Karl Kempton's Sun Plus Moon

Another example of Karl Kempton's Visual Poetry 

New From Karl Kempton

This is a new little diddy from Karl Kempton. I am not sure if he had a title for it but if I could title this piece, I would title it: "I don't trust language"

The Question of De Chrico

I have noticed many small mathematical poems on the internet that are in the form of A+B=C . This form is a perfectly legitimate form however, there are times when I think the author intended you to understand it in terms of A*B=C . There is some confusion as to what is the difference between addition and multiplication within the realm of mathematical poetry. I would love to hear anyone try to explain the difference between the two. In the mean time I have posted a piece above that asks that very question.

The piece is titled: “THE QUESTION OF DE CHIRICO” and it poses the question: “Is the image on the right side of the piece equal to the ideas of Baltimore times De Chirico or is the image equal to the ideas of Baltimore plus De Chirico?

I invite anyone to choose between the two statements and explain why and I will post the answers.

Introduction To ‘Visual Mathematical Poetry’

"Americana Mathematics" (above)

-Details Views (below)-

Introduction to ‘Visual Mathematical Poetry’:
I would like to introduce another category for mathematical poetry related nomenclature. This delineation I would like to call 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. There are plenty examples of math type poems out there that use elements of visual mathematical poetry however, I have seen none that are done with the intent of having a didactic element within them and most if not all are too abstract to show the mechanics of visual mathematical poetry. Furthermore, I have not seen any that are ‘purely visual mathematical poetry to serve as clear example.
Verification of logic:
I have tested the logic in this piece on a group of aerospace engineers to see if the artistic aesthetic interfered with the logic. All of them clearly saw the logic and understood the mechanics of the piece however, a couple asked, in perfect stereotypical engineering demeanor, why would I bother.
I also presented this to the mathematician Paul Gailiunas who replied below:
"It goes further - there are special numbers if we do multiplication (the primes), but none in addition. Number theory follows. We can set up other systems that work like this, but the elements need not be numbers. They are called rings. Division is a further complication. Sometimes it works, and we have a "division ring", sometimes it doesn't. The integers do not form a division ring because things like 2/3 are not integers."
The mechanics of this piece:
What motivated this piece was some conversations with a few people who have trouble visualizing mathematical poetry in general and the difference between addition and multiplication in particular. I decided to create this piece to possibly help those people approach this nebulous concept. For if we look at addition we see 2 concepts put together in such away that the original concept is easy to remove from the other and both concepts are easy to identify retain their original identity. I think most people do not have much of a problem comprehending this idea. However, multiplication is much trickier to embrace. Using the operation of multiplication augments the result by integrating the identity of both elements being multiplied. That is in the example of 4 x 5 = 20. ‘Twenty’ can be seen to have been augmented by both 4 and 5 and one can see this by dividing up 20 by cutting out 5 pieces of 4 or 4 pieces of 5. What is important is that we recognize that 20 is a higher magnitude relative to both 4 and 5 but has the ‘identity’ of both 4 and 5. “Americana mathematics” operates the same way for in addition one can easily recognize and conceptually separate both identities. Furthermore, the multiplication operation has a result that is an augmentation of both separate identities but obviously is more powerful than the original ideas, has its own identity however; it retains the original identities of both.

For a web page version click here

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