Five Types of Mathematical Poetry

These are some delineations of "types" of mathematical poems that I have constructed from my experiences through my survey of mathematical poetry and mathematical poets. While it is true that I am writing these delineations they are not necessarily based on my personal beliefs they are based on what I have gathered from others who claim to be mathematical poets. Personally I have problems with some of these ideas and I may or may not address my objections later. However, I think it is important to draw some lines in the sand for discussion. Obviously these lines may move through further discussion and I can imagine that this page will be edited in the future.

I might add that numerous mathematical poems that I have experienced have facets or elements that extend into more than one of these types. In other words, very few "Mathematical Poems" can be described by just one category.

They are:
1.)“Mathematics Poetry”
2.)“Mathematical Visual Poetry”
3.)“Equational Poetry”
4.)“Visual Mathematical Poetry”
5.)“Pure Maths Poetry” which encompasses ”Number Poetry”


1.)‘Mathematics Poems’ are lexical poems that are influenced by the field of mathematics - There are many examples of these on the internet. This type of poem is the most lexical yet the least like “Pure Mathematics” in the sense of performing mathematical operations on the elements in the visual field. JoAnne Growney seems to be the biggest supporter of these types of poems on found on the internet.
Here is her blog

2.)“Mathematical Visual poetry” uses words and images mixed with/and/or mathematical symbols into a visual field. The mathematical symbols may or may not follow the rules for the formal language of mathematics. This type is much more open and encompasses everything between visual poetry and equational poetry. Because of the wide range of intent it is difficult to place a work on a scale between lexical poetry and pure mathematics However, I believe that if it is more toward visual poetry then it is less like pure mathematics and if it is more like equational poetry then it functions closer to pure mathematics. Or should I say it follows the rules of pure mathematics. Examples of mathematical visual poetry would be in the body of work from Karl Kempton, Scott Helmes, Pi.O. and Bob Grumman

3.)“Equational Poetry” is more rigid than “Mathematical Visual Poetry” in its use of mathematical elements. The rules of mathematics are explicitly used within the structure of the mathematical poem. The explicit use of mathematical rules is what separates “Equational Poetry” from “Mathematical Visual Poetry”. Within the equations words serve as metaphors as well as nested metaphors (metaphors inside metaphors) An example of this type of work would be the mathematical poems at this link. Also Bob Grumman approaches his work with elements of equational poetry and I must also mention the work of Craig Damrauer, which also falls into this catagory. If there are no words in the equation then it is not equational poetry

4.)“Visual Mathematical Poetry” follows the rules of mathematics the same as ‘Equational Poetry’ however the terms for the mathematical poem are purely visual as opposed to textual. In other words the metaphors are visual as opposed to lexical, yet, in essence they function mechanically the same.

5.) “Pure Maths Poetry” is the viewpoint that pure mathematical statements are a poetic expression. What
separates Pure Maths Poetry from the other types is that there are no words/lexical statement. Relative to all types of mathematical poetry “Pure Math Poetry” is the least like “Lexical Poetry.”
Number Poem is a visual formation of numbers who have a verifiable mathematical relationship to each other. The main poetic element in number poems is rhythm or pattern and can be seen by repetitions of certain numbers or operations. Number poems function correctly only when the rules of mathematics are observed. Richard Kostelanetz work from the 1970’s serves as one example of these poems yet, Magic squares and Yang Hui’s Triangle would be examples that are hundreds of years old. Number poems Number Poetry would be a subset of pure math poetry.
Toni Prat also does number poems, however, where Koselanetz focused on mathematical beauty, Prat focuses on paradox which some say is the crux of mathematical metaphor.

On Scott Helmes and Mathematical Visual Poetry

The following is a blog entry devoted to another comment on June 4, 2010 from Pioh concerning my review of Scott Helmes work originally posted on May 30 2010

Dear Kaz
I'm sorry, but it all sounds like damning praise to me, concerning Scott Helmes. You are both "slighting" and "dismissive" while magically "marginalizing" re his influence, (or if not influence, then his status as a precursor). Too,ooo,ooo schizophrenic for my liking. (I wonder what he truly thinks!) (Or for that matter, others!) (Come on, lets open this thing up!) (I know others are reading/listening/thinking) (If we can't do it now, when?!). I would be loathe to describe Helme's work as "light hearted". You seem to be floundering with all due respect.
John Cage is good, but not really relevant in this discussion. If mathematical poetry is to be what "you like" then the subject is closed from what I can see. If there is something larger at stake then lets examine it, seriously. I don't mind being wrong.
Your emphasis on whether an equation is synchronicity or coincidence is not really helpful either. Once used, we have to deal with it; real or imagined!
Variables in an equation DO NOT have to be defined, anymore that WORDS in an equation. The EQUALITY sign DOES NOT mean EXACTLY THIS or EXACTLY THAT (as it does in masthematics) --- it would be a sorry day when we insist that an EMOTION or a THOUGHT or a ANYTHING is so simply put. I think that in MATHEMATICAL POETRY the equal sign (a) suggests, and/or (b) implies a possible ACTION. There are many ACTIONS of course in mathematical poetry (of the equation variety) that are NONSENSICAL, but…. we know what you mean. Which brings me back to the fact that mathematical poetry is better viewed as a system of linguistics. Dividing the MOON by the OCEAN to equal a PALMTREE is understandable as an "image" but multiplying the OCEAN with a PALMTREE only gives you the MOON approximately one-thirteenth of the time --- cos its not there. From my point of view the "equational" poem is of value cos it ALLOWS various JOURNYINGS and SOLUTIONS. Exactitudes are a myth.
You are right, REALITY is not POETRY (tho it contains it) and it isn't THINKING (tho it contains it), and POETRY isn't REALITY (tho it contains it) (… I hesitate to go on). But if a poetry purports to be THINKING, it’s a sorry state of affairs when it borrows contaminated LANGUAGE and pretends that they are context-less, connotation-less, and irrelevant to REALITY. Why bother!? I suggest we BOTHER cos the matrix of all of it still has a pull on us.
Thanxs for letting me talk
Love + anarchy
TT.O.


Dear Pioh,
I think you are missing the point in all of this. It is true that I am dismissive of a particular kind of aesthetic for which we are talking about yet you make it sound like I am being dismissive to Scott Helmes in a personal matter. I assure you that this is not the case and even Scott feels this way.
As far as marginalizing Scotts influence; there is only one person I know who claims to have been influenced by Scott’s work and that person is Bob Grumman. I would guess that Geof Huth was influenced as well but I have not heard him say so. That is not to say that there are not others; however, I have not heard the claims.
But, ultimately we can all have our delusions of Grandeur but the bottom line is that hardly anyone seems to be interested in doing Equational Poetry or Mathematical Visual Poetry for that matter. The most popular form of mathematical poetry (at least in the number of poems found on the internet) seems to be what I call ‘mathematics poetry’ which is lexical poetry influenced by mathematics. The torch for this genre seems to be carried by JoAnne Growney, Kate Stange and Sarah Glaz.
The reason that these blog posts seem critical is not necessarily to demean the genre of mathematical visual poetry but drive a ‘functional’ wedge between it and ‘equational poetry’ and what I mean by ‘functional’ is how each functions or the mechanics of this type of poem. Equational poetry has rules that must be followed this is quite different than mathematical visual poetry which may or may not possess mathematical rules. If this sound confusing well I would have to agree. No one has written any formal criteria for judging mathematical visual poetry. I on the other hand am trying to define criteria to use in determining the aesthetic foundation for ‘equational poetry’. Furthermore, these criteria can be used to determine the aesthetic value for a mathematical poem.

Pioh says, “Variables in an equation DO NOT have to be defined, anymore that WORDS in an equation. The EQUALITY sign DOES NOT mean EXACTLY THIS or EXACTLY THAT (as it does in mathematics) --- it would be a sorry day when we insist that an EMOTION or a THOUGHT or a ANYTHING is so simply put. I think that in MATHEMATICAL POETRY the equal sign (a) suggests, and/or (b) implies a possible ACTION. There are many ACTIONS of course in mathematical poetry (of the equation variety) that are NONSENSICAL, but…. we know what you mean.”

The equation sign in mathematics has a particular meaning and if you try to loosen its definition then it ceases to be mathematics and falls into some other category. Here again we force this type of viewpoint into the realms of mathematical visual poetry as opposed to equational poetry that follows explicitly the rules of mathematics. As far as the term nonsense goes I use it loosely when discussing metaphor and primarily to mean ‘not rational’ – an example of this would be the statement: Joe is a deer. Well, this seems a bit odd sense we all know Joe is a man. This I would consider nonsensical due to it not seeming to be a rational statement. However, ultimately, ‘nonsense’ is not a good term for this situation because metaphorically speaking Bill could be a deer. The type of nonsense that I am critical of is that in which you have rules for a system, namely mathematics, and then you don’t follow the rules. There it ceased to be mathematics and thus become gibberish, vague or decoration at best.

Pioh says, “Dividing the MOON by the OCEAN to equal a PALMTREE is understandable as an "image" but multiplying the OCEAN with a PALMTREE only gives you the MOON approximately one-thirteenth of the time --- cos its not there."

I say, “While I am not terribly excited about this poem, it does function as an equational poem however, I cringe when you put out this arbitrary number of ‘one-thirteenth’ – on another note; I really see limited use of numbers in equational poems. I see numbers only working as coefficients for emphasizing magnitude within a poem” If you say: 4lovemaking x 2arguments = 12emotions then you better have a very good reason to say 12 instead of 8 – Yes you can do it but I find it very cumbersome from an aesthetic view.
I hope this clears some things up.
K
Oh on another note yet related to Pioh’s understanding of the equation sign – Here is a ‘Mathematical Poem’ that he sent me.

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