Tuesday, June 29, 2010

A great quote by Douglas Hofstadter that I think is pertinent to the debate I’ve been having with Kaz Maslanka and Bob Grumman over my use of analogy in my “mathematical poetry”:

“Analogical thought is dependent on high-level perception in a very direct way. When people make analogies, they are perceiving some aspects of the structures of two situations — the essences of those situations, in some sense — as identical. These structures, of course, are a product of the process of high-level perception.”

From the essay  The Pedagogical and Epistemological Uses of Analogy in Poetry and Mathematics by Marcia Birken and Anne C. Coon (and which cites work by fellow mathematical poet JoAnne Growney).

For the debate, see the comments attached to my essays, “On Mathematical Poetry.”

Friday, June 25, 2010

Three works in sculpture by the American artist Joseph Keppler.

From the Seattle Group show Spirit Resonance at the Ouch My Eye Gallery, Seattle, WA.

Thursday, June 24, 2010

Thanks go to JoAnne Growney for taking notice of my posts on mathematical poetry at her blog Intersections -- Poetry with Mathematics. I had the pleasure of meeting JoAnne at the Bowery Poetry Club at the opening of the Mathematical Graffiti wall a couple weeks ago on Friday, June 11. Thanks, JoAnne. What a pleasure meeting you!

“The processes of mathematics offer themselves to the Beckett protagonists as a bridge into number’s realm of the spectrally perfect, where enmired existence may be annihilated by essence utterly declared.”

    — Hugh Kenner,  Samuel Beckett A Critical Study

Tuesday, June 22, 2010

The math-art graffiti wall at The Bowery Poetry Club is taking shape.  (If you are reading this, you are invited to get down to the BPC and write some math-graffiti of your own!)

John Sims.

“Here is a poem I did with my NYU students in response to the Sol LeWitt / Adrian Piper show. Each student including myself wrote and recorded a small poem that was stitched together into a hyper poem. Visually each poem was mapped into a binary visualization of pi (see my pi quilt work — same idea). These crossword-looking forms were then mapped back into the original binary form (this gives a sense of self-similiarity as seen in fractals). Now, we created a model of this in animation space. The default flight path is associated with the sequence of pi in base two. As you travel over each section you will hear the voice of the student associated with that sub-poem. However the program allows for any path.” — John Sims

Thursday, June 10, 2010

On Mathematical Poetry (Post Three)

Our third type of “mathematical poetry” — or, rather, of “mathematical poem,” because within the mathematical poetry genre there exists different types of mathematical poem and our three types are but one family type and this expressly concerned with the analogy between “the grammar” of the mathematical proposition and the grammar of the linguistic statement.

Our third type of mathematical poem is based on the “parallel lines” situation in geometry. Our formal symbol, here, will be two horizontal lines, the one parallel to the other, that make for the “parallel lines” situation; however, as we progress, that formal symbol will change, and the change will represent an actual situation come into being, as distinct from a potential situation or from what is simply the place or topos for a future situation, and we will call this actual situation a “transversal.”

So while we may speak of two formal symbols, we will actually be using only one formal symbol. Why then still speak of a first formal symbol and what does it mean in relation to our poem? To that end, let’s gain some perspective on this first formal symbol (and on formal symbols as such):

In my Logoclasody Manifesto I included a brief addendum entitled “On Mathematical Poetry” and there I put forth a proposition, a challenge of sorts, to myself and to the mathematical poet. Every good student en route to Aquinas via Copleston will have come upon this proposition, which in situ is for the relation between substance and accident, namely those qualities and relations which exist only as qualities and relations of that of which they are predicated. Here is my rendering of that proposition — and in the form of a challenge, of sorts, to myself and to the mathematical poet:

Write for me the mathematical sentence equivalent of the sentence, “Peter is sitting on the chair.” Write for me the mathematical sentence equivalent of “sitting on” existing as an entity apart from any sitter.

There is a distinction here, between “Peter is sitting on the chair” and “sitting on” per se. We might speak of “sitting on” as a position without magnitude, or, as abstract as opposed to concrete (and indeed in that you cannot picture it!), or, as empty, or, as without specification, or, as being in the same position as a formal symbol. The formal symbol, per se, is empty; it is without circumstance; it is like a predicate without a subject (thinkable only in the abstract); and in the case of our first formal symbol, the parallel lines, what we have is a situation in posse, a place in posse, a topos in posse, awaiting some action or state of affairs. This state of affairs is brought on by the transversal line, which crosses both parallel lines thus bringing them via their formal relation into an actual relation, or, indeed, into many possible relations, each signaled by the angle and by analogy with the angle the many possible poetic and ideational senses.

Formally, parallel lines are situational, they are the place, the topos, where things come to happen. That happening is the transversal line (and the angles or by analogy the poetic and ideational senses it carries with it). Our poem, then, which we will name “the transversal poem,” requires a formal symbol other than the two horizontal lines that indicate the parallel lines situation; our symbol will have to indicate or show or signal to the reader that here is an actual situation; that here is a poem, and that here we must consent to the intention of the poem; that we must as it were enter into the confidence of the poem. Our formal symbol then will be thus


and will thus be known in this context as the “transversal poem.”

And our poem will take this structure, or, syntax or arrangement:

     lines ≠ spirals

     particles ≠ waves

     constancy ≠ change

     permanence ≠ transience

The transversal line, along with the angles it suggests, is then analogous to the many senses brought about by the juxtaposition of our words (of the poetic elements or ideas or images we bring to our formal symbols situation). Those angles, or, senses, or, “transversals,” if you will, exist side-by-side, and as often do complementary, competing and contradictory ideas. Some of these ideas can be said to exist in a state of “perpendicularity” or to be at right angles with each other, which is to be “at odds with each other.” Such as:

     multiculturalism ≠ ethnocentricity

     government ≠ media

     determinism ≠ character and motive

     turpitude ≠ enlightenment

     a poetics ≠ an attitude

     creationism ≠ evolution

     god man ≠ monkey man

Some “transversal poems”:

     the order of ideas ≠ the order of causes

     the causal relation ≠ the relation of logical implication

     word ≠ memory

     paradox ≠ semantic tension

     attractive ≠ repulsive

     force ≠ matter

     edgèd words ≠ edgeless words (sounds)

     milquetoast ≠ white bread

     iteration ≠ chromaticism

Our next post will be about “mathematical prose.”

Monday, June 07, 2010

On Mathematical Poetry (Post Two)

So we set ourselves a task — to work by way of the analogy between the grammatical and the mathematical — and we formulated a 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 — and we posted a set of examples of a “mathematical poetry.” Let’s name this type of math poem “mutually inverse operations.”

     Change + purse = church.
     kite + propeller = wing.
     to + to = too.
     am = be + I
     secrets = ? + whispers

Now let’s move on to another type of “mathematical poetry.” This type will also be based on our analogy, only here our analogy undergoes a slight modification.

The idea is to write a “mathematical poetry” based on the analogy between the “grammar of the number system and of the mathematical equation” and the grammar of the linguistic sentence.

So, whereas the "mutually inverse operations" were concerned with the formal symbols and operations of our math, here we’re going to be concerned with structure, which is to say, with arrangement, with system, with the rules for writing math in analogy with the syntax or with the rules for the arrangement of the words in the linguistic sentence.

NB: Grammar is concerned with the structure of a language and the rules and principles of its use. Morphology is concerned with the forms and formation of words. Semantics is concerned with the relations between words and the changes in the meanings of words. Syntax is concerned with sentence construction, with the relation of words as parts of the structures of sentences. Our concern, here, is going to be with syntax.

So, this is our task:

The idea is to write a “mathematical poetry” based on the analogy between the “grammar of the number system and of the mathematical equation” and the grammar of the linguistic sentence.

To do this, we’re going to take the “place value” system in arithmetic (where within a number each digit is given a place value depending on its location — for instance: millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, units) as an analogue to the syntax (the syntactic structure, or, arrangement) of grammar (where sentences are generated by means of a series of choices made from left to right as after the first, or leftmost, element has been selected, every subsequent choice is determined by the immediately preceding elements).

Consider the “place-value system” of the Fibonacci numbers:

     0, 1, 1, 2, 3, 5, 8, 13, 21, 34 . . .

Each number is the sum of the two numbers before it. Each number in the sequence is the sum of the previous two.

Let’s name this type of math poem, “place-value poems” and we’ll call our first one, which is also a haiku,

“Molotov’s Sister”

a blonde bomber,she.smokes filterless,plays upright bass & writes haiku

NB: There is no space before and after the comma and the decimal point.

The separation of sentence elements takes this form:

noun,pronoun.verb,verb conjunction verb

Here are some more “place-value poems”:

undistorted,Zeno’s perceptions.so says Simplicius

Iamblichos,AKA “ruffian,”slew.old Apollodoros

Anaximander’s walking stick,his evening constitutional.

Semele,importunate summons,the environing naught

Sos’thenes,our brother.called by God

Next, in post number three, we’ll see another type of “math poem” and we'll take a look at “mathematical prose.”

Friday, June 04, 2010

On Mathematical Poetry (Post One)

I’m titling this series of posts “On Mathematical Poetry” and in the days and weeks to come I’ll be revisiting and revising and emending my thoughts as necessary.

In my Logoclasody Manifesto I included a brief addendum entitled “On Mathematical Poetry” and there I stated what I hold to be the most important point in the whole mathematical poetry endeavor:

There has to be considered the analogy between the grammatical sentence (the linguistic sentence) and the mathematical sentence (the mathematical equation). Already (“mathematical sentence”) I’m thinking analogically.

There has to be considered the analogy between the grammar of the sentence and the “mathematics” of the equation (i.e., of the mathematical statement).

And these are the examples I gave:

     Change + purse = church.
     kite + propeller = wing.
     to + to = too.
     am = be + I
     secrets = ? + whispers

Here I offer a working definition of “mathematical poetry”:

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.)

If these are my formal symbols (and as such indicative of operations):

     +, =

What then are my poetic elements?

     ideas and images

(i.e., “to,” “am” and “be” are ideas, while “kite” and “propeller” are images, and an image can at the same time be an idea, and be as general or abstract as it can be specific or concrete)

Wednesday, June 02, 2010

This Saturday, June 5, 2010, will be “Jack Foley Day” in Berkeley, California. On this day Jack Foley will receive a Lifetime Achievement Award from the Berkeley Poetry Festival .

Congratulations, Jack Foley.

Walking Across Brooklyn Bridge

by Jack Foley

As we walked across the Bridge,
  I thought of Hart Crane
    (poor suicidal poet)
      & of Joseph Stella
whose paintings are like chords struck
  on the harp strings
    of this amazing edifice
Crane saw The Waste Land
  as a condemnation
    of modern industrial society
      (“so negative”)
    His answer was
      this marvel
    of spidery, delicate cables
      which swoop us into skies
of unspeakable beauty
“sleepless as the river under thee”
(Eliot: “Fear death by water”)
  Our guide, Gregory,
quietly told us stories,
      raged against the sometimes reckless bikers,
        & watched our wonder
            as we walked
        across this passageway
        from busy life to busy life—
            this “between”
          suspended over water—
            that took us
            into the sky
          & home to Brooklyn

With Jack Foley in NYC, 2005.