A special session of the 2017 Annual International Conference of the Royal Geographical Society in London
This year marks the centenary of the first edition of D’Arcy Wentworth Thompson’s book On Growth and Form. Thompson was a mathematically inclined biologist who spent the whole of his academic life in Dundee and St Andrews but who also served for a short while as President of the Royal Scottish Geographical Society (1942–46). So why should we mark the centenary of his work? On Growth and Form was a major influence on the development of the spatial analysis tradition in geography during the 1960s and 1970s, most notably in the work of Haggett and Bunge and in inspiring Tobler to develop cartogram projections. Despite this early work, most subsequent quantitative geography has concentrated on the analysis of the attributes of places, treating their geometry as in some sense fixed. However, aided by advances in geocomputation and greater data availability, recent years have seen a re-discovery of the importance of a geometrical tradition in geography associated with ideas that date back to 1917 to do with the relationship between geometric form and process, similitude and rates of growth, and transformation/projection as an analytical device. This session will examine recent work in the Thompson tradition and along the way celebrate the centenary of a remarkable and stimulating book.
Introduction to On Growth and Form
David Unwin (Birkbeck, University of London, UK)
“Together with Charles Darwin, Thompson is the most culturally influential English-speaking biologist in history” (New Scientist, 11 Feb 2017) but we have only one book, On Growth and Form, first published in 1917, to sustain that assertion. This short talk will introduce the session by tracing the introduction of Thompson’s ideas into the geography of the 1960s and now, fifty years on, into what has been called ‘the new quantitative revolution’.
Shaping geographic enquiry – D’Arcy Thompson’s On Growth and Form
Alan Werritty (University of Dundee, UK)
D’Arcy Thompson’s seminal monograph On Growth and Form (1917) is widely acknowledged by biologists as the first successful biophysical explanation of the size and shape of organisms. In explaining how the shape of plants and animals is determined, Thompson gave mathematical rigour to the concept that forms follows function. His two fundamental ideas – the concept of allometric growth and the theory of transformations – not only radically influenced the development of biology but also stimulated cutting edge advances in fine art, urban design and engineering throughout the 20th century. Thompson’s ideas also played a significant role in the development of spatial analysis in geography during the late 1950s and 1960s, most notably in influential monographs by Haggett and Bunge and Tobler’s liberation of map projections from the constraints of Euclidean geometry. A century after the publication of On Growth and Form Thompson’s ideas continue to inform geographical scholarship in Batty’s studies on the size, shape and scale of cities, Dorling’s World Mapper project and fractal-based analyses of the morphology of river basins. This paper re-assesses Thompson’s contribution to geographic enquiry from the 1950s through to the present time.
Beyond physical form: geocomputational approaches to map projections
Chris Brunsdon (University of Liverpool, UK)
Thompson’s ‘theory of transformations’, articulated in On Growth and Form, has inspired the development of many innovative map projections, of which the cartogram is the best known. A cartogram is a map in which a thematic variable (such as population size, or total land value) is substituted for physical area or distance. The technique can be a powerful tool, in particular when the thematic variable is population-based and used as a proxy for physical area. In this case, other variables can be used as standard thematic variables – but if they are based on characteristics of the population then the choice of a cartogram as a base map ensures that the characteristics of highly populated smaller physical areas remain visible. To those familiar with more usual map
projections of a region, use of other thematic variables to define the cartogram can provide a striking visual contrast, emphasizing the geographical distribution of the variable in use. Thus, cartograms represent an approach to spatial representation that has a geometry, but not the usual geometry of points in a Euclidean plane or on the surface of a sphere. A number of algorithmic approaches to cartograms have been attempted – starting with physical models, and progressing to advanced computer algorithms. This talk will provide an overview of cartograms, including examples of their use and a brief history of approaches to creating them. Finally the `getcartR’ package in the programming language R will be described. This package, written by the speaker, provides a freely available and flexible front end to the Gastner and Newman cartogram algorithm, allowing users to experiment with the cartogram methodology, and providing reproducible, publication-quality spatial data visualizations.
Evolution and Transformation in Cities: Re-evaluating Patrick Geddes and D’Arcy Wentworth
Michael Batty (University College London, UK)
Despite being members of a small community of biologists at University College Dundee in the last decade of the 19th century, Patrick Geddes and D’Arcy Wentworth Thompson did not refer to each others work as far as I can tell. Geddes published the pioneering book Cities in Evolution in 1915 and despite some reservations, preached the message that cities should be observed and planned as evolutionary systems. Wentworth Thompson published his seminal book On Growth and Form two years later in 1917 and to an extent provided the foundations for mathematical biology but also established the notion that physical and natural objects, cities included, evolved to different shapes as they grew. They must have known each other rather well and it is unlikely that they would not have discussed cities and biology at least in passing. I will not solve this riddle in this essay – probably nobody can – and it is possible that the coincidence of their working in the same department for so many years did not make any sense until much later as both Geddes and Wentworth Thompson have come to play such a central role in complexity theory, particularly in the complexity theory of cities. I will attempt to show how early ideas in the theory of evolution resonated in both their works and then illustrate how their work was picked up in the 1960s, in particular by the design theorists such as Christopher Alexander, by those studying geometric form in spatial and city systems such as Waldo Tobler, and by those beginning to fashion a theory of cities from the bottom up such as Jane Jacobs. I will attempt to pull all these threads together especially in contemporary ideas about the morphology of cities such as that which focusses on scaling, self-similarity, and connectivity
First published one hundred years ago, On Growth and Form is almost certainly the most influential book ever written in Dundee. It pioneered a whole new area of science – mathematical biology – but has also influenced artists, scientists and thinkers as diverse as Alan Turing, Salvador Dali, Buckminster Fuller and Claude Levi-Strauss, to name just a few. In this illustrated talk, Matthew Jarron (curator of the D’Arcy Thompson Zoology Museum) will discuss the book and its extraordinary impact.
Admission £2 (£5 to whole series). No need to book – pay on the door.
2017 marks 100 years since the publication of D’Arcy Thompson’s landmark book On Growth and Form – “the greatest work of prose in twentieth century science” (Stephen Jay Gould), written by possibly “the most learned polymath of all time” (Richard Dawkins).
One of the key works at the intersection of science and the imagination, it is a book that has inspired scientists, artists and thinkers as diverse as Alan Turing, C H Waddington, Claude Lévi Strauss, Norbert Wiener, Henry Moore and Mies van der Rohe. It pioneered the science of biomathematics, and has had a profound influence in art, architecture, anthropology, geography, cybernetics and many other fields.
To mark the occasion, a three-day interdisciplinary conference is being organised at the Universities of Dundee and St Andrews, where D’Arcy spent most of his career and where his surviving collections are held. It will feature a range of presentations covering every aspect of D’Arcy’s own work and the various fields that it has influenced. The conference will also include visits to the D’Arcy Thompson Zoology Museum and the Bell Pettigrew Museum of Natural History and there will be a special preview of a new exhibition exploring On Growth and Form and its legacy.
The conference will be followed by a Newton Institute workshop hosted by the University of Dundee 16-20 October 2017 on Growth, Form and Self-Organisation in Living Systems – see https://www.newton.ac.uk/event/gfsw02
This workshop, closely related to D’Arcy Thompson’s legacy, will focus on recent advances, mathematical challenges, and promising new directions in research on mathematical aspects of form in living systems. Stochastic models and topological approaches, including knot theory, have been employed to study shape evolution, for example the structure of the DNA. Cellular and developmental biology have recently seen a surge in the use of mathematical models and new conceptual frameworks for problems such as the self-organisation of the cytoskeleton or gradients of morphogens in embryos. However, the constitutive features of living systems pose unique technical and conceptual challenges. Some of these challenges concern construction of a multiscale framework for agent-based models, and employing non-equilibrium physics to address non-conservative nature of living systems, using continuum models such as the (visco)elasticity of growing bodies.
2017 marks a hundred years since the first edition of D’Arcy Wentworth Thompson’s classic book “On Growth and Form” was published. This seminal publication marks the beginning of modern mathematical biology. The overall goal of this workshop is to bring together a multi-disciplinary community inspired by D’Arcy Thompson’s work, with participants from the fields of developmental and mathematical biology, science history and philosophy, mathematics, art, and architecture.
Important questions we would like to discuss during the conference include:
The role of genetics and mathematics in understanding growth and form.
The role of generative models of pattern formation and morphogenesis in biology, bio-inspired art, architecture and engineering.
What kind of mathematics are needed to understand growth and form? What are the philosophical implications?
The On Growth and Form 100 conference website is now live at https://www.ongrowthandform.org/conference/0 We’re also delighted that Dundee & Angus Convention Bureau are kindly supporting the conference, and will be helping speakers and delegates with...
The BBC are marking the centenary of On Growth and Form with two programmes on Radio 4. An episode of Inside Science was recorded earlier this week at the University of Dundee and was broadcast yesterday – you can listen to it here:...
On this day 100 years ago the journal Nature received an advance review copy of On Growth and Form – now they’re celebrating with a centenary special which will be available free online for one month, along with other relevant items from their archives....
ON GROWTH AND FORM CENTENARY CONFERENCE 100 years on and still growing! 13-14 October 2017 University of Dundee and University of St Andrews 2017 marks 100 years since the publication of D’Arcy Thompson’s landmark book On Growth and Form – “the greatest work of prose...
On March 11, 2017 artists, psychologists, biologists, mathematicians and many others come together at De Balie on the theme of “transformation”. The reason for this evening is the 100th anniversary of the famous work “On Growth and Form” by...
Some of the anniversary activities have been covered by the New Scientist in a feature by their culture editor Simon Ings. It includes a spotlight on our on-going project to create 3D scans of some of D’Arcy’s original specimens. Read the article here and...
The anniversary year has only just begun and already we know of several major conferences taking place around the world that will include sessions celebrating the impact of On Growth and Form. They include: CAA conference, New York on 18 Feb MBI Emphasis Workshops,...
The biology journal Development is planning a special issue titled “On Growth and Form – 100 years on”. This special issue will be guest edited by L. Mahadevan (Harvard University) working alongside Editor Thomas Lecuit, and is scheduled for publication in late...
The Edinburgh City Art Centre exhibition A Sketch of the Universe: Art, Science & the Influence of D’Arcy Thompson is now open and looks great! Lots of events coming up to accompany it – check out the Events calendar on this site for more...