The Dificulty In Bridging The Genres of Mathematics and Poetry

    The creative process is one of bridging concepts together to create an expression. I have always wondered if I was indeed bridging mathematics and poetry. So, I put a poll together on this blog to query the readers and find out what end of the spectrum they reside. It turned out that the blog consistently had a 50% split between both mathematics and poetry for the 5 years the poll existed. I feel lucky to have landed in this spot yet, existing in the cracks of genres is never a popular place to be. That said I feel confident that bridging is extremely worthwhile. Creativity is always spawned in the cracks of genres. 

    I would like to share evidence of bridging this gap between the institutions of mathematics and the institutions of poetry. On one hand I had a poem published in the "page a day" calendar for the American Mathematical Society. Here is the letter requesting the poem for Basho:

    Here is the mathematical poem Evelyn chose for the calendar:

 

    And on the other hand, I had one of my mathematical poems nominated by the prestigious literary journal ZYZZYVA, for a pushcart prize in poetry. Here is the letter notifying me that the poem was nominated:

     

    Here is the math poem they nominated:

Joint Meeting of the American Mathematical Society and Mathematical Association of America Conference 2009

This blog entry is to share a few moments and images of the AMS and MAA Joint Meeting held this year in Washington D.C. The first lonely image is a view from my hotel room bed as I tried to get to sleep by counting the sheep jumping over the Washington Monument. The weather for the most part was cold and rainy and made my three-quarter mile walk to the conference a little trying at times. However the last day was nice and offered the image below which was shot from my hotel room window as the sun was rising in the east.

The shot below is a 180 degree panoramic view of 21 images sewn together to provide an overview of the entire show of mathart. The show is always modestly done due to its modest budget (relative to art galleries) but it is always done well and the people who work on it are wonderful enthusiastic individuals who feel mathart can make a difference. They even gave out prizes this year.
The shot below is of the past president of the Mathematical Association of America, Joseph Gallian as he was browsing the show.

Speaking of browsing the show … The next image (below) is of our friend Ivars Peterson who writes about mathart for many publications including Science News.

From left to right: Reza Sarhangi the nucleus of the Bridges Conference on mathematical connections in art music and architecture , Annette Emerson, the Public Relations Officer of the AMS and Anne Burns, one of the Judges for the mathart exhibit and webmaster for the mathart exhibit webpage.
The next image is of Robert Fathauer who curates the mathart show each year and also owns and operated Tessellations a company devoted to selling objects that inspire the math aesthetic.

Here is Nat Friedman and one of his knots displaying a minimum surface by spanning a soap bubble film across the knot. Very interesting and simple stuff showing complex concepts.

The next image is of Reza Sarhangi with Arthur Benjamin who happens to spend a lot of time on stage racing calculators … I have seen him in action and yes, he can calculate in his brain faster than you can calculate on your hand calculator. Check out this video.

JoAnne Growney and Sarah Glaz recently edited an anthology of mathematical love poems titled “Strange Attractors”. The book was published by AK Peters and can be seen in the above photo at the bottom right of the image. Also in the photo are Klaus Peters (left) and his lovely wife Alice (Thus AK). The conference also provided a poetry reading session to deliver poems from the book. The event was organized by co-editor JoAnne and you can see the crowd gathering for the reading in the image below.

In the image above you can see JoAnne standing and speaking to the crowd and Sara sitting and listening (lower right). The image below is of fellow mathematical poet Bob Grumman as he delivers one of his long division mathematical visual poems.

The image above is of me delivering my poem "Prometheus's Epistle to Job"

Here is a link to a review of the poetry reading by Karren Alenier.

See the Mathart show in Washington D.C.

Here is the link for the mathart show in Washington D.C. this January. You can see the variety of work from the links presented. The image I chose to show (above) is titled:
“A Strange Dream”
Oil crayon on paper, 20" x 24" (framed), 2008. "

The work is by Karl Kattchee, Associate Professor of Mathematics, Mathematics Department, University of Wisconsin-La Crosse, La Crosse, WI

Professor Kattchee says, "I generally work in the abstract and typically with oil crayons or pencil on paper. Each drawing has an internal logic, mathematical in nature, which usually evolves while I work. My mathematical instincts urge me to keep the internal logic consistent, but my artistic side wants to bend the rules. The soul of my drawings is the balance between the two."

The American Mathematical Society has accepted “The Empty Paradox”

I am grateful and honored that the American Mathematical Society has accepted “The Empty Paradox” to their annual art show which will be held in Washington D.C. this year. (To see The Empty Paradox click here)

The American Mathematical Society Show Is Up And Running

View the show here




The AMS show is now visible in it physical construction in Exibit Hall B at the San Diego Convention Center. The good news is that you don’t have to be in San Diego to view it you can go to the link here. The bad news is that the internet destroys some of the subtleties in the images. For example, the image by Andy Lomas (above) has beautiful delicateness that cannot be imagined here on the internet.

Andy’s image is composed of layered trajectories followed by millions of particles. Each individual trajectory is essentially an independent random process, with the trail terminating when it reaches a deposition zone. Collectively the paths combine to form delicate complex shapes of filigree and shadow in the areas of negative space that the paths don't reach. Over time, as particles deposit they create a growing region that future particles will not be able to enter. There are no actual defined boundaries, simply intricately structured gradients of tone formed by the end points of trajectories.

Andy Lomas, Digital Artist, London "These pieces are part of a study into how complex organic forms can be created from simple mathematical rules.
The base algorithms used to generate the forms are variations on Diffusion Limited Aggregation. Different structures are produced by introducing small biases and changes to the rules for particle motion and deposition. The growth like nature of the process, repeatedly aggregating on top of the currently deposited system, produces reinforcement of deviations caused by forces applied to the undeposited particles as they randomly move. This means that small biases to the rules and conditions for growth can produce great changes to the finally created form. All the software used to simulate the structures and render the final images was written by the artist in Visual C++."
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The image above is of a three dimensional piece by Carlo Sequin in which he explores the geometrical relationships of a hole to a surface moving through a tube-like structure.
" Scherk's 2nd Minimal Surface" is a way to weave together two intersecting planes so that an infinitely long chain of holes and saddles replaces the intersection zone; it is possible to do that so that the resulting single surface has everywhere zero Gaussian curvature. The same basic scheme can be used to also blend together three planes that share a single intersection line. A small region, comprising just 5 monkey saddles and 4 Y-shaped holes, has been cut out of such a minimal surface; it has been artistically stretched and twisted to make a towering sculpture. Carlo H. Séquin, Professor of Computer Science, EECS Computer Science Division, University of California, Berkeley

Mathartist statement:

"My professional work in computer graphics and geometric design has also provided a bridge to the world of art. In 1994 I started to collaborate with Brent Collins, a wood sculptor, who has been creating abstract geometrical art since the early 1980s. Our teamwork has resulted in a program called "Sculpture Generator 1" which allows me to explore many more complex ideas inspired by Collins' work, and to design and execute such geometries with higher precision. Since 1994, I have constructed several computer-aided tools that allow me to explore and expand upon many great inspirations that I have received from several other artists. It also has resulted in many beautiful mathematical models that I have built for my classes at UC Berkeley, often using the latest computer-driven, layered-manufacturing machines. My profession and my hobby interests merge seamlessly when I explore ever new realms of 'Artistic Geometry'."

Reza Sarhangi - At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January. The following image is by Reza Sarhangi and Robert Fathauer (see Robert's work)
Reza is one of, if not the most important person in the vismath genre for Reza is the nucleus of the Bridges conference on mathematical connections in art music and science. He is a very special man and I really appreciate everything he has done and continues to do for the genre.

This print was inspired by Abu’l-Wefa Buzjani's (10th Century Persian mathematician) construction of a regular heptagon contained in his treatise, “On Those Parts of Geometry Needed by Craftsmen”. His construction is illustrated by the linework in the center portion of the print. The characters around the perimeter of the design repeat Buzjani’s name in Farsi.

Reza Sarhangi, Professor of Mathematics, Towson University and Robert Fathauer, Small business owner, puzzle designer, and artist, Tessellations Company

Reza Sarhangi is interested in Persian geometric art and its historical methods of construction, which he explores using the computer software Geometer's Sketchpad. Robert Fathauer creates digital artworks on a Macintosh computer, primarily using the commercial programs FreeHand and Photoshop.

Gary R. Greenfield - At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January. The following image is by Gary Greenfield who also happens to be the chief editor of the Journal of mathematics and the arts. I really enjoy Professor Greenfield no nonsense approach concerning this genre.

Virtual interacting particles are realized as small paint droplets encased in hard shells. Particles move under the influence of artificial gravity. When a particle touches the canvas it adheres, its shell disintegrates, and the particle's footprint becomes visible. Particles stream from fountains located slightly above the canvas. Back scattering and dispersion occur when particles from two or more intersecting streams collide. This series of images was made by sequentially turning on and off 120 pairs of streams where some collision potential existed. Each stream contained 400 particles, all particles in a stream were of the same color, and four colors were available. The resulting "fountain paintings" lie on a spectrum somewhere between simulated Pollock style drip paintings and simulated air brush paintings.Gary R. Greenfield, Associate Professor of Mathematics and Computer Science Mathematics & Computer Science Department, University of Richmond, Richmond, VA 23173

Mathartist Statement:

"Many of my computer generated algorithmic art works are based on visualizations from simulations that are inspired by mathematcal models of physical and biological processes. Examples include cell morphogenesis, swarm behavior, diffusion limited aggregation, and interacting particles. By experimenting with the parameters affecting simulation settings and drawing attributes, I try to focus the viewer's attention on the complexity underlying such processes. "

Michael Field - At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January.

The following Image is by the mathartist Michael Field. Looking at these small jpegs is quite an injustice to these works. If you see them in person, you will be amazed at the complexity of texture. I have loved professor Field’s work since the first time I saw it at Bridges.




Part of a repeating pattern of type pmg. The pattern was generated using a smooth symmetric torus mapping and then lifted to the plane. The colors reflect the density of an associated absolutely continuous invariant measure.
Michael Field, Professor of Mathematics, Department of Mathematics, University of Houston


Mathartist Statement:


"All of my art work is based on ideas rooted in dynamical systems, chaotic dynamics and invariant measures (part of my field of research). I developed all the software, algorithms and coloring used for these images. I also built the computers used to generate the images and printed these images myself.
My interest primarily lies in the ways in which one can achieve certain desired artistic effects using a "mathematical palette" (as opposed to using images toilluminate the mathematics)."

Robert Fathauer At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January. The following image is an M.C. Escher homage by Robert Fathauer. Also to note that Robert has curated many mathart exhibitions around the world.

"Angels and Devils" is a digital artwork based on a fractal arrangement of circles within circles. Two half-scale circles are placed within the starting circle and rotated by an angle of π/4 in opposite directions. These steps are then repeated in the smaller circles, etc. The motifs pay homage to one of M.C. Escher's most famous prints, "Circle Limit IV", which also contains angel and devil motifs. Escher's print is based on hyperbolic geometry, which distorts the motifs as they get smaller. All of the tiles in "Angels and Devils" are similar in the Euclidean plane.

Robert Fathauer, Small business owner, puzzle designer, and artist, Tessellations Company

Robert Fathauer makes limited-edition prints inspired by tiling, fractals, and knots. He employs mathematics in his art to express his fascination with certain aspects of our world, such as symmetry, complexity, chaos, and infinity. His artworks are created on a Macintosh computer, primarily using the commercial programs FreeHand and Photoshop. More recently, he has been exploring fractal arrangements of polyhedra

Anne Burns At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January. The following image is by Anne Burns who is a prominent figure in the vismath world and I continue to find her fractal imagery extremely fascinating.

I use mathematics to invent algorithms and recursive subroutines that model structures found in nature such as clouds, trees and flowers. The program that generated this picture was written in Visual Basic.

Anne Burns, Professor of Mathematics, Long Island University.Mathartist statement:

"Just out of high school I entered Pratt Institute to major in art. For a number of years I painted in oils and water colors. I returned to college in my thirties and found that I loved mathematics. I never realized the connections between math and art until I bought my first computer and began writing computer programs. This enabled me to combine my love of art with my love of mathematics. Another of my interests is identifying wildflowers; this led to writing programs trying to imitate the structure of plants and other forms found in nature. I love programming and I am fascinated by the process of recursion and how it can be used to create pictures of astonishing complexity with very little code."

Robert Bosch - Outside Ring - At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January.

While we are looking at space filling curves … The following piece is another space filling curve image similar to the last blog entry yet this one has a different premise.

"Outside Ring" is a continuous line drawing constructed from a 3000-city instance of the Traveling Salesman Problem. The line is a simple closed curve drawn with white ink. It divides the plane into two regions: in (drawn with red ink) and out (drawn with black). From afar, the piece looks like an alternating link, a knot formed from two interlaced loops, one red and one black. Robert Bosch, Professor of Mathematics, Robert and Eleanor Biggs Professor of Natural Science, Department of Mathematics, Oberlin College, Founder of http://www.dominoartwork.com/

Mathartist Statement:

"I specialize in "Opt Art", the use of mathematical optimization techniques to create pictures, portraits, and sculpture. I have used integer programming to create portraits out of complete sets of dominoes, linear programming to create pointillistic pieces, and instances of the Traveling Salesman Problem to create continuous line drawings. What all my pieces have in common---aside from how they were constructed---is that they look very different up close than they do from afar. I create my artwork out of a love of optimization---the theory, the algorithms, its numerous applications. I believe that optimization can be applied to virtually every imaginable field, and I believe that my artwork does a good job of helping me make that point!"

Douglas McKenna - Thirteenski - At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January.

The following vismath piece is by Douglas McKenna who was kind enough to invite me to visit his studio a couple of years ago. Since then I have been a fan of his 'space filling curves'.

Mathartist statement:

The original Peano and Hilbert Curves represent two out of three techniques for "threading a square". The generalized third technique I recently conceived connects square corners with side centers. "Thirteenski" is an asymmetric, recursive traversal of 13 symmetrically arranged sub-squares that eventually converges as a space-filling curve at different geometric scales according to a Sierpinski Carpet-like pattern. The resulting pattern wonderfully illustrates a struggle between symmetry and asymmetry, arising from the underlying combinatoric constraints governing the solution space.

Slavik Jablan At The AMS Show in San Diego - January

Graphical work based on links and interlaced structures.

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January. The beautiful piece below is done by Slavik Jablan

Graphical work based on links and interlaced structures.Slavik Jablan, Professor of Mathematics, The Mathematical Institute, Belgrade, Serbia.

Mathartist Statement:

"For many years I used almost all painting techniques (oil, watercolor...), painting in a color-expressionist manner. Later I transferred to computer graphic and mathematical art, trying to preserve the individuality and originality of math-art works, so my math-art works are not computer-generated. In fact, I am using a computer only as a tool for producing artworks."

개꿈 The American Mathematical Society Has Accepted “DOG DREAM” And “TEMPTATION”

I am grateful and honored that the American Mathematical Society has accepted “DOG DREAM” (above) and “TEMPTATION” (below) to the 2008 art exhibition, which is concurrent with the 2008 AMS conference which takes place in January of 2008.

Both poems are in the form of an orthogonal space poem.

Polyaesthetics and Mathematical Poetry

I am pleased to announce that the paper I wrote on “Polyaesthetics and Mathematical Poetry” was accepted into the Journal of Mathematics and the Arts. It is now available at the following link :

http://www.informaworld.com/smpp/title~content=t755420531