Here is a visual poem with mathematical facets done by Karl Kempton and titled "The Root of Pi"
Here is a couple of pieces of Mathematical Visual Poetry in the Bridges Pecs show by Henry Segerman. The vispo folks may like these as well. The first one is a sphere made from a tessellation of the word Sphere. See if you can find one reiteration of the word (it is right in front of you)
The second one is the same idea with a torus.
Here is a link to his work the Bridges 2010 show in Pecs Hungary.
Heck as a last ditch idea I went ahead and colored the spheres so that it would be easier for some of you to see the words. Here ya go.
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.
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.
I received some interesting comments from TT.O. concerning my blog entry on the mathematical poetry of Scott Helmes. I have copied the comment below and below his comment I will address it.
Dear kaz
It always annoys me when people use words like "whimsical" it seems so demeaning to me. I looked it up and it said, 1. full of or characterized by whims or whimsy 2. oddly out of the ordinary; fanciful; freakish 3. subject to sudden change; unpredictable. Is the implication that other "mathematical" poetries are the opposite of "whimsical" i.e. the antonym "nonarbitrary"???? I think it unkind. In Scott Helmes's "Second Order Programming" the churning up of the linguistic elements with the mathematical elements is a powerful poem in the "imagist" style. I can sense the aeroplane's engines, the timetables, schedules etc and the sense of urgency in them --- that is, if I read the poem as a whole and not separate it into "five" singular equations. I can sense the pilot going thru their routines etc. You say the equation "serves as nothing more than a real mathematical equation that could be used for something had all of the variables been defined beforehand" --- I don't see why the variables should have to be defined beforehand. The sense of "alienation" from those variables are very much my (your?) experience of aviation. There is a sense of anticipated hope and faith every flyer has that those equations are correct and will work. And whose to say that those "equations" are NOT correct, i.e. REAL equations used in AVIATION? Equations as metaphor are perfectly acceptable "mathematical poetry" I would assume. Further to that, the "sequencing" of equations (i.e. one equation leading on from the one before and so on), builds a "model" i.e. an "object", it "manifests"; takes it out of the realm of the non-substantive, even "spiritual" (say). You say "it seems to me following that path really leads to nowhere"; hypothesizing dead-ends seems to me to be a dangerous art-practice, or at least not wise. It might be asserted (I dare suggest) that the World (or the emotions contained therein) cannot bare or endure the myth of a single equation. It would seem to me that reality or emotions only exist or can be interpreted as a "cluster" of equations, and that each and every equation may be "trivial" on its own, but collectively creates a simulacrum of sorts, an "evocation" of sorts. I find Helmes's poems extremely liberating and full of potential AND mathematical poetry to boot! That is not to exclude other kinds, but the "family" is growing! I'll send you a small offering of mine via attachment on an email. Thanxxxxs for the continued talking.
Love + anarchy
TT.O.
Dear TT.O.
1. Wiktionary.org says this about it -- Given to whimsy; capricious; odd; peculiar; playful; light-hearted or amusing.
Personally I see nothing pejorative about this term. When I used the word, “Whimsical” my intention was playful; light-hearted and amusing. Although some may think so, I think very little of my work is light-hearted – only two pieces come to mind that may fit that category. What I am doing here is stylistically comparing his poetry to mine. I am not making judgments on different types of mathematical poetry. His mathematical poetry appears to be equational poetry yet it functions quite different. Now when the dust settles I think that the bottom line will yield that we have a different view of what is important when it comes to aesthetics. All forms of mathematical poetry are valid but that doesn’t mean that I personally am interested in the aesthetics employed by them. While John Cage was a huge influence on me when I was young and I have always enjoyed his work, yet, his indeterminate processes don’t interest me - at least not the process itself. The beautiful thing about John Cage is how he teaches us to focus on the moment. I have always felt that he was not interested in you being excited about his systems for they are not the point. All of his work was to get you to not focus on art but focus on the moment that you are experiencing. Randomness and stochastic systems are only a tool to help you experience your experience. I have very little appreciation for random gizmos. In other words stochastic systems in general bore me as well as artists who make aesthetic decisions based on “warm and fuzzy feelings” Every inch of the canvas, every word in a poem, every symbol in a mathematical statement has meaning and as an artist I believe you should have a very good idea of what it means to you for your expression.
2. What is important about Scotts work is WHEN it was done and how much of it he was doing -- about ten years before I was doing mathematical poetry but then again my work is quite different than his. There have been a few who have done mathematical poetry before him even as early as the year 1800 however none that I know did as much as Scott had done in the 1970’s.
3. You say; --- “I don't see why the variables should have to be defined beforehand.” I say, “of course you don’t need to define them if you don’t want to; however, at that point they function as pure mathematics and operate as such … if they have meaning you have to bring it to the equation yourself. This seems to be what Scott wishes as well. This issue really begs the question; how much should one have to bring to the table for the piece to work ‘well’ and of course what does ‘well’ mean? It seems to me that if I have to bring a lot to the table and I can view it a number of different unrelated ways then I will see the piece as vague. I would much rather the poet say something in particular – point at something. What turns me on is an artist or poet who points at an archetype but does it in a new fresh way.
4. As far as you said, “who says those equations are not used in aviation? “ Even though I would not find it that interesting if they did; the probability of an aerospace structural engineering equation having those exact variables that spell out words would be astronomically unlikely. However there are equations that do spell out things for instance Energy = mad (mass times acceleration time distance) – again, as curious as these are I don’t find them that interesting. I think my aesthetic boils down to this: Synchronicity is much more interesting to me than Coincidence.
5. In reference to: "it seems to me following that path really leads to nowhere"; you said “hypothesizing dead-ends seems to me to be a dangerous art-practice, or at least not wise.” I say, “The reason I say it is a dead end is because the equation variables are not defined – There is no place to go mathematically speaking. It is too ambiguous - the equation can be solved in too many ways to have any meaningful relationship with the words. Yes you can imagine that it is an aerospace equation but that says more about you and your imagination than it does the equation or the art.
6. You said, “It would seem to me that reality or emotions only exist or can be interpreted as a "cluster" of equations.” I say, “Reality has nothing to do with equations – in fact Reality is just the opposite of equations. Reality is not thinking.”
7. All this said – I don’t want you to think that I don’t like what Scott has done. I like it and especially for the time it which it was done – it is extremely important work.
Here is a new'Mathematical Visual Poem' by Karl Kempton - first published in Turkey here
I met the visual poet Karl Kempton face to face for the first time last weekend (he is on the right). My wife and I experienced a wonderful dinner/picnic with Karl and his wife on the shore of Pismo beach. He gave me a stack of his books and publications to read. It was a grand meeting however; it went by way too fast. Here is a shot (above) of Karl and I located in the beautiful garden designed by Ruth Kempton.
Here is a link to one of my favorite essays of his.
The following four images comprise a new minimalist visual poem by Karl Kempton. It could easily be said that each slide is a separate poem as well. I would like to draw our attention to the first slide which certainly can be viewed as mathematical poem in its own right. What is signature in this first slide (poem) is Karl’s use of text (there is no image as a rendering, there is just text, yet the images come through). It has a lot of the same simple and elegant features that remind me of Marton Koppany’s work.
The other three slides add an artistic breadth to the original idea in the first slide. It’s a very nice piece Karl! Thanks!
