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 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.”


  1. Dear Gregory,
    You didn't answer my question.

  2. Hi, Kaz.

    For technical reasons beyond my control, this is part one of my reply. The other parts will follow directly.

    The reason I did not answer your question(s) is because your question(s) is the sort of question(s) that begs the question

    Did you read the essay?

    and I did not want to seem rude. But since you insist: You ask where are the “mutually” inverse operations (did you mean to emphasize mutually, Kaz, as though the “mutually” aspect is what you do not get, or did you wish me to write them, the operations, out, as I would write out the permutations, the combinations, the pieces are suggestive of?) and you ask which elements are the formal symbols. My answer: Gee whiz, Kaz, if these points are not obvious to you, then the entire concept, nay the wit of it, is lost on you.

  3. Hi, Kaz.

    This is part two of my reply. The other parts will follow directly.

    The entire concept, nay the wit, of these pieces, “turns” on the understanding of “mutually inverse operations” (it is “a play” on the “mutually inverse operation”) and to a small degree the play on “verse” which it pains me to have to point out — it’s as though I have to remind you that you’re reading poetry and all the things to look for when reading poetry, and that you must read differently than if you were reading a mathematical equation, which is to say if you are going to read this “literally,” in spite of that I make it perefectly clear in what sense (metaphorical, allegorical, figurative — these are the way of poetry) I am to be taken, then the failure to launch is yours, not mine.

    The “poetic” elements (the words that are the ideas and images) share (they must share) a common, consistent logic (enabling at once an integration and a differentiation), or else they would not be able to survive, semantically, their outcome. And this should be obvious to the reader without any permutations taking place. All the more frustrating when my audience is a mathematician, as I expect the mathematician to see it and to get it immediately. Mathematical poetry is a form of “conceptual poetry,” if you will, and if you do not get the concept, or if you simply refuse to grant the concept, and be smugly conventional about it, then you will not get it. Without the concept, you can’t see it.

  4. Hi, Kaz.

    This is part three. More to follow.

    I must say, my friend, I think your thinking in this matter is remarkably two-dimensional. You have to think three-dimensionally, and that third dimension is the analogy. That’s the getting of perspective. That analogy makes for the metaphor and for the allegory and above all for the poetry. It’s the zen. It’s the ch’i. It’s the wit. It’s “the poetry.” If you can’t get the analogy, then you can’t see the poetry. And curiously enough, I think it is the same analogy at work in your own “mathematical poetry,” and that you do not see this, well, my reaction is the logical equivalent of a raising of the eyebrow. (The same for Bob Grumman’s “mathematical poetry,” but with Bob I am convinced he simply does not know what an analogy is.)

    When you use words in place of numbers, which is to say, when you assign quantity- or magnitude-values, so to speak, to words, or when you assign grammatical or semantic outcomes to what are otherwise mathematical operations, you are working analogically, whether you realize it or not. (That’s the way language works.)

  5. Hi, Kaz.

    Last part.

    Another point: The “sum” of a mathematical poem need not be the same for everyone. If we’re going to make up mathematical poetry rules, then that’s mine.

    And btw, to “write out the permutations, the combinations, the pieces are suggestive of” is not necessary for the getting, or, for the appreciation, of the concept. That is not the point of the poems and indeed I do not expect it or require it of my reader.

    The idea, the task, is to take a mathematical operation and by analogy create a trope, a sort of formula, for making poetry out of it.

    Peace, Kaz.

    Yrs, Gregory

    PS: I wish to repeat here something in my reply to Bob:

    When I state, “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,” that is not meant as an unqualified assertion on the order of, “This is a poem!” That would be ridiculous. It is, rather, an invitation.

    In my Logoclasody Manifesto I speak of a passage from the creative intuition of the poet to the receptive intuition of the reader and state that this requires a sort of previous, tentative consent to “the poem” and to the intentions of the poet, without which we cannot be taken into the confidence of the poem. And that this requires a certain relaxing of the critical intelligence, for how can you reflect upon an experience if you have not first had that experience? But once you have had that experience, you are free to judge it as to whether it has satisfied your expectations, critical or otherwise.

  6. Gregory,
    I never question your poetic insight however when creating double-entendres they both must make sense – mutually “in verse” operations make perfect sense however you mislead your readers by creating a mathematical context to which meaning must be gleaned. Inverse operations have a specific meaning which has nothing to do with the equations that you have supplied. You say that ‘verse’ plays a small role yet it seems to me verse plays the entire role. You feel that I am taking the literal path yet how can I ignore the mathematical meaning of inverse operations when you supply the mathematical context - yet you ignore mathematics and the meaning of inverse operations. There are no mathematical inverse operations in your examples. This is your biggest sin that I see. You have supplied the poetics yet failed the math or at least mislead the math. Furthermore you did it again with your transverse lines by redefining the “does not equal” symbol to mean “transverse line” If your use of “transverse lines” also made some sense with the idea of “does not equal” then I would be happy to embrace the clever move you believe you made- yet, it makes no sense to me. Your “Transverse lines” is an extension of your logoclasody manifesto, a trope or analogy to a simple geometrical form. Ok you are going to claim that this whole discussion is over my head - and if that is true we will really never know until our audience is a bigger one well versed in both poetics and mathematics – we can both claim the higher ground, however, for the time being this conversation looks like no more than three artists with no audience and delusions of grandeur. Can you, I or Bob speak to both artists and mathematicians simultaneously? That is the real question and real challenge. Can we bridge the aesthetics between these two fields? I find it has become much more difficult than I had imagined ten years ago when I first saw the quest. This conversation is a reminder of how difficult it is.
    As far as getting your analogy – I get it or let’s say I get something from it yet I have to ignore those areas where you mislead me. I see how you are connecting your mathematical analogy to logoclasody, I see how you are connecting the analogy to a geometrical form and I get how the poetry is in the breaking out of the eidetic through your analogy. It just dawned on me that what you are doing is much like or the same thing as the mathematical poems of Catherine Daly. In fact I should include this as a 5th type of mathematical poetry in my list which lies between mathematics poetry and equational poetry. It points at the possibility of the equation but does not fully realize it.
    The bottom line for my aesthetic or should I say “the muse that I follow” demands more; I want to see the equation, I want to feel the mathematical operations, ponder the units of measure and I want to taste the symbols. You point at the possibility of this in your transverse lines yet I want it to be realized mathematically not just described by analogy.

  7. Gregory says, ”When you use words in place of numbers, which is to say, when you assign quantity- or magnitude-values, so to speak, to words, or when you assign grammatical or semantic outcomes to what are otherwise mathematical operations, you are working analogically, whether you realize it or not. (That’s the way language works.)”
    Kaz says, “Of course we are using analogy, however, we are using more than analogy, we are using metaphor” It seems that you are missing that.

  8. Hi, Kaz.

    Only it’s not a sin against God; it’s a sin against Kaz.

    I'm happy you know you are using analogy. That's all I wanted to communicate.

    Yrs, Gregory