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Karl Kempton, whose math-related poems will be the subject of this entry, and I have been friends for some 30 years. It’s been an odd relationship. On the one hand, we’ve both made all sorts of different kinds of poems, particularly visual and mathematical ones, written about such works, and run money-losing enterprises committed to the advancement of the same kinds of otherstream poems, as I call them, he with his famous newsprint magazine, Kaldron, now become a website, I with my Runaway Spoon Press. On the other hand, when it comes to philosophical outlook on existence . . . Well, maybe a few words about the following two poems, one I wrote for him, and one he wrote for me, may best reveal our differences there:

Mine is pretty straight-forward, just a long division in which an attempt is made to divide Psyche, the goddess of the mind whom Cupid fell in love with, into summer. But it’s a joke: Karl’s favorite bird (I believe), the crow, who should be the quotient, flies into what I call the dividend shed, breaking up and scattering the summer—and yielding, when multiplying Psyche, just a fragment of autumn, the latter equaling the scattered pieces of summer when a fragment of laughter is added to it.

The idea of the poem goes along with a favorite belief of Karl’s, which is that western math and science can’t significantly help us understand things like summer or crows. A dividend shed can’t contain summer, nor can a long division example keep a crow from acting up.

The irony of the piece is that I completely disagree with what it’s saying. Okay, not completely disagree. What I believe is that the use of mathematics (and other scientific techniques) not only can get us as close to absolute truth as it’s possible to get, but that they are the sole effective means of understanding existence. I know, even scientists haven’t believed that for the past hundred years or so. But I do agree that some forms of science—scientism, some call it—are awfully superficially at explaining things like summer and crows. So my poem works, for me, as a portrait of science going wrong, as it sometimes does.

Karl’s poem for me shows how close we are as artists, in its playfulness and—of course—its moves beyond conventional poetry. But, unlike most of my poems, it is didactic, focused, as so much of Karl’s work is, on the value of selflessness. It flares out of its mathematics into eastern mysticism, too, as I, strictly a scientific materialist, never let mine do (although some of those can get a bit metaphysical). When it comes to philosophical outlook on existence, Karl and I are not at all on the same page: think Plato versus Aristotle, Hamlet versus Horatio, Eastern Mystic versus Scientific Materialist. The arguments we have!

Note: the backward parentheses are intended to emphasize what they enclose; they have no mathematical meaning. The j represents the selfless devotee of bhakti, the I the brash individualist, “proud of its muse numerology,” by which I suspect Karl means the rationalism of mathematics-based science. Basically, it is a celebration of his spiritual way of life, which I can empathize with as a celebration of the search for meaning.

Karl had what he considers a “timeless, spaceless, non-duality, Bliss-filled” mystical experience at the age of 14 that didn’t take; in fact he left his childhood religion shortly after having had it. Later, on first meeting the man who become his guru, he had the experience again, and has spent his life refining on it, and expressing in his art the spiritual outlook which, for him, makes such experiences possible, and opposing outlooks he deems more limited—generally in a quiet, non-confrontational way. It has made him an active advocate of sane ecology, a defender of sacred Amerindian sites from what he considers archaeological abuse, a committed student of various ancient stone monuments he believes were used as sophisticated astronomical observatories, a champion of women’s rights, and long ago an opponent of the Vietnam War, which his first (very conventional) poems were about, among other things. What’s most important as far as my blog is concerned, though, is the importance of his spirituality for his poetry.

That spirituality thrives most for him outside established, religious organizations. Hence the following work that I had at my first installment of this blog:

Here he compares Buddhism as an institution versus what he terms “its mystical ch'an/zen paths to enlightenment. religious setting has its closed gates and no trespassing signs.”

“the spiritual path,” he goes on to say, “is such that the temple is wherever one sits or stands, i.e. within. there and here are the same or have no real difference--the words themselves are identical when one is deep in meditation.”

This makes sense to me. Where the gulf between us shows up most is in the few works of his that take on the conflict between the idea of realities mere rationalism is helpless at dealing with such as the following:

What to say about the above? It’s one of the visioconceptually most interesting pieces in Karl’s Three Cubed, an extensive selection of his mathematical pieces my Runaway Spoon Press published in 2003. I struggled mightily trying to figure it out, though, finally giving up and asking him for help. Here’s what I first got from him (slightly modified for clarity):

T stands for the edifice, the central architecture of the piece

on the lefthand side are 3 less-than signs and 3 identical signs, the right = signs

empty sets divided by over-lapping empty sets

full sets divided by empty sets

squashed empty sets = two overlapping empty sets divided by full sets

right side 3 greater than signs and 10 equal signs equaling nothing and zero

right side under the cross bar or bridge of the T is an array of empty sets and sets with a mark that is open to interpretation. the same mark also free in places

all this adds up to or down to the metaphor for philosophical and mathematical architectures of rational interpretation made by the mind within the mind that can not explain that which is outside the mind.

I’m afraid this left me more beleaguered than I’d been before. I needed more details. As we continued discussing the piece, a bit heatedly at times, I learned that the T stood for "Truth" which made the piece a satire on science's attempts to come significantly close to it. I felt it wasn't at all fair to science since it didn't show any process close enough to actual science effectively to mock it. We ended at the same nowhere our discussion had begun at.

That wasn’t the case with Karl’s “The Root of Pi”:

The first version of this I saw had no labels. It made no sense to me. With labels, it’s clearly an “visioarchaeomathematical” poem tracing the source of the invention of pi to ancient like Stonehenge. How valid it is archaeologically I don’t know, although the ancients’ use of circles may well have originated when their study of the sky caused them to create their observatories—the first buildings for science? In any case, the piece certainly works as art.

A useful sort of comment on it is Karl’s poem, “Ka”:

taking away the hands

the egyptian glyph for soul



stands as a doorway

measured by those hands

taken away

the value of

the golden section

and pi

the greek letter

stands as a doorway

the three poles |||

the number ka makes

the call of the crow

(Note the crow.)

Probably my favorite mathematical poem of Karl’s is the following poem for Amy Francheschini, his “bonus daughter,” an artist who seems to be at least partially influenced by him if the title of a book she recently contributed to, Variation on Powers of Ten, is any indication.

Clearly, verbo-visual puns are a key element of Karl’s tool kit. One you may have missed in the preceding is the black dot’s representation of the sound “awe.”

Next up is one of the first math-related poems Karl made that he was satisfied with:

When I sent a copy of this to a friend of mine on the Internet who calls herself, “Knit Witted,” and blogs at http://knitwittings.wordpress.com/, we had a discussion about it after which she sent me the following, which I liked enough to add it to this entry. Another good reason for its presence is the way it illustrates my understanding of Karl’s piece. I take it to be showing Zeno’s four steps from his starting place, which we can assume is zero, any line’s starting point, to . . . zero—as his famous paradox proving change is impossible because it requires a thing to move and nothing can move, because in order for it to move from anywhere at all to anywhere else, it would first have to move to the point halfway between its starting point and its goal; and in order to do that, it would have to move to the halfway point between its starting point and the halfway point to its goal; and so on ad infinitum. In other words, it would always have an infinity of points to reach before it could get to its goal, so would never get there, or get anywhere.

Since there seem to be philosophers who still believe that Zeno was on to something of intellectual importance rather than merely revealed an example of the kind of paradox every system of thought will have, but the real world will never have, like Georgi Cantor’s infinities that are larger than the number of integers, I feel compelled to point out why Zeno was wrong. It is that in the real world there is no such thing as an infinitely small distance. There is, so far as we’re concerned, a smallest possible distance—I imagine it as a sort of quantum locus in space. In any case, it is a space without any halfway point between it and the similar space right next to it. An object in that second space can get to it without first being at a halfway point. And that, my friends, is why our eyes tell us thing move.

I would add that the fact that we can see things moving demonstrates that not everything true in mathematics is true in the real world, as many mathematicians and physicists seem to think. That mathematics has an infinite number of dimensions does not mean our reality has more than four.

Okay, if all that doesn’t at last get me some comments here from mathematicians, nothing will!

That Karl’s poem got me going the way it did, and inspired Knit Witted’s zany piece about the relationship of infinity and zero is really the important thing here. I contend that a prime value of it, and other works like it, is their power to trip those encountering them into offbeat—perhaps even preposterous but interesting—otherthinking like Knit Witted’s about the inter-relationship of zero and infinity, and mine about absolute positions in space.

Another of Karl’s earliest works is the following:

Here’s what I said about this many years ago when I first saw it: “When in the poem above Karl Kempton repeats his first word in steps distributed through three lines, a reader not familiar with his work might be puzzled. Of course, the sentence that the poet has converted his small word to should soon become apparent. But that sentence makes no sense--the "1" that Kempton has punned out of the letter "I," can't equal ten. Is his stunt only clever, then? I say no, for to me it buoyantly shows, even as it asserts, the multiplicative power of both "listen," the word, and listen, the act: if only we listen, truly listen—not only to a text, but into it, down to its very letters, and the cracks between them--our world will increase tenfold.

“No, wait. Not tenfold but fiftyfold! Or so the poem goes on to state, whereupon the poetic rightness of Kempton's claim suddenly marries the counter-poetic rightness of a roman numeral l's equaling fifty.

“Through this rich interplay of the intuitive and the rational, the poem draws us into the concrete heard of "loose and klinking chanj" (like the loose and clinking letters in Kempton's repetition of "listen")--and at the same time into the high generality of change, as a pocketful of pennies becomes a boy's magico-economic version of the"magico-esthetic transformative device that words and letters are in the pockets of poets. Thus does Kempton's trinket deepen dozens of colors beyond mere cleverness into a full-scale lyrical celebration of boyhood, coins, letters, Rome, mathematics, English--and the secret of listening things into poetry.”

I still think I know what I was talking about.

While some not in sympathy with mathematical poems call them puzzles as though that were some kind of mordant disparagement, I’ve always tended toward the belief that a poem that is not a puzzle is limited. True, if a poem is nothing but a puzzle, then one might properly argue that it lacks the substance to be considered a Major Poem. To which I say, “So what?” Puzzles are fun!

They are more, too, not that fun should ever be considered not enough. They are good exercise for the brain. In the case of the following, they give a viewer exercise at something hardly anything else does, reading and seeing a path to a solution, or a kind of double scrutiny that too few are good at, or even capable of doing—or, worse, even aware can be done—and, I hold, can sometimes lead to a solution nothing else will.

Be that as it may, the first of Karl’s puzzles below is also a joke (as I hope some of my visitors will instantly know). The second is a variation on the first in which the eye becomes more important.

Then we have a similar joke. Explanations of the three at the end of my entry—because I want you to think about them for a while (as I had to, not being that swift in spite of how familiar I am with Karl’s work).

The next joke by Karl is mainly verbal:

For Karl at his pop art best there’s this:

Now for a rouser to end our tour of the Works of Karl Kempton::

I take it to be a dynamic representation of gravity in all of its infinitesimal manifestations down & up the three spatial dimensions of our world.

That’s it for our too-brief visit to one of the odder but most profound frontiers of the meeting of mathematics and poetry. I hope you enjoyed it.

P.S., Karl’s first math joke shows an eight as the square of a zero—since the eight is a sort of sideways multiplication of two zeros. The poem under it finds the eight to be zero taken to the fourth power, but this time the zero is one- rather than two-dimensional. The key to solving the poems with 180 degrees in it is that the 180 degrees should be taken as rotating the E—to go with one-half of an 8 to make a 33.

Previously in this series:


M@h*(pOet)?ica: Summerthings

M@h*(pOet)?ica–Louis Zukofsky’s Integral

M@h*(pOet)?ica—Scott Helmes

M@h*(pOet)?ica—of Pi and the Circle, Part 1

M@h*(pOet)?ica – Happy Holidays!

M@h*(pOet)?ica—Circles, Part 3