On Mathematical Poetry (Post Four)
(On Mathematical Poetry (Post Four) was originally going to be about “mathematical prose.” I’ll post those notes in the near future. In the meantime, regarding “mathematical prose,” see below for paraphrase and the mathematical statement.)
Notes on Bob Grumman’s Christmas Mathemaku
and on mathematical poetry generally, or, how to deconstruct a division sign
First things first: I think the only fair and general term that one [that we?] should use is “math-themed poetry.”
I think the term “mathematical poetry” ought to always be in quotation marks. And one [and we?] should use the term, “math-themed poetry.”
I think it is fair, and within our power, to maintain that this poetry is “influenced” by mathematics. But the claim that this poetry is “carrying out a mathematical operation,” has, in my opinion, not been substantiated and is, in my opinion, false.
The reasons for these things ought to be immediately obvious (and if they are not, then I think we’ve gone beyond the usual skepticism and cynicism and have entered the realm of the incredulous).
If there is indeed something we can locate and identify as the math-themed poetry community, then it is in no way a “close-knit” community, but is made up of quite various and distinct individuals (not all of whom are established poets) with quite various and distinct ideas as to what a math-themed or “mathematical” poetry should look like, and a constellation of probably only three so-dedicated blogs. I am concerned here with just one creator of math-themed poetry, Bob Grumman, because Bob has probably been doing it the longest and his is the work that I am most familiar with (having interviewed him on the subject and, probably, having written more words than anybody else on his work), and because Bob claims that his “mathemaku” “in long division” is actually “carrying out a mathematical operation.” And because Bob has a blog at the Scientific American Blog Network, with respect to which I am writing this in the spirit of a peer review.
Which raises an interesting question: Who is the “math-themed” poet’s peer? The poet or the mathematician?
One particular opinion, which I have frequently encountered, holds that only the capital M mathematician is a real mathematician while anybody and everybody (who tries his hand at poetry) is a poet. This opinion is held by mathematicians. (I’m tempted to rest it there, but I’ll go on.) The fact is there are instincts for poetry just as there are instincts for mathematics, only the instincts for poetry cannot be taught; they can be aspired to but they cannot be won by rote.
As for who is a mathematician, it is my opinion that anybody and everybody is a mathematician who uses math. We are surrounded by math and mathematical concepts; anybody who has ever taught math to a child with zero interest in math knows that the way into his “mathematical heart” is to awaken him to the fact that he is already a mathematician, and this is done by demonstrating to him that he is already using, and being used by, mathematical concepts all the time, only now he is going to be aware of it and from now on he will avail himself of it with facility. Plato’s Meno, anybody? (This is not to downplay the difficulty in teaching math to a child, boy or girl, with zero interest in math, or with zero attention span.)
Rather than “math-themed” poetry, I think math art is better suited for teaching math. I don’t put math art in quotation marks because with regard to the math art object the claim is not being made that it is carrying out a mathematical operation; it seems one can demonstrate a math concept in action without actually doing any math.
About paraphrase: To see a mathematical statement is one thing while to speak a mathematical statement is another, in that when we speak it we paraphrase. (Seeing / listening. We see the sign (a physical form), the signifier / we hear the sense (a meaning), the signified.) *
With regard to the claim that the mathemaku (a lovely name, by the way, that I have suggested might mean “learned-” ku) is “carrying out a mathematical operation,” Bob’s only evidence, his proof, ultimately, is the mathemaku itself.
This is not to downplay that steady stream of interpretation (the paraphrase, restatement and what is ostensibly establishing argument) that surrounds the mathemaku and the other examples of “mathematical poetry” that Bob exhibits. On the contrary, this steady stream of interpretation is quite imaginative and ofttimes fascinating, if more poetical than mathematical. Which is to say, literary exegesis is not the step by step, sequential analysis and elucidation we expect in mathematics, which may, however, and with regard to Bob’s interpretive wit, ultimately prove to be inappropriate for the math-themed poem (in particular, the “mathemaku”), which asks to be known in its entirety, to be apprehended as a unity—given more readily to sight than to intellection, and this despite the three-step division-multiplication-subtraction usually associated with the long division problem.
Recourse to the mathemaku itself, and to the reader’s technical expertise in mathematics, as the final determinant of whether the mathemaku, or as to whether any such “mathematical poetry” is actually carrying out a mathematical operation, is, in my opinion, a dodge—it is tantamount to saying, You don’t see it as I intend it because, mathematically, your knowledge is not equal to mine. Or else, who is the “mathematical poetry” for? Is it for capital M mathematicians, or for readers generally? (If it is only for capital M mathematicians, then I would expect that it was actually carrying out a mathematical operation. If it is for readers generally, then I would expect, and I would settle for, an analogy based on the semantics (the meaning, the content), if not on the syntax (the order, the address), of the words and the mathematical operations of, in this instance, the long division problem (yea, the long division table).)
As for the level of technical expertise required to “read” and to comprehend the mathemaku, we are reminded that we are at the “level” of the long division problem, and Bob’s mathemaku, or, rather, let’s just stick with the “Christmas Mathemaku,” never goes beyond the first step in the long division procedure, namely, the division step. (There does not follow a multiplication step, nor a subtraction step.)
Why do I say never goes beyond the division step?
We can say that when it comes to long division, Bob is taking poetic license—he is departing from the conventional rules in order to create an effect. ** If we left it at that, there would be no debate. But Bob’s blog is not just anywhere, Bob’s blog is a part of the Scientific American Blog Network. And why (is Bob’s blog a part of the Scientific American Blog Network)? Apparently it is because his mathemaku is carrying out a mathematical operation. (Someone at the Scientific American Blog Network must agree with him!)
Well: That IS the question. Just what IS Bob’s “long division poem” doing?
Let us then begin at the beginning, and to do so we begin at the “division sign.” Here we see not an obelus, but what we will for our purposes refer to as “the long division sign” (or what is, technically, a vinculum attached to the top of a close parenthesis). We begin here because this “long division sign” immediately identifies the poem as a specimen of “mathematical poetry,” and we have to ask, What role does it play?
What role does the division sign play in the mathemaku?
The first time I laid my eyes on Bob’s “Christmas Mathemaku,” I mistook the division sign for a toboggan. Now that’s not hard to do when you consider a toboggan, in profile, anyway, is made up of a vinculum and a parenthesis—just turn the profile upside down and change the open parenthesis to a close parenthesis. And I thought, What a lovely Christmas postcard!
I was focused on the long division sign. My eye instinctively, learnedly, went straight for it. And I was asking, What do I know that I should know to begin here? What role does this sign play?
I know that, beyond identifying the poem as a specimen of “mathematical poetry,” the division sign signals that here, at this place, this is my point of departure. It signals that here is where I am to begin if I am “to read” the poem, and it signals that here is where I am to begin if I am “to solve” the long division problem. And it does this without contradiction. The division sign, as point of departure, holds true for both the poetical and the mathematical “operations” of the mathemaku. And so: If the division sign is going to operate both mathematically and poetically, and without contradiction, then the division sign needs be so construed, so interpreted, that both poetry and math can share in its operation. And so it is, first of all, a point of departure.
But it would not suffice to end it there. For beyond indentifying, beyond locating, the division sign is also instructional, indeed it is prescriptive—it is in that the division sign also signals a rules for procedure. Most importantly of all, the division sign signals a rules for procedure.
What is this long division sign signaling, expressing, here in this “Christmas Mathemaku”? Is it not at once stating a problem and a poetry? Is it not stating:
“Christmas divided by children,” or, “[how many times] children [will go] into Christmas.”
If so, how then reconcile, how then make the one consistent with the other, this poetical idea and this mathematical statement? (Indeed: How apply these rules for procedure?)
“Christmas” cannot be “divided by children.” Not literally, which is to say, not mathematically. But if we read it as “children into Christmas,” and rethink it as “children” and “Christmas,” we begin to see what our poetical steps are leading to.
But this is not a mathematical demonstration, let alone the procedure for long division. Rather, this is a demonstration of semantics! (One might here object, that this is not a matter of stating a long division problem at all, because long division problems are made up of numbers, not of words. But that would be to miss the point of “mathematical poetry,” which is to use semantics in a way that is analogous to mathematical operations!)
Let us return to the division sign and ask once more, What role does this division sign play? Because it is here, I think, we’ll see just where our poetical-cum-mathematical steps are leading.
Now consider, that just as the long division problem is said to have, or to unfold, if you will, a table, the “Christmas Mathemaku” may be said to have, or to unfold, a tableau. What must be the case for this to be so?
We have seen how if taken as “a point of departure,” the division sign can be both mathematical and poetical without contradiction. And yet, where concerns “a rules for procedure,” we must have recourse to semantics if we are to proceed beyond the contradiction of using words in place of numbers. What other role, then, might the division sign play in the carrying out of the operations of the “Christmas Mathemaku” in its unfolding of the mathemaku tableau?
Now consider, that just as the long division problem unfolds its table by proceeding by way of an analytical calculation, the mathemaku unfolds its tableau by proceeding by way of a collocation of images.
This collocation of images, thusly arrayed, which is to say, expressively visually arrayed, adds up to a tableau, a picture.
The mathemaku picture is quite distinct from the long division picture, and not only because the one is made up of words while the other is made up of numbers. The mathemaku has its own dynamics and its own sense of coherence. Its dynamics are not those of an analytical calculation and reasoning, but are those of semantics and word association. Its coherence is not a mathematical coherence, but an emotional coherence.
There is a sense in which numbers are evocative (certainly, certain numbers we associate with certain events in our lives—birth dates, death dates, anniversaries and such), but as to any sentimental appeal, the number as number, notwithstanding a certain platonic appeal, the number as number cannot move us to reverie and to reminiscence, it does not bring to mind such memories and feelings as of tenderness or sadness or loss, it is not associative.
In its proceeding by way of a collocation of images, the mathemaku moves by content, not by address (which is to say, it moves by virtue of what these things are, and by the sentiments they in turn evoke, rather than by where they belong, which is to say, by their place in the long division table). This is the movement of a poetical expression, not of a mathematical expression. This movement, in analogy to the calculative steps in the long division equation, is by association.
And now we ask: What must be necessary for this analogy between the long division table and the mathemaku tableau to work? What other role must the long division sign play—and play without contradiction?
The division sign signals to be the equivalent of to rule lines on paper. That is its most significant role, for without that there would be no structure upon which to find the poetical tableau that is the entire visual and semantic field of the mathemaku poem. The division sign signals to be the equivalent of to rule lines on paper. That is its most significant role, for without that there would be no structure upon which to find the long division table, for without that there would be no structure upon which to find the poetical tableau that is the entire visual and semantic field of the mathemaku poem.
* About paraphrase: To see a mathematical statement is one thing while to speak a mathematical statement is another, in that when we speak it we paraphrase. (Seeing / listening. We see the sign (a physical form), the signifier / we hear the sense (a meaning), the signified.) Indeed we hear a word, a name, what is representative of that physical sign, and from this we construe a meaning. Not counting the name as a sound form, we are some steps removed from that physical sign, and are in the realm of mental representation, and so perhaps we ought to speak of this as meta-phrase.
** Bob writes in a footnote: “ . . . I am proud of the way this poem slops [sic] anti-mathematically out of the extremely formal and rule-bound structure than [sic] a long division example is. I bring this use of carefree art against rigorous science not for the first time to advertise the long-division poetic form as often as possible in hopes of inspiring other poets to use it.” (Capital M mathematicians may leave it at that.)