With apologies to Steven Shapin, there is no such thing as a medieval diagram, and this is a book about it. Shapin’s point in The Scientific Revolution (Chicago, 2018) is that there was no single moment of “revolution” in the development of modern science, and that those elements of scientific practice considered most characteristically “modern” were contested in the seventeenth century by historical actors with equal claims to modernity. The Diagram as Paradigm likewise promises something straightforward--a consideration of diagrams across the Aristotelian epistemic regime as scientific exemplars--only to problematize the notion of diagram as a stable concept across cultural, textual, linguistic, and epistemic boundaries.

This substantial volume, comprising four introductory and fifteen focused essays, includes cosmological, medical, logical, and religious diagrams from late antiquity to the Safavid Period, with methodological approaches drawn chiefly from the history of art, material culture, and the history of science. Likewise, the contributions--all scrupulously researched and argued--engage and continue the established scholarly conversations concerning diagrams across disciplines, reflecting the visual and material turns in the historiography of science, and the material and scientific turns in the history of art. The editors have divided the book into sections on scientific, cosmological, medical, and mathematical-philosophical-theological diagrams, with each section including at least one essay on the Latin, Arabic, and Greek traditions, each, and headed up by three introductory essays, by each of the editors on Byzantine, Islamicate, and western medieval diagrams, respectively. The distinctions among these different sections are more loosely conceptual than rigidly concrete, reflecting the porous boundaries among genre, purpose, and even topic in the textual culture of the period.

Taking a comparative and necessarily incomplete approach to the topic, the editors aim for a volume that provides multiple examples and perspectives across time, type, and text. It is clear from reading the essays that there is no consensus in the scholarly conversation--within the pages of this volume and beyond--on what constitutes a medieval diagram. Nor was “diagram” a stable or self-evident category in the longue durée under discussion; something as simple as a diagram’s use or purpose could be contingent and context-dependent. Several contributors invoke Potter Stewart’s famous definition of obscenity (“I know it when I see it”) in their discussion of diagrams, while others look to Peirceian semiotics, W. J. T. Mitchell’s “imagetext,” and Michael Evans’ spectrum from typographical to emblematic diagram, and Adam Cohen’s from “imagistic diagram” to “diagrammatic image.” [1] As several of the contributors make clear (Jeffrey Hamburger, Benjamin Anderson, and Christiane Gruber), the ways that diagrams are defined and discussed, both by contemporary historical actors who first engaged them and by later scholars, informs how they are constructed and understood as objects of inquiry. What these different frames all have in common is a binary sense of whether something is or is not a diagram. Yet, upon reading this impressive volume, we found that the indefinable, non-paradigmatic nature of the medieval diagram motivates a relational account, whereby the diagram explicates a complex pattern of relations between constituent parts. In other words, a diagram features as an emergent and transhistorical aspect of a relational pattern. This account, implicit within and between the volume’s individual essays, maintains conceptual precision and discursive rigor while enabling a nimble manifestation of the diagram across cultures and time periods. In building the account, we respond to the editors’ explicit injunction to “construct, as it were, diagrams of [our] own: a web of connections linking the points represented by the individual contributions together into a larger pattern” (9-10).

In what follows, we explore the main themes of this volume and demonstrate how they allow for a relational understanding of medieval diagrams as connective shapes and possibilities existing across multiple dimensions. This relational, or network, account substitutes for a binary account and a spectral account (one-dimensional lines or axes between image and text, diagrammer and reader, or theory and praxis). In contrast, the network account posits a taxonomy of feature classes (or parts) and relations (or connections) among those features. Indeed, this relational aspect is noted throughout the volume, and a simplified version can be found in the words of Charles Sanders Peirce: “‘Many diagrams resemble their objects not at all in looks; it is only in respect to the relations of their parts that their likeness consists’” (3). But what are the parts of a diagram? Classes particularly prevalent in this volume include content, structure, function, and time. Content stems from the field of knowledge being communicated, and that content is expressed through a structure comprising visual units that may include letters, words, geometric shapes, and images. Content and structure may be related, but the function of the diagram is not necessarily tied to these. A diagram might be meant to encode, to communicate, or to assist in the memorization of content. Moreover, this function might not remain stable over time--the final feature class--as a diagram originally made to encode could later be used as a mnemonic device. Time includes the time(s) of creation and communication, as well as of perception and processing. Together, features of content, structure, function, and time relate within and across classes to form the diagram.

Section headings in the volume designate taxonomies of content, whereby scientific diagrams are distinguished from cosmological diagrams, and medical diagrams are distinguished from mathematical, philosophical, and theological diagrams. Diagrams situated in each domain of knowledge may contain motifs, themes, or propositions characteristic of that area. For example, a medical diagram may contain themes of biological fluids, disease, surgery, or reproduction whereas a mathematical diagram may contain themes of shape and movement. Yet boundaries of these content categories are permeable and unfixed. Component parts of a diagram’s epistemic milieu do not function in isolation; they overlap with one another. A diagram can contain both philosophical and cosmological motifs, as is the case with the Islamic homocentric diagrams of the universe discussed by Anne-Laurence Caudano, or both theological and scientific themes, as Megan C. McNamee elegantly demonstrates through later copies of Boethius’ De arithmetica. In fact, not only can content areas or motifs overlap in a single diagram, but they can also interact with one another in a way that can determine the philosophical conclusion. For example, the mathematical structure (geometry) of the Shield of Faith, a common theological diagram in medieval Latin Christianity, discussed by both Hamburger and Safran in this volume, recasts Trinitarian theology as a set of logical propositions. Interactions between content features can also occur throughout a codex; for example, as Caudano points out, a planetary diagram located in a medical codex “offers not only an overview of the world but, in a medical codex, it was also fully consistent with a field whose premises rested on the influence of the macrocosm (the heavens) on the microcosm (the human body) through the humoral system” (218). Throughout this volume, the authors demonstrate that content features realize cognitive work by the manner of their relation; the parts of the diagram exert force with, between, and upon one another to produce meanings that are irreducible to the features themselves. The more-than-the-sum-of-parts nature of diagrammatic content forecloses an account of diagrams as sets of features or even as sets of overlapping features; rather it demands a network account wherein relations produce meaning not attributable to the parts of the diagram alone.

Whereas diagrammatic content is clear from the volume’s section headings, diagrammatic structure comprises features defined and studied in the discipline of art history. Drawing upon the methods of that discipline we can ask: What patterns of ink are present on the page? And then, how might typographical, figural, geometric, and other features encode and communicate content? Borrowing from Faith Wallis’s definition of diagrams as “visual text” (153, cited in Divna Manolova’s contribution on Eratosthenes’ calculation of the earth’s circumference), we can consider textual elements from letters and numbers to words and phrases, or from shapes and geometries to notations and grids. Additional structural elements discussed in the volume include balance, visual proportion, pattern, scale, and style (e.g., mimetic or abstract, pictorial or aniconic). Any of these components alone can convey meaning. For example, two colors can highlight operative opposition; the physical size of a diagram can indicate theoretical importance; a Greek letter can give the impression of scientific or mathematical precision and render the universe finite and comprehensible; a number can be a structuring agent that shapes and orders the physical world; and a grid can make the abstract concept of number concrete and visible.

In addition to the meaning that single components can transmit, the alignment of components, formal symmetries between components, and the relations between content and structure all also create meaning. Indeed, Meekyung Ruth MacMurdie deftly shows how the geometrical patterns of text and mise-en-page in copies (illustrated or not) of the Kitab al-diryaq (known in English as Book of Antidotes) were central to the book itself. Hamburger discusses how meaning arises from content-structure relations, pointing out that incarnational theology in the Latin Christian West employs a mode of argument both relational and oppositional, which in turn manifests in a diagrammatic juxtaposition of figural and line drawings. Of course, meaning can also be obscured by a mismatch between content and structure, as evinced by the examples in the volume in which diagrams make text even more opaque than it was in isolation. Collectively, the ways in which structural features interact with one another and with content features, whether in a way productive of or detrimental to meaning, underscore the relational or network nature of diagrams.

But what are diagrams for? As this volume makes clear, diagrams function in ways that are multiple, context-dependent, and can be mutually exclusive or mutually reinforcing. Those functions can be ordered along cognitive, informational, and sociopolitical dimensions. Cognitive functions of diagrams range from representation to memorization, and from encoding the old to creating the new. For example, diagrams function representationally when they are used to visualize the invisible; rectify the incorrect; designate content; organize information; illuminate patterns; or reflect experience. Several of the contributions explore the mnemonic function of diagrams as discussed by ancient and medieval scholars, such as Ptolemy and William of Conches. But even beyond representational and mnemonic functions, diagrams are dynamic instruments of many other cognitive processes. In the general introduction to the volume, Hamburger notes how diagrams shape, construct, and constitute the process of thought, enabling so-called diagrammatic thinking wherein (as in diagramming) one employs a sequential method of defining and drawing relationships that point toward particular conclusions. As Alexandre M. Roberts points out in his essay on Byzantine astronomical diagrams, in this context, as in mathematics, the diagram functioned as the proof itself, rather than just an aid for comprehension. Other contributors note the capacity for diagrams to generate new thought by forming the basis for different questions, being a tool to create new knowledge, and serving as machines for illumination.

The cognitive work that diagrams perform also supports and complements informational and sociopolitical functions of the diagram. Diagrams house information that can be communicated or transmitted between people. In addition to serving as mathematical demonstrations or proofs, diagrams provide explanations, reconcile ideas, proffer visual solutions, enable understanding of complex theoretical concepts, and codify underlying operations or patterns of thought. Thus, across the long medieval period diagrams were frequently used as didactic instruments, spaces for mathematical practice, and effective objects of transmission. Importantly, diagrams’ informational functions are both static and dynamic, guiding the eye and mind through pieces of information in sequence to enable certain kinds of thought. Diagrams can force a pace of reading and intensification of sight, such that as the eye and mind take in a diagram distinct mental operations can occur separately from one another. Moreover, these distinct mental processes operate differently at different locations within the diagram. Certain diagrams invite or even require mental manipulation, whether of the diagram itself (or components thereof) or of the objects or concepts in the real world to which the diagram alludes. Collectively, these informational capacities allow the diagram to be used as an ideological vector, whether to drive affective goals, lend legitimacy, establish authority, elevate status, or compel the reader to perform specific epistemic actions.

Critically, the multiple possible functions of diagrams are not independent, but instead directly depend upon one another. Different representational styles can determine a diagram’s memorability. The degree to which a diagram represents the world can determine whether the diagram is better used to support abstract or concrete thought processes and mental manipulations. The sorts of cognitive functions supported by a diagram can determine its uses. Furthermore, the sociopolitical functions of diagrams can depend on both affective and cognitive functions in individuals, as well as functions of transmission across humans. Thus, diagrams have network functions: meta-functions composed of sub-functions that depend upon one another relationally. Moreover, both meta- and sub-functions can interact with content and structural feature classes in complex ways, meaning that the network of relations among the constituent parts interpenetrates the network of relations about content and structural features, forming a multilayer network of dependencies. McNamee describes Boethius using number (content), placing it into a grid (structure), and thereby playing the role of Reason (cognitive function) such that the reader’s mind can exercise its natural inclination to seek truth, ascending like Christ (sociopolitical function). This and other examples throughout the volume emphasize the ways in which diagrams exploit relations among content, structure, and function to enable an emergent human process that is more than the sum of the parts.

Although diagrams are commonly thought of as static objects, dynamic processes occur with, upon, and through them, as canvassed extensively in the volume. Perhaps most simply, diagrams can address the challenge of encoding time (and information about time) while being confined to a two-dimensional material surface. But beyond the page, there is also the time of the creator: whether diagrams were written off the cuff in the margins, or sketched out in advance; whether the creator spanned across time as multiple scribes contributing to a single corpus; whether the creator listened back in time to the author’s instructions for drawing the figure; whether the viewpoint depicted in the diagram was their own, or someone else’s from a different time. Then there is the time of the reader: between seeing the diagram and generalizing it to new contexts, appreciating the layers of meaning built through multiple modes of visual representation, drawing out or retracing step by step in the imagination; to read through each component; to read a diagram in one direction versus another; to rotate either the manuscript or one’s body to engage the diagram; the time-lapse of psycho-ocular movements; of turning (and returning to) the page; and for sustained contemplation or meditation (or the split-second relief one feels when, weary from long debates, one can simply look at a diagram). Beyond a single reader, there is the time of diagrammatic dialogue; diagrams can offer a (sometimes posthumous) schematic expansion of the source; a diagram can be a nexus of meaning, while gesturing both within the page to surrounding text and outside the page to other images, texts, and authors. Because of this connectivity of diagrams, the timescales involved broaden to the historical. Diagrams, and the relations between or among content, structure, and function, are subject to historical, cultural, and social context, which in turn define iconographic possibilities and practices of intellectual production. In addition to these mutual articulations, diagrams can emerge as acts of intercultural communication and thus are influenced by cross-cultural fertilization. Diagrams also change over time as different elements were brought together, altered, and selected, as different materials were used for construction, thereby reworking material into new forms, and as a range of colors and artistic techniques were applied, in turn broadening and changing the audience, the intended function, and the diagram’s basic meaning. Throughout these examples, time is a conduit for relation, adding a fourth and final layer to the network account of the diagram.

The Diagram as Paradigm offers a deep, multi-layered and multi-perspective account of the medieval diagram. The breadth and depth of the volume as a whole and the individual contributions render it required reading for scholars of visual culture, cognitive processes, intellectual history, and the history of science. Indeed, as we have tried to demonstrate here, the impact and importance of this volume arise from the relations between and among the individual contributions and different themes and subsections. Like a diagram itself, this volume is more than the sum of its parts.

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Note:

1. On Peirce’s theory of semiotics, see e.g. Albert Atkin, (2013), “Peirce’s Theory of Signs,” in the Stanford Encyclopedia of Philosophy (Spring 2023 Edition), ed. by Edward N. Zalta & Uri Nodelman, online at <https://plato.stanford.edu/archives/spr2023/entries/peirce-semiotics/>; for Mitchell, see e.g. Christine Wiesenthal, Brad Bucknell, and W. J. T. Mitchell, “Essays into the Imagetext: An Interview with W. J. T. Mitchell”, Mosaic: An Interdisciplinary Critical Journal, 33.2 (2000): 1-23; for Evans, see e.g. Michael Evans, “The Geometry of the Mind: Scientific Diagrams and Medieval Thought,” Architectural Association Quarterly, 12.4 (1980): 32-55; for Cohen, see Adam S. Cohen, “Diagramming the Diagrammatic: Twelfth-Century Europe,” in the Visualization of Knowledge in Medieval and Early Modern Europe, eds. Marcia Kupfer, Adam S. Cohen, & J. H. Chajes (Turnhout: Brepols, 2020): 383-404. The original version of this review misattributed Cohen’s typological spectrum to Evans.