Editing On Growth and Form (section)

==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>