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A poem that fully demonstrates the value of a poem's including mathematics.is Scott Helmes's "Non-additive postulations." It consists of ten equations full of Greek symbols, square root signs, and terms like "noosphere / RBF." Their over-all subject, it seems to me, is sex. Probably the most accessible (and my favorite) of them is the one just quoted (which I posted in my first entry to this blog and now will try to make sense of, as I then said I would).
This equation at first seems strange, to say the least. But once one begins mathematizing, interesting things happen. First, "rudders" divided by "udders" becomes a simple "r." This being the first letter of "relationship," the sole term on the left, it brings one quickly and vividly to the "relationship" that shares that word with "r." And one begins whirling into thoughts of the complexity of human love, with its tension of leadership ("rudders") versus nurture ("udders") that is at the heart of all relationships' being, or "are-ness."
The square root of “alphawakes” over “oscillations” is tougher to make sense of. According to the logic of the poem so far worked out, it should equal “elationships” (which it’s wonderful to believe that some relationships would have!) Mathematically, this means the quantity “alphawakes” over “oscillations” squared should equal “elationships” squared.
If we want to get anywhere with this, poetic intuition must take over from mathematical reasoning (or the strange cousin of it I’ve been using). First, we must explicate “alphawakes." If we let the “wakes” part of it stand for both the opposite of going to sleep and for something associated with funerals, and have the right background in literature, we can grant it the rich ambience it has in the title of Joyce’s Finnegans Wake. Moreover, with ships of sorts involved, "wake" has yet another meaning with at least a little metaphorical aptness.
Finally, the "alpha" part of the word strongly brings to mind (as my friend Stephen-Paul Martin noted when reading an earlier version of this analysis) the "alphawaves" of the dream-state, and the "goddess" of that state, and of Intuition in general, Joyce’s Anna Livia Plurabelle (ALPha). The "alph" injects a bold sense of firstness into the meld, too.
I’m a little foggy as to how “oscillations" fit into it. It seems to me they would tend, by their division into the alphawakes, to reduce the latter’s bounciness—perhaps to tone down the frivolity of the relationships it is contributing to the meaning of.
In any event, the equation stirs varied images and ideas into the mind, which for me is a main function of poetry, and art. Its mathematical formulation not only serves vivifyingly and freshly to condense its message but to provide an almost absurdly
rational background structure to a subject about as beyond rationality as there is, the human male/female “relationship.” But here with another point of view on works like “relationships” (my name for it) is Scott Helmes his own self, in the afterword he wrote to Non-Additive Postulations and the Square Root of Other Poems, the book “relationships” was in—and my press published:
In the late 1960s and early 1970s, I had been reading a number of books relating to communication and inter-disciplinary approaches to education, such titles as Two Cultures and a Second Look (C P. Snow), Cybernetics or Control and Communication in the Animal and the Machine (Norbert Weiner) and The Medium is the Message (Marshall McLuhan) stand out. One afternoon, it occurred to me that mathematical symbols and instructions represented a separate independent language and wouldn't it be interesting to combine this language with the spoken and written English language. Not ever having written a poem previously, I then proceeded to compose/write about 15 poems dealing with mathematical ideas. Some of the works contained just written words and some contained a combination of mathematical symbols' and words. Wiener's book was probably the most influential, serving as inspiration as it contained mathematical equations which described communication.
What struck me about mathematics as a language was that the symbols are “translanguage.” For example, a Russian and English mathematician, neither knowing the other's spoken language, could converse for days about mathematical issues using the symbols. When the poems were first written, their visual appearance did not appear as striking as I thought they might have seemed in concept; maybe because I had taken physics, acoustics and other engineering courses as part of my college requirements. There was an “understanding” of them at least visually.
From this, and my own intuitive response to his poems, it seems to me their main function is to suggest the something beyond mundane reality as words wrenched (almost entirely) free of their denotations into nexuses of connotations by their equational re-contextualization rather than used with mathematical symbols in mathematical operations to poetically express old beauty from a new angle.
Ordinarily, I’d strike the preceding paragraph as pretentious, incoherent and dopey, but I’m choosing to leave it as is. I think it a good example of how a critic finding himself in a kind of art as yet rarely if ever effectively written about can have valuable things to say (as I believe I do), but fail to do anything but repel the intelligent reader, or at least make him shake his head in dismay, when he tries to use words to express those valuable things. (Although, alas, many critics will depend, successfully, on texts like the above to dazzle their readers!)
Okay, now for what I hope will be a better try. Like Duchamp putting a urinal into a museum, shearing it of its normal denotations so its attributes as a sculpture became visible (not that Duchamp seems to have realized that’s what he was doing), Helmes puts his poem into mathematical equations to minimize its ordinary denotations and release its connotations. It is equally true that he detaches the math in his works from their technical concerns to allow them . . . to have fun.
He is not concerned that a reader find the kind of story in what he does that I did, although I’m sure if that happens, it’s fine with him. He mainly wants to take his readers on mathematical adventures pure mathematics will never open into, adventures that are also verbal adventures no linguexpressive poems (i.e., poems that are linguistically expressive only) can open into.
In any case, here is the full set of “non-additive postulate” the poem I dealt with is from:
Notice what “relationships” equals in his second equation. Does that help you with it in the third equation? I think it rather contradicts what I said about relationships, which I thought positive! I’ll leave it to better mathematicians than I to decide. All I can say is that the concept of a “blueberryohio” even if not taken to the “tenth power,” makes being with these things worthwhile! And what about the multiplication of “recognition” by “without?”
I hope in a later entry here to return to these sorts of works by Scott, with improved ideas about them thanks to the world-wide discussion these remarks of mine on them will surely ignite. (Sorry, I don’t believe in emoticons, so you’ll have to guess whether or not I’m being sarcastic here.) Right now, however, I’m going to turn to something recent of Scott’s mathematical poetry in color!
I am proud to state that I commissioned this! “Do something in color for me,” was my command. So, to construct the above, he turned to the work Kasimir Malevich (1878-1935), the inventor of a kind of visimagery (i.e., my idiosyncratic term for “visual art,” you may recall) known as suprematism around a century ago, and considered (with Piet Mondrian) the most important pioneer of geometric non-representational art. Below is a detail from an early work of his called, “Supreme.”
I would describe Scott’s work first of all as a variation on a mathematical proof: a surrealization of such proofs that presents us with two equations we are to take as true, and told that from them the final equation follows. That final equation seems to me a wry squaring of the circle. In any case it gives us something quite fascinating to think about, those of us, that is, with the right short circuits in our brains: the question of just what a flat circle divided by a circle facing us would equal. Visually. Mathematically, I’m sure there are trig tricks, or vector manipulations, or the like, that would take care of the matter. Obviously, because computer programs can use math to re-orient images. But thinking only about a simple arithmetical fraction like this one, what might happen strikes me as rather profound.
Of course, that’s only me—but it’s still important because one of the principal things poetry is good for is nudging an engagent of a specimen of it into thoughts and ideas that seem to him profound, however ditzy they may seem to others. One might even go from my simple wonder into the larger wonder at the magic of exactly what it is mathematically that allows computer software to manipulate images.
While still on the final equation of Scott’s set, the question of how the yellow of the outward-facing circle and the grey of the flat circle will affect what they equal, and why what they equal should be black? Does the fact that the yellow circle has to go through a black division-denoting line have anything to do with it? Silly, yes—but a reminder that details count in poetry!
Much in the “proof” is left out—no doubt to be considered standard knowledge for poetimeticians, such as the value of “A.”
Another thought, inspired by the title of the piece, “Malevich Today”: that Scott’s piece offers us an escape from cut&dry math the way suprematism offers an escape from cut&dry realistic painting—which gives our pleasure in the latter a chance to revive.
The last piece by Scott I want to treat here is another one in color, done some time ago, after I’d shown him some of my long division pieces:
This is almost entirely a visimage (visual image)—but the barely noticeable infiltration of what I call the “dividend shed” (there doesn’t seem to be a formal name for it, unless it’s the “guzzinto sign” my friend Sid Glaser told me he knew it as—because it tells us what a divisor “goes into”), and the even less-noticeable infiltration of the decimal point. So aside from being a wonderful collage with enough triumphs of design to keep us in the thing for days combined with intriguing ever-deepening narratives beginning and ending, we have these two alien features problematizing it. The dot may be the more important of them, but it requires the dividend shed to assert its identity as a decimal point. As such, it decisively mathematicizes the top line of images, transforming it into a sequence of ever diminishing importances, a blank, or zero, amount of tenths being one of them, it would seem.
Granting this, what are we to make of the rectangle with what seems to be an umbrella in it outside the quotient, and the rectangles directly under the divisor, which is the rectangle with the clock in it? Why is the first term in the dividend blank? Against, it would seem we have a surrealization of a mathematical event, in this case, a long division.
Always trying to find what I call a unifying principle in a work of art, I am now going (for now) to abandon my attempt to interpret it as an actual long division the way those of my pieces like it mostly are (see below), for something more subtle. Is it perhaps a fairly formal arrangement of a moment, or perhaps several years, into which Mathematics has stolen in an attempt to find out what makes it tick (and it does tick in a lovely serene way)—to perform something I suddenly see as almost a surgical operation. Some of the arrangement’s magic is becoming susceptible to the reasoning mind the two mathematical elements represent—the sequence ordering itself, and some of the rectangles easing the situation by leaving the main scene, others perhaps finding where a multiplication has set them . . .
What about the alternative idea of the dividend shed as a ray of sunlight?
Do I know what I’m talking about? A little bit, I believe. Mainly, I’m letting my mind drift in the slow currents of the collage—with the hope that I will encourage others to have similar fun not worrying about properly solving the work as a problem, but let themselves be carried away by their mathematical brains, their visual comprehension and poetic story-telling ability into lazy “para-solutions” of it, or solutions apart but associating with whatever correct solution there is, if any.
Next, here is my “Long Division Poem for Scott Helmes,” which was inspired by his many adventures in collage:
I’ve used up my interpretive skills on Scott’s works, so can’t say much about this right now. Know, however, that it is absolutely correct! Oh, also let me inform you that Aurora was the ancient Romans’ goddess of the dawn. I should also confess that this may be unfinished. I’m not sure its quotient is entirely right. . . .
Finally, to demonstrate that Scott isn’t the only one doing artworks that are fascinatingly not mathematical and mathematical at the same time, as well as much else in divers arts and sciences, here’s “function,” by Carlyle Baker:
You want an explanation? You gotta be kidding! Seriously, I plan to say something brilliantly insightful about it in my next installment, which will be about circles! Study up on them until then!
Previously in this series: