When a Greek mathematician discovered that the square root of two was irrational, his fellow-Pythagoreans threw him into the sea (so the story goes). If only those philosophers could see the exquisite drawings of this San Francisco-based artist, who, armed with straightedge and compass, transmutes the mysteries of geometry into dense meshes of colored lines, alive with spiritual intensity. The drawings are marvels of harmony, their beauty compounded by Reynolds’s subtle pastel shading. In the margin of one thicket of rectangles, the artist has scribbled a note that would make a Pythagorean proud: “There is always order. The trick is to find it sometimes.” Through July 12.
http://www.newyorker.com/goings-on-about-town/art/mark-reynolds
Deeper Secrets and the Aevum of Geometry
Mark A. Reynolds – Pierogi June, 2015
In his second show at Pierogi, Mark Reynolds continues explorations into uncharted areas of geometric systems and harmonic grids resulting from joining unrelated ratios that share a common element. “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, do they still sound good? My solution to the 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 originally worked out. I love making the grids, and having all the intersections coincide. For me, it’s like making a map of night sky.”
Mark is further motivated by marriages between systems that actually do resolve mathematically. These are somewhat rare. As he moves into more uncharted territories, he has found constructions that can be proven mathematically, with most 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 these works may be seen in the current show.
One of Mark’s 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.
The “aevum” in the title for this exhibition is the “mean between time and eternity”. Aevum was defined by philosophers of the Middle Ages who cited the age of angels as an example of the aevum, believing angels were originally created by a divinity but will live forever. Mark isn’t positive about the angels, but he believes that geometry is another example of the aevum. The ever-present question for him is whether geometry is a part of time or is itself eternal. If it is a temporal issue, exactly when, where, and how did geometry, and number, come to be?
For Mark Reynolds, the presence of geometry in the systems and forms of nature and space-time is evidence of an underlying order that exists even in the turbulent birth and death of stars. Geometry has been a constant in evolution, a proof of order even within disorder. In the scientifically reductionist world view currently running rampant, Mark finds ever deepening spiritual components in his drawings. He believes in geometry’s ability to work well with the human mind. He senses that geometry may share consciousness with mind and spirit, and that geometry may in fact be an organic, living substance. Drawing geometric structures are a respite for him, and a joy to experiment with. His drawings bear witness to his enjoyment of the process of resolving those incommensurable relationships in marriage. And, while he continues to compose with his already tested rational relationships, like the musical ratios or the haunting marriages of several irrational ratios found in the Great Pyramid, he remains excited about his new discoveries and those that await him. For Reynolds, geometry is evolving, and we are all a part of it.