`DIAGRAMS`

Diagrams are schematic figures or patterns comprising lines, symbols, or words to which meanings are attached. Throughout human history they have been used to represent concepts, objects, processes, or systems as linear forms of information. Early examples include prehistoric engravings such as the crisscross patterns incised on ochre rocks in the Blombos Cave in South Africa around 70,000 BCE (figure 1). Diagrams exist within most systems of communication. As noted by anyone who has attempted to follow IKEA assembly instructions, the longevity of a diagram is closely linked to its utility and to the presence of other competing forms of representation.

Diagrams are often not self-explanatory. Those made during the past three millennia featured labels, or they required descriptions that were memorized, inscribed, or printed. The Babylonian “Pythagorean theorem” tablet of 1900 BCE, for instance, consisted of a transected square that was labeled with cuneiform numeric headings. Even though modern scholars have been able to translate the headings, there is still debate as to how to interpret the diagram, thereby illustrating the fact that the meanings of diagrams, both ancient and modern, are often influenced by the context in which they were made and used.

Some of history’s most iconic diagrams were remarkably simple and based on efficient combinations of long-standing visual elements such as circles, squares, chiasms, crosses, squiggles, arrows, and branches. The oldest known diagram from the geometry of Euclid (active around 300 BCE), found at Oxyrhynchus, Egypt, consisted of only a square and a rectangle. The sixteenth-century astronomer Nicholas Copernicus used concentric circles to represent the orbs of planets in his new heliocentric system. Charles Darwin visualized the process of speciation with a branching tree. The physicist Richard Feynman used H-shaped and Y-shaped arrows and squiggles to represent quantum relationships. All these diagrams blended simplicity and familiarity. The lineages depicted in Darwin’s diagram, for instance, were presented as an evenly spaced array of branching lines. This kind of tree diagram was a form of representation that had been used for centuries to depict family genealogies.

The accessibility of a given diagram throughout history was often influenced by how it functioned in relation to other diagrams. As evinced in the first printed edition of Euclid’s Elements, published by Erhard Ratdolt in 1482, different combinations of squares, circles, and rays could operate collectively as a group, a visual system, of Euclidean geometry presented in one place. Some of Ratdolt’s quattrocento contemporaries, notably Leonardo da Vinci, argued that diagrams could provide information more clearly and more usefully than prose. This notion would continue to grow within the new knowledge economies that emerged as the printing press spread across the globe during the sixteenth and seventeenth centuries.

By the time of the *Enlightenment, reference works regularly displayed hundreds of thematically related diagrams. Those presented in the French *Encyclopedia, one of the era’s most recognizable publications, ranged from a key to all human knowledge to schematic depictions of farming ploughs. Though diverse, the Encyclopédie’s diagrams were used together in a way that allowed readers to make links between different kinds of useful knowledge. For instance, D’Alembert’s chart of the disciplines in the front matter of the work, presented branching dichotomies grouped according to three categories: memory, reason, and imagination. Within the tree of reason, “raison,” included agriculture, among many other fields, a categorization that helped explain why the plough diagram was conceptually relevant to the publication.

`Figure 1. Ochre stone etched with a geometric pattern, Blombos Cave in South Africa around 70,000 BCE.`

The diagrams of the Encyclopédie and Euclidean primers worked best as visual systems when they were used in real time, when viewers flipped the pages and compared them with each other. In recent centuries the real time aspect of diagrams has come to play an increasingly important role in the ways that they are used to represent data, blurring the line between what counts as a diagram and what counts as a graph. In many respects this interface was a reoccurring feature of diagrams from the *Renaissance forward. Though Copernicus’s circles were neatly presented as singular shapes, other kinds of diagrams, especially those based on copious data, were not presented as freestanding forms, nor were they constrained by the binding of a book. Perhaps most notable among these were the rectangular, gridded, unfoldable charts used by chronologers to represent data as timelines.

Concurrent with the rise of quadriform diagrams, early modern diagrammers increasingly turned to circular, graticuled, and rotatable volvelles to represent everything from planetary motion to months of the year: these printed circles were cut out and mounted on the page around a string in order to demonstrate the effects of circular motion. Using charts and volvelles diagrammatically required bodily movement. Charts often needed to be scrolled out of a book across a desk. They were often large and required users to either move them around with their hands, or move around them as they sat on a table. Volvelles needed to be rotated so that new connections between different kinds of information could be made. Though they became popular in the *early modern period, charts and volvelles continue to be used as real-time diagrams today.

Diagrams were of course not confined to technoscientific settings. Geometric, geographic, and metric diagrams played an important role in the everyday life of learning in schools and literate households. Johannes Amos Comenius’s Orbis sensualium pictus (World of the senses in pictures, 1658), arguably the most influential Latin primer across early modern Europe and its colonies, featured diagrams of numbered objects that students could match to vocabulary words presented in sentences above or below the image (figure 2). Frontispieces of popular Enlightenment primers and manuals such as George Fisher’s The Instructor featured students in classrooms with diagrams hung on the walls around them.

`Figure 2. Johannes Amos Comenius,` `Orbis sensualium pictus: Hoc est, Omnium principalium in mundo rerum, & in vita actionum, pictura & nomenclatura, translated by Charles Hoole (1705), 130. Image courtesy of the Boston Public Library.`

Outside schools, domestic and commercial diagrams from the sixteenth century onward visualized everything from sewing patterns to the place settings of dining-room tables. By the nineteenth century, books like Eliza Acton’s Modern Cookery (1860) featured diagrams of utensils, kettles, pots, saucepans, ovens, “smoke jacks,” “weighing machines,” ingredients, and various dishes. Advertisements in Victorian magazines such as the World of Fashion invited readers to buy diagrammatic sewing patterns, a trend that continued well into the twentieth century. Like those used in scientific settings, domestic diagrams were interpreted and used communally, oftentimes in shared spaces like parlors, kitchens, and gardens.

The components of diagrams evolved over time in relation to the knowledge possessed by their designers and users. Lines and labels were removed and added. Meanings were attached and detached. Most diagrams operated within communities, and their designers often took this factor into account. Here educational or training practices played a key role in influencing how diagrammers came to understand how to make and use diagrams as key elements of coherent visual systems. It would have been difficult for Newtonian calculus, for instance, to take hold in Britain were it not for the diagrams developed by several elite tutors based at Cambridge University. Likewise, Newton’s younger contemporary Joseph Black would have struggled to communicate his discovery of carbon dioxide to his University of Edinburgh students were it not for a collection of simple diagrams that he used to explain chemical affinity.

Until recent times diagrams were made by hand, which means that designing or replicating one through copying was an adaptable and kinesthetic mode of knowledge acquisition, formation, and circulation. In this sense diagrams were similar to written notes in that they were thinking tools that allowed diagrammers to manipulate information on paper in real time. The Victorian astronomer John Herschel recognized this function in the meticulous diagrams of nebulae that he observed and then drew. He called them “working skeletons,” a term that gestured to the long-standing interactive and schematic facets of handmade diagrams. His sketches built on diagramming traditions present in his own family, which also doubled as a scientific community. Caroline Herschel, his aunt who helped raise and educate him, had been making diagrammatic star charts since the 1780s to plot the movement of comets. Whether they were drawn in a notebook or read in a book, diagrams played an increasingly prominent role as thinking tools after the invention of the steam press. The proliferation was often countered or mediated through iteration. Marie Curie, for instance, employed diagrams to remember the specialized apparatus that she used for her radiation experiments. Indeed, the diagrams she drew in her circa 1900 laboratory notebook are still radioactive. The direct interface between diagramming and drawing remains with us to this day. The ribbon diagrams used by scientists and the public alike to illustrate the structures and functions of protein molecules, for example, were first hand drawn by the molecular biologist Jane S. Richardson and then photographed so that they could be printed in articles (figure 3). Like Herschel, Richardson used diagramming as a mode of thinking. In her words, “making a drawing can change one’s scientific understanding of a protein.”

`Figure 3. Jane Richardson, ribbon schematic (hand drawn and colored, in 1981) of the three-dimensional structure of the protein triosephosphate isomerase. The barrel of eight beta-strands is shown by green arrows and the eight alpha-helixes as brown spirals.`

Richardson’s view on the relationship between thinking and diagramming resonates with the ways in which diagrams have been employed ever since humans began using visual forms of representation. The twentieth-century philosopher Ludwig Wittgenstein acknowledged this point when thinking about the relationship between logic and language. He was especially fascinated with arrows, perhaps one of the most popular forms of representation used in modern diagrams. In his words, “The arrow points only in the application that a living being makes of it.” In many respects, this view accurately pinpoints the essence of diagrams and the role that they play as dynamic entities that are usually designed or iterated for a specific purpose. Whether carved with a stone tool in a rock or crafted on a screen with a mouse, they work best when they are adapted to the needs of their makers and users. As such, they are multistable artifacts that will remain indispensable informatic tools for years to come.

Matthew Daniel Eddy

`FURTHER READING`

Michael Baxandall, Painting and Experience in Renaissance Italy, 1988; John Bender and Michael Marrinan, The Culture of Diagram, 2010; Lee E. Brasseur, Visualising Technical Information: A Cultural Critique, 2003; Matthew Daniel Eddy, “How to See a Diagram: A Visual Anthropology of Chemical Affinity,” Osiris 26 (2014): 178–96; Reviel Netz, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History, 2003; Theodore W. Pietsch, Trees of Life: A Visual History of Evolution, 2013; Daniel Rosenberg and Anthony Grafton, Cartographies of Time: A History of the Timeline, 2012.