[1] The following article is based on a series of interviews conducted by Jacob Nyman with John Duff, at the latter’s studio in New York City, between December 9^th 2009 and January 29^th 2010. All quotes attributed to the artist are taken from those transcripts. 

I. Fine Arts Magazine 

There exists an urgent and foreboding anxiety in art today- and so the anticipation of a reciprocal anxiety in the artist, and a consequent anxiety in us, the spectator. On its grandest scale this anxiety intuits the responsibilities of ownership, predicting the tragedy of man’s arbitrary nature. Arbitrary, not as anguished loss or random meaninglessness, but rather the profoundly human dread of the artist – the individuating unease of fully embodied and creative selfhood. The arbiter goes to see, looks into and then decides. This anxiety is the self-conscious bounding of nature (Necessity) into small, comprehensible images; viz., into knowledge. 

above: John Duff, Inside the Kepler Conjecture III 2010. Urethane resin, steel ,47” x 22” x 22”  

 The Necessity of the world- those conditions upon which its existence depends – the way in which the world holds together- is ultimately that image which explains life to himself. Religion as arbiter once crafted its world, it defined its Necessity and sculpted a universe that helped, for a time, to bridge an uncomfortable gap. Science too has assumed its own image – one of necessary laws; those secrets bequeathed to man as regularities, unlocked from their enigmatic workings with patient observation and measurement. In ancient Greece, a time when art and science were coextensive to human understanding, an inclusive Necessity was set upon, utilizing a far more sensitive tact to arbitrate the world than our own disparate and exclusive mentality of today. It is this original and mutual dialogue that is re-articulated in the sculpture of John Duff; art which speaks in the unitary intuition of the artist and scientist. 

Duff says of his art that “it works on the level of necessity” – his nature is one of a world connected and interconnected, its laws relied upon to unfold consistently and uniformly. In the language of science, one might say Duff’s conception of Nature resembles something between Liebniz’s Principle of Sufficient Reason and Newton’s Laws of Motion. 

 Sculpting this Necessity, Duff has erected an ideological threshold for himself, whose lintel reads: “imitate nature in its manner of operation”; his works can be comprehended effectively only against that Necessity, which acts as a measure for a world of mechanistic inevitability. This adage is a horizon, an expectation against which the sculptures will be gauged and by means of which they will succeed or fail. In this way Duff labors, philosophically, in a way similar to the scientist; and as if obligatorily his recent sculptures model current mathematical and scientific discourses. The art itself has assumed the very literal imagery of certain contemporary ‘scientific’ projects. Thus these works can not help but to instantiate a discourse between two radically divergent dialogues, granting to art its unique ability to comment on the science. 

II. 

Not just geometricians but mathematicians philosophers and physicists have conceived of space geometrically since Antiquity. Johannes Kepler, an Enlightenment thinker who early in his career conceived of the five Platonic Solids as the constitutive influence of the Solar System’s form, also less famously, worked on a mathematical arrangement of spheres in three-dimensional Euclidean space, searching for their ‘closest packing’ known today as ‘Kepler’s Conjecture’. The close packing of objects, asks for the most efficient way to pack solids in an infinite space; arranging solids in configurations that minimize the resulting empty spaces. Thus, for example, one can easily imagine how it is that hexahedrons (cubes) ‘pack’ with 100% efficiency, whereas spheres, as they stack side-by-side, one on top of the other, give rise to lacunae. Importantly for both the mathematics and the sculpture these vacant spaces lack uniformity, they generate irregular patterns. In fact it might be said that they are the irregular complements to the perfection of the spheres themselves. 

Modern physics has inherited the conceptual problem of close packing, surprisingly taking mathematicians almost four hundred years to prove Kepler’s Conjecture- which visually is a simple, almost intuitive formation. The Conjecture can be proved, it turns out, when all the solids are arranged in a regular lattice. However, irregular arrangements provide for denser packings under differently manipulated spatial determinations. Even as it stands today with a density slightly greater than 74% this proof must be relied upon with trepidation and incredulity. Over and again with mathematical assertions, coupling larger computers with more creative computing frequently disconfirm proofs; the exact scenario in the case of ‘packing’ tetrahedrons – a mathematical study resembling a Guinness Book of World Records competition more than scientific demonstration. The closest packing began with a density of 72%, increased to 78%, then 85% and now at last count has achieved 85.63%. Saliently there always looms the very real possibility for packings of ever increasing density; illustrating again arithmetic’s primary function as tool of measurement always in the hands of a measurer.  

above: A pyramid of 35 spheres, illustrating part of Kepler’s theory of maximizing spherical density in a three-dimensional Euclidean space.  Note the same optimization strategy with oranges in your local supermarket. 

The central work of Duff’s current series of sculptures is entitled Tammes Project, a work predicated on an issue in physics known as the Tammes Problem, a puzzle of theoretical mathematics involving a type of ‘close packing’. The Tammes Problem entails ‘packing’ two-dimensional circles onto the surface of a three-dimensional sphere. 

 Tammes Project, then, is a sculpted sphere, 3’ and 1/16’’ in diameter. Duff, beginning from these original measurements (an arbitrary inception) has calculated that 101, 8’’ hemispheres will pack onto the sphere’s surface. Once packed, Tammes Project will be cast in black, urethane resin. In the process the original sphere will be lost and so exist only as an absence. Thus the sphere’s new constitution will be formed by the skin of those 101 hemispheres resting on the now absent 3’ sphere. Looking out from inside the cavity of the sculpture – the packed circles (the feet of the hemispheres) sitting in their closest packing, will create the surface of the new imperfect sphere. 

Duff chose a moment, a place to begin a discourse and then allowed it to unfold under the direction of its own mandated expectation. The mathematical foundation of Tammes Project, the Necessity of the 101 8’’ spheres, forces an inevitability but only after the original 3’ sphere has been decided upon. In this way, the sculpture shares the same contingent Necessity as Kepler’s Conjecture; an arbitrated construction of space and solids. The mathematical proof of the conjecture is predicated on the exclusion of any configuration other than what Kepler manufactured. Those four hundred years of mathematical toil were finally relieved by computers making Kepler’s ‘Proof by Exhaustion’ feasible – a proof however, which still only confirms an original decision. The philosopher at the center of the project, as artist and mathematician, is deeply implicated in both regularity and irregularity, perfection and imperfection. 

Duff works on the level Necessity such that one consequence forces the next, like the image of the sphere which itself effects the image of an ideal perfection. Yet Tammes Project forces an image of irregularity, of imperfection. The abstract perfection of the sphere gives rise to irregularity and in sculpture it’s much more than the abstract image – it’s a functioning symbol of perfection. Moreover, exactly in this relationship art exercises its insightful leverage on its intentional object, in this case science. In fact Tammes Project, as it articulates the entire project of the close packing, compels the very unsettling and uncanny realization that the seat of these irregularities is actually not the sphere but rather the expectation which it motivates; man’s relationship to this Necessity. The irregular and the necessary are projected onto the world- they are assumed and sublimated into art- and the work of art evokes this uneasy tension. 

Duff, himself, says that art is born of man’s inexorable relationship to Necessity, to the world; i.e., art as the distinction of the birth of a post-Eden consciousness. The arbiter’s interminable ejection from the garden is not coincidental to those desirous expectations moored to the ideal sphere. Yet perversely, that very image appropriated by the mathematics of close packing is strangely abysmal. Somehow the sphere has become menacing; grafting the Tammes Problem to its surface, obscures and drains its deceptively flawless façade – its Eden fantasy. 

 Instead, the sphere has become abysmal in its un-attainability. The irregularity induced on its surface is the reluctant insistence of an ineluctably arbitrated irregularity. This recalcitrant righting of a wrong in the absolute language of mathematics seems at once the doleful pronouncement of a dangerous projection as well as the mourning of its collapse. The sphere is no longer selfsame, its symbolic weight is subject to effacement, an effacement with mathematics – the language of the eternal. Mathematics is the progenitor of the sphere, the symbol in which the creator meets the beyond, where Necessity meets the arbitrary. Historically this convergence is the inception of a great tragedy in which the arbitrary recognizes his own arbitration; the artist assumes the responsibilities of the hand. There is no perfection, there is no sphere, even when mathematics is the tool of the arbiter, Eden is only an illusion. 

Interestingly, Tammes Project can not be completed, echoing the unconsummated ideal of mathematics and auspiciously validating art’s symbolic foresight. The unfinished nature of the sculpture was itself inevitable. As Duff became more deeply implicated in the sphere’s mandates, he realized that successfully accommodating all 101 hemispheres, necessitated by the original 3’ inception, was only possible as a theoretical abstraction (an accomplishment of mathematics alone). Realizing this Duff, shifted the goal of the work, but actually in it’s most profound meaning finished it by re-sculpting the arbitrary. 

The revised Tammes Project will accomodate as many of the 8’’ hemispheres on the surface of the sphere as he, the sculptor, can manage by both hand and intuition. Duff will apply them and make adjustments so that the consummation of the work will be mediated directly by the artist, rather than mathematically. By shifting the original decision- by arbitrating the hemispheres not by algorithm but by hand Duff has subtly re-emphasized the artist’s intimate relationship to science. The seeming Necessity that mandated the 101 hemispheres was always absolutely contingent on the arbiter, generating an uncomfortable tension between an ideal perfection and those irregularities that are a pre-requisite for its manufactured realization. Only on the surface of the sphere could this drama play out. 

 Duff anticipated this exact tension in an earlier work entitled Missing Man Formation; a sculpture built, quite simply, from one hundred beer bottles arranged in a ten by ten grid. The title of this piece refers to the pre-established formation in which a returning air force sortie flies to indicate it has lost a member of its squadron, or the pattern it flies in an aerial salute performed as a memorial event for a fallen pilot. The same themes of arbitrary Necessity are as front and center in this piece as Tammes Project, but the role of Necessity in the former has been resolved upon more ambiguously. The thought is that bottles will inevitably break, leak or just go missing over the course of the work’s lifetime. Installation, shipping, crating and all the usual fuss involved in showing, transporting and storing art, especially sculpture, will over the years, naturally force irregularity in the constitution of the piece. Each bottle is numbered and then placed on its own shelf in a regular grid that hangs on the wall. As bottles break, the sculpture itself, in its purpose will remain selfsame, but the indices which define its image are no longer regular as the corresponding shelf remains empty once its occupant ceases to be. In this way Duff accommodated originally, an inevitable imperfection. Lacunae would surely occur, perhaps even whole veins of irregularity would eventually form. The sculpture has adopted a specific expectation of the world- namely one in which human imperfection is bound inexorably to his own expectation of perfection. With out the sacred weight of the sphere in Missing Man Formation however, the museum’s clumsy carelessness can only be understood as an indifferent pessimism – the consequence of an ever expanding and random universe in opposition to the moral imperatives demanded by the self-bound, eternally generating spherical universe of Tammes Project. 

Duff’s work, which is to say both his sculpture and the burden of his labor, are inculcated by an ambivalence about his implication in the profanation of the sphere and all that it portends. In response he has tried to subtly dissemble the presence of his hand; evidence of the moral struggle of the arbiter in his ownership of the world. Sensitive to the opprobrium of the artist Duff has said: “I would like to erase [my] original decision, so that original decision is buried in [the work]”. As if ratcheting up his own incrimination he goes on to describe his art as “Conceptual, Geometric, Abstraction” a characterization of the sacred undoubtedly – its potential for a deflation, exceptional. However deflation and salvation are two sides of the same coin and intuiting again that “if there were not irregularity in the universe, life would not be possible… I want to see how the experience of irregularity necessarily [develops]. Wondering how and why and the nature of it. It’s arbitrary but is it arbitrary? What’s the nature of arbitrary? What’s the role of arbitrary? Is there such a thing as arbitrary?” Duff straddles a rift, holding the tension between Necessities and bridging the antagonism of two worlds. Like the image of nature whose mysterious regularities reward the scientist’s patient observation he has likewise been granted a similar reward, but as an artist seen something different. In the unitary discourse of the scientist and artist, the original logic of the arbiter is bound together in this sculpture, preserving the peculiar proof of Kepler’s Conjecture. 

III. 

The tension-producing anxiety of this sculpture ultimately stems from art’s primordial privilege in the foundation of man’s understanding of the world, which although different from science, is every bit as sure. However, unlike science, it is best described a unique logic characteristically enigmatic and elusive. The condition for the possibility of art’s success is precisely as an un-scientific and non-discursive appreciation of the world articulating its meaning through a logic which works by a kind of indicative implication. Framed more traditionally art is symbolic operating in the logical structure of the symbol. 

Contrarily, science mediates understanding by means of a very familiar and recognizable logic – that ‘scientific-type mediation’. Scientific logic mediates consciousness and the world according to the prescriptions of analysis and synthesis, induction and deduction and mathematics is, needless to say, this logic’s most reliable tool. 

The marvelous and distinctive successes of science reside in carefully constructed worlds of rules, unfolding either as predicted or else not. With any failure comes the possibility of a correction; an engagement with the series of choices and assumptions determining them. In this way the mathematician is a humanitarian- a historian, and in this role he allows his failures to generate new artifice; the world building architecture historians both inherit and endow, ad infinitum. Necessity is the finite extended infinitely. 

 The circumstance of modernity has nurtured a seeming distinction – a false dichotomy between the discursive logician and the artist, effectively conflating logic with the logician – the measure with he who measures. As the examiner seizes upon and pursues his phenomena he is always already immersed in a world of assumptive expectation. It is only within a world that already holds together that he can search out relationships and regularities, finally extending beyond into theoretical abstraction; the building blocks of ideas. The artifice of the scientist’s world are those ideas (laws, theories, hypotheses, assumptions, etc.), which laid as a measure against the expectation of their truth allows them to unfold; i.e., allows them to be true. Science is precisely methodical in its expectations and subsequent measurements and in this way its logic intentionally mediates the world, bringing the artifices of Necessity to consciousness. The logic of science is a super-conscious intentionality. 

Of course it is never the object (math or sculpture) that mediates understanding, but rather a mediation which an understanding consciousness brings to bear on an object. Thus, one can view Tammes Project as either a work of art or as a model of scientific study. In the latter it not only succeeds or fails against a determinate (logical) measure, but grants the apprehending viewer a ‘scientific’ understanding of its intended subject. Consequently, relinquishing the scientific mediation instinctively liberates the possibility for the art-mediating consciousness; i.e., the symbolic logic of art to function. The symbolic is ever-present and always prepared to propound its portents, it requires only to be yielded to. 

Art comments about the universe with equal force and verity as does science; however, it appreciates them with a dissimilar logic. Art understands the world outside of a conscious mediation, that is im-mediately, and retains its power as art, in its uniquely unmediated and so also ‘unscientific’ method. Im-mediate logic is mystic in its effected union of the artist or spectator to his world. (Any incredulity in regards explanations other than causal-mechanistic need only inquire after the mechanistic or chemical explanation of gravity, or say the Id). To be sure, this is not an attempt to cede to art an obscurantic absolution, as there does exist a real but fine line between a credible mysticism and an incredible metaphysics. The common language of ‘birth’, the organic image of the artist’s ‘giving birth’ is comprehensible only by respectfully toeing the that line. Moreover, the progeny of the artist remains enigmatic only by the standard of induction/ deduction, analysis/ synthesis. The logic of art is that condition which has already allowed the work to be art. Art has already chosen its world, it has articulated its meaning – it has already spoken. 

The world art’s un-mediated logic articulates is not only indubitable, but profoundly recognizable, and exactly within that moment of recognition art has demonstrated its unique arithmetic, it has proved itself to be a symbol. In recognition the work of art expounds the truth whence it was born, the Necessity against which it acts as a measure. Just as mathematics articulates in its language the Tammes Problem, giving the thought body, enabling it to participate in a world, so too it is with the case of art. Once recognized the work of art itself functions as a measure of knowledge, incarnating that image, whose meaning functions in the world. The Artist is the arbiter of knowledge and Necessity. 

In its consummate form the un-mediated logic of art can take the same objects that the mediated logic of science does: man and the heavens, plants and animals, death and chemistry. Tennyson for example, in his poem Ulysses, grasps the idea of ‘experience’, in the logic of art when he writes: 

Yet all experience is an arch wherethrough 

Gleams that untraveled world, whose margin fades 

For ever and for ever when I move. 

The image of the infinite evinced by these few lines summon by analogue a world of experience. It itself is an arch wherethrough finite nature comes into urgent and melancholy focus as an achievement more penetrating than any vulgarly mechanistic description of time or consciousness. 

IV. 

 Duff, by conflating these two mediations has instigated a dialogue between art and science, affording a unique interpretative opportunity. The first question these particular sculptures must ask is about the claim art makes relative to the claims of science, as the viewer must decide how he will negotiate, hermeneutically an art which is of science. Duff has conferred upon science the logic of art, apprehending the former symbolically and so granting a retrieval of the anxieties, tensions and anguish of an influential and powerful world view. What does the art say? 

Take as an additional example a work from the same period as Missing Man Formation called Daddy’s Dice. It’s a sculpted set of five dice, imagined from the inside. Each individual die is crafted as a nexus of avenues crossing at what would be its center. The viewer comes to see that each of the avenues designates one face of the cube; thus there are six interweaving threads. Then each of these avenues splits again with either one, two, three, four, five or six of their own termini, representing those recognizable dots which make cubes dice; a sculpture that imagines the internal logic and constitution of the die. 

These dice are, in a sense, the implements of the scientist. They are the mechanism of a canned chance; an instrument to bound the infinite for the purposes of a game – for the flick of the wrist. Like Tammes Project here the looming menace of an unresolved consequence, the responsibilities of conscience, resound in a static despair. In the same dejected way Dürer’s Melencolia I and Blake’s Newton contend with the nervous relationship between measurement and the new-measured world, so too does Daddy’s Dice affect a visceral deflation by the recollection of an impossible Eden and the dissolution of an objective Necessity- a calling to one’s projections. In the face of this work the viewer must also account for what Newton and the melancholic genius so nobly confronted. “We’re the people in my work” Duff once reminded a lethargic and despondent spectator who had lost the measure of his art; forgetting that only by means of a viewing participant can the sculpture work. Likewise, these dice demand a person, and when seen they can not help but to incite again the sobering memory of Necessity as the tool of the arbiter. 

The primordial affinity of the artist and scientist is a forgotten and uncomfortable truth John Duff’s sculptures remember. Choosing for himself a science thing, understood from the perspective of art he manifests one moment out of an infinite many, choosing and prioritizing certain relationships which all rest on a nexus of hypotheses, pre-conceptions and prejudices. For both the scientist and the artist, a world already exists and Duff’s sculptures come to be, due to his series of expectations. He explains why are some artists interested in theatrical physics and some landscapes, why are some scientists interested in astrophysics and some biological evolution- he explains the world. 

The anxieties inherent in this explanation are articulated in a segment of contemporary art, and Duff’s work surely assumes the responsibilities of the owner. His sculptures however, only reflect a false dichotomy, which originally is really the shared project of the artist and scientist. Although both are every bit the arbiter of their worlds, the latter refuses the burden of the anxiety. As it has come into itself over the last two hundred years, its confidence has also grown, usurping the historical terrain of art’s understanding. Dangerous attempts to explain other logics by means of science, perhaps as a complex, but reductive chemical processes have already appeared, and will undoubtedly continue. Against their meanest incarnations Duff’s sculptures will naturally arise, arguing as a bulwark and antidote against the limits of the science’s understanding. They remember the original affinity of two disparate logics and of the limits of he who creates the world. Reminding a science, which claims exclusive authority over truth, requires the authority of art’s logic – as it is that arbitrary Necessity which is centrally reflective of man’s ascendant power. 

by Jacob Nyman, Contributing Writer 

learn more about the fascinating geometry of the icosahedron at www.en.wikipedia.org/wiki/icosahedron and Kepler’s Conjecture at www.en.wikipedia.org/wiki/kepler_conjecture