Posts Tagged ‘Mathematical Poetry’

Entry 159 — Two Poem Poems

Wednesday, July 14th, 2010

The following are the Poem poems I composed as a response to the mathematical graffiti wall.  I consider them rough drafts although the first may be almost finished.  I started it after figuring out the poem I planned to add to the wall, which is the poem’s main subject.  I’ve revised both slightly since the reading–and misread the poems a couple of times there.  Note: both are meant to be funny, sometimes Very Funny, in spots.  I now believe I ought to have read the second one first at the Bowery Club, for it did get laughs.  The first got none that I heard.

.

At a Wall, 10 July 2010

On a wall in
the lowest winds of his weirdness
Poem noticed a long
division example.
It showed “mathematics”
being divided by “number,”
giving a qoutient of “spring.”

“Uhn,” he thought out loud
after a moment’s reflection,
shaking his head in incomplete comprehension.
“To get mathematics from number,
you must multiply number by spring.”

“No,” quoth Criticism, suddenly
at his side that a dialogue might transpire.
“Note the term, ‘arithmetic,’
beneatht the term, ‘mathematics.’
The term, ‘spring,’ times ‘number’
equals only ‘arithmetic.’
To that you must add
the remainder to get ‘mathematics.’”

“Ah, so it’s a joke since the remainder
is the term, “hubris,’” responded Poem.
“Mathematics is arithmetic with hubris.  Ha ha.”

“You absorb learning most speedily, Poem,
but surely the text is more thanjust a jest.
Surely, it suggests most cogently
how number may majestically ascend
from where it usually winters all the year,
incommunicative, inert,
and almost less than winter,
to what the woods and meadows
celebrate into when multiplied by spring!”

“You’ve paved my grope across this text
most winningly–e’en to the utmost bound
of perfect reasoning,” cried Poem.

“That heartens me, good friend,”
responded Criticism.  “But tell me,
does the meaning of this text
completely satisfy you, as a work of art?
For such, I’m sure, its author
has intended it to be.”

“Why, yes, I think so, Criticism.
Wherefore should it not?”

“Ah,” smiled Criticism.  “Verily, you may be right.
“Yet I have still a question: how
can such a quantity as spring,
supreme among the seasons,
themselves the rulers of our earth,
be less in value than arithmetic,
however admirable the underknitting
that the spring carries out
of so much of
our scientific understanding?”

Poem paused for three full minutes.
“I must concede that you
could not be more correct,” he finally said.
But surely what the author wants to say
could not more skillfully be rendered;
ergo, how could it be be amiss
to overlook so trivial a flaw?”

“Because, iwht thought, it can
more skillfully be rendered,” shouted Criticism,
producing a magic marker
and with it slashing out “spring,”
replacing it with “1 laneful of May”;
hesitating, then changing “1″ to “2.7″–
then angrily changing “lanefuls” to
“meadowfuls.”

“There,” quoth he. “The author’s carelessly
implied disparagement of spring
impales the sensitivity of those
of us with taste no longer.
Do you not agree, good friend?”

“I do,” said Poem.  “You, once again,
have forcefully repaired my wayward wits.  That done,
O learned one, I ask:
would it be possible for us
to not exchange our views less stiltedly?
Or must we keep on parodying Socrates
and some dull blunderer that Plato
has inserted to make his hero seem astute
to his admirers?”

Poem’s show of resistance
to the instruction
Criticism had been trying to
improve him with came too late.
Criticism had been ignoring him,
concentrating on
calling up Number from before
the universe’s oldest axiom.
The winds ceased,
all words exceeded
the last syllable of enumeration
and a winter commenced
whose value was less
than the absolute value of zero.
Poem steeled himself
for the sort of epiphany
he so frequently
had to undergo,
but if one occurred,
he was not aware of it.

Criticism soon left.  For an hour–
or century–after that,
Poem felt Number’s continued presence,
although he could no more see him
than he could see his sibling, light,
there being no longer any matter
for light to bounce to him from–
and he himself had mostly gone,
only his awareness
remaining with whatever it
and light and Number were in,
as invisible as they,
but aching with internalness–
as, for all it knew, were they.

.

Poem & Number Discuss Mathematical Poetry

The ocassion was the official unveiling
of a large artwork called
the mathematical graffiti wall.
Number, somberly clothed
in the equation defining the sine function
that he might be visible to the audience
gathered to listen to him and Poem
discuss the wall, opined
that while it was arresting as visual art,
and illustrated the Pythagorean Theorum,
the origins of differential calculus,
and other aspects of mathematics
with commendable charm and skill,
some of the applications of that science
depicted onit, involving, for instance,
the square root of a valentine heart, or a tree(!)
made little sense.

“I disagree,” said Poem.  “I’m new to the various forms
of mathematical art, but I like the parts you mention..
According to my knowledgeable friend, Criticism,
they marry the purely conceptual
with the exhiliratingly sensual to result in
a wonderfully fresh kind of art,
an art which, among other things,
unghettos any mind flexible enough
to live in two perspectives simultaneously.”

“on the contrary,” retorted Number.
“It merely relieves the creator of such ‘art’
from any need to be coherent.”

“You’re wrong,” snapped Poem.  “The effective maker
of such art is forced to be coherent in two ways.
A good example of this is the poem
“to plus to equals too,”"
which was composed by a scholar
in the philosophy department of
Fordham University.”

At this point Asterrisk interrupted from off-stage:
“Gregory Vincent St. Thomasino,” said he.  “And
it’s Franklin University, not Fordham University.”

“Thank you,” smiled Poem.  “Now, what this poem does
is simple arithmetic, which it certainly does
correctly and coherently.”

Number reddened.  “Correctly!?
You’re telling us that it performs an addition
that yields ‘too’ as the correct answer?!”

“‘Too’ is a correct answer.  But when
I said it does arithmetic correctly,
I meant it performed its operation
according to the rules–it added ‘to’ to ‘to,’
or at least I’m intuitively convinced it did,
as I am intuitively convinced
the answer it got, coherently,
is one correct answer–
the way, it suddenly occurs to me,
4 is the correct answer to what is 2 + 2,
but not the only correct answer,
others being 2.5 + 1.5, and 17.3 – 13.3, and 2 squared.”

“Or your IQ,” he wasn’t crude enough
to say out loud.

“You’re being absurd.  Mathematics does
mathematics, poetry does poetry.
This thing does neither.  Only someone
of unsound mind could think otherwise.”

“Sorry, idiot, but it does both.”
At this point, the moderator had
to step between the two.
Fortunately, he had anticipated
just this sort of fireworks
when the two confronted each other,
so had two security men on hand.
With their help he managed to keep the peace.
Number, however, refused to continue.
So the unlucky audience was
denied Final Illumination regarding
the main matter of the discussion.

Entry 150 — More Discussion with Gregory

Saturday, June 19th, 2010

Gregory Vincent St. Thomasino and I are continuing our discussion about mathematical poetry at his blog. Below is the reply I made to his latest comment (with a little minor editing), him in regular type, me in italics:

You say you are “speaking of the set of language-objects used to represent the real world and that you and I differ in what those objects are.”

Would you explain that, please. And, by “language objects” do you mean words and symbols? Are numbers language objects? Are the names we call numbers by language objects?

The things used to express oneself with language: words, punctuation marks, numerals, whatever things like ampersands are called, square root symbols, etc.  Numbers if you mean numerals–that is, written numbers.  But there are also the numbers in the environment the words for numbers, and numerals, represent.

You say, “poets can be ungrammatical and not wrong but logicians, using words, can’t. You’re just finding users of language who use certain rules and ignore others, and other users whose use and non-use is different.” Would you explain that, please.

All great animals are male.  George is a green animal.  Therefore George is male.  Those are a logical statements.  They have to be grammatical.  Mathematicians similarly have to abide by their rules–their “grammatical” rules if you want to call them that.  Actually, anyone using words has to be reasonably grammatical in order to communicate.

A point of difference between “math grammar” and poetry grammar is that in the case of poetry grammar we can be ungrammatical and still be poetical — and not only that, we can still be meaningful — while if we are “mathematically ungrammatical” we then fall into error. I wish you had addressed this more fully.

I’m afraid I don’t see how I could have discussed it more fully.  I’m saying so what if a poet can be ungrammatical and still be meaningful, and a mathematician can’t.  A logician can’t, either.  I’m saying different specialists use different parts of the grammar of a language, and use it with different degrees of rigor.  Actually, I would say that poetry grammar is specialized grammar and that poets don’t break the rules when they break schoolroom grammatical rules.

I wonder:

Is the correctness of math but a matter of the correctness of “grammar”?

Is the correctness of math but a matter of the correctness of operation (of application of operational principle)?

I don’t know.  I don’t see what this has to do with your definition of mathematical poetry.

(Axiomatical?)

When I write math I am “doing” math. (So to be “mathematically ungrammatical” would apply here.)

When I read math I am “doing” math. (How could it apply here? Or does it: what if I don’t know the rules?)

Sorry, Gregory, dunno where you’re going.

So according to you “mathematical poetry” is a sub-category of “visio-textual art”?

I can’t imagine where you get that.

According to me, “mathematical poetry” is a sub-category of poetry.  It has

no more connection to visio-textual art than to music.

Sometimes you make up your own terms (“texteme”) and other times you use common terms or combining forms like “visio” and “textual.”

Why don’t you use, for example, “semanteme,” “sememe,” “morpheme,” “phoneme” and so on?

I try to use the available terms I know.  I believe there is no term for what I mean by “texteme.”  I’m not understanding why you are bringing this up.

You say, “no analogy need be involved.” How then do your math poems work, how do they signify, how do they function? Or are they, in the end, just pictures? (Visio-textual pictures.)

When I said no analogy need be involved, I meant–as the context, I think, makes clear–an analogy between the “mathematical sentence” and the “linguistic sentence.”  My mathematical sentences don’t act LIKE linguistic sentences, they ARE linguistic sentences.  Or so I claim, and that’s why I (at this point) don’t fully accept your definition of mathematical poems.

My mathematical poems work, signify, function just like any poem: they provide a reader with words and symbols (and sometimes other elements, when, for example, they are also visual poems) which the reader decodes just as he would a conventional poem.

How would you describe the grammar of your math poems?

One side of an equation has to equal the other.  I don’t know.  Some of my math poems use verbal grammar.  The “grammar” of mathematics is very simple, for the most part–at the mostly sub-calculus level of my math poems.  You follow algebraic rules like multiply both x and y by z in the expression z(x + y).  These rules, for me, are just an extension of “normal” grammatical rules, like putting an adjective next to the noun it modifies, using a pronoun in such a way as to make clear what its referent is, etc.  I don’t think of them as I use them.

My brain may not be working well, which may be why I’m having a little trouble following what you’re saying here and there.  (My doctor thinks I may be anemic.  It’s being checked.  In the meantime, I’m using that as my excuse.)

all best, Bob



Entry 148 — Response to Gregory Vincent St. Thomasino, Part 2

Thursday, June 17th, 2010

You say, “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.”

I don’t understand why you have, “if it is to be, or to contain, poetry.” If you call it a poem, claim I, you are saying that it is a poem, so much have poetic elements, however defined. That such a poem should have “some formal symbols and operations of math,” follows from its being called a “mathematical poem.” Ergo, I would rephrase your definition as “A mathematical poem is a poem containing mathematical elements.”

I would then ask you to say what you mean by “having” mathematical operations in a mathematical poem. That is, would a poem about a child who has to do five long division problems for homework “have” a mathematical operation in it?

Also, to be fastidious, I would want you to spell out whether the symbols and operations should be overtly in the poem. Some, as you probably know, seem to think a sonnet is a mathematical poem because the poet has to be able to count up to 14 to make one.

Which leads to the next important thing I think needs to be done: sort out all the kinds of math-related poems it seems reasonable to distinguish from one another. I would list the following five:

(1) poems that discuss math

(2) poems generated by mathematical operations.

(3) poems that use mathematical symbols but use them unmathematically: e.g., a poem with a square root sign next to the word “Sunday,” which is followed by seven plus-signs, whereupon the poem becomes standard verbal expression.

(4) poems that one or more persons claim arouse some kind of “mathematical feeling.”

(5) poems that perform one or more mathematical operation central to its aesthetic meaning.

Entry 146 — Discussing Mathematics and Poetry

Wednesday, June 16th, 2010

Gregory Vincent St. Thomasino has been blogging about mathematics and poetry at his Eratio blog.  When he told me about it on the phone yesterday,  I said I’d check it out, which I’ve now done.  I left my first comment on it.  Fortunately, for once I cut what I said before hitting the button telling his blog to accept it, for my post got rejected.  I’ll try in a little while to post it again.  Meanwhile I want to post it here, to make sure it’s somewhere, and because maybe one of my two regular visitors doesn’t also read Gregory, or misses posts to it because it’s irregular, which is my excuse.

Hi, Gregory.  I’ve decided to tear into your commentary on mathematics and poetry Very Slowly, one idea at a time, to facilitate coherence.

I’ll begin with your statement that “Already (‘mathematical sentence’) (you’re) thinking analogically.”

This is where you and I first disagree, for (as revealed in our long & interesting phone conversation of yesterday) I believe numerals and mathematical symbols are part of our verbal language, just as, in my opinion, typographical symbols for punctuation or to abbreviate are.  The mathematical symbol, “+,” for instance, is just a different way of writing, “plus,” or “&.”  It therefore follows that for me, a mathematical equation is a literal sentence differing from unmathematical sentences only in the words in it.  “a – b = c,” for instance, is a very simple sentence and not significantly different from, “Mary cried when she lost her lamb.”

Obviously, it’s just a case of your opinion versus mine, but I think acceptance of my opinion makes more sense, because it keeps thing more simple than your does.  I would say that what most people mean by “words” are “general words,” while words like “sineA” or “=” are “specialized words” or mathematical words–like punctuation marks.

I think in my linguistics, these “words” are all called “textemes,” But it’s been a while since I read Grumman on the matter, so I’m not sure.

Hey, I found a glossary in which I define many terms like “texteme.”  It’s not a word but a typographical symbol: “any textual symbol, or unified combination of textual symbols–letters, punctuation marks, spaces, etc.–that is smaller than a syllable of two or more letters: e.g., ‘g,’ ‘&h(7:kk,’ ‘GH,’ ‘jd.’”  I coined the term for discussion of various odd kinds of symbols and symbol-combinations like some of those among my examples that not infrequently occur in visual or infraverbal poems.

So, I don’t have a special term for word, as I define it.  Yet.

To continue my argument in favor of my take on mathematical expression as an extension of verbal expression, not something different in kind, I would saimply ask what is special about mathematical symbols that should require us to think of them as elements of a special kind of expression?  They do nothing that ordinary verbalization can’t do, although they do it more clearly, compactly and elegantly.

Graphs would be mathematical expression–a form of visio-conceptual expression, as is written music.  Chemical diagrams but not chemical notation. . . .

I don’t see that there’s any difference between the syntax of mathematical expression (other than graphs and probably other similar things I’m not into Math enough to think of right now) and normal verbal expression.  There’s no inflection, I don’t think, in mathematical expression.  Which is a triviality.

Conclusion: we need a carefully formed taxonomy of human modes of expression.

Entry 40 — #675 through #670

Saturday, December 12th, 2009

In #675, I posted Endwar’s “Ten X Ten,” having liked it so much, I assume, that I’d forgotten I’d posted it a week of so before at my blog.  Under the Endwar piece, I had three mathematical poems by Kaz Maslanka, one of which is also a visual poem but too large to reproduce here without losing most of the text.  One of the others has the same problem, but the one below should be readable:

a-mans-intelligenceOops, you may need a magnifying glass.  My choice of reproduction seems to be the size above, or four times as large.  Anyway, it’s called “A Man’s Intelligence” and may be more informrature–a specimen of informratry–than poetry.  Let me quote what it says: “A man’s Intelligence” equals “intelligence Quotient” divided by the product of “The measurable level of Dionysian blood transfused in a saffron masseuse boasting whispers through the cool crystal shot glass of the finest golden tequila” times “The amount of passion fueled by a young pink Venus–her hand wandering in slow circular patterns, a seemingly aimless whistle up the man’s inner thigh.”

#677 and #678 are about the Christmas mathemaku I’d done a draft of the previous year, and worked some more on at this time (December 2005), and have worked on since then, finishing it, I believe.   Then a reproduction and revision of a long division poem I used in the autobiographical essay in the mainstream series of such things I got it into many years ago, without its making any difference whatever in my vocational reputation.  I don’t like it well enough to reproduce it here.  I had another of my mathematical poems in #680 that I don’t like enough to reproduce here.

Entry 33 — Yesterday’s Poem

Friday, December 4th, 2009

Here’s yesterday’s image again:

17Aug07B

It’s one of my mathemaku, of course.    I’ve actually been working industriously  on it, trying get it right enough to submit to some sort of  anthology Nico Vassilakis and Crag Hill are putting together.   The version above is a recent revision of my first draft of 2007, a variation on “Frame One” of my Long Division of Poetry series.

17Aug07D-light

“Frame One” is similar to the top image except that its divisor is “words.”  It had long bothered me because (and make sure to write this down, students, because it’s an excellent example of the way I think about my poems) its claim was that “words” squared (basically–although it’s really distorted words, or words told slant. times regular words) happened to equal an image having to do with summer rain.  Why that and not, say, a Pacific sunset?   Obviously, the quotient times the divisor could equal anything.  That, I didn’t want.  Off and on I thought about this, but could think of no way to take care of it.  Until a couple of days ago, when I finally concentrated for more than a few minutes on it.  I came up with several pretty good solutions, one of them changing everything in the poem but the sub-dividend product (the image).

My final solution (I hope) resulted in the above poem.  All I did was add “memories of a long-ago summer day” to the quotient.  That assured that the sub-dividend product would have to do with summer–that it would be, that is, a visual poem about summer.  And, as a poem, it would be poetry.

No doubt in due course I’ll think of something else I find illogical about it and want to revise it again.  For now, though, I’m happy with it.

Oh, I’ve made several changes to the main image in it, too.  One was to combat the darkness in the top version (which wasn’t in it until I put it out here).  I’m as fussy about getting my graphics looking the way I want them as I am about everything else in a poem–except the choice of font, and things I can’t do anything about with my equipment, like density of resolution.

Entry 25 — Old Entries 641 through 651

Thursday, November 26th, 2009

azily back to old blogs again, this time beginning this mathematical poem by Andrew Topel taken from #641:

add3-small

A very slightly revised version of one of the mathemaku in yesterday’s entry not worth posting here was the feature in my next entry.  Then some minor autobiography.  In #644 & #645 I posted 3 more of Andrew Topel’s addition poems, including:

add4-small

On September 24, 1997, I started my first blog, an actual log for my poetry website, Comprepoetica.  In entries #646 through #651 I reprinted my (few) entries.  OF great historical interest, no doubt, but too boring to post here.

Entry 24 — Old Blog entries, Again

Wednesday, November 25th, 2009

The question I battled in #632 was what to call the emotional state which is neither painful nor pleasurable.  I came up with a few coinages but didn’t like any of them, and still haven’t one that I consider worth keeping.  My next entry had to do with my semi-addiction to Civilization, the computer game I play too much of, and almost always lose.  In #634 I returned to my quest to find a word for the feeling of no feeling and came up with a coinage so bad I refuse to tell you what it was.  Next I discussed the difference between what a poem is as an object, and what it is as (I guess) a signifier–which is what most people take it only as.

Out of one of my more and more rare episodes of creativity the following mathemaku came into being, and I posted them in #636, #638 and #640:

frame-xx01

frame-xx02

frame-xx03

I consider all of these unsuccessful drafts with potential that I hope to work on over the next few days.  In #637 I had a variation I don’t now think much of on something of Geof Huth’s.  Two entries later, this, which I no longer understand although I’m positive I did when I made it:

Comma-Duo

Which takes me to the end of another set of ten entries from my old blog.

Entry 14 — Back to My Old Blog Entries

Sunday, November 15th, 2009

I remain blank in the brain, so will return to my old project of revisiting old blogs in hopes that will get me going again.  A check of my back-ups indicates I made my last entry to the old blog 27 October.  In it and the entry just before it, I reported on my last trip to the hospital.  My entry for 25 October was the last in which I discussed old entries, getting to #610.  So I will turn now to some fumbly work with letters I did in #611:

Letter-Blocks1These seem to me like they ought to be interesting but they don’t grab me, at all.  In #612, I reported that I’d gotten an e.mail from an old literary friend (and early buyer of A StrayngeBook), Fred Stokes.  A not-too-interesting entry on Me followed, then this, which I quote in full more to give an idea of where my head was at the time than because it says very much:

“7 October 2005: Or, to continue my musing of yesterday (about the effectiveness of my aging brain), maybe I’m just recycling ideas I’ve had for decades. Whether original for me or just recycling, I think my putting literature into four classes, narrature, anthroture, evocature and poetry was nutty. Just a momentary aberration, I hope. I have nothing against the over-all concept, however. Ergo, I am rephrasing it today in a single statement: Every poem has four zones of operation: (1) the sagaceptual (or narrative) zone, (2) the anthroceptual (or people-related) zone, (3) the protoceptual (or imagery-centered) zone and (4) the reducticeptual (or technique-focused) zone. What the poem does as a story, what it does as self-expression, what it does as an evocation of a scene or object, and what it does as a mechanism or (i.e., how its grammar works, what its form does, what–in the case of my mathemaku–its mathematics does, and so forth). Right now, I can think of no other operational zones it might have (but would not be at all surprised if it had others, even very obvious others).”

I should have mentioned that there’s no such thing, in my poetics, as an idea-centered poem.  That’s because a text primarily about an idea would not be a work of literature but of what I call “informrature,” the use of words in pursuit of some truth.  Ideas can be important in poems, as is the case with many of Wallace Stevens’s, but only for what they allow the poem to do as (usually) protoceptually.

#615 and #616 continue my discussion of zones with the addition of two new ones, one (the verbo-protceptual zone) for verbally-mediated sensory perceptions (as opposed to direct ones like the sound of the words used), and one (the verbo-reducticeptual zone) for the ideas or thought of a poem. I had scanted the latter because I believe any text with a significant amount of ideas disbarred from being a poem–it must be either advocature or informrature (i.e., propaganda or nonfiction). I now realize that all poems have ideas, however vague, and some them to a significant degree (although, I contend, never are they the most important elements in the poems).  So almost every poem will to some degree enter an idea-zone.

The center of interest in #617 was the zero-onset, which is the blank onset (or absense of consonant) that begins some syllables–as in “out,” or “or,” for instance.  Next I took up vowels that act as consonants the way the u in use does, and the o in “one.”   My last two entries in this set of ten have two versions of a mathemaku I was working on:

12Oct-A12Oct-BIt’s not quite there, but I think it has the potential to be Major.  The pond, it should be obvious, is a cousin of Basho’s.

Entry 7 — My First Long Division Poem

Sunday, November 8th, 2009

FirstLongDivision

The poem above is my very first long division poem, composed around 1990. It’s on display here as an example of how complex a seemingly simple poem can be. According to the rules of long division, the poem says, on the surface, that spring divided by woods equals rain, with a remainder of robins. It further states that woods multiplied by rain equals green, and that robins added to green also equals spring. A set of rather simplistic metaphors, in other words. But is it? Certainly the idea of green as a near-simile for spring is about as banal as can be. As is the idea that rain is its cause. But the rain is not merely added to the woods it affects, it multiplies them. For me, this is a terrific metaphor, or was when I first used it. Multiplication. It’s so much more than addition. I, at any rate, get a sense of individual raindrops intricately interacting with limbs, and expanding the woods, not just lying on them.

More important, as one verbally experiences of Nature as rain, woods, greenery and robins–sensual and organic, careless and carefree, the poem’s structure should make one increasingly aware of the eternal mathematics underlying everything . . .