In his second show at Pierogi, Mark Reynolds continues his explorations into uncharted areas of geometric systems and harmonic grids resulting from joining unrelated ratios that share a common element, through a series of drawings.

“I experiment with geometric relationships. Many of my drawings combine geometric systems that are from different families, similar to music written in different keys without the advantages of equal temperament, yet sounding beautiful together. Or, perhaps, one piece of music is written for an Indian raga and another for a Delta Blues song. If they are played together, can they still sound good? My solution to this problem is to find a common link between the conflicting or incommensurable ratios (notes or keys) and to build on this shared unit. It may be a specific length of line, like a side or a diagonal, or the anatomy of a square or a triangle. My goal is to create harmony that resolves the initial numeric conflict, and my resolution is to draw the resulting compositional grid – a harmonic composition generated by the union of the two ratios, their shared unit, and the parts I select to join with straightedge and compass. The grid is unique to the marriage. I call them, ‘Marriages of Incommensurables,’ unions of ratios that cannot be measured together but can be constructed so that they work together. And, although the marriage is a vital component, the ‘grid’s the thing,’ for it is the grid that manifests the relationship I originally worked out. I love making the grids, and having all the intersections coincide. For me, it’s like making a map of the night sky.” (Mark Reynolds)

Reynolds is further motivated by marriages between systems that actually do resolve mathematically. These are somewhat rare in the infinite number of choices available. As he moves into more uncharted territories, he has found constructions that can be proven mathematically, with many of them at the outer reaches of the golden section family of ratios. Examples are his Mu Series, Mu Root Two Series, and Phi Root Three Series, some of which are included in this exhibition.

One of Reynolds’ early inspirations came from the idea of “Squaring the Circle,” that is, a square that has length of pi for its area or perimeter, a mathematical impossibility involving pi’s irrationality. Reynolds determined that it may be possible to square the circle when drawing in the physical world where lines must have thickness, and therefore break the mathematical rule for lines: a line has no thickness. He compounds the art/mathematics conflict inherent in drawing geometrically by regularly working with irrational numbers, numbers that cannot be measured precisely with any measuring system known. By line thickness and precision, Reynolds can compensate for almost all the discrepancies. By bringing the drawing into existence, this opportunity is presented. Also, many irrational systems used in art and architecture can be found and generated from the anatomical parts of the square, itself rational and measurable. At the same time, he always attempts to remain faithful to his original mathematical calculations. His goal is to make the drawings as beautiful and truthful as his discoveries and inventions, in spite of any art/math debates.

An aevum, according to medieval philosophers, is “the mean between time and eternity.” They used it to describe the age of angels. “I’m not sure about the angels, but geometry fits nicely into the aevum for me as well. In all my new experiments and…discoveries with geometric systems, I’m hoping that this one deeper insight is slowly coming to me: Is geometry temporal, or is it eternal? The drawings you see in the show are the result of this singular question. The complexity of the grids reflects the complexity of the question.” (Reynolds)

Mark Reynolds is an artist, geometrician, and educator. He has Bachelor’s and Master’s Degrees in Art and Art Education from Towson University in Towson, Maryland. He received an Andelot Fellowship to the University of Delaware for post-graduate work in drawing and printmaking. Additionally, Reynolds has been teaching courses in geometry and philosophical geometry to graduate and undergraduate classes at the Academy of Art University in San Francisco for over twenty years.