Marriage of Incommensurables Series: Serlio and KCW Triangles, Triple Root Five, 6.21
Marriage of Incommensurables Series: the Serlio and KCW Triangles, 4.21.21
Marriage of Incommensurables Series: The 1.382, 2.1.21
Marriage of Incommensurables Series: The 1.382, 4.7.21
NNJ_v10n1_Reynolds_pp051-076 Leonardo
Thales Series: ATROW, the 1.118, 8.12.19
Theta Series: Molecular Drop, 1.19
Thales Series: ATROTW, Sq. Rt. 5, 5.8.19
Minor Third Series: Another Nod to Pythagoras, 12.18
Thales Series: ATROTW, Three Metallic Means, 7.19
Thales Series: ATROTW, Sq Rt Phi, Mu, and Compounds, 6.18.19
Thales Series: ATROTW, The 1.111, 5.19
Thales Series: ATROTW, The Great Square, 5.19
Thales Series, ATROTW, Root Rectangles and the DROC System, 6.19
Thales Series: ATROTW, Quadruple Square Group, 6.19
Thales Series: ATROTW, Sq Rt Three Family, 7.7.19
Thales Series: ATROTW, Gold and Silver Means, the Triple Square, 7.18.19
Square Root Phi Series: Movements in the Pyramid, # 49, 4.25.18
Link to the show here:
Order Chaos Disorder
My drawings present a determined search for new levels of order. However, as is often the case in my work, when hostile environments are present in the form of competing geometric systems or from pushing the limits and boundaries of known geometric shapes and ratios, order may be jeopardized. Potential chaos or even disorder may lurk behind the next line that is drawn. When constructing grids of increasing complexity, the issues of order, chaos, and disorder become more relevant to the success or failure of the internal harmonics of the grid and the overall appearance of the drawing. Coupled with variations in line thicknesses, the physical limitations of drawing mediums, and irrational lengths (lengths that cannot be measured with a ruler) that exist in many geometric forms and systems, the effort necessary to keep the grid orderly becomes more demanding. Although the initial ratio can be managed in a fairly easily way to create an orderly space, as the grid grows in complexity, a state of chaotic relationships may possibly be generated, and may then pass into a complete state of chaos. Chaos can then lead to disorder in the details and eventual misalignments of the intersections and placement of lines. Any further development of the grid only serves to advance the disorderly state.
At times, chaos has hidden order within it. This sometimes becomes evident by changing one’s perception of the space that the chaotic conditions appear to be in. Usually, the repeated applications of order can make things somewhat chaotic, but still manageable. Disorder, however, is a “point of no return” to order. Disorder is the opposite of order. It is at the point of no return that the drawing must be abandoned or begun anew. Erasure is not an option due to nature of the work. Time and daily practice have made the issue of disorder far less common for me, but it still occurs on rare occasion. Still, it is a humbling experience, as are many things in the production of art.
I work this way because the rewards are great, especially when discoveries are made that did not exist before.* There are also times when a grid will reveal some surreal or yantra-like (yantra: Sanskrit for a machine, a “contraption”, a mystical diagram) imagery in the lattice work, or when some problem in geometry has a solution with a very low percent deviation, or even when some hitherto unknown solution to a classical problem is discovered that can be mathematically proven. But more than all this, I draw these geometries because they are unique, intriguing, and beautiful to me. I believe the drawings would lose these qualities if I were to use computer technology to assist me. Because my ancient brethren in Egypt and Greece drew their geometry by hand with only compass and straightedge, out of respect for them and for tradition, I do the same. I think the drawings carry more authority and weight because of this. I also like to see the artist’s hand in the ways pencil and paper meet.
The presence of geometry everywhere inspires me. Geometry and numbers are, among other things, ordering systems found throughout the universe. Grids are related to geometry and numbers, and are themselves ordering systems. They can bring order to a space by defining the structure and energy within the limits set by that space, and by generating the specific geometric qualities that are present within the space. The structure of these geometric details is sometimes called a lattice or armature, and may be referred to as a harmonic deconstruction. These constructions and the forms and relationships that are manifested within them are mechanisms that bring me into close contact with the universal qualities of geometry.
I am an artist, not a mathematician, but I know that geometry is a bridge that can connect the two disciplines. For me, art and mathematics are two sides of a coin composed of geometry and numbers, and as such, geometry provides both the artist and mathematician with an elegant and beautiful system that offers solutions to questions of space and time, and a way to order like no other.
Drawing grids requires an understanding of the power of the limits and the geometric “content” of a particular space. The resulting compositional grid has a certain beauty and quality unique to the specific space in which it is contained. The question is always just how simple or complex the grid should be, and if something wondrous and worthwhile comes from the effort of maintaining order over chaos and disorder in the grid structures and the specific ratios I develop.
——
* A recent discovery of mine is an irregular tetrahedron (four triangular faces) I created that combines two well known musical ratios with the well-known irrational ratios: the square root and golden section families. This tetrahedron can be seen in my 2018 show at Pierogi Gallery.
Minor Third Series: Meson Shift 100, 1.17.17
Phi Series: Primal Moment of the Square, Rectangle, and 90 Degree Angle, 6.15
Square Root Phi Series: Further Disruptions, IV, 5.17
Marriage of Incommensurables Series: The Equilateral Triangle and The Khufu Pyramid Elevation, 7.17
Square Series: Union with the Minor Third Series, 5.17
Square Series: Golden Ogees, 7.17
Thales Series: All the Rectangles of the World with the Yin-yang, 9.17
Square Series: Curvature of a Harmonic Progression, 8.19.16
Square Root Phi Series: Clusters of Music with an Eclipse, 9.17
Minor Third Series: Meson Shift 99, 1.17.17
Mu Series: Anniversary 28, 12.10.10
MARK A. REYNOLDS
E mail: [email protected]
Website: www.markareynolds.com
Pierogi Gallery: https://www.pierogi2000.com/artists/mark-reynolds/
CHRONOLOGY
Education
1971 Master’s Degree in Art and Art Education, Towson University, Towson, Maryland
1970-71 Andelot Fellowship, University of Delaware, Printmaking/Drawing, Newark, Delaware
1967 BS, Art and Art Education, Towson University, Towson, Maryland
Exhibitions – Solo
2018 Order Chaos Disorder, Pierogi Gallery, New York, NY
2015 Deeper Secrets and the Aevum of Geometry, Pierogi Gallery, Brooklyn, NY
2013 Compositions, Pierogi Gallery, Brooklyn, NY
2000 New Monotypes; Ancient Ratios, Ebert Gallery, San Francisco, CA
1999 Movements in the Pyramid, Mill & Short Gallery, San Francisco, CA
1998 Sacred Geometry, Mill & Short Gallery, San Francisco, CA
1995 Recent Prints, Mill Valley Arts Commission/Mill Valley Library, Mill Valley, CA
1993 Gallery Route One/LAP Project Resource Center, Point Reyes, CA
1992 School of Humanities & Sciences, Stanford University, Stanford, CA
1987 Kaiser Rich Gallery, Baltimore, MD
1974 One Man Show, Taylor Manor, Ellicott City, MD
1966 First Works, Church of the Redeemer, Baltimore, MD
Exhibitions – Group
2022 Make Art Not War, Pierogi Gallery, Brooklyn, NY
2021 Pulp at Pierogi, Pierogi Galley, Brooklyn, NY
2021 Naked in Brooklyn,. Pierogi Gallery, New York, NY
2020 First, Second, and Third Person, Pierogi Gallery, New York, NY
2018 Courtesy of, Transmitter Gallery, New York, NY
2018 The Idiosyncratic Pencil Resharpened, Stone Harper Gallery, Presbyterian College, Clinton, SC
2017 Double Down, Pierogi Gallery, New York, NY
2017 The Armory Show, Booth 740, New York, NY
2016 UNTITLED, Miami, Florida
The Armory Show, New York, NY
Rage for Art (Once Again), Inaugural Exhibition, Pierogi Gallery, New York, NY
2015 The Armory Show, New York, NY
2014 Twentieth Anniversary Show, Pierogi Gallery, Brooklyn, NY
Volta 10, Basel Art Fair, Basel, Switzerland
The Armory Show, New York, NY
2013 Unhinged, Pierogi Gallery, Brooklyn, NY
2007 Narrative and Geometric Paintings and Drawings, Atrium Gallery, San Francisco, CA
2005 Hanlon & Reynolds: Two Person Show, City Picture Frame Gallery, San Francisco, CA
2004 California Society of Printmakers Annual Show, Bay Model, Sausalito, CA
2001 Sacred Images: Spirituality Through Art, (Jurors’ Section), Artisan’s Gallery, Mill Valley, CA
2000 California Society of Printmakers Annual Show, College of Marin, Greenbrae, CA
Guarding/Discarding Traditional Techniques in the Digital Age, Marin Civic Center, San Rafael, CA
1999 Myth and Magic, Fetterley Gallery, Vallejo Community Arts Foundation, Vallejo, CA
1998 Under Pressure: Prints and Books from LAPS Exhibition, Cerritos College, Norwalk, CA
California Society of Printmakers: 85th Anniversary Exhibition, Academy of Art College Gallery, San
Francisco, CA
1997 The Workshop Show/Sight and Insight, the O’Hanlon Center, Mill Valley, CA
Beyond Boundaries, Richmond Art Center, Richmond, CA
1996 Altar-ed Images, Falkirk Cultural Center, San Rafael, CA
Fifth Annual Marin Arts Council Exhibition, Town Center, Corte Madera
The Human Figure (Clothing Optional), Artisans Gallery, Mill Valley, CA
Watermark: Works on Paper, Gallery Concord, Concord, CA
Two Person Show: The Marin Theater Company, Mill Valley, CA
1995 Fourth Annual Marin Arts Council Membership Exhibition, Town Center, Corte Madera, CA
1995 Membership Show: California Society of Printmakers, Concepts Gallery, Walnut Creek, CA
Fall Faculty Show, Academy of Art College, San Francisco, CA
Janet Turner National Print Competition Exhibition, Janet Turner Print Gallery, California State
University, Chico, CA
All Saints, All Souls, Falkirk Cultural Center, San Rafael, CA
Second Annual Marin Images: Inside & Out, Marin Community Foundation, Larkspur Landing, CA
1994 Third Annual Marin Arts Council Membership Exhibition, Town Center Corte Madera, CA
Fifth Annual Miniature Invitational Exhibition, Bolinas Museum, Bolinas, CA
Altars and Masks, Skyline College, San Bruno, CA
Diversity and Vision of the Printed Image; California Society of Printmakers, Triton Museum of Art,
Santa Clara, CA
Fine Arts Faculty Show, Academy of Art College, San Francisco, CA
Marin Images: Inside and Out, Marin Community Foundation, Larkspur Landing, CA
Art as a Mirror for the Soul, San Francisco State University, San Francisco, CA
Spring Faculty Show, Academy of Art College, San Francisco, CA
1993 Fourth Annual Miniature Invitational Exhibition, Bolinas Museum, Bolinas, CA
California Society of Printmakers: 1993 Members Show, Mission Cultural Center, San Francisco, CA
Second Annual Marin Arts Council Membership Exhibition, Corte Madera, CA
California Small Works 1993, CA Museum of Art, Luther Burbank Center for the Arts,
Santa Rosa, CA
Printmaker’s Fine Impressions, Center for Global Spirituality, Tiburon, CA
Self Portraits in Black & White, Edith Caldwell Gallery, San Francisco, CA
1993 Lenten Arts Festival, First Presbyterian Church, San Anselmo, CA
Foundations Dept. Faculty Show, Gallery 99, Academy of Art, San Francisco, CA
Fine Art Faculty Show, Gallery 625, Academy of Art, San Francisco, CA
1992 Third Annual Miniature Exhibition, Bolinas Museum, Bolinas, CA
Calif. Society of Printmakers: 1992 Membership Show, Art Concept Gallery, Walnut Creek, CA
1st Annual Marin Arts Council Artists’ Exhibition & Readings, College of Marin, Kentfield, CA
Living Arts Project Exhibition, California Arts Council, Sacramento, CA
Sacred Image/Sacred Space, Bolinas Museum, Bolinas, CA
1991 The Great Marin String Along, College of Marin, Kentfield, CA
1991 Miniature Show, Bolinas Museum, Bolinas, CA
Something Small for the Wall, SOMAR Gallery, San Francisco, CA
Surrealist Salon, Rayko Photo Center, San Francisco, CA
Artists Look at War, Bolinas Museum, Bolinas, CA
Black and White, Gallery Sanchez, San Francisco, CA
Printmakers, Artisans, Mill Valley, CA
1991 Faculty Show, Academy of Art, San Francisco, CA
Claudia Chapline Gallery, Stinson Beach, CA
1990 1990 Miniature Invitational Exhibition, Bolinas Museum, Bolinas, CA
Small Works Annual Juried Exhibition, Bolinas Museum, Bolinas, CA
Facades Imaginaires, Place Feliz-Poulat a Grenoble, Grenoble, France
Bolinas Living Artists Project: Stinson Beach, Bolinas Museum, Bolinas, CA
1989 Ninth Autumn Annual, Gallery Sanchez, San Francisco, CA
Eroticism: West Coast Expression, Gallery Six-Oh-One, San Francisco, CA
Art of the Automobile, Sears Point National Raceway, Sonoma, CA
Open Fine Arts Exhibition, 1989, Marin Society of Artists, Ross, CA
14th Annual Juried Exhibition, Falkirk Cultural Center, San Rafael, CA
1988 Christmas Show, Cuisine Perel Gallery, Tiburon, CA
Christmas Show, Cafe, Cafe, Mill Valley, CA
Dundalk Art Festival, Dundalk, MD
1987 Fells Point Marine Art Gallery, Baltimore, MD
Fells Point Art Festival, Baltimore, MD
Towson Art Festival, Towson, MD
1984 Maryland Biennial Show, Annapolis, MD
1980 Towson Arts & Crafts Show, Towson, MD
1978 27th Courthouse Arts Festival, Towson, MD
1976 art & animals, art etc., inc., Baltimore, MD
1972 Baltimore Museum of Art Regional Show, Baltimore Museum of Art, Baltimore, MD
Employment:
Education
1990-2015 Art Instructor, Graduate/Undergraduate Schools, Academy of Art University, San Francisco,
CA (Classes include Sacred Geometry, Drawing, Printmaking, and Perspective)
1980-81 Lecturer in Art History, Catonsville Community College, Catonsville, MD
1973-75 Instructor in Mandala Drawing, AUM Esoteric Study Center, Baltimore, MD
1967-69 Art Teacher, Baltimore Public Schools, Baltimore, MD
Art Related
2008 Nexus VII: Architecture and Mathematics Conference, 2008; Presentation: “The Salk: A
Geometrical Analysis Supported by Historical Evidence”; San Diego, CA
2004 Nexus V: Architecture and Mathematics Conference, 2004; Presentation: “A New
Geometric Analysis of Teotihuacan”; Mexico City, Mexico
2003 Participant in the scholarly project, Leonardo: Mathematics and Architecture, Vinci, Italy
1999-2006 Contributing Editor for www.nexusjournal.com, writing the Geometer’s Angle Column
2001-present Mentor: Faculty Mentoring Program, the Academy of Art University, San Francisco, CA
2000 Nexus III: Architecture and Mathematics Conference, 2000; Presentation: “A New
Geometric Analysis of the Pazzi Chapel”; Ferarra, Italy
1999 On site geometer, Egyptian Cultural Heritage Operation (ECHO), Cairo and Alexandria, Egypt
1991-93 Member, Board of Directors, Bolinas Museum, Bolinas CA
Chairman, Living Artists Project, Bolinas Museum, Bolinas, CA
1980-89 Freelance Commercial Illustrator/Designer (Baltimore/New York Corridor)
1986-89 Independent publishing & marketing of limited edition prints from my original artwork
1975-76 Member, Maryland Bicentennial Committee for the Arts
1975 Coordinator, Beautiful Walls for Baltimore Mural Project/Mayor’s Office, City of Baltimore
1974 Mural, AUM Esoteric Study Center, Baltimore, MD
1972-74 Artist/Illustrator, Becker Corporation, Baltimore, MD
Bibliography
“Deeper Secrets and the Aevum of Geometry” reviewed in The New Yorker Magazine, July 6, 2015
“Deeper Secrets and the Aevum of Geometry” mentioned in Beauty and Well Being, “Summer in the City”, July 24, 2015
“Deeper Secrets and the Aevum of Geometry” previewed in NYC Ephemera, June 3, 2015
“Deeper Secrets and the Aevum of Geometry” mentioned in ARTnews’ “9 Art Events to Attend in New York City this week”, June 9, 2015
Three articles on geometric analysis published by Springer Publishing,, Architecture and Mathematics from Antiquity to the Future, 2015
Interview in ARTnews Magazine, September, 2015 issue, “Mark Reynolds: Rational Art About Irrational Numbers”, 2014
Article and six drawings published in the 13th Annual Issue of Fukt Magazine for Contemporary Drawing, 2014
Interview with “The Bottom Line” blog, produced by The Drawing Center, 2013
“Compositions” reviewed in Whitehot Magazine of Contemporary Art, 2013
“Compositions” reviewed by New York Art Beat, 2013
“Compositions” featured in Wall Street International , 2013
Awards and Honors
2011 Accepted into the Viewing Program at The Drawing Center in New York,
www.drawingcenter.org/viewingprogram/ in 2010
1993 Outstanding Educator of the Year, Academy of Art University, San Francisco, CA
1987 Second Place, Professional Artists – Fells Point Art Festival, Baltimore, MD
1978 Second Place, Professional Artists – 27th Courthouse Arts Festival, Towson, MD
1970 Best-in-Show Award, 17th Annual Baltimore Outdoor Art Show, Baltimore, MD
1970 Andelot Fellowship, University of Delaware, Newark, DE
Collections
Eleanor D. Wilson Museum, Hollins University, Roanoake, VA
Achenbach Foundation for Graphic Art, The Fine Arts Museums of San Francisco, San Francisco, CA
Biblioteca Comunale Leonardiana (The Leonardo Da Vinci Library) in Vinci, Italy
Crocker Art Museum, Californian and American Art: Permanent Collections, Sacramento, CA
Saginaw Art Museum, Works on Paper Collection, Saginaw, MI
University of California-Davis, Nelson Gallery, Davis, CA
University of Maryland Print Collection, College Park, MD
Public Collections
AT&T
Baltimore Sunpapers
Becton Dickinson, Inc.
Black & Decker
Citibank
Coldwell Banker
Johns Hopkins Hospital
Legg Mason
Marriott Corporation
Mayor’s Office, City of Baltimore
McCormick & Company Spices
Proctor & Gamble
USF&G
Warner Brothers/Warner Communications
Westinghouse
Williams & Wilkens Publishing Company
Phi Root Three Series with the Rho Rectangle (2.8025).2.18.15
The 1.111 Series: 5.5.14
Phi Square Root Phi Series: 11.27.13
Mu Nu Series: Aperture Overture, 11.11.14
The 1.366 Series: Ode to Matins, 5.29.16
Phi Series with The Minor Third and The Golden Section, IV, 4.21.16
Square Root Phi Series: Pulsations on the Horizon, 5.1.16
The 1.111 Series: Archways and Columns, 4.14
Musical Ratio Series: Minor Third and Major Fourth, 11.14
Greater and Lesser Dyad Series: Nocturne, 3.27.16
Mu Nu Series: Tulpa Twenty-Three, 5.13.16
Mu Nu Series: Tulpa Twenty-Two, 5.1.16
Spiritual Jukebox Series: Ode to Dr. Hawking, 5.4.16
Mu Series: Rising Stars, 6.16
Root Five Series Transfiguration Mound, 5.16.16
Phi Root Three Series, the Rho Rectangle in a Phi Rectangle, 11.15
Phi Series: Earth Tulpa, 9.4.15
Phi Series: What Would Hilma Do? 11.15
Phi Series: Alchemical Still with Alembic, 10.4.15
It’s an adorable subject for me,” Mark Reynolds says about geometry. “It has a consciousness. It’s not dry; it’s musical, poetic, and speculative.” The San Francisco–based artist is known for his obsessive, seductive drawings that derive primarily from mathematical relations, expressed, as he describes it, in “shape, size, relative position of figures, and the properties of space.”
Dizzyingly shifting perspectives and kaleidoscopic effects entrap viewers in such a way that their eyes can never rest. Reynolds likes to work mostly with 15-by-22-inch paper, and he draws primarily with powdered pigments, graphite, pen and ink, and pastel—“usually dry media,” he says.
The 69-year-old Baltimore-born artist teaches at the Academy of Art University in San Francisco in the liberal arts department. He spends considerable time in Italy and is represented by Pierogi Gallery in New York.
Reynolds attended Towson University in Maryland, where he studied fine art and art education. He started out doing freelance illustration and design, including advertising art and romance-book covers. “At the beginning, I was doing kind of surreal work—I looked for subject matter in clouds,” Reynolds says, emphasizing how he focused on color, line, and shape—“not narrative.” And that inclination persists in his art, which draws inspiration from music, art history, and architecture.
His drawings are distinguished by the disjunctions between their soft-colored lines and sharp angles. Filled with surprises, his work disarmingly calls to mind that of Piero della Francesca, in its colors and deep perspectives, Paul Klee, in its musicality and lyricism, and Sol LeWitt, in its varying geometries. Reynolds’s most recent pieces, he says, are based on the golden section family of ratios, or divine proportion, which governs ratios in patterns found throughout nature and the human body. “One new series has put mirror symmetry—bilateral like our faces—into my work, big time. It’s taken some getting used to for me.”
Explaining his approach, Reynolds says, “I deal with irrational numbers that can’t be measured. I try to begin with two ratios and put unlikely ones together. It’s like rap and Mozart, or Beethoven and the Beastie Boys—you put them together and something new emerges.”
Music itself, with its emotional and spiritual associations and effects, is very much a part of the work. The relationship between two lines of different lengths could equate with the strings of a piano, for example. The compositional grids in his drawings can be viewed as the result of the vibrations of two strings. “I’m working with harmonics,” Reynolds explains, “which change based on the lengths of the lines.” A high sound is produced by a short string on an instrument, whereas a long string yields a low sound. Reynolds can hear sound through such visual cues as the length of lines, as in his Marriage of Incommensurables Series: 1.902 and Root 2, 4.13 (2013).
Studies have shown that “the minor third is the saddest sound in music,” he says. So if you produce an image of a minor chord, visualizing it can have the effect of the sound, and that’s one source of emotional resonance in his work.
“While many art students go through their drawing courses working from life,” Reynolds says, “I don’t have many external references.” Geometry enables him to avoid, he points out, “narrative, social, political, sexual, athletic, hierarchical, fashionable, and other debate-filled issues.”
“I know I’m an artist, not a mathematician,” Reynolds says, “but sometimes when I’m around artists, I feel that I am a mathematician. The funny thing is, I’m not gifted with numbers, just geometry.”
A version of this story originally appeared in the September 2014 issue of ArtNews on page 56 under the title “Rational Art About Irrational Numbers”.
I am represented by Pierogi Gallery in Williamsburg, Brooklyn, New York, www.pierogi2000.com
My work can also be seen and purchased at The Dryansky Gallery on Union Street, San Francisco, www.thedryansky.com galleries
Square Root Phi Series: Evolution of the Planetary Fan, 11.13
New Yorker Magazine, July 6 & 13, 2015
Galleries-Brooklyn
Mark Reynolds
Pierogi
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.
The 1.111 Series, 5.5.14
Greater and Lesser Dyad Series: Integration of the Phi Family and the First Three Roots, 1.30.15
Minor Third Series: Nods to Pythagoras, 2.1.15
Phi Series: Root 5 Grouping, 1.15.15
The Phi Root Two Seies: Tulpa XII, 12.13.14
Minor Third Series: A Grouping of Root Fives, 2.1.15
Marriage of Incommensurables Series: the Roots and Phi, 2.18.15
The 1.111 Series: 5.9.14
The 1.111 Series: 2.9.14 2014
Phi/Square Root Phi Series: 1.3.14 2014
Greater and Lesser Dyad Series: Square Root Phi and Root Two, 7.13
Greater and Lesser Dyad Series: Phi and Root Three, 7.13
Spiritual Jukebox Series: Ode to Turing Patterns, 2013
Mu Root Two Series: Wedge, 2013
Minor Third Series: Vortex Sound, 2013
Minor Third Series with Related Notes, 2013
Greater and Lesser Dyad Series, 8.13
Double Mu Series: Square Root Phi Space, 2013
Dear friends and visitors to my site,
I am now represented by Pierogi Gallery in Williamsburg, Brooklyn, New York. Here is the link to the Pierogi homepage:
http://www.pierogi2000.com/
Also, here is the link to my most recent show there:
Thank you, and please feel free to contact me at [email protected] with questions or comments.
Best wishes,
Mark A. Reynolds
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.
Artist’s Statement
Mark A. Reynolds
Compositions
Pierogi Gallery
June, 2013
Light is to the Natural World as Abstract Space is to Geometry.
– Robert Grosseteste 1112
Where there is mathematical form, there is consciousness and spirit, and there is the hope of an experience with the Eternal. When mind encounters this mathematical form, it often takes the form of geometric constructions and harmonic systems.
– Mark A. Reynolds, 2012
Many of the drawings in the Pierogi show are taken from different meldings of systems of geometry that are not related or numerically commensurate, and attempting to make them so. I call these compositions, ‘Marriages of Incommensurables’, and some of them, ‘Unions of Opposites’. I am interested in the structures and the images – the forms – that result from these meldings.
I also explore the armatures of specific ratios found, for example, in the whole number/musical ratios, the golden section family of ratios, and the square root rectangle series. Sometimes, I look into the more unknown ratios within these three families, or I may invent ratios of my own that I find intriguing.
Great care is given to the drawing because I want to know exactly what the relationship will look like, what it will become, what harmonies, tonal qualities, or discordant passages it will contain. These structures have never been seen before, even though the history of geometry goes back probably to the beginning of time itself. The nature of geometry is to compose. Each resulting composition is uniquely harmonic by the method in which it was drawn and what was chosen to be the unifying geometric principle for that drawing. Much depends on this original marriage, what specifically was being employed in the geometric construction involved in the union. Certain principles of geometry – ratios, proportioning systems, harmonic resonances or discordances – interface within the relationship. I make it visible by drawing the resulting geometric forms.
Approaching the geometry this way is also an exciting journey into the world of geometry that is so old as to be eternal. We don’t know when or where the forming of geometry first took place, and what the nature of the creative forces were that brought geometry into our universe. I do know that drawing these various systems of geometric structures is exciting, meditative, exhilarating, and humbling.
Double Square Series: Roots and Harmonics
Minor Third Series: Harmonics, 8.22.11
Square Series: Piston Effect, 12.10
Minor Third Series: Transitions from Diagonal and Half-diagonal, 1.13
Square Root Phi Series: Meanders, 2.13
Spiritual Jukebox Series: IX, 8.12
Square Root Phi Series: Ode to Crustaceans, 8.12
The 1.111 Series: Ode to John Cage, 2.13
Minor Third Series: Phi Harmonics and Overtones
Marriage of Incommensurables Series: 1.902 and Root 2, 4.13
The 1.111 Series: Warmth, 3.11
Greater and Lesser Dyad Series: Two Ogee Curves
“Musical Ratios Series: 6 to 7”
“Spiritual Jukebox Series: Ode to Moons”
Square Root Phi Series: Disrp.7.2.10B
Geometry means “measure of the earth” but it is in fact far more than just this. Geometry is interdisciplinary, multidimensional, universal, absolute, eternal, elemental, and essential. At the same time, geometry is a noble and exalted gift, not base, crude, or sinister. It is the most pure of art forms, and pays homage to eternity and the cosmos. It may suggest a greater reality yet is complete wherever it is found. Geometry is the visual representation of numbers in their most elementary form, whether these numbers are rational or irrational. Without geometry, disorder would overwhelm order, the cosmos as we know it would not exist, and art would have no form. No one knows when and where geometry first came into existence in the universe. We only know that geometry was discovered, not invented.
I use geometry in my art work because of its universal, clear, and spiritual nature, for its ability to address and unify the formal aspects of art: point, line, shape, ratio, light, and color, and for its avoidance of narrative, social, political, sexual, athletic, hierarchical, fashionable, and other debate-filled issues.
There are several sources for my work:
1. My own discoveries, explorations, and inventions using geometric systems
2. Geometric analyses of ancient and classical architecture and painting
3. Geometric systems found in the natural world and in the human body
4. Classical and contemporary studies in number and geometry
Paramount in my work is the art and science of grid making: perimeters, fields, intersections, and relationships of structures and patterns within defined areas. These areas are set by sacred ratios that can be discussed in metaphysical terms, and their grids are linear representations of the various energy fields found in all geometric shapes and forms. These fields are generated by the relationships of the geometric parts and by the mind’s involvement in perceiving and defining those parts. All grids are selected from an infinitely large number of possibilities, edited, and developed.
The spiritual qualities of geometry and the physical aspects of drawing and painting geometric systems are key aspects of my efforts to take geometry farther than any artist in history. I have come to know that it is as much the geometry working with me as me working with it. I am humbled to be a part of this process.
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