This is an artistic research project that presents a number of challenging problems, both in terms of the representation of the concept, and in its execution. The thumbnail sketches presented here (Fig.1, for example) are best understood as sketches, that is, as the result of the intricate material process of exploring and experimenting with a preliminary capture or mapping of ideas in visual form. Sketching taps into the artistic intuition, allowing a kind of playful revealing of ideas with all the tics, hesitations and flourishes of the act of drawing itself. These sketches were made in a search for salient characteristics that allowed me to formulate a number of questions that address scale and scaling, and by extension, drawing as a way to know about such things. The sketches began as generative play at the tip of a pencil, but as always in the drawing studio, when it’s good, the play becomes the work. So this project of tracing inconceivable trajectories and spaces turns on a series of humble doodles that have led me to a number of insights into futility and the limits of representation, that overlap mathematics, astronomy and art.
Here is a simple tone-setting observation: emerging from his research on early human artefacts of bone and stone, marked-up with lines and circles, the anthropologist Alexander Marshack (in 1972, p.406) remarked that “The sky is a calendar,” a pithy reminder that we have come to use the apparent features of that mysterious expanse for a kind of codex of other, invisible things. Of course the sky is really only a calendar when its features are drawn together in the mind’s eye, and represented by the workings of graphite on some surface. At that point, the sky enters into the call and response of symbolic exchanges, allowing reading. With this in mind, I will first provide some context for this project, and then attempt to describe some insights gleaned from the sketches, and the implications and entailments for a program of theory and artistic practice.
Context and terms of reference
Key terms in the project are adopted from the literature on art and representation. The difficult term “representation,” for example, is defined here by Nelson Goodman (in 1976, p.43), as a ‘symbolic relationship that is relative and variable;’ while David Marr writes that representation is ‘a formal system for making explicit certain entities or types of information, together with a specification of how the system does this’ (in Riley, 2001). Here, Marr simply recapitulates Goodman’s crucial idea of efficacy, that ‘What matters with a diagram… is how we are to read it,’ (1976, p.170). In this sense, a representation is not some thing, but ‘a process in which the thing is a participant’ (Mitchell, WJT, 1994, p.420). Of course representation is a product as well as a process, and the term “external representation” will refer to such a product, including pictures, writing, and diagrams, any of which may be made or experienced in Mitchell’s dialectical relationship (Cox, 1999).
Stenning and Lemon (2001, p.36) describe diagrams as ‘plane structure(s) in which representing tokens are… directly interpreted as relations in the target structure.’ The research cultures growing around diagrams, denotational drawings (Willats, 1997, p.4), and diagrammatic reasoning, are well documented, and converge on questions of their benefits in reasoning tasks, and their uses in “amplifying the mind’s eye” (Fish and Scrivener, 1990). Simply note their sustained in the STEM subjects (Science, Technology, Math, and Engineering), and then read Goodman, who proposes that the key difference between pictures and diagrams is that, while pictures are freely interpretable along a number of lines. diagrams limit interpretation, seeking a more articulate display.
Anyone who uses drawing in his or her work, either as proposition or presentation, comes to understand that measurement is a primary motivation. In my own practice as a painter, for example, I have identified this value in the representation of entities and forces, or even the felt scaling of body to body in the life-drawing studio. The impulse has its clearest application in geometrical drawing, a visual-mathematical method developed to take a measure of reality as a wireframe diagram of location and passage. A well-constructed geometrical illustration exploits capabilities of the visual system, replacing logical, memory, and search requirements with a perceptually grounded context for making judgments (Stenning and Oberlander, 1995).
It is a well-understood aspect of working with diagrams that they permit users to hold in hand, so to speak, things that are otherwise quite difficult to grasp. As a key example, in 1735 the mathematician Leonard Euler sought a solution to the problem of whether a route could be plotted to cross each of the town of Königsberg’s seven bridges without doubling back. In his work, Euler addressed the question using the simplest of mark-making strategies. He did not actually cross the town’s bridges, but used them as schematic characters to resolve questions of connectivity, after which diagrammatic representations have been understood to permit inductive reasoning in logical problems (Carlson, 2009).
A character-string notation for some posed physical problem writes forward, line-by-line, and depends on important background-symbolic knowledge (of algebraic notations, for example). In contrast, a diagram shows us problem and solution together. As a ready explanation of contemporary interests in data-visualisations, then, by working over such representations, we have gone from exploring natural principles in terms of location and motion, to computational visualizations of vast data-sets, allowing insightful experience of a different kind of organic system — which is to say, information (Lau & Vande Moere, 2007; Bresciani & Eppler, 2009).
Over the past five years, my work has explored drawing as a bridge-building method between sound and vision, seeking a blended visual-musical practice. I have produced graphic music composition systems from bits and pieces of pictorial and diagrammatic drawing systems (for example Griffin, 2013). To underpin that work, I proposed a structural classification of drawing methods that clearly positions music notations relative to other graphics, arguing that music notations are “space-time drawings.”
To “draw music” is to translate from the multi-dimensional space of audition into the secondary space of marking, encoded for further passage in the playing of the score (an instructional element), presented to performers and audiences in a future-subjunctive tense. The paper stands for silence, for Cage’s underlayment of duration (1973, p.19); it is the surface on which we work. But as we calculate the performance, the paper becomes a space of time. A music notation is therefore a control interface, by which users trace through a conjunctive space of time: a space-time notation.
Of course, all things are both spatial and temporal, but in drawing a tree we do not target temporal dimensions, except as interpretive content (in a tree-picture), or as time-factored sequences (in a tree-diagram). Even Duchamp’s strangely lucid “Nude Descending a Staircase” (1912) can only suggest duration through metaphors of fanning lines, tonal transitions, and repetition across and down: we read Duchamp’s composition from a context of Western painting traditions, in his impish terms. In contrast, the staff music notation is a tally-sheet, generating readouts in which the performance is factored in timeline and pitch-space axes. Thus music notations are differentiated from the ambiguities of pictures, or the way-finding of maps and other system-diagrams, not because those graphic practices are not temporal in some way, but because time is not a character in their schemes.
Among the insights gleaned from this graphic and scholarly work, a novel stream of research has emerged that oddly, excitingly blends analysis and creativity, extending the focus on drawing space-time into a context of cosmological discourses, rather than artistic performance. The key outputs of the project are a portfolio of three colossal, collaborative drawings with complex timing and execution requirements, expanding views on Fine Art drawing as a conceptual practice. The mark-making tools for each of the drawings in the portfolio harness the coherent light of Laser, here used for its linear values, which is to say, as lines of energy applied to the geometry of space itself as support, in a process of marking-up incredible proportions.
Beyond the systems analysis of Euler’s elegant solution, drawing has long been a core component practice for many disciplines, each of which benefits from the blended space of seeing, thinking, and making that happens on the page. The sketch, once again for example, is a robust research method in design, providing a haptic search space useful for conjecture, for testing against experiential knowledge (Goldschmidt, 1991; Tversky, 2002), and for reconstruction of what design-researcher Nigel Cross has called “ill-defined” problems (2001). But what if the target of such a working graphic (bridging theory and practice) is simply incomprehensible in terms of the handfuls and footfalls to which we are naturally bound? What if we place Euler’s node-links into a context where their pragmatism is met with a kind of senselessness?
The three collaborative, publically performed diagrams that result from this work simultaneously inhabit and trace the spaces of their inscription, perversely smearing the distinctions between “attribute” and “relation” which are key conceptual labels in reasoning with diagrams.
The first of the three is a node-link diagram consisting of a one-second Laser burst, aimed at the centre of our Milky Way Galaxy. This single line will have approximately 300,000 kilometres of length, resulting from questions related to orientation, distance, and other physical matters, in support of an event that taking one second to begin, and something on the order of 25,000 years to complete, assuming a definition for the word “complete” that allows room for the provisional.
The second and much smaller (briefer?) drawing inscribes a network between our small planet and the other planetary bodies in our local physical space — a cascade of metaphors allowing us to extend our grasp to scales that are otherwise incomprehensible in the terms to which we are accustomed. This quasi-semantic diagram actually connects us to those seven mythically charged bodies, for a period of time computed from relative distances. This network will ultimately have the absurd property of around 10 billion kilometres of total length, tied to about four hours of active drawing.
Finally, the third drawing in the portfolio builds from professional principles of multi-view Orthographic Projection, an analytical design-drawing method that constrains to parallel views of an object’s sides. Orthographic projections are spatialized images of distribution, not unlike a music notation in spirit, if different in targeted output. Reading from an orthographic drawing, fabricators are enabled to make the desired object in accord with the compound needs of designer and client. In this final drawing, three bisecting Laser lines are drawn through polar points on the planet, forming twelve “wedges” that flare outward from the Earth, amounting to another set of absurdities, delivered in the soft fiction of metaphor.
In geometrical diagrams “the circle of the proof is drawn, not imagined to be drawn,” writes Reviel Netz, so ‘the action of the proof is literal… for it is only in the diagram that the acts of construction literally can be said to have taken place’ (1999, p.53). In the case of these colossal diagrams, their acts of construction are both in the moment of their performance, but also over spans of time that simply exhaust our descriptive capacities. Inscribed on spaces we can know only in conjecture, these Laser drawings interrogate epistemologies of science, and in some sense, of empiricism.
Location and Duration
The psychologist William Ittelson pragmatically describes a mark as an artefact of human intention, “decoupled” from its real-world source (1996, p.171). And while a fine artist’s marking can be an act of rhetoric and abundance, an engineer generally seeks to reduce the oscillations of meaning; Euler ultimately sought a proof, after all, while the painter Rembrandt (or Cy Twombly, or John Cage in his music notations) sought potential.
Among contemporary artists, working in a post-digital climate of social engagements and institutional support, marks are made with pigment (Felice Varini) or footprint (Richard Long); through the influence of primary physical forces (Haines and Hinterding) or coding for hardware-software systems (Maurizio Bolognini); and with foreknowledge of dissolution (Robert Smithson). But while the linked-to works of these artists hew to Ittelson’s essentialist characterizations of marks, they also blur whatever differences in motivation actually exist between the marking applications of Euler and Rembrandt.
These Laser drawings, however, show Ittelson’s decoupling to be deeply and perversely problematic. In broad terms, pictures represent objects and spaces, while diagrams map systematic relations. But these drawings map space and time in a peculiar form of conjunction, simultaneously tracing and inhabiting the multi-dimensional surfaces on which they are inscribed. They cannot be held in hand, not because they are too big, but because the hand that holds (or the eye that sees) is subsumed in the surface of the drawings themselves.
As experimental drawings, they supply frameworks for a hybrid art-science discourse, but how are we to judge their success or failure? What is the relationship between such drawings and their objects? Entering into flows of metaphor, where are these drawings?
Methods and timeline
What is the significance of an external representation that we cannot interact with, not because it is hidden away, but because it is simply beyond us? We know that our bodily measures actually prohibit direct mappings of our experience onto structures at either end of cosmic scales (Dawkins, 1999). We are prisoners of this incomprehension, but we also know that certain drawing practices have developed which play key roles in recording and understanding challenging relationships in Physics. Well after Euler’s parsimonious road-trip, quantum theories, for example, present us with notoriously strange tableaus to negotiate. Crossing bridges, as Euler did without doing, is the least of our problems in this problem space. Yet Niels Bohr’s simple projection-diagrams of atomic motion (Miller, 1995), or Richard Feynman’s diagrams, mapping probabilities (Feynman, 1983, p.78), have proven themselves useful as simple visual metaphors that illuminate the invisible complexities of natural forces.
The preparatory work is underway, emerging from conversations and collaborations with experts in the physical and mathematical areas that the drawings themselves will overlay. Leaving aside earth-bound issues, for example, I will need to answer questions about diffusion or interference in the spaces between such enormous edges: what are the odds? In brief, there will be the rigorous preparation of a scientific-experimental use of resources, tied to outputs that reach around pragmatism, seeking knowledge that may not be possible to know.
In deliberating how to track and present this work, with their strange timelines and oddly prosaic performance, I offer a bit of collaborative text from the novelist John Steinbeck and marine biologist Ed Ricketts, in which artist and scientist worked together to re-present their experiences sailing the Sea of Cortez, surveying its flora and fauna.
We could, if we wished, describe the Sierra thus: “D. XVVOL.II-15-IX; A. VOL.II-15-IX;” but we could see the fish alive and swimming, feel it plunge against the lines, drag it threshing over the rail, and even finally eat it. And there is no reason why either approach should be inaccurate. Spine-count description need not suffer because another approach is also used. Perhaps, out of the two approaches we thought there might emerge a picture more complete and even more accurate that either alone could produce (Steinbeck J, Ricketts E, 2001).
The fragment gives us a cascade of images, reflecting the needs of the researcher, and the tinkering of the novelist, but also the desire to eat. There is a numerical map of the fish, but also an image of what it is to struggle with, and haul in the animal. In the task of representation of complex relations, character-string notations (D. XVVOL.II…) are powerful instruments for learning; in the case of the Sierra, encoding spine counts to simplify classification and correlation. But for Steinbeck this cannot tell the whole story, and he suggests the incompleteness might be resolved by reflective and analogical approaches from the mind’s eye of the fisherman, and the novelist. Steinbeck and Ricketts are here engaged in dialectical admixture of their disciplines for that: to include the sea and the struggle to better know the fish.
Drawing into space
Exercising insights from the Steinbeck-Ricketts partnership, then, the performance of these drawings are the culmination of a rich bed of writing, drawing, and other forms of documentation that track their features and development, and ultimately their dis-appearance in space.
Taken as spectacle, what viewers will see at the time of their execution may not be particularly exhilarating. The phrase “point and shoot” about sums it up. But just as watching paint dry is not thrilling, in itself, a deeper understanding of the facts of the matter – for example oxidizing, polymerization, and molecular cross-linking, delivered in a range of representations from microscopy and animations, to time-lapse photography — enhances the experience with a compelling back-story, and an often beautiful, more complete (in Steinbeck’s terms) present of physical knowledge.
In the end, there are three drawings, graphs writ (absurdly) large, with an existence that is actually dubious from the point of view of the traditional consumers of Art production. Yet they are no less marks on surfaces than any other objects of connoisseurship in a frame, even if mark and surface are inscrutable, and the frame is a slurry of words and other representations.
Drawing in this deeply problematized context, the contemplation of their performance generates questions with intriguingly unstable answers — a condition to which any productive 21st art practice aspires. They are external representations with which we can only interact, so to speak, in the plan. In their essential in-visibility, they are free of aesthetics, cannot be directly apprehended (or at least, not for long). They are utterly free of use, cannot be exchanged, cannot exemplify or denote anything but some view on limitations.
And of course they may be wrong. But the diagrams are not merely rhetorical; they are drawn in fact. So we must also recognize a kind of impossibility built into the project. Their marks, somehow incorporated in the surfaces on which they are inscribed, are moving into place, following a deeply flawed plan, formulated under absurdly limited conditions of perspective. Long after artist and viewers are dead, long after their potential is exhausted, they will be tracing the fabricated cosmos of a small set of utterly ephemeral beings. Among other things, they finally represent a kind of romantic futility, reflecting something of the general condition of representation, at least from the perspectives of a painter and a cosmologist.
In short, they are graphical gestures that are equally matters of time and space, and fantasy as a function. Through their application onto the tangle of distortions and misunderstandings between what we know and what we do not, and perhaps cannot know, witnesses will have an opportunity to see drawings of becoming.
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