 228]–241|isbn=978-0-19-217726-1 }}</ref> Williams then attempts a "gross simplification" of Medawar's evaluation:

{{quote|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."<ref name=Williams>{{cite journal |last1=Williams |first1=George C. |title=On Growth and Form by D'Arcy Wentworth Thompson; On Growth and Form by D'Arcy Wentworth Thompson; John Tyler Bonner |journal=The Quarterly Review of Biology |date=June 1993 |volume=68 |issue=2 |pages=267–268 |doi=10.1086/418080 |jstor=2830008}}</ref>}}

=== Modern ===

The [[architect]]s 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."<ref name=Beesley/> They note the "extraordinary optimism" in the book, its vision of the world as "a symphony of harmonious forces",<ref name=Beesley/> and its huge range, including:

{{quote|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.<ref name=Beesley/>}}

Beesley and Bonnemaison observe that Thompson saw form "as a product of dynamic forces .. shaped by flows of energy and stages of growth."<ref name=Beesley/> They praise his "eloquent writing and exquisite illustrations"<ref name=Beesley/> 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."<ref name=Shalizi>{{cite web|last1=Shalizi|first1=Cosma|title=Review: The Self-Made Tapestry by Philip Ball|url=http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/self-made-tapestry/|publisher=University of Michigan|access-date=12 November 2014|archive-url=https://web.archive.org/web/20130916185520/http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/self-made-tapestry/|archive-date=16 September 2013|url-status=dead}}</ref>

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'",<ref name=Shalizi/> 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

{{quote|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.<ref name=Shalizi/>}}

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.)".<ref name=Shalizi/> 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",<ref name=Shalizi/> and comments that we have forgotten other early twentieth century scientists who scorned evolution. In contrast, he argues,

{{quote|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.)<ref name=Shalizi/>}}

The [[anthropologist]] [[Barry Bogin]] writes that Thompson's book

{{quote|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.<ref name=Bogin>{{cite book|last1=Bogin|first1=Barry|title=Patterns of Human Growth|date=1999|publisher=Cambridge University Press|isbn=978-0-521-56438-0|page=53|edition=2nd|url=http://assets.cambridge.org/97805215/64380/sample/9780521564380WS.pdf}}</ref>}}

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.<ref name=Bogin/>

Peter Coates recalls that

{{quote|[[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."<ref name=Coates>{{cite web |last1=Coates |first1=Peter |title=An Elegant and Original Idea |url=http://thesecondpass.com/?p=7447 |website=The Second Pass |date=2 May 2011 | access-date=13 November 2014}}</ref>}}

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";<ref name=Coates/> it is in his view

{{quote|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.<ref name=Coates/>}}

The science writer [[Philip Ball]] observes that

{{quote|Like Newton's ''[[Principia Mathematica (Newton)|Principia]]'', D’Arcy Thompson's ''On Growth and Form'' is a book more often cited than read."<ref name=Ball>{{cite journal |last1=Ball |first1=Philip |title=In retrospect: On Growth and Form |journal=Nature |date=7 February 2013|volume=494 |issue=7435 |pages=32–33 |doi=10.1038/494032a |bibcode=2013Natur.494...32B |s2cid=205076253 |doi-access=free }}</ref>}}

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 Stories|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.<ref name=Ball/>

The [[philosophy of biology|philosopher of biology]] [[Michael Ruse]] wrote that Thompson "had little time for natural selection."<ref name=Ruse/> 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 [[vitalism|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"<ref name=Ruse/> – with the important proviso that Thompson apparently felt there was no need for natural selection. Ruse at once adds that "people like Darwin and [[Richard Dawkins|Dawkins]] undoubtedly would disagree";<ref name=Ruse/> they would insist that

{{quote|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 [[Orthogenesis|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.<ref name=Ruse/>}}

==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.<ref name=Elliot>{{cite web | title=Daniel Giraud Elliot Medal | url=http://www.nasonline.org/site/PageServer?pagename=AWARDS_elliot | publisher=National Academy of Sciences | access-date=16 February 2011}}</ref>

''On Growth and Form'' has inspired thinkers including the biologists [[Julian Huxley]] and [[Conrad Hal Waddington]], the mathematician [[Alan Turing]] and the anthropologist [[Claude Lévi-Strauss]]. The book has powerfully influenced architecture and has long been a set text on architecture courses.<ref name=Beesley>{{cite book |last1=Beesley |first1=Philip |last2=Bonnemaison |first2=Sarah |title=On Growth and Form: Organic Architecture and Beyond |url=http://www.philipbeesleyarchitect.com/publications/ogf/ogf_sample.pdf |publisher=Tuns Press and Riverside Architectural Press |date=2008 |isbn=978-0-929112-54-1 |pages=7 and passim |access-date=13 November 2014 |archive-date=4 March 2016 |archive-url=https://web.archive.org/web/20160304024028/http://www.philipbeesleyarchitect.com/publications/ogf/ogf_sample.pdf |url-status=dead }}</ref>

''On Growth and Form'' has inspired artists including [[Richard Hamilton (artist)|Richard Hamilton]],  [[Eduardo Paolozzi]], and [[Ben Nicholson]].<ref name=About>{{cite web |title=About D'Arcy |url=http://www.darcythompson.org/about.html |website=D'Arcy Wentworth Thompson |access-date=14 October 2016}}</ref> 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.<ref name=Museum>{{cite web | title=The D'Arcy Thompson Zoology Museum | url=http://www.dundee.ac.uk/museum/collections/zoology/ | publisher=[[University of Dundee]] | access-date=28 February 2013 | archive-date=31 December 2020 | archive-url=https://web.archive.org/web/20201231064759/http://www.dundee.ac.uk/museum/collections/zoology/ | url-status=dead }}</ref>

To celebrate the centenary of ''On Growth and Form'' numerous events were 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.<ref name=Website>{{cite web | title="On Growth and Foerm 100 | url=https://www.ongrowthandform.org/ | publisher=[[University of Dundee]] | access-date=15 March 2017}}</ref>

==See also==

* [[Evolutionary developmental biology]]
* ''[[Kunstformen der Natur]]''

==References==
{{reflist|30em}}

==Bibliography==
* Thompson, D. W., 1917. ''[https://openlibrary.org/books/OL6604798M/On_growth_and_form. On Growth and Form]''. Cambridge University Press.
** [https://archive.org/details/ongrowthform00thom 1945 reprint] at [[Internet Archive]]
** [https://books.google.com/books?id=_9NMM9l5FMUC 1961 abridged edition] at [[Google Books]]

==External links==
*[https://web.archive.org/web/20041027081318/http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Thompson_D%27Arcy.html D'Arcy Wentworth Thompson]
*[http://www.dundee.ac.uk/museum/zoology D'Arcy Thompson Zoology Museum] {{Webarchive|url=https://web.archive.org/web/20120414221727/http://www.dundee.ac.uk/museum/zoology |date=14 April 2012 }}
*[http://www-groups.dcs.st-and.ac.uk/~history/Miscellaneous/darcy.html Using a computer to visualise change in organisms]
*[http://www.darcythompson.org/ D'Arcy Thompson 150th anniversary homepage]

{{Patterns in nature}}

[[Category:1917 non-fiction books]]
[[Category:Mathematical and theoretical biology]]