Are abstractions also “real”? Or, put another way, do such varied non-material things as physical laws, mathematical formulae, consciousness, and religious faith have independent existence, even if they emerge from or are representations of physical processes? While questions like these have been debated by both professional and amateur philosophers for centuries, the work of artists may help move that conversation a step or two away from being “academic” and towards to being more immediately practical. In particular, chemist and sculptor Susan Van der Eb Green’s hands-on explorations of the worlds that are normally unseen and—more—untouched, direct our attention towards our peculiar human identity as creatures who dwell in both the abstract and the concrete.
For the past several years, Sue Green has been creating sculpture and furniture based on ideas and structures known from science and mathematics, part of a group of scientist-artists known collectively as ComplexUs that exhibited together in 2010 at the Washington, D.C. headquarters of the American Association for the Advancement of Science. But Green’s first career was as an analytic chemist, specializing in liquid chromatography and centrally interested in how the three-dimensionality of molecules effects their function in biological systems. Indeed, as it was her childhood interest in visualizing and rendering forms in space that first led her to chemistry, the transition to sculpture based on her years of lab work and continuing studies in complex mathematics represents the completion of a circle in her life interests.
But perhaps it is more accurate to think of her sculptural work as the next turn of a continuing spiral of interests, rather than a completion; for, rather than being attempts to visualize only the very small (“the microscopic, molecular, and subatomic structures that define what we see in Nature,” as she says), Green also grapples with how to give extraordinarily tactile forms to abstract concepts that are not apparent to our ordinary senses. Some of these, like Mobius strips and knots will seem familiar even to non-specialists; others are forms particular to the field of topology.
The sculpture pictured here, for instance, takes a complex topological shape—a genus 2 orientable manifold—and translates it into an object that can be seen, but more importantly, touched, held, turned, even smelled. While some of her work involves building up a series of laminates that will allow sculpting and bending wood into elegant curves and twists, this piece was carved from natural mahogany—a wood with historical associations of both richness and exoticism, beauty and utility. The work has a satiny finish that accentuates the grain of the wood, and a surprisingly solid lightness as it is turned over and over in the hands. Twisting and rotating the object allows the beholder to look down through the two parallel voids that pierce the wood and around which it turns. With both eye and finger one can trace the flat surfaces that are first inside, then outside the curves, flowing into each other seamlessly but also seeming to pass through one another. While a computer simulation of such a shape might convey its general contours, and let us imagine how inside becomes outside, this is an object with presence in the material world, the world of human relationships as well as mathematical ones. It was made by hand, can be handled, and even given into the hands of another.
So what, then, does this work of art, and craft, and abstract mathematics have to do with the first question posed about the reality of immaterial forms, or with the appropriateness of mixing science and faith? Green has described her work as a “pursuit of truth and beauty,” and further said that “scientists, mathematicians, and artists all have an awareness of the infinite and eternal in the finite." It would be easy to hear that and affirm the complementarity of the infinite and the finite, which is nevertheless a gentle way of reasserting their distance. Indeed, a form of Platonism in which the abstract (or spiritual) realm is assumed to be the source of perfect forms, which must necessarily be debased (rather than just limited) when translated to the material is the default position of many today, whether they claim to believe or disbelieve in God.
The Christian view of the relationship between matter and spirit, the infinite and the finite, requires a complicated and on-going struggle to live out that confluence, not just argue about it. There is not one pure “spiritual ideal” in a heavenly “out there” for which we must always be ever striving in vain on account of our material selves. Rather, our ideal is the “ordinary” way spirit overlaps with matter, exemplified in the extraordinary person and life of Jesus. His example was not just to be the confluence of matter and spirit, to demonstrate that the one must flow into the other to fulfill God’s own claim on the whole creation as “very good,” but also to be the source of a flow of such integrated living in the entire human community. It was not enough for him to represent an ideal, an “abstract” of obedience, or love, or compassion; God’s purpose was that He be the material form of those things, and give Himself to be touched, and held and pierced and broken.
Debates over how mind emanates from the brain, whether consciousness is another thing in itself, and whether art, literature, and culture are “real” in the way wood and chisels are real will continue. But the solidly fine-grained work of Sue Green and other artists can help us literally hold onto the otherwise-immaterial and direct our attention to the fact that it is a hallmark of our humanity—of the imago Dei—to exist at the intersection of what we are and what we believe.
Susan Greene graduated from Wellesley College with a degree in Chemistry. She taught high-school mathematics before turning to a career doing research in both university and industrial laboratories as a liquid chromatographer. After early retirement in 2001 Susan studied sculpture at Virginia Commonwealth University in Richmond, Virginia, and with sculptor, furniture-maker and teacher Stephen Cooper. She continues to inverstigate mathematics and keeps her hand in the sciences through tutoring and lecturing. A longer article on her work (from which the quotes above are taken) appeared in the Spring 2011 issue of Hyperseeing, the journal of the International Society of the Arts, Mathematics, and Architecture. Several additional images of the Genus 2 Manifold being rotated in space by the sculptor may be seen here.