Miscellaneous Mathematical Visual Poetry Links

Stratigraphy and Significance in the Fibonacci Sequence

click on the word algebraic

Mathematical Poetry Visual and Verbal

MNMLST POETRY: Unacclaimed but Flourishing

Bridges 2006 Abstracts

Bridges Conference on Mathematical Connections in Art, Music and Science starts Aug 2 2006 --- Click Here to list the Abstracts for the 2006 proceedings.

Bernar Venet

I had mentioned that Bernar Venet influenced me in the late 1970's. I have always enjoyed his work. I found a very nice essay about Venet by the Mathematician Karl Heinrich Hofmann. What I liked the most about this essay is its illumination of the fact that Venet does not present math as art but math as it is. However, the context in which Venet displays his work is in an art gallery or museum.

Click here for the essay

Karl Kempton Links

The Mathematical Visual Poetry of Karl Kempton links:
Revista de Poesia

M is for Mathematica

Runes about Karl's runes by Karl Young

The Root of Pi

Mathematical Poetry links:

Buddhist Mathematics

My Big Mouth

Mouth

Dusk

Six Alone In

Zen Poems

About Karl Kempton:

dbqp

North America's Longest Running Visual Poetry Magazine Edited by Karl Kempton, Harry Polkinhorn, and Karl Young -- Kaldron

Critical writings of Karl Kempton:

VISUAL POETRY: A Brief History of Ancestral Roots and Modern Traditions

CARRYING POETRY INTO THE 21ST CENTURY

Centered in London

My piece “Centered” was accepted in the Bridges Exhibit of Mathematical Art.

There is a lot of very interesting Mathematical Art in the Show Check out the other Art at the following link.

Righteousness

I have always found Mytho-spiritual aphorisms to be beautiful and every time I discover a new one if feel my life has new depth. They seem to me to be the archetypical fabric in all mythologies / religions as I have found them to be translatable and transmutable between the myths. I have also found that translating them into the language of math to be aesthetically rewarding. The piece righteousness above is one such aphorism which basically states that the more you display righteousness the less you really have. Of course this aphorism can be said for many disciplines for it seems we have all experienced the braggart who is more interested in covering his insecurities than setting an example for us to follow.

The equation is 'D' is proportional to 1/r ... or in otherwords 'D' is inversely proportional to r

New/Old Math Humor

I don't know where this came from but it reminds me of the logic used by a mathematical poet I know.

click here for the video

Early Karl Kempton visual poetry (plotter poems)

Here we have some interesting early visual poetry from Karl Kempton which used mathematical programing to plot these poems the link takes you to a page on Dan Wabers wonderful minimalist concrete poetry site. Here is the main page: minimalist concrete poetry

Mobius Poem by Endwar

Here is a link to a wonderful Mobius Poem by Endwar. Very Nice!
Click here for the Mobius Poem

Prometheus Epistle to Job

Do the muses scatter ancient fragments of thought or do they just perpetuate them. How is it that the ancient Greek Titans can still speak?

also see Orthogonal Space Poem

The Virtuous Sphere (part two)

The Virtuous Sphere (part two)
This blog entry is a continuation of “The Virtuous Sphere” please read the last blog entry so that today’s will make sense.

On the last blog entry, we had just finished talking about the equation of a sphere. However, the next question one may ask is, “why are there words in the equations instead of numbers?” To answer this question, you should read my essay on verbogeometry. I am going to republish some of the essay that relates to “The Virtuous Sphere” but if you have not read the essay on verbogeometry then you may not get as much out of this as you would if you were to read it.

Distance Formula and Verbogeometry: As we have seen, to calculate the distance between two points, we need to describe our points by its coordinates using the nomenclature of the coordinate pair. Let me reiterate, describing a point in verbogeometry is no different from numerical coordinates except we use words. Lets look again at the example in figure 15 where we used the midpoint formula to find the exact point between the points: P1(love,praise) and P2(hate,punishment) but instead of putting them in the midpoint formula lets put them in the distance formula. (See below)

Here we have an expression for the distance between the points P1(love,praise) and P2(hate,punishment) in two dimensions. But we can also use verbogeometry in any number of dimensions including hyper-dimensions. But before we look at hyper dimensional verbogeometry lets look at another example which we will express in the third dimension. The following example uses a three dimensional Cartesian coordinates system with 3 simple antonym word-axes. (See below) The first axis is noble / ignoble the second axis is just / unjust and the third axis is loyal / disloyal.
Now lets look at the expression for the distance between the points P1(noble,just,loyal) and P2(ignoble,unjust,disloyal) (see below)
Notice the green line in figure 33 is the visual representation for the mathematical expression above. However, it would be much easier to visualize if we were able to rotate the axis. Figure 33 is an isometric view, which I chose to use because it is best for viewing the axis but unfortunately at the expense of viewing the spatial orientation of the green line.

(The virtuous sphere is written in the language of three dimensions. What I find interesting is that we can write a spherical equation in hyper dimensions. The following shows the distance formula written in a hyperdimension.)

Now let us look at verbogeometry in a hyper-dimension. Let us look at the distance formula used in seven dimensions:Figure 35 shows the mathematical poem 1+1+1+1+1+1+1+1 =1 This is a metaphorical piece that creates a metaphoric path from the concept of confusion, to where seven deities meet. The piece uses the analytic geometry distance formula in a seven dimensional space where each dimension is a gradation from confusion to a point where a deity exists.

Here is a detail:

Lets look at the coordinate pairs for these two points P1(confusion, confusion, confusion, confusion, confusion, confusion, confusion) and P2(Allah,Buddha,Jesus,Spider woman,Vishnu,Yahweh,Zeus)

The Virtuous Sphere (part one)

The Virtuous Sphere (part one)

I thought it would be a nice idea to post "The Virtuous Sphere" and talk some about it. First of all I would like to say that I believe there are many ways to define virtue, this is only an artist rendition of one way. Please do not get bound up here in the idea of some absolute truth… remember the Hindu saying: “All wars are Just on both sides” When this piece was originally mediated to me my intentions were not so much interested in an answer of denotation but in the aesthetic inherit with the structure of a mathematical sphere and the coloration and distortion of that sphere by the personal ideas of integrity, justice, nobility and of course virtue.

Today's blog entry will talk about the analytic geometry involved in the piece and the next blog entry will discuss the verbogeometrical ideas needed to approach this piece.

Let me talk a little about the mechanics of this piece. This piece is a standard verbogeometry piece so obviously I will be borrowing sections from my essay on verbogeometry to help open this up for you that are not familiar.

We all should be able to recognize a sphere, but did you know that a sphere has a relationship to the Pythagorean Theorem? To see this relationship we first should talk about the relationship between the distance formula and the Pythagorean Theorem. Then we will look at the relationship between the distance formula and a circle and after that the sphere. The distance formula uses the Pythagorean Theorem to calculate distances on the Cartesian coordinate system. The Pythagorean Theorem says that the square of the hypotenuse of a right triangle is equal to the sum of the square of it sides.

Solve for c and we get the following:


Let us look at little closer at how the Pythagorean Theorem works in a Cartesian coordinate system. Here is an example: Plot two points on a two-dimensional axis system P1(-9,10) and P2(4,3) and If we draw a lines between the points and lines parallel to the axes we can obtain a right triangle.

To solve the length of the hypotenuse we first find the difference between the x values and the y values to create the sides of the triangle then we plug the values into the Pythagorean Theorem. The x value is 9 - 4 = 5 and the y value is 10 - 3 = 7Now we plug it to the equation and we get the expression in the following figure:

The distance or length of the hypotenuse would be the square root of 74 or approximately 8.602

The distance formula in two dimensions is thus -- Given two points (x1,y1) and (x2,y2):

To reiterate -- you will notice that the distance formula is nothing more than Pythagorean Theorem placed on a Cartesian coordinate system! The x1-x2 in our equation actually shifts the line horizontally and the y1-y2 shifts the line vertically. In effect if we start at the origin for our point (x1,y1) then we can simplify the equation as shown below:

Let us look at the equation for a circle: (below) --- Doesn’t it also look remarkably like the Pythagorean Theorem? In essence it is the Pythagorean Theorem! Notice that the radius of the circle corresponds to the hypotenuse of the right triangle. What we do is sort of ‘nail down’ one end of our right triangle at the hypotenuse and spin it around so that the other end of the hypotenuse follows the form of a circle.
All of the equations that we have been looking so far function in two dimensions but what if we wanted to use the Pythagorean Theorem in three dimensions? To use the Pythagorean Theorem or the distance formula in three dimensions we append another term at the end of the equation so it looks like the one below.

The Pythagorean Theorem in three dimensions is the same as it was in two dimensions except that we add another term at the end to give us the extra dimension.

Let us look at the equation for a sphere (below):

Notice that it looks just like the Pythagorean Theorem in three dimensions? It follows the same thought that we did in two dimensions. Where we ‘nail down’ one end of the triangle and spin it around in a circle but since we are in three dimensions, we also spin the circle around an axis and so it goes that the end of the triangle we started with now follows the form of a sphere.

This concludes discussing the analytic geometrical aspects of “The Virtuous Sphere” You can see that I used the equation for a sphere as my mathematical language for this piece. The only thing we haven’t discussed is the verbogeometric properties of the piece. The next entry in my blog will discuss some of the mechanics of verbogeometry that are needed to approach this piece.

A Screening of Super-8 films by Robert C. Morgan

I studied with Robert C. Morgan in the late 1970’s and he is responsible for much of my earlier artistic development. He exposed me to the conceptual art movement in general and Benar Venet in particular. Venet noticed that science had aesthetics as well as art and was bold enough to re-contextualize these scientific aesthetics as Art. It wasn’t until I read the Dancing Wu Li Masters by Gary Zukav that I experienced an epiphany that drove me into mathematics and science. Prior to that event I had no interest in mathematics and some disdain. However, I must say I loved math up until I was seven years old then, as I mentioned, I abandoned it until 1979.
Robert has always been supportive and I always wish the best for him.

Millennium Film Workshop

presents


A Screening of Super-8 films by Robert C. Morgan

Saturday, June 17, 2006, at 8 PM



Although known today primarily as a critic and curator, Robert Morgan
emerged as a "post-conceptual" artist in the mid-seventies. Between 1974 -1989,
Morgan worked in a variety of different media, including an extensive body
of work in Super-8 film. He regards his films as "counter-narrative" in that
they deconstruct both Hollywood and commercial television -- the two primary
forms of visual narrative in the entertainment industry -- by laminating appropriated
footage against a personal and often political narrative. This is a rare opportunity
to see films by one of the formative "appropriation" artists of the seventies.

A reception will precede the screening in the Millennium Gallery at 7 PM

Admission: $8 / $6 (members)


For further information, please contact:

Millennium Film Workshop
66 East 4th Street, NYC 10003
Tel & Fax: (212) 673 - 0090
Email: cinema@millenniumfilm.org

The Transformation of Poison

The image above has been simmering in the background for a few years now and has finally come to fruition. It came about in December 2001 over a cup of coffee while taking a break at the ASCI conference in NYC. At the conference I met a very interesting Poet/Artist Philosopher and NASA scientist named Farzad Mahootian. We had a wonderful conversation between sips of dark java in mid town Manhattan and talked of many things. I shared my ideas on verbogeometry while he shared his ideas on sculptures that purify the environment. In our mutual excitement he thought it would be a good idea to incorporate the two ideas into a piece of Art. The piece above is the result. I decided to make a symbolic wedge from a verbogeometric prism and have it cleaning the air with chrysanthemum power.

Terminology for Mathematical Poetry and Related Endeavors*

‘ Visual Art Aesthetic’ is the aesthetic that concerns itself primarily with the beauty or horror expressed in direct sensory experience, whereas the ‘ Mathematics Aesthetic’ concerns itself with the beauty in the structures of logic and thinking.

‘Mathematic Aesthetic’ is the aesthetic that concerns itself with the beauty in the structures of logic and thinking, whereas the ‘Artistic aesthetic’ is concerned primarily with the beauty expressed in direct sensory experience.

'Mathematical Conceptual Art’ This form of Art focuses on the Math aesthetic and re-contextualizes it as Art personally I feel conceptual art is not art however, it is aesthetic but. That does not necessarily mean that Math is art. The main difference between ‘Mathematical Conceptual Art’ and ‘Visual Mathematics’ is that in the former the artist presents their the work as Math, where as in the later they display the mathematical object as Art. In both types, they display the object in the context of an Artistic space. A good example of “Mathematical Conceptual Art’ would be the work in the late 1960’s of Benar Venet in which he would study Math and Physics and present what he had learned purely for the aesthetic of the topic involved. There are many works of Sol Lewitt that could be considered “Mathematical Conceptual Art’ as well. A contemporary Artist who I would consider a ‘Mathematical Conceptual Artist’ is the British artist Justin Mullins although he does some work that could be considered as ‘Mathematical Visual Poetry’. The main difference between Mathematical Conceptual Art and Mathematical Poetry is that the Conceptual Art movement as a whole was not concerned with the intention of metaphor in any form and Mathematical Poetry relies mostly on metaphor to make its connection to poetry in general

‘Mathematic Constructivism’ Is one of the most popular forms of Mathematically related Art. It is a term I will use to sum up a conceptual thread that started with the Russian constructivists and ended up in the modern movement of visual mathematics. The former started in the political and social upheaval of the 1920’s with the emergence of Artists such as Naum Gabo, Vladimir Tatlin and ended up in the latter movement with mathematicians such as Donald Coxeter who felt their mathematical work is a form of Art. Donald Coxeter imparted much mathematical assistance to M C Escher.
The conceptual idea of Cubism pushed visual Art into a process of abstraction whereby the artist removes unnecessary visual layers of an object in order to point to a metaphysical idea of the object. Art Constructivism moved to push the methodology of abstract Art more and more abstract to the point of the object being something not found in nature -- a “construction”. If we push this idea further we end up in realm of ‘Visual Mathematics’ where the object of Art is pure logic, a reflection of the logical structures of language in our mind. Today ‘Mathematical Constructivist’ work has moved more toward ‘Visual Mathematics’ and can be seen in the work of Max Bill, Helaman Ferguson, Rinus Roelofs, Robert Fathauer, Brent Collins and many others.

‘Mathematical Poetry’ – Mathematical Poetry is a umbrella term that covers any poetic expression involving Mathematics. An initial list of categories is as follows: Equational Poetry, Mathematical Visual Poetry, Visual Mathematical Poetry, Mathematics Poetry and Number Poetry


‘Equational Poetry’ – This is literally performing mathematical operations on concepts whether they are words or images. A good example would be my page at the following link: Mathematical Poetry

'Visual Mathematical Poetry' -- This is a mathematical poem where the elements in that poem are visual objects. The difference between mathematical poetry and visual mathematical poetry is that the former uses words and the later uses images. Visual mathematical poetry is more similar to mathematical poetry than it is to mathematical visual poetry. However, one could create a poem that has aspects of all three of these types. For an example check out "Americana Mathematics"
‘Mathematical Visual Poetry’ – This is more difficult to define because of the vast areas and the many competing definitions of visual poetry. However, I consider mathematical operations on text as well as mathematical textual information composed for aesthetic purposes to be ‘Mathematical Visual Poetry’ Also words, text or textual elements mixed with mathematical symbols or formulae that are not performing mathematical operations on the word meanings. Although Karl Kempton has worked in many categories, I feel the following is a good example of ‘Mathematical visual poetry’: Another good example is Marko Niemi’s fractal poem described in the following link: Midwinter nights dream Scott Helmes was one of the first visual poets that moved into mathematical motifs. Bob Gruman has probably been the most prolific in this catagory.

‘Mathematics Poetry’ -- This poetry is what I would call traditional language poetry about or inspired by or uses mathematical imagery. I also would consider this catagory to include language poetry that has an interaction of numbers with words. There are numerous examples all over the web but the most popular from google's perspective seems to be Marion Cohen: other sources would be JoAnne Growney and Katherine Stange:

'Polyaesthetics' is a word used in relation to aesthetic works which incorporate many diverse aesthetics. This is not limited to but includes the aesthetics of Mathematics, Art, Music, Science, Religion etc.

'Visual Mathematics' Is one of the most popular forms of mathematically related art. It sometimes has been called “Concrete Art” This is a form of Art that focuses on the Math aesthetic and re-contextualizes it as Art. The main difference between ‘Mathematical Conceptual Art’ and ‘Visual Mathematics’ is that in the former the artist presents his/her personal/emotional relationship with the aesthetic of Mathematics where as in the later the display is less personal and more cerebral. In both types the object of that presentation is displayed as a form of Art. The hero of visual mathematics is M C Escher whose work is so strong anything that resembles it looks cliché. Fortunately there are other arenas in Visual mathematics. A good example of contemporary Visual Mathematics is found in the work of George Hart, Paul Gailiunas, Carlo Sequin, Robert Krawczyk, Michael Sussna and many others. This type of work is primary interested in visualizing mathematic structures. These structures could be anything from computer algorithms not limited to fractal Art or polytopes to hand drawings, plastic sculpture or origami.


*Disclaimer: These are the views of Kaz Maslanka and are a rough attempt at trying to put mathematical poetry in context with most of the mathematical influences in visual Art of the last 100 years

Polyaesthetic example

Boeing 747 Landing gear in the process of being manufactured

Walt Gillette of Everett, the lead engineer on the 787 program and a man Business Week recently called a "plane genius," announced his retirement from the Boeing Co. on Wednesday.

You may ask what does this event have to do with mathematical poetry? … Not much however, the following quote of his is a perfect example of polyaesthetics whereby aesthetics comes in many forms even in engineering and technology.

Walt Gillette says,
"One of the most incredible experiences is to go out ... and stand in the middle of full landing gear of a Boeing 747," he said. "To stand there, right there under that big, fat, huge machine, and you think this thing goes 625 miles an hour and a little-bitty human brain ... tells it exactly what to do and where to go, and it follows just like a docile family pet."

There are many forms of beauty in concepts and some say that if the concept is beautiful then it must be considered as a form of Art. I personally don’t find beauty and Art to be synonymous but I will admit that it is a nebulous concept and very difficult to nail down. Art for some reason seems to be a ‘catch all’ for anything anyone wants to call Art. I wish there was a better ‘catch all’ term other than Art. If you can think of one then I invite you to comment.

More Math Humor

click on it to read

It seems I have found myself in a sexist corner again … I was feeling a bit guilty for posting "girls = evil" so I had to post the cartoon above to give equal voice to our lady friends.

smile! its not that bad :)

Fabulous Finnish Fractal Flooring

Nokturno.org has a new fractal poem titled Palasista!
by Saara Lehto. The piece is written in Finnish and is in the form of a Sierpinski Carpet. The words are all anagrams of each other as well as the title.

Thanks to Marko Niemi for bringing this to us!

Rescuing Metaphor

Gregory Vincent St. Thomasino has sent me a math poem that I would like to share with you.

to + to = too

This is a nice little poem that has three Important elements that strike me right off the bat:
1.) it plays on the words to and too … in other words we have too many to's
2.) is the clever addition of o's … o + o = oo
3.) the most important element of any mathematical poem is the equal sign.**

I really like the feeling in this piece … metaphor is so hard to describe without using another metaphor and if we do then we miss the point.

By the way … eratio seven is now available! Check it out!


** It is the equal sign that creates the metaphor in mathematical poetry. It is the fact that a poem of the latter form says a + b = c and we know that a + b IS NOT c

There exists a mathematical form that is the logical crux of all metaphors in all poetry mathematical or otherwise:
A = B
Given: We know for a fact that ‘A’ does not equal ‘B’

There is also one more key ingredient for metaphor to exist. That ingredient is connotative intention. In other words, the physics equation d = vt is not metaphorical because the intention of the equation is denotative.

‘A’ is similar to ‘B’ is not a metaphor
‘A’ is proportional to ‘B’ is not a metaphor
‘A’ looks like ‘B’ is not a metaphor
‘A’ is compared to ‘B’ is not a metaphor
Simile is not metaphor that is why they are different words

Marius de Zayas

Marius de Zayas and Francis Picabia, FEMME!

Karl Kempton shares some links with us:

Marius de Zayas, Agnes Meyer. Eye Contact: Modern American Portrait Drawings from the National Gallery, Nov 2005

Picabia. Between Music and the Machine: Francis Picabia and the End of Abstraction, fig 28 mathematical formulas. Nov 2005.



I really am not able to tell whether Zayas was trying to express something mathematically or not. I have seen an abundance of artists decorating their work with equations in order to express a math feeling or maybe add a cryptic quality to their works and that may be what Zayas is trying to do as well …These days the latter idea is a bit trivial however, the case with Zayas is probably one of the first times that equations are inscribed within visual work … (I wouldn’t put it past Hieronymus Bosch … but I don’t think he did it)

Thanks Karl for passing this on!