Toward Diagrams
This essay is concerned with the diagram as a tool of inquiry and as an expres-sive and causal form. I use the term “diagram” here in its widest sense, including hand-drawn diagrams, phase diagrams, maps, graphs, open and closed logical and circuit diagrams, and wider applications such as large and small-scale biological and physical network theory and the study of diagrammatic thinking, whose use in the selective processing of eidetic and physical choices is necessary to all theories of consciousness. To diagram is to intentionally compare and link alternatives, to indicate potential choices and boundaries, typically using a conceptually clear line or boundary to indicate the limits of the comparison underway. A successful diagram not only expresses an underlying topology but also produces a manifold where otherwise invisible force relations between pluralities of subjects can be articulated. Diagrams, seen and hidden, constitute the pivotal means, or body, by which we can move through the overlapping topologies of prediction, memory, language, and metaphor without contradiction. Over the last two centuries, the diagram has become the essential mechanism for our collective efforts to articu-late and negotiate an almost impossible circumstance: reality itself.
John Bender and Michael Marrinan identify the reemergence of the diagram in the seventeenth century as an essential tool of research whose openness and ability to cut across boundaries can be clearly distinguished from the rules that govern access to the closed disciplinary arrays that Michel Foucault describes as inherent to any system of knowledge.1 As Bettina Funcke observed, Foucault’s archive, or “dis-course of rules,” is “inscribed on a hidden carrier taken up in the materiality of the medium”; and there exists an unarticulated contradiction between the materiality of signs and the indestructible identity of this hidden carrier (the diagram) that for Foucault induces a fear of “the proliferation of meaning.”2 Boris Groys describes this hidden carrier as “a figure of suspicion” that can only be imagined.3
I am indebted to the Getty Research Institute, Columbia University, the Mellon Foundation, Dr. David Brafman, Natilee Harren, and Andrea Rosen for supporting my interest in this entire area of research—and most especially to the editors for their tireless efforts.
1 John Bender and Michael Marrinan, The Culture of Diagram (Stanford, CA: Stanford University Press, 2010); Michel Foucault, The Archaeology of Knowledge, trans. A. M. Sheridan Smith (New York: Pantheon Books, 1982).
2 Bettina Funcke, Pop or Populus: Art between High and Low, trans. Warren Niesluchowski (Berlin:
Sternberg Press, 2009), 47.
3 Boris Groys, Under Suspicion: A Phenomenology of the Media (New York: Columbia University Press, 2012).
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In contrast, for Bender and Marrinan the open form of the diagram is the basic form of what Krzysztof Pomian calls the “elements of discourse” in science4—the propositions, images, and theories that allow us to connect objects, forces, and interac-tions that would normally be inaccessible to us. Beginning with Newton and Maxwell, the cumulative articulation of a complex series of otherwise humanly inaccessible object-to-object relations has been accomplished through the proliferation of a vast series of diagrams—the isomorphic manifolds of increasing abstraction shown in Max Tegmark’s diagrammatic classifications of formal systems (fig. 1). This is not simply a disguised essentialism: for Tegmark the scientific pursuit of higher and higher orders of formal abstraction definitively does not necessarily point toward a final “Theory of Everything”; rather, each generation of diagrams offers radically new perspectives on local nature.
Figure 1. “Relationships between various mathematical structures. The arrows generally indicate addition of new symbols and/or axioms. Arrows that meet indicate the combination of structures—
for instance, an algebra is a vector space that is also a ring, and a Lie group is a group that is also manifold. The full tree is probably infinite in extent—the figure shows merely a small sample near the bottom.” (Reproduced by permission from Max Tegmark, “The Multiverse Hierarchy,” in Universe or Multiverse?, ed. Bernard Carr [Cambridge: Cambridge University Press, 2007], 4.)
4 Krzysztof Pomian, “Vision and Cognition,” in Picturing Science, Producing Art, ed. Peter Gallison and Caroline A. Jones (London: Routledge, 1998), 227.
Through a precise definition of inherent topological relations, a new diagram can ultimately produce a radical reduction of local complexity and a corresponding change in relative accessibility as the defining local force relations become apparent and newly accessible, as for instance in the way Richard Feynman’s famous diagrams reintegrated the confusing bestiary of particles and interactions that pre-ceded the standard model (fig. 2).
Figure 2. “Electron-electron scattering is described by one of the earliest published Feynman diagrams. […] One electron (solid line at bottom right) shoots out a force-carrying particle—a virtual photon (wavy line)—which then smacks into the second electron (solid line at bottom left). The first electron recoils backward, while the second electron gets pushed off its original course. The diagram thus sketches a quantum-mechanical view of how particles with the same charge repel one another. As suggested by the term ‘Space-Time Approach’ in the title of the article that accompa nied this diagram, Feynman originally drew diagrams in which the dimensions were space and time; here the horizontal axis represents space. Today most physicists draw Feynman diagrams in a more stylized way, highlighting the topology of propagation lines and vertices.” (Reproduced by permission from David Kaiser, “Physics and Feynman’s Diagrams,” American Scientist [March–April 2005]: 153;
diagram from Richard Feynman, Physical Review, 1949.)
As Manuel DeLanda noted, a diagram contains all its possible expressions; the inventorying of natural properties may be suddenly and effectively replaced by a higher order of unity.5 The recent discovery of the “amplituhedron” is another such example (fig. 3).6 This remarkable jewel-like form replaces the need for hundreds of Feynman diagrams with a single graphic equation.
5 Manuel DeLanda, “Deleuze, Diagrams, and the Genesis of Form,” ANY: Architecture New York 23 (June 1998): 30.
6 Nima Arkani-Hamed et al., “Scattering Amplitudes and the Positive Grassmannian,”
arXiv:1212.5605, 2012.
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Figure 3. “A sketch of the amplituhedron representing an 8-gluon particle interaction. Using Feynman diagrams, the same calculation would take roughly 500 pages of algebra.” (Reproduced by permission from Nima Arkani-Hamed, “A Jewel at the Heart of Quantum Physics,” Quanta Magazine, September 17, 2013; www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/.)
By proposing new conventions of dimensional connection across an infinite sheet, such exploratory diagrams also reinvigorate theories of picture and the possibili-ties of agency within them. Frederik Stjernfelt, in his magisterial Diagrammatology, characterizes the diagram as a form of hypostatic abstraction, demonstrating that any painting or sketch always indexes another group of terms, even as it moves away from it, always referring back reciprocally through a kind of sublated or hidden dia-gram.7 Stjernfelt goes on to link C. S. Peirce’s theory of diagrams, premised on the concept of an isomorphic continuity or transformation across an invariant structure (such diagrams being co-extensional with mathematics and theories of picture), to Edmund Husserl’s analysis of representational forms and his series of time-diagrams (fig. 4) that describe a separation of objective and experienced time and seem to promise a final reconciliation with the infinite.
7 Frederik Stjernfelt, Diagrammatology: An Investigation on the Borderlines of Phenomenology, Ontology, and Semiotics (Heidelberg: Springer, 2007), 306.
Figure 4. (Reproduced by permission from James Mensch, “A Brief Account of Husserl’s Doctrine of Time Consciousness,” available at: www.academia.edu/590652/A_Brief_Account_of_Husserls_
Doctrine_of_Time_Consciousness_with_Accompanying_Translations.)
Like Feynman’s and Tegmark’s diagrams, the diagrammatic conventions used by Husserl and Peirce are semasiographic, not dependent on the conventional organi-zation of meanings linked to human experience of time and space.
So effective is the diagram as a scientific tool, it might be easy to mistake its functions for a basic condition of informational space. But the diagram (a diagram, all diagrams) is neither a simple expression of the terms of the space it occupies, nor simply a useful metaphor for a hidden bridge between the local manifolds or ordering system and the proliferation of localized difference that constitutes the primary operating system of conscious thought. It is something more than a trans-lator; in the presence of diagrams, the profound questions of relative time, scale, distance, gauge symmetry, proximity, and imagined immunity from discontinuity and relationality that define our use of any shared informational space become painfully evident. This discontinuity has recently entered a new and increasingly ubiquitous sphere of influence, making it more relevant than ever. Computational space, the hidden substrate and indexical basis of contemporary culture, is built from highly ordered diagrams of microstates that physically integrate quantum force relations, relying on directed movement and a central ordinator to make the letters we see into lines of code, patterns of electrons—an architecture of pure energy.
As an artist, I’m most interested in the extent to which this environment, with its simultaneous advantages and problems, can be properly understood and utilized, both physically and metaphysically, as an exploratory tool. Despite the familiar com-plaint of “information overload,” the humanly experienced web largely duplicates,
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juxtaposes, or compresses what we already know into degraded “sensory appear-ances,” while the non-human, object-to-object force relations that sustain it (tem-poral, physical, political, and environmental) are increasingly hidden. The culture of diagrams introduced through publishing, globalized in the nineteenth century and now radically extended by computational space, is becoming a continuously edited substrate, a form of shared creation whose extended use might powerfully affect how reciprocal relationships between material and concept are understood. As the horizontal force relations of networks become increasingly predictable, as shown in the scale-free network theory of Albert-László Barabási,8 and our own responses become more and more conditioned to the limited options within it, will this highly programmed and increasingly predictable computational environment come to
“know” us better than we will ever know ourselves? Given the growing reliance of contemporary art culture on computational management systems, performance metrics, and financial engineering, the stealthy but steady emergence of an essen-tially eidetic or algorithmic art culture makes the review of underlying concepts of diagram all the more urgent. Hand-made diagrams have tellingly begun to vanish from the visual tool-kit of artists and architects to be replaced by the invisible hands of programs; the concepts of network, distribution, and hub are becoming central to art historical presentation. For a discipline whose basis is the movement away from the index and toward the proliferation of meanings, surely the only unacceptable trajectory is a too complete belief in the current diagram, one that would abandon its exploratory modes and become fixed into the rules of discourse.
Toward the Maelstrom
The ways of God in Nature, as in Providence, are not as our ways; nor are the models that we frame any way commensurate to the vastness, profun-dity and unsearchableness of His works, which have a depth in them greater than the well of Democritus.
—Joseph Glanvill, “Against Confidence in Philosophy and Matters of Speculation,” in Essays (1676)
This epigraph was used by Edgar Allan Poe in 1841 as the introduction to “A Descent into the Maelstrom,”9 exemplifying his theoretical project to elaborate the difficulties faced by a rational author in a chaotic universe. In Poe’s tale, a fisherman recounts his
8 Réka Albert and Albert-László Barabási, “Topology of Evolving Networks: Local Events and Universality,” Phys. Rev. Lett. 85 (2000): 5234–37. Available at www.barabasilab.com/pubs /CCNR-ALB_Publications/200012-11_PhysRevLtr-TopologyEvolNetworks/200012-11_PhysRevLtr -TopologyEvolNetworks.pdf.
9 Edgar Allan Poe, “A Descent into the Maelstrom,” in The Collected Works of Edgar Allan Poe—Vol. II:
Tales and Sketches, ed. Thomas O. Mabbott (Cambridge, MA: MIT Press, 1978), 574–97. Available at www.eapoe.org/works/mabbott/tom2t044.htm.
experiences surviving an enormous whirlpool, describing how he had coolly observed the various features of the terrifying gulf with an “unnatural curiosity,” and then, fol-lowing the principles of Archimedean physics, had lashed himself to a barrel, the only geometric form that can be successfully propelled out of the abyss. Poe’s “Maelstrom”
has been characterized as an early form of scientific fiction or “science fiction” (a term whose inverse complement might easily be the phrase “weird realism” coined by H.
P. Lovecraft—or even Speculative Realism itself). Poe’s text contains no fantastical or supernatural elements. It is only his narrative rigor and personal distance when describing phenomena extending beyond human terms of reference that make it “sci-entific fiction” at all. It is in this superposition of informational space and imaginative space that we find the accompanying premise: that human cognition needs metaphor-ical technologies to extend itself effectively into transitional areas and new sensory experiences, which we may find only partially comprehensible and hence “weird.”
As Poe’s contemporary and admirer Gustave Flaubert wrote in The Temptation of Saint Anthony, “somewhere there must be primordial figures whose bodily forms are only symbols. Could I but see them, I would know the link between matter and thought; I would know in what Being consists!”10 Flaubert’s tortured hermit, besieged by an encyclopedic parade of gorgeous visions, still hoped to reconcile Bouvard and Pécuchet’s later confusion between sign, symbols, and reality at a time when diagrammatic thinking and behaviors were moving from symptom to syndrome. Fifty years later, Poe’s story and Flaubert’s vision would collide in Stéphane Mallarmé’s poem “Un coup de dés,” which features another shipwreck survivor, this time consumed by the whirlpool of chance and myth. When Mallarmé, another admirer and translator of Poe, wrote that “the poetic act consists in suddenly seeing that an idea splits into a number of motives of equal value and in grouping them,”11 he almost seems to be echoing Poe’s “The Philosophy of Composition”: “It is my design to render it manifest that no one point in its composition is referable either to accident or intuition—that the work proceeded step by step, to its completion, with the precision and rigid consequence of a mathematical problem.”12 And so Poe, already well known for his “incalculable influence on succeeding generations of writers of horror and science fiction,”13 must also be given credit for his role in the introduc-tion of systematic thinking into ficintroduc-tion, a concept that would lead to the so-called death of the author, so vital to the linguistic turn against which Speculative Realism sets itself. The emergence of derealization as a widespread clinical condition, closely linked to depersonalization and the ensuing disbelief in the world as a continuous
10 Gustave Flaubert, The Temptation of Saint Anthony, trans. Lafcadio Hearn (New York: Modern Library, 2001), 179.
11 Stephane Mallarmé, “Crise de vers,” trans. Rosemary Lloyd, in Mallarmé: The Poet and His Circle (Ithica, NY: Cornell University Press, 2005), 231.
12 Edgar Allan Poe, “The Philosophy of Composition.” Available at www.eapoe.org/works/essays /philcomp.htm.
13 Joyce Carol Oates, “The King of Weird,” New York Review of Books 43 (October 1996). Available at www.nybooks.com/articles/archives/1996/oct/31/the-king-of-weird/.
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phenomenological whole (which disbelief Speculative Realism so ardently refuses), can also be definitively located in the latter half of the nineteenth century. Cotard’s syndrome, a complex form of schizophrenia where the patient believes they possess a body that is dead, or without physical limits, was first diagnosed in 1880.14 The contemporary impulse in philosophy and art was to produce a similarly deperson-alized algebra of signs that would support the messianic and exponential proposals of the nineteenth century, through whose geometries, graphs, and encyclopedias the possibility of totalizing, multi-positional strategies of art production (and every-thing else) would became a historic inevitability in the twentieth century. As Wassily Kandinsky wrote ecstatically from the heat of the crucible, when time and space were collapsing as fast as precision-guided munitions could eliminate them, “the life of the spirit may be fairly represented in [a] diagram.”15
The exploded geometric spaces of Gaspard Monge’s technical drawings and Nikolai Lobachevsky’s non-Euclidean geometry converged into Kazimir Malevich’s squares and his statement that “the artist who wants to develop his art beyond the potentialities of conventional painting is forced to resort to theory and logic,”16 then exploded into Kurt Schwitters’s Merzbau. Under the misnomer “machine drawings,”
diagrammatic connections were critical for Francis Picabia, Raoul Hausmann, Marius de Zayas, and Marcel Duchamp. For Duchamp, the universal connectivity of the dia-gram became an essential tool in the dimensional isomorphism of the Large Glass and ultimately the only stable referent in the construction of a project as scale-free as the world itself. Over time, Duchamp produced a hidden web of imprisoned connections, an unstable pseudo-archive, variable in meaning, legibility, scale, and materiality that could be projected (in reverse) into the art history of the twentieth century, constituting a series of isomorphic manifolds far exceeding the terms of a private language.17 This essentially diagrammatic premise, the superposition of multi-positional formal and temporal terms, of a passive carrier and active body in a single practice or volume, would eventually give rise to a wide range of different sculptural possibilities and ways of contemplating pictures, depending on which abductive, bodily, or intellectual stance was adopted. The combines of Schwitters and Robert Rauschenberg led to the combinatorial logics of Sol LeWitt and Mel Bochner. If the diagrammatic program began with an artist becoming the world, it reached some kind of conclusion with the world being diagrammed as a potential space for art in the practice of Joseph Beuys, an artist in whose practice diagrams and drawings are indissoluble.
14 Jules Cotard, “Du délire hypocondriaque dans une forme grave de la mélancholie anxieuse,”
Annales Médico-Psychologiques 4 (1880): 168–74.
15 Wassily Kandinsky, Concerning the Spiritual in Art, trans. M. T. H. Sandler (Toronto: Dover, 1977), 6.
16 Kazimir Malevich, The Non-Objective World: The Manifesto of Suprematism, trans. Howard Dearstyne (Mineola, NY: Dover, 2003), 51.
17 “This experiment [of the Three Standard Stoppages] was made in 1913 to imprison and preserve forms obtained through chance, through my chance.” Marcel Duchamp, “Apropos of Myself,”
in Marcel Duchamp, ed. Anne d’Harnoncourt and Kynaston McShine (New York: Museum of Modern Art, 1973), 273.
As is evident in the range of diagram projects, there is a price for this freedom.
Diagrams of universal conditions produce a further superposition, one of ludic con-fidence, simultaneously encouraging limit-case thinking and a hermetic withdrawal from the conventional taxonomy of the world. With its properties as universal trans-lator, limit-case eidetic, Peircian abduction-deduction-intuition machine, fantasy generator, and “thing-in-itself,” the diagram as model-of-thought offers one final fantasy, of omni-directional potency. Rhapsodic thinking, quasi-science, suspicious topologies, and mathematical inconsistencies can all be elided with a confident group of gestures and terms. There is no requirement for rationality, only mutuality—or isomorphism of parts. As Deleuze wrote: “A diagram is a map, or rather several superimposed maps. And from one diagram to the next, new maps are drawn.”18 Without a gauge theory to discipline it, every new diagram displaces the author horizontally to the “authority” of the diagram and cloaks the anthropomorphic centrality of the rules or local regime.
This is not to suggest that diagrammatic thinking constitutes an easy escape route for the visionary or fantastical impulse (far from it!). Poe, Duchamp, Flaubert, Mallarmé, Beuys, and a thousand others labor under infinite obligation to the freedoms, compulsions, and intensities of their own universes and achieved varying degrees of mutuality. Whether we are truly accessing higher orders of reality or
This is not to suggest that diagrammatic thinking constitutes an easy escape route for the visionary or fantastical impulse (far from it!). Poe, Duchamp, Flaubert, Mallarmé, Beuys, and a thousand others labor under infinite obligation to the freedoms, compulsions, and intensities of their own universes and achieved varying degrees of mutuality. Whether we are truly accessing higher orders of reality or