Iteration

Here is one of my new proportional poems titled "Iteration"

What is Mathematical Poetry?

Lately, there has been a bit of passionate yet conflicting talk debating the definition of Mathematical Poetry among those who care. I will present six definitions. You pick what you like best or come up with your own.

Here is Bob Grumman’s:
A mathematical poem is a poem some or all of whose verbal elements undergo a mathematical operation centrally important to the poem that is simultaneously both significantly mathematical and significantly verbal–in the opinion of those capable of appreciating the poem.

Here is Karl Kempton’s:
A visual poem must contain a visual element consciously composed so that the poem must be seen to fully grasp meaning and experience, a mathematical poem must contain a mathematical operation, such as a addition, to fully grasp meaning and experience. a mathematical poem can or not be a visual poem.

Here is Gregory Vincent St. Thomasino’s ‘working’ definition:
The “mathematical poem,” if it is to be, or to contain, poetry, must have some poetic elements, as well as some formal symbols and operations of math.
I want to emphasize that by “operations of math” I do not mean that the poem will be “doing math.” What I mean is that the poem will be, in some way or in some sense — be that metaphorical, allegorical, but for the most part figurative — mimicking or imitating or finding a trope in that operation (whichever that operation may be). (I emphasize: I do not mean that the poem is “doing math.” Math does math. The poem is representational.)

Here is Kaz Maslanka’s: Mathematical Poetry is a umbrella term that covers any poetic expression involving Mathematics. Maslanka has broken mathematical poetry into five categories – they can be viewed here

Here is Sarah Glaz's: Mathematical poetry is an umbrella term for poetry with a strong link to mathematics in either imagery, content, or structure. -click here for more-

Here is JoAnne Growney's: Years ago when I first began to bring poetry into my mathematics classrooms, I used the term “mathematical poetry” to refer to poems in which some of the imagery involves mathematics; it was a sort of “applied mathematics.” Now, after lots of reading and exploring, the possibilities for math-related poetry seem nearly endless--including shaped poems, functional poems, permutation poems, various Oulipian structures, and then--on the Internet--a myriad of possibilities including animated poems, interactive poems (including linked hypertext), and so on. These days, I mostly avoid the term “mathematical poetry” (since I can’t formulate a definition that satisfies me). Instead, I think of the multiple possibilities as intersections of mathematics and poetry. (See, for example my blog: “Intersections -– Poetry with Mathematics.”)

A Thought For Today:

Nothing which does not transport is poetry. The lyre is a winged instrument. -Joseph Joubert, essayist (1754-1824)


taken from wordsmith.org

Does Mathematical Poetry Do Math?

The comment Below was originally posted as a comment on Bob Grumman's blog but it did not show up on his comments so I will post it here.
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Does mathematical poetry ‘do’ math?

This is an excerpt from Bob Grumman’s blog where he and Gregory Vincent St. Thomasino are debating mathematical poetry. I have taken a small yet important few lines from the discussion to add my own thoughts. Gregory is green text Bob is Blue and I am white.

Gregory says: And I would offer, for starters:
1) It is a fallacy to think mathematical poetry is “doing math.”
Bob says: What is it doing?
Gregory says: The “sum” of a mathematical poem need not be the same for everyone.
Bob says: As in pure mathematics, it has to have the same value for everyone although it need not be “the same” for everyone. Just as in pure math, two plus two can be eight minus two as well as four.

Here is where I have inserted my responses:
Gregory says: And I would offer, for starters:
1) It is a fallacy to think mathematical poetry is “doing math.”
Bob says: What is it doing?
Kaz says: I feel very strong that Gregory’s viewpoint on this is too narrow. Mathematical poetry does do math the same as any applied mathematical problem does math. It just requires more math operations than pure math problems of the same size.
Gregory says: The “sum” of a mathematical poem need not be the same for everyone.
Kaz says: This is not what I would consider the correct verbiage for Gregory’s expression yet the essence of what he said is very true. Let me refine it a bit: “The answer of a mathematical poem is never the same for any two or more people.” In fact it is never the same for one person. There are different levels of answers for the reader if the mathematical poem is of any poetic value.
Bob says: As in pure mathematics, it has to have the same value for everyone although it need not be “the same” for everyone. Just as in pure math, two plus two can be eight minus two as well as four.
Kaz says: I have a question for you Bob. Would you say the value of a poem has to be the same for everyone that reads it? Of course not – everyone gleans different meaning from the metaphors among other things based on their own past and personal experience. It is no different for equational poetry/mathematical poetry. Not only are there different values for each reader of the mathematical poem there are also a multitude of different values for a single reader of a mathematical poem. (If it is read correctly) However, to Bob’s credit, I believe that he is using the right word to describe the terms in a mathematical poem. That very important word is “value”. Value is what makes it mathematical. A year ago, I erroneously thought that we were using words as if they were numbers and stated so in the introduction on my blog even though my intuition told me they were numbers, I could feel the numbers, yet, I didn’t push my mind to the realization that they were indeed numbers. I have now made the connections to realized it. I have realized that Value is quantity. In other words quality is really a cluster of quantities, however, all of the quantities have not been defined, and in addition, they don’t have to be. As long as you realize that each element in the cluster can be defined as quantities. For example in Gregory’s mathematical poem “ to+to= too” the poem has values in it yet you have to ‘see’ it that way. In other words you have to assign it value if you want to literally ‘do’ the math. In this example “to” and “too” both have value. One example is that the poem reads “2 + 2 = 4” it also can be read as “great + great = greater” and we can assign “great” to equal 100 so his poem can also mean 100 + 100 > 100 ; I can go on and on assigning new values - The bottom line is that the math is embedded in the poem but one must realize there are many answers – of course! This is why mathematical poetry is poetry (or art) instead of science. If poems had only one answer they would be science not poetry. One brings value and meaning to any poem that one reads and one brings value and meaning to mathematical poems the same way. The numbers are there you just have to assign them or just feel them the way you would a physics problem.

Top 40 Poetry Blogs (we are third)

I am excited to announce that this blog is rated third in the top 40 poetry blogs at “Guide to art schools.com” check it out here.

The Ancient Dual

There exists an ancient battle of polarities within the human psyche – They were once symbolized as the Sun/Moon; Lion/bull ; eagle/snake The equation shown is a dance of the total. The structure used for this mathematical poem is the expanded similar triangles form.
Flavor three A= (D(B+H)/E)-G

Here is the detail of it.

Toni Prat

Here is one visual mathematical poem and some mathematical number poems from Toni Prat there are some other very interesting work at his blog: http://www.poemesvisuals.com

At the Bowery Poetry Club NYC

I got back from NYC last week after being invited by John Sims to participate in the “Mathematical Graffiti Wall” at the Bowery Poetry Club. I scrawled out my proportional poem titled “Afghanistan” on the wall as well as giving a short lecture intended to impart the necessary tools to access the piece. Below is an (poor quality)image of me delivering my lecture -- you can see Poet/Historian Richard Kostelanetz underneath me and mathematical / visual poet Bob Grumman to his right. I am not sure who was wearing the white hat.
After the gig myself, Richard Kostelanetz, Geof Huth, Bob Grumman, JoAnne Growney, and others went for coffee and discussion – I think we all had a great time - I certainly did.


Here is a photo of the wall taken from the stage.


Here is my poem Afghanistan

And you can see it here inked onto the wall.

Speaking of graffiti – here is a photo I shot in the men’s room at the bowery poetry club.



On another note the day before I gave my lecture I went to MOMA to see my old friends (The Tanguy, Magritte, Ernst, Dali, and De Chirico paintings) - I went up to pay my twenty dollars when the man behind the counter told me if I waited twenty minutes I could get in free. He said that I just need to wait in line outside. It was quite a long line and as we were coming in I noticed Bob Grumman about seven people up in front of me. So as fate turned out, I ended up hanging out with him as we viewed the art work. I had a nice chat with him as we covered a lot of territory in our discussions. Below is a photo of him and me in front of the De Chirico Painting “Gare Montparnasse” (The Melancholy of Departure).

Dear Sir

Issue 4 of Dear Sir, is up! I have some images in the current issue - Check it out at: http://www.dearsir.org

John Sims' Mathematical Art Poem

Here is John Sims and company doing their mathart poem originally performed at the Bowery Poetry Club NYC.
Check it out!

Afghanistan

Here is a new proportional poem titled “Afghanistan”

I find that you can switch Hope and Empire and get different results that still provide something interesting

Venerate Your Experience

Here is a new twist on one of my older proportional poems based on the the statement form is to emptiness as emptiness is to form. This is an example of solving the equation for "1"

John Sim's Mathematical Graffiti Wall

John Sim's Mathematical Grafitti Wall is taking shape at the Bowery Poetry Club in NYC. If you are Mathy and in NYC drop by an put your favorite equation on the wall. If you are in the NYC area on July 10 2010 drop by for a night of Mathematical Poetry Reading with visuals. There will be all of the most active Equational Mathematical Poets in America reading there!

Bob Grumman expresses what he calls True Mathematical Poetry

The following is a comment by Bob Grumman on my delineations for four types of mathematical poetry; with his vote that the only real kind of mathematical poetry is what I call Equational Poetry. I think his argument is pretty good so I am posting here so that everyone can see it.
I also agree with his assessment about number poetry … to me the beauty of number poetry IS the beauty of mathematics. Sure it has rhythm in it but so does virtually everything that the mind can remember due to memory's existence being dependent of repetition. And sure it can be visualized but does visualizing something make it art? Once again I will express that I think art is an expression of culture and ‘Pure Mathematics’ is cultureless.


VizPo-Central has left a new comment on your post "Four Types of Mathematical Poetry":

Number poetry gives one an appreciation of pure math but doesn't seem to me to be poetry. Appreciation of it takes place in one's mathematical awareness only, it seems to me.

The more I think about it, the less I know what to call it. It's not visimagery (i.e., visual art). I guess I would call it number art--it's numbers arranged in order to elicit mathematical pleasure. It's not a kind of mathematical poetry, but an equal art.

As for who "dominates" the term, "mathematical poetry," I say let there be competition; let all who want to define it have their say, and hope that reason prevails. What usually happens in picking terms for kinds of art is what has happened with the term, "postmodernism." A catchy worthless term is coined, probably by an ignorant academic, and someone even more ignorant but with a lot of readers makes it fashionable, and the morons run with it before people of intelligence have had a chance to analyze it and perhaps find a better term.

I will admit that my definition of mathematical poetry fits the kind of math-related poems I compose. So what? What matters is not whether my self-interest is involved, but whether the definition is effective or not.

Aside from what I'm calling "number art," it seems to me there are three kinds of math-related poetry: poetry that is about math, poetry that is generated by some kind of mathematical formula (like make a poem out of every third word in a given dictionary, and poetry in which some mathematical operation is aesthetically central.

I don't think poetry about math should be considered poetry because, to make it simple: poetry about chemistry is not called "chemical poetry," poetry about Bach would not be called "musical poetry," poetry about Picasso's paintings would not be called "visual poetry," poetry about Maria Tallchief would not be called "choreographical poetry," and so forth.

Similarly, mathematically-generated poetry (like sonnets, which are generated in part by the rule that they be ten by fourteen unit rectangles, or that kind of poem each of whose lines has a number of words in it equal to the sum of the number of words in the preceding two lines, or whatever it is) are no more mathematical poems than a bridge of building is a mathematical bridge or mathematical building because generated in part by mathematics. The end product is not mathematical.

Sorry about the slip up regarding "mathematical visual poetry," and I do see the difference. I wasn't able to type my post and read your entry at the same time, and forgot your designation. Anyway, my opinion remains the same: a visual poem that has mathematical symbols in it that don't carry out any mathematical operations is simply a visual poem with mathematical content.

I agree that my long division poems are equational. But some of my other math-related poems are just terms, Like one that is just an ampersand with an exponent of three. "Andness" multiplied by itself twice. I suppose you could call it an equation, half of which is implied.

Yes, I'm sure our little controversies will disappear into some void or other--"exiled history" sounds okay. Better than "non-history."

all best, Bob

Henry Segerman - Mathematical Visual Poetry

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.

Bridges Pecs 2010 - Pecs Hungary

I am happy to report that my pieces “Salvation” and “Whispers” were accepted to the Bridges show in Pecs Hungary opening this July 24th Unfortunately we didn’t display the detail image so that you could read the poem. So I will post it here.

Here is the full Piece "Salvation"


Here is a link to the other artwork that was accepted into the show. Check it out there is some good stuff in there.

Whispers

Here is a recent polyaesthetic piece utilizing a "proportional poem" titled "Whispers"

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.

Number Poems and Richard Kostelanetz

A 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. (And in this case Arithmetic)


The following number poems are early works from the Poet/writer Richard Kostelanetz. These works are from the early 1970’s and he was kind enough to share them with us.

The following is titled "Parallel Intervals"




This piece is titled "Two Intervals II"

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.