Compelled by the Diagram Thinking through C. H. Waddington’s Epigenetic Landscape

Between 1940 and about 1960, Conrad Hal Waddington produced several illustrations to explain a concept central to his theories of developmental biology. The concept Waddington explained, the epigenetic landscape, was not based on settled science, and its implications were not easy to grasp. Unlike proponents of the most successful contemporary biological theory, Waddington was committed to including all biological phenomena–no matter how complex or unusual–in a single theoretical system. His intellectual style and use of images matched his ambition. Waddington used compelling images to get his readers to engage with and work through his theories. His images used a shifting, even contradictory, set of metaphors and analogical models, from train yards to crafted topological surfaces. Through an analysis of Waddington’s images and theories, I show that taking a close look at what scientific images show and how they show it is important for the historiography of science. Images can be effective at drawing viewers in, confounding them, and prodding them to ask questions; this is one reason images are necessary for science.

tackled broad questions ranging from philosophy to art. 5 Early on he picked up a dialectical style of thinking from the philosopher Alfred North Whitehead, which manifested itself in his conversational style of prose. Waddington is often described as "ahead of his time"-he is best known as a grandfather figure for the evo-devo movement, which remains controversial. 6 Because his work was against the grain, and thus in constant danger of being dismissed, Waddington employed images to draw viewers in and get them to unpack and think through his theories. He used images to keep possibilities open in a situation in which his audience might otherwise settle on simple-and, in Waddington's view, false-certainties.

Two Styles
Biology in the 1930s, the period of Waddington's intellectual formation, was dominated by the modern evolutionary synthesis. 7 The neo-Darwinian evolutionary theory that was an outcome of the synthesis has proved extremely successful-so successful that popular understanding has dropped the "neo-" and equated the modern synthesis biologists' theory with Darwinism itself. 8 The modern synthesis embodied a distinctive style. Richard Lewontin, a prominent twentieth-century biologist, offers this description: "The modern skeletal between individuals, who can exhibit goal-directed behavior because they have been "programmed" by their DNA to do so, and "the overall harmony of the organic world" (the domain of evolution), which cannot. 16 Mayr raises very reasonable points-his prose reads as a model of reasonableness. Mayr proposes the type of simple, clear-cut distinctions that allowed the modern synthesis to create a working consensus and eventually to triumph over competing theories of evolution. 17 It is no surprise that Waddington wrote a response to Mayr's essay in the following issue of Nature: by 1961 Waddington had been in the habit of writing opinionated letters to the journal for more than two decades, and Mayr's distinctions cut to the heart of Waddington's theories. But Waddington's engagement went beyond the usual letter.
Waddington also circulated Mayr's essay before a conference he organized in 1966 -and he later published it in the conference proceedings bookended by two critical essays of his own.
Here is part of his response, on the topics of final causes: It is becoming inadequate to point out, as Mayr does, that natural selection is not purposive. In itself it is of course no more purposive than is the process of formation of interatomic chemical bonds. But just as the latter process is the basic mechanism underlying the protein syntheses which are integrated into the quasi-finalistic mechanism of embryonic development, so natural selection is the basic mechanism of another type of quasi-finalistic mechanism, that of evolution. The need at present time is to use our newly won insights into the nature of quasi-finalistic mechanisms to deepen our understanding of evolutionary processes. 18 Waddington demands that "chemical bonds," "embryonic development," and "natural selection" be taken into account, all at the same time. For Waddington, there is no way to separate functional biology from evolutionary biology, and he adds to these a third approach to biology that Mayr ignored entirely: developmental biology. While Mayr argues for theoretical synthesis by way of diplomatic compromise, Waddington asks for speculation unencumbered by practical divisions. Mayr later mentioned that embryologists failed to create a "viable bridge" between disciplines, implying that if a concept from developmental biology was not useful for evolutionists, then its exclusion from the synthesis was justified. 19 This is the context in which Waddington argued for what he calls "theoretical biology." He objects to Mayr's "cleavage between types of phenomenon," and he suggests that the "newly won insights" of developmental biology may offer a way to bring all of biology back together. 20

The Epigenetic Landscape
To say that Waddington and Mayr employed different styles is to say more than that their prose is different. Waddington and Mayr also had different ways of constructing and 1 2 4 C o m p e l l e d b y t h e D i a g r a m testing theories, which lead to different ways of using images. 21 If a skeletal theory like the modern synthesis is developed through logical propositions, more fleshed-out theoretical styles often employ analogical models. The place of models and metaphors in scientific inquiry was a subject of heated debate in the 1950s and 1960s. 22 Critics of logical positivism noticed the slippery relation between features of models and theoretical propositions. 23 Thinking of an atom as being something like a solar system, for example, helps explain some theoretical observations (which is why Ernest Rutherford and Niels Bohr proposed the model in the first place), but it also raises questions. The planetary model may help describe hydrogen atoms, but what about atoms with more than one electron? Testing questions raised by models is often productive, sometimes by leading to a new model and different questions (as happened with the Bohr-Sommerfeld model and eventually the Schrodinger model of the atom). Models, metaphors, and thought experiments pervade science, but some scientists engage with them more than others. Waddington was a serial modeler, a strategy which supported his approach to theory. The concept Waddington is best known for, the epigenetic landscape, was developed through analogical models over the course of four decades. Waddington first used the term, which he coined, in 1940. It drew on familiar associations. Epigenesis was a common concept from eighteenth-century biology, and biologists in the mid-twentieth-century would also have known of Sewall Wright's adaptive landscape, which explained adaptation as a genetic drift up and down humps and pits on a topological surface (Fig. 2). 24 Waddington's major theoretical contribution was to insist that a complex "landscape" acts as the mediator between genes and an adult organism, emphasizing that all of the "environmental" (or "epigenetic") influences that occur during development cannot be ignored (as they would be by a geneticist thinking in terms of population, as the modern synthesis biologists were).
Waddington used a handful of illustrations to help explain his concept, drawing on metaphors of train tracks, streams of water, and, of course, landscapes. His images and metaphors changed as his theories evolved, and they contradict one another in various ways. It is not always clear whether or not a feature of one of his illustrations refers to something important about his concept; the author of Waddington's retrospective in Nature notes that "scientists are still confused by this today." 25 As I explain below, this tension between concept and representation does important cognitive work for Waddington. 21 The different ways images are used by biologists is a matter of emphasis rather than clear-cut distinction. Though an analysis of, e.g., Mayr's use of images is beyond the scope of this study, a quick look at his publications suggests that he uses illustrations of analogical models less frequently than Waddington. While Waddington typically includes a wide variety of analogical imagery, Mayr's canonical 1942 text, Systematics and the Origin of Species, for example, has only one that clearly falls into this category: a rather straightforward depiction of a phylogenetic tree.  In research leading up to the epigenetic landscape, Waddington sought to work out the mechanisms by which an animal develops from a single cell into an organism with groups of specialized cells. First the single cell divides, and then the resulting two divide, then the resulting four, and so on. At certain points, cells begin to specialize: one region in the developing embryo becomes brain cells, another becomes liver cells, etc. Waddington began illustrating this process with cell-fate bifurcation diagrams (Fig. 3). 26 His explanation is that cellular specialization occurs as a "series of branching decisions, taken under the control of genes." 27 This explanation was based on his experiments with fruit flies-experiments in which a mutant gene would, for example, make a leg develop on a fly's head in place of an antenna (Fig. 4). 28 Waddington suggests that the mutant gene flips a switch, causing a different developmental pathway to be followed.
Grizzly as these experiments were, Waddington's diagram of the process is relatively straightforward. That is, its semantic content is limited; Waddington could easily have described all the paths and switches in words. But his images also carry unstated connotations that nudge the viewer down particular interpretive paths and incidental features that suggest areas for further investigation. The importance of representational choices becomes evident when the different images Waddington used to describe the same concept are compared. One other illustration Waddington used in this early period was a photograph  This is Waddington's first use of the landscape metaphor (a hump, after all, is a landscape feature), and it raises some new questions. What is the biological equivalent of gravity? What are biological switches made of, and who is switching them? In the era before the discovery of DNA, how exactly something could be "under the control of genes" was a matter of speculation. 30 A satisfying description of developmental pathways (which Waddington represented as lines in a drawing or tracks in a photograph) turned out to be illusive at mid-century.     There are a few ways Waddington's 1940 illustration of the epigenetic landscape could be elaborated or changed. One would be to show the stream swelling as it proceeds through the valley (embryos grow, after all). Waddington chose to focus attention elsewhere: on the mechanics of buffering. To do this he switched to yet another metaphor. Waddington's next illustration of the epigenetic landscape, from 1956, represents the developmental process as the path followed by rolling eggs (Fig. 8). 36 Unlike a stream of water, which can split and recombine, and soil, which would require a feat of engineering to control, this new image suggests well-defined paths and hands-on control. It implies that someone will release the eggs at the top and watch them roll down. The surface looks like a crafted artifact that could be altered to create different developmental pathways. The suggestion of hands-on control hints at the life of an experimental biologist at mid-century, tweaking the developmental environment and running trials on millions of fruit flies.
Waddington produced several versions of this illustration. The most refined, published in 1957 in Waddington's best-known book, The Strategy of the Genes, shows a single ball and a single set of branching paths as well as the system of "guy ropes" attached to "pegs" that shape the surface from below (Fig. 9). While the first illustration of the epigenetic landscape varied line-type and tone to create a naturalistic image, the ones that followed look like highly stylized engravings of artificial surfaces. These latter illustrations employ a linear technique popularized in the nineteenth-century with fine art reproductions (Fig. 10). 37 This style of engraving was developed so publishers could ensure consistency across illustrations even if more than one engraver was employed. Every line looks the way it does for a reason; no artistic license is involved. By using illustrations following this technique, Waddington implies that his epigenetic landscape is as logical and under control as the lines cut into steel plates by a team of engravers. If the earlier drawing of a system of streams fits the big-picture holism of nineteenth-century evolutionary biology, the engraved version fits the hard-nosed experimentalism of mid twentieth-century developmental biology. 38 Because Waddington's work was aimed at both camps, it is no surprise that he used illustrations with both connotations. But the fact that he settled on illustrations suggesting precise experimental control reveals his deepest disciplinary affiliation. Waddington used his illustrations to raise questions and to convince others that these questions would be productive avenues of research. For a question to be productive to an experimentalist, it must be precise enough to be tested. Waddington used topographical diagrams with connotations of precision and control to make his most controversial theoretical points. Figure 11, for example, shows a black line that remains in a fixed position in space while the landscape around it is shifted. Waddington used this to help explain an unusual phenomenon, genetic assimilation. This is now an accepted concept: Faced with changes in their environment, organisms have the capacity to physiologically adapt to these variations by modifying the epigenetic landscape.
Genetic assimilation is the subsequent stabilization by genetic variations of this initial physiological adaptation. 39 shape the epigenetic landscape. 42 Waddington explains how the arrows in another diagram ( Fig. 15), match up with one of these arrows. 43 Toggling conceptually between the cybernetic metaphor of the former diagram and the landscape metaphor of the latter is no mean feat.

Figure 10
Waddington's concepts have not gotten any easier to explain. Updated versions of these diagrams (e.g. Fig. 16) involve the same convoluted causality. 44 To engage with these diagrams and the concepts they explain, readers have to slow down and think their way carefully through a complicated theoretical terrain. Even the shortcomings of Waddington's images reveal key aspects of his theory.

Compelled by the Diagram
We can now see the efficacy of Waddington's particular visual practice. Waddington created a set of illustrations of a series of (contradictory) analogical models to condense a career-spanning theoretical conversation into a set of visual "proofs" that required unpacking, effectively drawing out the duration of his colleagues' engagement with his concepts. Waddington's diagrams focused and directed the conversation. They gave him and his colleagues something to ponder, something to talk about.
The effect of a compelling diagram, and why it is said to be compelling, begins with the capturing of a reader's attention. Historians of science have tended to downplay the importance of singular, compelling images. Bruno Latour sums up the reasoning: "One should not isolate the scientific imagery and shoehorn it into the types of questions raised by iconography. There is nothing visual in scientific visual imagery. Literally, there is nothing to be 'seen.'" 45 Latour and others argue that images are typically used by scientists as links in chains of reasoning, and that they are meaningless outside of these chains. 46 Latour makes one exception: the (in his view rare) case in which "one isolated image extracted out of the chains as 'the definitive proof' of the phenomenon they wish to describe," for "pedagogical purposes." I suggest that images are more often meant to be seen (and, more to the point, grappled with, thought through, and questioned) than Latour allows. Images can put a theoretical proposition "all in one place," rather than spread throughout a text. This condensation is a powerful feature. What Latour identifies as the "pedagogical" use of images is really the function of analogical models: to condense theories and multiply questions. And, analogical models are pervasive in scientific practice. 47 Illustrations such as Waddington's only work if the reader feels compelled to pause, look closely, and work through the detailsthat is, to pull the image momentarily out of the chain to which it belongs and to treat it iconographically.

Figure 14
Epigenetic Action System of Cell, from Conrad H. Waddington, New Patterns in Genetics and Development (New York: Columbia University Press, 1962), 7 (photo: author).  What makes an image or illustration or diagram compelling? Understanding this requires a description of what exactly is being seen and the cognitive work of seeing. 48 There are two dangers along this analytical route. First, the analyst may appear to be appreciating visual features for their own sake. Second, he may seem to be projecting his thoughts into another's head. I think these dangers are unavoidable and that the analytical results justify the means. Anthropologist Alfred Gell has gone further down this route than most. In his 1998 book, Art and Agency, Gell attempts to explain the cultural phenomenon of decorative patterning. Why put a complex pattern on a Persian rug? His answer is that the viewer feels a "pleasurable frustration" when trying to decipher the pattern. 49 Figuring out one part of the pattern (one figure/ground relationship, for example) means losing sight of another. The viewer is drawn into the pattern on the rug as she tries and fails to hold everything in mind at once. As Gell explains it, "We are drawn into the pattern and held inside it.... The pattern is a mind-trap...." 50 Trying to match up features of an illustration of an analogical model to concrete biological phenomena is a similarly frustrating, pleasurable, and productive mental exercise. Waddington's reason for putting complex diagrams in his books is not so different from the reason someone might want a decorative pattern on her rug: "the application of a decorative pattern to an artefact multiplies the number of its parts and the density of their internal relationships." 51 One final example from Gell, trying to understand a type of Indian chalk drawing (Fig. 17), describes the end result: [E]ven if one 'knows' (intellectually) that this design is made up of four separate, but identical loops differently oriented, it is extremely frustrating to attempt to abstract individual loops from the overall design. ... Where simple geometric figures are concerned, 'seeing' (a triangle, say) is tantamount to mentally intending or projecting  Waddington used a strategy that involved compelling diagrams because he was committed to the project of including all biological phenomena within a single theoretical system; this was the point of his late-career work on "theoretical biology." He wanted biologists to be able to talk about genes, development, and evolution at the same time.
Complex images helped him manage this process. Again, Gell describes the intention: Patterns, by their multiplicity and the difficulty we have in grasping their mathematical or geometrical basis by mere visual inspection, generate relationships over time between persons and things, because what they present to the mind is, cognitively speaking, always 'unfinished business.' 53 Waddington's diagrams and concepts present biological phenomena as complex "patterns" that cannot be distilled into simple rules. Thinking of biology this way is a matter of style. Waddington's distaste for pragmatic compromise and his preference for inconclusive conversations matched his visual practice.

Figure 17
Matthew Allen, Kolam Threshold Design: The Pattern as Topological Snare and The Constitutive Element of the Kolam, after a diagram in Alfred Gell, Art and Agency (Oxford: Clarendon, 1998), 85 and 86 (photo: author).

Conclusion
Taken together, Waddington's illustrations of the epigenetic landscape suggest an unusual type of synthetic project. While modern synthesis biologists produced a simple framework for dividing up biological knowledge, Waddington sought to bring all biological phenomena together in a way that does not always make immediate sense. He insisted that, in principle, nothing should be left out.
The legacy of logical positivism in analytical philosophy and history of science continues to privilege well-formed sentences, explicit argumentation, and conclusions that follow one another in a linear way. By contrast, a compelling illustration condenses a great deal of conceptualization into a small, non-linear space. Sometimes Waddington's most important questions are raised by his illustrations. Looking again at a diagram of the epigenetic landscape ( Fig. 1), the questions multiply. Where exactly is the embryo? What represents the cell? What is the role of time? What is the landscape itself, in biological terms? Because these questions are not always raised explicitly in the accompanying text and a satisfying answer may not exist, they may be ignored rather than thought through. Against explicit, step-by-step argumentation, Waddington favors the risky move of raising too many questions to answer. He gambles that biologists will not settle for simplified, straightforward explanations in the meantime.
In answer to the perennial question of whether images are necessary for science, I propose that images function effectively at drawing viewers in, confounding them, and prodding them to ask questions. Images are often thought of in science and technology studies as links in chains of reasoning, but images do not always play the role of providing positive bits of information. As I have shown here with Waddington's epigenetic landscape, sometimes images get in the way of knowledge by bringing up inconvenient complications and suggesting alternative interpretations. Compelling images draw out the process of understanding and help ensure that conclusions are not jumped to too quickly.