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Today’s lesson will start with something of mine that is so elementary I won’t bother to try to explain it:
More complex is the following poem by the only other mathexpressive poetry specialist besides myself that I know of, Kaz Maslanka, “Beginner’s Mind”:
Kaz kindly agreed to provide a brief lecture on this for presentation here:
“There are two ideas of perfection and they both take the form of a circle.
The mathematical expression shown in the piece is the analytic geometrical equation for a circle and it is so perfect in its conception that nothing in nature comes close to its perfection – it is infinitely perfect in its denotation yet, ultimately it is a manifestation of the mind.
The circle is also used as a symbol of infinity.
The swirling circle image was originally done with ink on paper and later digitized. The image is of the Korean Il Won Sang or Japanese Enso. It connotes the perfect idea of emptiness. Many Zen monks practice drawing this circle as an exercise to focus on the present moment.
The Chinese characters in the background literally say beginner’s mind.”
I love its title. “Beginner’s mind.” That, I feel is exactly what we should all be using when encountering a poem—especially what I call an “otherstream” poem, the otherstream being where poems of a kind (like mathexpressive poems) not yet certified by the Poetry Establishment can be found.
To pin down (tediously) what Kaz’s poem objectively is most exactly, because I deem it worthy of a full-scale examination, I say it is first of all something to be read since it consists of Chinese words, and mathematical symbols I consider likewise to be words because they represent sounds those understanding them will interpret as words (e.g., “squared”--and “ex,” which here is a letter used as a word rather than just a letter). It is also what I call a “visimage”—a visual image in a much larger sense than printed words are. The verbal and the visual interacting: hence, a visual poem.
This is important to know; otherwise one may take it as just an equation with a pleasant design as a background—an equation with no aesthetic significance. But, to me (aided by its author’s commentary on it), the equation, by existing all by itself in otherwise empty space, poetically represents something reduced (but also intensified) to the perfection of the wholly symbolic.
Below it is the clearly unabstract, roughly and swiftly made, incomplete circle, acting as a specific specimen of what the equation universally denotes. It, too, is alone in otherwise empty space. I think what it connotes is especially vivid in comparison with the equation’s lack of connotative value—of sensual connotative value, at any rate. (Nothing can avoid being in some way connotative. One thing this, or probably any, equation, connotes—as the image on the page it can’t avoid being--is a kind of philosophic ethereality). As Kaz points out, his Zen circle speaks in an oddly earthy way of infinity, of rushing somewhere it will never get to as the infinite does, but speaking of the never-beginning, never-ending structure that it attempts to portray.
Note that the circle has a texture, as the equation does not. Width and thickness, too.
Then we have what suggests to me a calendar behind the equation and uncompleted circle, an implicitly unending repetition of durations. A mind, eternally churning—at its beginning, turning a seen circle into a felt image, then ascending into an equation for, its perfect essence.
Final result: the marriage of the physical and the conceptual in a manner almost impossible for either words alone or mathematical symbols alone to achieve.
With Connie Tettenborn’s “Staying Centered,” we return to the formula for a circle’s circumference, “pi times twice the radius,” which she makes equal to the never-beginning, never-endings circle Kaz Maslanka had in mind, as a way of evoking what the inner remoteness of jogging long distances is like. Nicely adding to the experience are the repeated glimpses of the ground the countless footsteps are covering, covering, covering.. But note how these glimpses ever so subtly suggest where the wandering thoughts may be going. . . .
Next up, “The Mind of Wallace Stevens,” a work of mine inspired in part by “Beginner’s Mind,” but also by a fear I might not have enough poems for a full entry this time around. As is the case with all mathexpressive poems, it has a good deal to do with the abstract versus the material. To the left of the equals sign is the standard formula for the volume of a sphere, using “the eternal sky” as the radius of the sphere involved, which the righthand side of the equation says equals the mind of Wallace Stevens. The sky seemed appropriate to me because above us, and seemingly close to being abstract because so unsensual, as well as huge, the way Stevens’s poetry so often seems.
Note that I didn’t use just “sky” for the radius, I used “the sky”—because I meant the whole thing, not what might be only a local piece of it, or less. And I said, “the eternal sky,” even though aware how that risked sounding pretentious, because I wanted to underscore the size of the sky in time as well as in space, thus implying how much sensual matter it must have, and Stevens’s poetry and mind must have (clouds and birds being only the most obvious of this matter). To repeat that point, I give the words denoting Stevens’s mind color, color which at times cannot be contained by it.
Working with the letters on the other side of the equation, which include the Greek pi (which is also in this case a full word), I provided outlining to them in hopes of subtly making what they denote more than what they denote. Again, the concern in my work with the idea of the difference between a mathematical symbol (or any other kind of symbol) of one color and the same symbol colored differently. And of employing color where it normally is not in poems to make a poem new, which is by now a boringly unnew idea, but still valid.
Now for a circle whose area rather than circumference is what’s important, Andrew Topel’s Sound1. He did not plan it as a mathexpressive poem, but I liked it so much that I made it one so I could show it here without guilt feelings. It was easy: I just determined the value of its radius:
I did the same with a second circle of Andrew’s that I liked, coming up with:
Okay, let me be honest: neither of the values of these radiuses is completely accurate. The first, in fact, is off by more than a quarter tone. But do keep in mind that this is only Mathexpressive Poetry I. And if you use an exponent of the correct color, you’ll be off less than a trillionth.
I couldn’t resist including the untitled work by John Moore Williams above, so ordained that the symbol for infinity is two circles to make it fit the circle theme of my entry. I laughed when I first saw it—laughed in awe of it! And at its sheer cleverness. The plainest element of arithmetic, one, is shown in contrast with the weirdest (if zero isn’t, and zero is visually there, too!) Matter and anti-matter as well as a kind of negative/positive dichotomy. And the wonderfulness of scientific symmetry (however incomplete physicists may be finding it of late). Somehow it describes the entire cosmos for me!
Speaking of which, here, from Sue Simon, more explicitly, is such a description:
According to its creator, “this painting describes the 4 dimensions that we know: first, second, third and the fourth, which is time. String theory proposes several more dimensions so I thought this painting would ask the question ‘how many are there?’
“The equation: time dilation. In the equation t=time, v=velocity, c=speed of light.”
(Note from Blogmeister Grumman: there are only 4 dimensions.)
I included this because it has a circle—a sphere, too! I find it extremely visually appealing, but especially delight in the tension between ethereally Platonic visual representations of geometry and colorful ungeometry—with the simple red 4 and the elegant equation taking the work beyond visuality into pure thought. On one hand, too, it is crazy—but so carefully, uncrazily laid out in nine squares (for 9 dimensions?) The way the outlined square (as I take it as) in the top left interacts with the also white non-square in the middle is just one little move the work carries out that makes it a continuing source of fun simply as a painting, as well as being what I consider to be a visiomathexpressive poem.
It suddenly occurred to me to bring back the circle below, Carlyle Baker’s, “Random Number,” because I think it works interestingly with “Are There Only 4 Dimensions?” Maybe someday I’ll be able to say why.
I was so pleased with Sue Simon’s piece, by the way, that I asked her if she had any pieces with circles in them that I could use here, and she sent me three really nice ones, including, “Black Holes,” which I decided to include because it was the only one of the three with explicit math in it.
About this, Sue says, “I am fascinated by the thought of a black hole where nothing can escape. This painting uses a bit of artistic license to think about these strange and interesting places. The equation: Maximum black hole angular momentum.” It is not really a poem so much as a labeled painting, but I’m not letting taxonomical rigor keep me from presenting first-rate material!
To finish off my entry, I thought I would show you three pieces by Karl Kempton, whose work will be the feature of my next entry. They aren’t mathematical, but they are circles, so not wholly off topic. The top two are from a series of his called Rose Window: 29 “windows,” the first three containing all the letters, the other 26 each built of repetitions of one of the letters of the alphabet and nothing else, ending with the same sort of views into the world around us that the best of cathedral windows provide—ergo: the alphabet as the means toward stained glass enlightenment. . . .
In his third piece, Karl uses the word for the rose and fragments of the flower to reach a similar peak.
I didn’t see the word, “rose,” at first, but assured by the author that it was there, I found it:
Previously in this series: