Artist’s Statement
4/25/13
There is a sympathetic magic between pencil and paper that is primordial. Many people have had an experience with this magic in some way. Bring geometry to the magical ceremony that we call drawing, and the power and energy of the union can be sublime and infinite, especially when geometric structures are drawn. The shapes, forms, grids, and structures that I sometimes call compositions are almost endless. Through decades of work with geometry, I have come to realize that drawing is a transformative act, and, that drawing geometrically is also a transcendental one.
Erwin Panofsky, in his Idea, a Concept in Art Theory, said that Plato conceived of the Idea as being, “in the world of shapes and figures something perfect and sublime, to which imagined form those objects not accessible to sensory perception can be related by way of imitation”. These shapes and figures of Plato’s were essentially geometric in form. If we consider the geometric aspect of reality and the structures of the universe, we are led to ponder just when geometry first became present in this universe, and that geometry may indeed be a gift from the gods. One may be led to ponder whether geometry, by its very nature, within its chi, there is a consciousness similar to our own. At least, there may be an awareness that geometry itself is a vehicle that connects the human mind with the universe of things and energies. Its mechanisms, its ways of structuring, of composing, may be inherent within geometry itself, for we did not invent geometry, we discovered it. (Perhaps there was an exception on mankind’s obsessive use of the straight line however.) I believe that geometry at least shares something with the human mind that makes mind aware of the eternal, the constant. We then ask when geometry first came into existence in the universe, and by what hand or energy or law.
Artist’s Statement
4/13/13
In art school, I loved drawing and constructing geometry enough to make it my life’s work. However, I didn’t want to go back over the techniques of Geometric Abstraction, Hard Edge Painting, Minimalism and other similar methods of drawing and painting. Although I have great respect for all of them (and I am aware that my work has elements of all these movements within it), my art is more involved with the origins of geometry, how geometry works, especially with the human mind, how it builds things, how it specifically orders space and records the development of an infinite variety of choices and structures because of the ratios and relationships inherent in the system of geometric forms.
The compositions also present these structures as composing in time as well. All things made by hand suggest this passage of time, but to me, none so acutely as the building of geometric structures, especially complex grid systems. These structures may be drawn or painted, woven, or even performed musically or poetically. All of these things mark the passing of time units. These geometries also demonstrate the process of ordering from disorder, that is, starting with the empty drawing space, then selecting an empty perimeter ratio or shape and drawing it into this bounded space.
Working with geometric systems is humbling and at times, even terrifying in its grandeur, yet always sublime and eternal. Drawing is the best tool we have for capturing the structures of geometry because of the ways the human mind interacts with this eternal force of nature. Geometry organizes the universe by number and geometric forms and shares in that creative process, giving the person drawing an ever deepening understanding of geometry’s complex workings throughout the universe.
Drawing (and the act of drawing), is a special language, and that drawing geometrically brings with it a specific kind of wisdom that includes an unspoken language of its own, a language that does not use words. Geometry is not narrative, even though we may talk about it. And, I believe, it is much more than an object, a thing. I sense that geometry is alive.
Even as the artist fulfills his function of geometrician and mechanic, of physicist and chemist, of psychologist and historian, so does form, guided by the play and interplay of metamorphoses, go forever forward, by its own necessity, toward its own liberty.
-Henri Focillon
The Life of Forms in Art
Artist’s Statement
April 7, 2013
The visual space between chaos and order have predominated my work for the last several years. I’ve always composed with both the rational world of whole number/musical ratios, and also the irrational systems like the golden section, the square root series, and other families of ratios. I became increasingly interested in the development of contrasting, conflicting, and incommensurable pairs of ratios to see if I can find – and construct – two different systems of geometry not usually found together in a family of ratios or as a part of a larger system of relationships and structures. The musical ratios can be easily measured and built, but an irrational ratio, like the golden section, is very demanding in its construction. The elements of the system – the relationships within the grid – are rigorously drawn. The irrational quantities cannot simply be calculated by reckoning, but only constructed. This may be ironic in the light of how wonderfully, and seemingly perfectly, geometry can structure and build so very many things in the world that are indeed based on numbers that cannot be measured.
My searches have brought me to being able to find one element in two vastly different geometric systems that have one thing in common, usually a specific length or shape they have in common. This element is the unifying agent between the two systems. But joining these systems together can also create chaotic relationships between and within the grids, the harmonics, of these two vastly different systems. And although there are precious moments where the two energy fields interact in astounding and beautiful ways that until now, have never existed before, there are also grid lines that behave almost like the tracks of subatomic particles in their erratic dances.
These demands of precision and the energy required to produce this type of drawing is motivated primarily by my pure curiosity and wonder about these new worlds of structures that are born from the marriages look like as drawings. I am fascinated by their appearance and structure. It’s exciting as can be, and it gives me a bit of insight about how it might have been like in the very beginning of the building of all things.
Without hands there is no geometry, for we need straight lines and circles to speculate on the properties of extension. Before we could recognize pyramids, cones, and spirals in shells and crystals, was it not essential that man should first “play with” regular forms in the air and on the sand? Man’s hands set before his eyes the evidence of variable numbers, greater or smaller, according to the folding and unfolding of his fingers.
-Henri Focillon
The Life of Forms in Art
Artist’s Statement
5/7/13
Lebbeus Woods is a great drawer. I see myself as being like minded on the geometric
level, but my drawings are not so politically or socially minded. We were fortunate to have
Woods with us.
Mark A. Reynolds
SFMOMA, April, 2013
I have a responsibility to the geometry I draw to be as perfect as I can be, and to make it as beautiful as possible. The task is difficult because of the physical limitations of attempting to draw something that only truly exists in the Platonic sense of the ‘absolute’, in a place other than the world’s physical limitations.
My physical lines are also a generation removed from the mathematicians’ have-no- thickness lines. I have to bring the geometry into the physical, and therefore, limited, world. So the drawing is faced with mathematical impossibilities. At the same time, it still must be as precise as is humanly possible in order to be true to the geometry’s measures, both rational and irrational numerically. I must draw as precisely as possible to try to bring all the irrational elements of an irrational system, like the golden section or the square root of two, into alignment and exactitude. All the points and lines must meet in a totally harmonious field of energy we call the grid, and that everything corresponds with all else, all working together to make a beautiful whole. Drawing to this end is transformative for body, mind, and spirit.
Pencil and paper have a sympathetic magic. Geometry, having always been drawn, enters into this sympathetic magic with its own unique qualities. Drawing geometrically consists of the construction of a specific group of geometric elements – shapes, ratios, lengths, angles – seeking harmony within that universe of geometric elements by specific selections of those harmonies, those structures, which are exquisite and sublime to the drawer. The choice of geometric systems becomes boundless by the power of human thought and creative action with the these geometric systems.
Geometry is one of the first things intelligent mind laid out and diagrammed. It can, and often does, intercede where disorder, chaos, and order are gathered.
Geometry has been with us for a very long time. It is a part of us. I have reverence for both it and its obscure and ancient origins in the universe. Because of this, my drawings deserve the best materials and my best hand to make them all as beautiful as I can. The Form/Light paradigm is a source of pleasure and intrigue for me. I love all forms and all light. But geometric form is my best way to enter into a relationship with the infinite, perhaps even into what Plato called the absolute.
My drawings are the result of years of study, experiment, exploration, and meditation. I have studied examples of thousands of years of geometry in art and architecture. Using what is already known in mathematics, nature, painting, and architecture, I have been able to take geometry farther now, yet there is no end to the explorations. Much more than I could ever do. Others can now go farther than I have gone. Geometry is a marvelous tool, a gift no doubt.