Friday, June 04, 2010

On Mathematical Poetry (Post One)

I’m titling this series of posts “On Mathematical Poetry” and in the days and weeks to come I’ll be revisiting and revising and emending my thoughts as necessary.

In my Logoclasody Manifesto I included a brief addendum entitled “On Mathematical Poetry” and there I stated what I hold to be the most important point in the whole mathematical poetry endeavor:

There has to be considered the analogy between the grammatical sentence (the linguistic sentence) and the mathematical sentence (the mathematical equation). Already (“mathematical sentence”) I’m thinking analogically.

There has to be considered the analogy between the grammar of the sentence and the “mathematics” of the equation (i.e., of the mathematical statement).


And these are the examples I gave:

     Change + purse = church.
     kite + propeller = wing.
     to + to = too.
     am = be + I
     secrets = ? + whispers


Here I offer a working definition of “mathematical poetry”:

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 want to emphasize that by “operations of math” I do not mean that the poem will be “doing math.” What I mean is that the poem will be, in some way or in some sense — be that metaphorical, allegorical, but for the most part figurative — mimicking or imitating or finding a trope in that operation (whichever that operation may be). (I emphasize: I do not mean that the poem is “doing math.” Math does math. The poem is representational.)


If these are my formal symbols (and as such indicative of operations):

     +, =

What then are my poetic elements?

     ideas and images

(i.e., “to,” “am” and “be” are ideas, while “kite” and “propeller” are images, and an image can at the same time be an idea, and be as general or abstract as it can be specific or concrete)



28 comments:

  1. 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.

    --Bob Grumman

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  2. 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.

    That's it for today's comment.

    --Bob Grumman

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  3. Hi, Bob.

    So you’re saying my analogy is false.

    I say there are similarities between the “grammar” of the mathematical statement and the grammar of the linguistic statement, and I base my analogy on those similarities.

    You’re saying that it isn’t even a matter of similarities, that they are all “part of our verbal language,” “not something different in kind,” and so no analogy need be involved.

    Math and language are both rule-following. Are the rules the same for each?

    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.

    Yrs, Gregory

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  4. Hi, Bob.

    I think, just saying “this is a poem” doesn’t make “it” a poem.

    When I state, “here is a poem, and that here we must consent to the intention of the poem; that we must as it were enter into the confidence of the poem,” that is not meant as an unqualified assertion on the order of, “This is a poem!” That would be ridiculous. It is, rather, an invitation.

    In my Logoclasody Manifesto I speak of a passage from the creative intuition of the poet to the receptive intuition of the reader and state that this requires a sort of previous, tentative consent to “the poem” and to the intentions of the poet, without which we cannot be taken into the confidence of the poem. And that this requires a certain relaxing of the critical intelligence, for how can you reflect upon an experience if you have not first had that experience? But once you have had that experience, you are free to judge it as to whether it has satisfied your expectations, critical or otherwise.


    “I would then ask you to say what you mean by ‘having’ mathematical operations in a mathematical poem.” “Ergo, I would rephrase your definition as ‘A mathematical poem is a poem containing mathematical elements.’ ”

    As I say in my essay:

    I want to emphasize that by “operations of math” I do not mean that the poem will be “doing math.” What I mean is that the poem will be, in some way or in some sense — be that metaphorical, allegorical, but for the most part figurative — mimicking or imitating or finding a trope in that operation (whichever that operation may be). (I emphasize: I do not mean that the poem is “doing math.” Math does math. The poem is representational.)

    Yrs, Gregory

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  5. Yes, I'm "saying that it isn’t even a matter of similarities, that they are all 'part of our verbal language,' 'not something different in kind,' and so no analogy need be involved."

    Or close to that.

    You ask if the rules are the same for both math and language. This starts to get difficult because I consider math a part of language. What I would say is that when mathematicians use their part of the language they share with writers, they have special rules that they follow--just as a sonneteer follows special rules when he uses his part of the shared language from the rules followed by a composer of a haiku.

    You say, "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'd say that (1) I'm speaking of the set of language-objects used to represent the real world and that you and I differ in what those objects are; and that grammar is something else. (2) 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.

    --Bob

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  6. Hi, Bob.

    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?

    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.

    I wrote above:

    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 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)?

    (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?)


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

    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?


    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.)

    How would you describe the grammar of your math poems?

    Yrs, Gregory

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  7. Gregory, I realize that all of this is addressed to Bob, however, I would like to stick my nose into the fray. There is a lot of talk here that I find nebulous and desire clarification. Gregory; I am not sure what you mean by a math poems not doing math. Is this the same thing as a sentence doesn’t read itself? One has to be engaged in it? – or are you thinking that if there are no numbers in an equation then you are not doing math.

    Bob: I don’t see how you can say a-b = c is not significantly different form “Mary cried when she lost her lamb” Even Mary – Lamb = crying is significantly different. a-b=c is about as abstract as one can get and “Mary cried when she lost her lamb” is very specific . a-b=c could mean 10-4=6 or henhouse – chickens = hunger or an infinite variety of other expressions. Big difference

    Bob: Most of your argument in your second comment seems superfluous for we know what Gregory means by mathematical operations. He means the same thing as you and I mean when we talk about math operations in a poem.

    Bob: In your types of mathematical poems – I see number 5 as being not relevant for I get a mathematical feeling from every poem I read. All I have to do is think about pattern and meter.

    Bob: it is true that you can recite a math equation in words and in that sense the both operate as verbal language, however, when you start performing the mathematical operations on the terms then you are following a completely different “grammar” if you can call it that. The rules of verbal language and the rules of math are very different – but you know that.

    Gregory: You say, "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 just had this argument with Pioh on my blog a few days ago. I agree with you if we are talking about equational poetry however, if we are talking about mathematical visual poetry then the rules of math may not apply. And there are those out there that enjoy that kind of gibberish. See my Four Types of Mathematical poetry to understand the difference between these two terms.

    Gregory: you said, “Is the correctness of math but a matter of the correctness of “grammar”?
    Yes if you can call the rules of mathematics “grammar”

    Gregory you said, “Is the correctness of math but a matter of the correctness of operation? Yes (of application of operational principle)?”
    Yes again.


    Gregory: you said, “When I write math I am “doing” math. (So to be “mathematically ungrammatical” would apply here.) “
    Yes as long as you are doing it correctly then you would be doing math

    Gregory: You said,”When I read math I am “doing” math. (How could it apply here? Or does it: what if I don't know the rules?)”
    If you don’t know the rules then you are not doing math.

    Gregory said to Bob, “So according to you “mathematical poetry” is a sub-category of “visio-textual art”?”
    I say equational poetry has nothing to do with visio-textual art. There is nothing visio about it.

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  8. Gregory Vincent St. Thomasino wrote:

    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.


    MAYBE SHORTER COMMENT IS REQUIRED, SO AM TRYING THIS.

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  9. HERE'S A LONGER SECTION OF MY REPLY:


    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. That's a logical statement. It has to be grammatical. Mathematicians similarly have to abide by their rule--their "grammatical" rules if you want to call them that. Actually, anyone using words has to be reasonably grammatical in order to communicate.

    I wrote above:

    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, dunno where you're going.

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  10. PART THREE:


    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

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  11. Hi, Bob.

    When I put up your other comments they all filed in above, so this here comment of mine will cover all of them. I'll reply to as much as I can.

    So far as "texteme" goes, I'm bringing it up because as I understand you terminology is essential to your endeavor, and so I don't understand why you seem to make terms up out of whole cloth rather than just consulting with a good dictionary of linguistics. It's okay to take an established term and then to explain how and why you are giving it a new sense or context or such that you are increasing our understanding and our use of it. What's more you seem to be constantly revising your terms and this is confusing and also unfair, my friend. Quite often when you can't explain yourself, you change a term here or there and thus you wiggle out of it. :)

    And Bob, when you say "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 are speaking analogically. It doesn't pardon you just because you put the word grammar in quotes. I don't think you know what an analogy is. I've been having this same go-round with you for nearly twenty years now.

    Regarding your “mathematical poetry” as a sub-category of “visio-textual art” and that you can't imagine where I got that, first of all I got that term from your list, the one on your blog, and second it's because I think your pieces function, if "function" is indeed the right term, like visual poetry, which is to say they have a certain dramatic logic to them, as when I'm looking at a picture say of a landscape — I see all the parts, the trees, the hill and dale — and seeing them together I "construe" they are a landscape. When I "read" one of your mathematical long division poems, I see words, and sometimes things (pictures of things), sitting on a mathematical structure, and as though they were sitting on a shelf, and it is via the integration and differentiation, the juxtaposition, the "decoding," of these words and things that I construe a, well, a sort of landscape populated by these particular words and things. That's how I think they "function," like a populated landscape. There are no moving parts.

    And btw, that list of "visio-textual artists" on your blog — it is so obviously arbitrary, so obviously based on your own personal biases and pet peeves, that quite frankly I am embarrassed for you.

    As for your other comments, the ones I do not directly reply to, I think they speak for themselves. Just as I think, in the final analysis, the poetry, the "mathematical poetry," will have to speak for itself.

    Yrs, Gregory

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  12. Your silly blog sent me a somewhat ill-tempered comment that I suspect is the one you removed, Gregory. No hard feelings. But, you were replying to the third segment of my post. I think this exchange will work better if you reply to my posts in order.

    I do want to reply to one thing you criticized me for in your post--my neologies. You overlooked what I said in my defense: "I try to use the available terms I know. I believe there is no term for what I mean by 'texteme.'" You implied "texteme" was unneeded. If so, I would sincerely love to know what term is around that I could replace it with. It means, in my poetics, "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." I coined it to facilitate discussion of certain of Cummings's poems. I find it to be a necessary term--unless linguists or some others in related fields already have a term that means what I have it meaning.

    --Bob

    --

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  13. Hi, Kaz.

    You say: Gregory; I am not sure what you mean by a math poems not doing math. Is this the same thing as a sentence doesn’t read itself? One has to be engaged in it? – or are you thinking that if there are no numbers in an equation then you are not doing math.

    I mean that my math poem is not doing math, math does math, poetry does poetry. That 1) my math poem follows the rules of math only insofar as to turn in analogy with those rules, and that 2) when one considers the expectations he or she brings to the math equation alongside the expectations he brings to the poem, to bring the math and the poetry together is to necessarily modify one's expectations of the math, but not to expect any less from the poetry. It is necessarily so.

    You say: equational poetry has nothing to do with visio-textual art. There is nothing visio about it.

    I say "equational" or no, there is a certain dramatic logic to it analogous to a populated landscape. There are no "moving parts."

    It is a fallacy to think mathematical poetry is "doing math."

    Yrs, Gregory

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  14. Hi, Bob.

    I think the term you are looking for is "lexeme" (a minimal distinctive unit).

    Yrs, Gregory

    PS: It is a fallacy to think mathematical poetry is "doing math."

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  15. Thanks, Gregory, for making me look up "lexeme," one of those words I know and use for a while, then forget after not using them for a while. Unfortunately, it does not mean anything close to what "texteme" does.

    As for mathematical poetry's "doing math," I may have lossely said that's what it does. More strictly speaking, it carries out mathematical operations. If one of my long division poems is not carrying out a mathematical operation, I would like to know just what it IS doing.

    --Bob

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  16. (Part One of Comment) "nebulous . . . desire clarification"--I agree with you on this, Kaz. A discussion of a rather complicated seldom discussed subject among (now) three people is bound to get confoozed.

    I can't think, to contribute more to the confoozery, how Gregory can hold that math
    poems are not doing math unless he believes "that if there are no numbers in an equation
    then you are not doing math."

    I hope (Kaz) that my rough answer to you about my Mary/a - b thought in my previous
    comment helps you see what I mean, or think I mean. Or may be not. I think what I'm
    saying is that . . . actually what I'm NOW saying . . . is that both mathematicians and
    writers function in the same large world, the world of language. (Or semantics? I really
    don't know.) But each functions in that world much differently from the other. Yes, this is what I said in the other post, or suggested. A painter does not function in the world.
    poets and mathematicians--and composers writing down their music--do. Mathematicians
    engaged in analytical geometry and mathematical areas based on analytical geometry are a special case. I'm not up to getting involved with them at this point. I suppose purely oral poets are a different case--but I would argue against that on the grounds that their work CAN be written down. Sort of analogous in reverse to the fact that mathematics can be orally expressed.

    I didn't want to get into my second comment until we had gotten through with my first
    comment to Gregory's three-parter. Maybe we have now. Actually, we haven't gotten through it, but Gregory seems to have stated his final position with the implication that
    he's through with the whole argument, although I didn't get through with even the first of his three posts about mathematical poetry.

    Anyway, I'll go ahead and try to deal with your comments. I deny that Gregory
    necessarily means "the same thing . . . I mean . . . (by) math operations in a poem. You may not, either. For instance, is there a mathematical operation in my poem about an &
    with an exponent of 3 and nothing else? I say yes. I really don't know what Gregory
    would say. I also don't know whether he'd consider a poem containing the line, "he
    was mystified by the binomial theorem," to "have" a mathematical operation. How about
    a poem describing how to prove two triangles which have two sides and the angle between them equal are congruent? I would say that even if such a poem showed the proof mathematically, it would be about math, not math. A borderline case, to be sure, and a math operation is being carried out. I simply subjectively state that it isn't
    aesthetically significant enough to make the poem a mathematical poem, for me. --Bob

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  17. CONTINUATION OF PREVIOUS COMMENT (which was rejected for being too long)

    I thought my number five was the same as your "equational poem," Kaz. Oops, you were
    referring to "(4) poems that one or more persons claim arouse some kind of mathematical
    feeling.'" (Aside: I hope eventually comment sections at blogs will allow a person to
    comment on a specific entry, and quote the entry commented on in the comment box--as
    happens at . . . newsgroups, I think they're called. One can then delete some or all of the quoted material--and answer the entry commented on--or the comment commented on--
    paragraph, or sentence, or phrase, by paragraph, sentence, phrase.)

    Okay, remember Kaz that I'm trying to list ALL kinds of math-related poems. My
    taxonomical procedure would then be to show that only one kind of them is what I call
    mathematical poems, eliminating number 4 because it's not even objectively math-related. This goes back to my dealing with people who say certain poems are visual poems for them because they cause them to see pictures of something.

    I think I've already given (perhaps twice) my understanding of math as part of the "language."

    Good point you make to Gregory about how one CAN be "ungrammatical" using math and be meaningful. At least, I think it was your point. It's mine, in any event. You were
    thinking of poems like some of Scott Helmes's that you consider (I believe) "gibberish."
    In some cases, I do, too--but knowing Scott am not so sure his poems are gibberish, and
    some I have found verbal meaning in. It strikes me now that his poems may be a form of
    asyntactical poetry, which in my poetic is a subset of language poetry. I tend to count
    them mathematical poems for carrying out mathematical invalidly but meaningfully, and by so doing bringing the operations of math sufficiently into what they're doing to be
    mathematical, or equational.

    This is one kind of thing that comes up in discussions like this that I consider fun: causing questions that otherwise could never have been asked. The one here, for me, is "would 7 + 9 = 45" be considered mathematics. I'm saying, yes. But in the case of "mathematical poems" like Scott's, it's difficult to tell.

    Going back to your answer to Gregory, I would say the rules of math SHOULD apply to the extent that we should be able to see what operation is taking place (and yielding a
    "wrong" answer, or being used incorrectly. The same as in asyntactical poetry, a text so
    ungrammatical as to be nonsense, is not a poem, but one almost as close to nonsense is, if some critic can plausibly interpret it.

    To be perhaps ridiculously picky, Kaz, I would disagree with you that “the correctness of math but a matter of the correctness of 'grammar,'” as Gregory put it? The mistake in 7 + 9 = 45 is not a mistake in grammar.

    Nor do I think reading math is doing math. Watching a ballet is not dancing. But you're
    using mathematical thinking. Yes, I'm splitting hairs. I don't know if I'm doing so
    productively but thought I ought to, anyway.

    --Bob

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  18. Phooey, Gregory, I was hoping you had realized you'd been in a bad mood when making the post that follows.

    About "texteme," I still want to know why you brought it up. It has nothing whatever to do with our discussion.

    For you (and Kaz), I say that I consider language to include ALL writable symbols. I am probably confusing (and confused) inasmuch as I'm leaving out grammar. I am making a distinction between symbols intended to represent things, and pure graphics. A depiction of a dog is different from "dog," and "9" or "&' or a square root sign are much more like "dog" than they are like the picture of a dog. I push this because I think mathematical poetry NOT visual poetry.

    Yes, a mathematical poet (or, for Kaz) an equational poet uses the part of language he uses in a way probably different in kind from the way a poet using words only does. I'm not sure of this, but will leave it as agreed to for the sake of argument (and because I'm to uncertain about it to discuss it cogently).

    My point is (I think) that the big difference between mine and your idea of a mathematical poet is that, for me, it is not the symbols he uses that make him a mathematical poet, but the way he uses them. And he uses them as a mathematician, by subjecting them to mathematical operations.

    If you want to say he uses a different grammar than a word-only poet, fine. I will only say that I am not sure of that.

    I will agree with you that I don't know what an "analogy" is. You may also get me to agree that I don't know what mathematics or poetry is, too.

    I would say that you look at what I call a mathematical poem the way you look at a picture seems subjective to me. I will only say that I don't see pictures when I view what I call mathematical poems.

    I would add that I "see" a landscape reading a good haiku but don't then consider it to be visio-textual.

    My definition of "visio-textual artists" is totally objective--but like any definition, tricky in some cases to apply. As I always say at some point in a discussion of vhat's visio-textual, what visio-poetic, subjectivity can't be avoided. But in most cases it's pretty easy to decide whether an artwork is literary or not--on the basis of whether it says anything significant verbally.

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  19. I'm not sure where we are in this discussion, but believe we've finished with my first comment and the responses it generated, so I'm going to turn to the one response my premature second comment got. It's from Gregory.

    He begins by saying, "I think, just saying 'this is a poem' doesn’t make 'it' a poem." I think he is responding to my statement that "If you call (something) a poem, you are saying that it is a poem, so must (here, I mistakenly typed 'much') have poetic elements, however defined." I was quibbling about Gregory's statement, which I quoted, that "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 thought he was using too many words to say a mathematical poem should be a poem with mathematical elements. My quibble, I think, was correct but stupid. He was defining his terms. I should have left what he said alone but I was going too fast, or somethin'.

    I think I agree almost entirely with what Gregory goes on to say about the invitation a poem is, etc., and as he knows, I am an implacable enemy of the idea that a poem is anything anybody advances as a poem.

    I have to confess I don't know exactly what Gregory means when he goes on to say, "I want to emphasize that by 'operations of math' I do not mean that the poem will be 'doing math.' What I mean is that the poem will be, in some way or in some sense — be that metaphorical, allegorical, but for the most part figurative — mimicking or imitating or finding a trope in that operation (whichever that operation may be). (I emphasize: I do not mean that the poem is 'doing math.' Math does math. The poem is representational.)"

    I would say that the whole point of mathematical poetry, as I define it, is to verbally represent AND in some way do math. Rather than describe a mathematical poem as "doing math," however, I would--as I previously have said--describe it as carrying out a mathematical operation--on what it verbally represents."

    At this point, I want to return briefly to the discussion Gregory and I got into about analogizing. I think the subject extremely complex and that we have been talking past each other. I admit to not yet being able coherently to express my point of view, yet I understand it, I believe, sufficiently to stick to it. One problem, is that I think in terms of metaphors--of course a form of analogy--so it's hard for me to convert to thinking about analogies. Metaphors, and therefore analogies, are central to poetry, though some poems manage without them. Mine don't. But where they are metaphorical is not where Gregory considers them analogical, in my opinion. I doubt what I've just said will help, but it's only intended to give a hint of where I am, and why we're having trouble discussing analogizing.

    --Bob

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  20. Hi, Bob.

    Before I forget, if Blogger rejected your comment, it's probably because it used too many characters, which I think you figured out by now. It did it to me—but it was welcome because it made me break my comment into parts and in the process I was better able to focus.

    I feel compelled to reply to what you say just above about analogy and metaphor. To quote you:

    "At this point, I want to return briefly to the discussion Gregory and I got into about analogizing. I think the subject extremely complex and that we have been talking past each other. I admit to not yet being able coherently to express my point of view, yet I understand it, I believe, sufficiently to stick to it. One problem, is that I think in terms of metaphors--of course a form of analogy--so it's hard for me to convert to thinking about analogies. Metaphors, and therefore analogies, are central to poetry, though some poems manage without them. Mine don't. But where they are metaphorical is not where Gregory considers them analogical, in my opinion. I doubt what I've just said will help, but it's only intended to give a hint of where I am, and why we're having trouble discussing analogizing."

    And especially this sentence:

    "But where they are metaphorical is not where Gregory considers them analogical, in my opinion."

    Okay. Quite simply: Analogy is not metaphor. Analogy makes metaphor happen, but they are not the same. Metaphor, simile, allegory, all figurative language works by way of analogy. Analogy makes possible the metaphor, but it is not the metaphor. The metaphor turns on the analogy, but analogy does not need metaphor.

    Okay, having said that: In the case with my math-po, it is by way of the analogy that they are "mathematical," not by way of metaphor, but if there is a metaphor, it would come by way of the poetry.

    And, I think your math-po, Bob, to the extent that it is at all "mathematical," is so by way of analogy, and I think the same goes for Kaz's.

    That you guys don't see this, and accept this, this most simple and fundamental point, disappoints me tremendously.

    For me: to theorize about "mathematical poetry" is to first "see" the analogy and then to create a trope out of it, and I think that's what I've done.

    If what I say makes sense to you, or if you feel you already know it, then use it to clear up your confusion.

    Yrs, Gregory

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  21. Gregory, Does a mathematical equation from Physics do math?

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  22. Gregory says, “That you guys don't see this, and accept this, this most simple and fundamental point, disappoints me tremendously.”
    Kaz says, This simple fundamental point may not be as simple and fundamental as you think. It seems to me that you don’t follow that mathematics on the axiomatic level is metaphorical. That is you don’t aspire to mathematics at its root foundation is metaphorical. What Bob and I are doing is mapping metaphors within metaphors. You may believe that we are only making an analogy but we are not. And yes analogy is different than metaphor. Now I have to admit that the metaphors we use may make analogies and furthermore may make a bunch of bad analogies but then that gets us into the aesthetics of the mathematical poems. Bad analogies make for bad mathematical poems. So bottom line is yes, there are analogies involved in our work but we are also mapping metaphors. The equation itself is a metaphorical structure where by the equal sign directly corresponds to the “IS” within the metaphorical structure of “target IS source” The conflation between the target and the source is where the poetic element resides. The poetry ‘lives’ in the equation yet the equation ‘lives’ in experience.

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  23. Gregory said, “For me: to theorize about "mathematical poetry" is to first "see" the analogy and then to create a trope out of it, and I think that's what I've done.”
    Kaz said, “Yes Gregory, that is what you have done however, I would not call it equational poetry and I doubt that Bob would call it Mathematical Poetry” because you are not doing math you are making an analogy between some geometrical elements (lines and a transverse line) and creating a trope to which points at analogy yet it seems that you are pointing at the possibility of having a mathematical experience - a ‘breaking out’ as you would say in logoclastics yet you really did not address the mathematical experience you just pointed at the possibility. This brings us to the next level which is a breaking out of the equation itself. Once the equation has been realized we have another level of breaking out when the metaphors in the equation bridge to a new signified. You did not address the later however that is where I come in and set up an equation showing how the transverse lines function mathematically. Of course I have already done a transverse line in my piece “Theta” see figure 18 in my paper on verbogeometry. Or http://www.kazmaslanka.com/Theta.html
    Back to metaphor – Metaphors have analogy embedded within them however the metaphors can be so confusing or poor in quality that the resulting analogies can be inconsistent creating many logical conflicts which can make the metaphor valueless. This is the aesthetic challenge within equational poetry.

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  24. Hi, Kaz.

    Your question is: “Does a mathematical equation from Physics do math?”

    I’m not sure what you mean by “Physics” and why you capitalize it. (I wish you had provided me with more information.) It makes me think of theoretical physics and then of the whole question of “meta” languages. The paraphrase in math is a sort of meta language and I should not want to be ungrammatical there. We ask: in theoretical physics, are errors a matter of grammar and of punctuation, or are they a matter of math? If the answer is both (sometimes the one, sometimes the other, as either can lead to error), then my answer to you is Yes.

    I think maybe the question should be, not is my poem doing math but is my math-poem doing poetry. (I’ve been very “liberal” with you so far as definition of “what is poetry” goes, but I know very well that if I ask you to point out the poetic elements in your poetry your reply will be to ask me what a “poetic element” is.)

    I think if you, Kaz, and Grumman too, are going to make up the rules for mathematical poetry, then anybody can. Me included. And I would offer, for starters:

    1) It is a fallacy to think mathematical poetry is “doing math.”

    2) The “sum” of a mathematical poem need not be the same for everyone.

    Now I know you disagree with the first point. But I wonder how you feel about the second: Do you really expect that two people reading one of your math poems will have, will reach, will come to the same identical outcome and impressions? I do not believe that is an expectation a poet brings, or should bring, to his work. (The mathematician, yes; the poet, no.) To the contrary, I think. The variations come about in the redding (please look that word up if you don’t know it — it means, “to put into order” — and know that I never create words out of thin air), or let us just say the reading, the variations come about in the reading in good part make for the poetic experience (which I maintain is to a great extent “personal” and even “private”).

    Maybe, in all fairness to you, Kaz, we need to reconsider the word “sum,” and ask, what is the “sum” of a math poem. Maybe we can divide “sum” into

    1) ?

    and 2) impressions.

    I write a question mark for number one because I really do not know the answer. I do know, however, that it would have to be separable from the impressions.

    Now speaking about your “mathematical poetry,” and the impressions it gives off, one would have to cite immediately the fact that you use pictures (and not “word pictures” but actual pictures of things, and I mean aside from your formal symbols) and the fact that you use color (whether color background or otherwise). So we’re definitely in the realm of vis-po or of some kind of collage. And while you do refer to your math poems as “equational,” I would have to say that, notwithstanding that you do that, that given how I think of my own math poems as “grammatical,” I have to, then, think of yours as “visual.” (And just as I think of Bob’s as “visual.” In fact I think yours and Bob’s are much akin.)


    Now you, Kaz, say your mathematical poetry is doing math. I say: if it is, it’s by way of analogy. Either way, I think St. Thomasino has just laid down the metaphysics for math-po.


    Yrs, Gregory

    PS: Phase in the Wagner. Big crescendo on the Wagner, then poof.

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  25. Gregory, I just wrote Kaz b/c that you have trouble focusing after seeing your latest. The only other thing I said what that I was going to stay away from the discussion until after my trip to New York.

    I now take back both. I do think you tend to wind around questions way more than you need to, avoiding the cut&dry for the metaphysical. You also digress into your opinion of your opponent and his thinking a lot too much.

    I just now want to throw in the comment that, yes, anyone can define "mathematical poetry." Eventually, though, the community of those involved will have to choose a definition. Kaz and I merely think our definition makes more sense than yours.

    Although I can't say I understand yours. One virtue of ours is that it's clear.

    I also beseech thee please to post one of your mathematical poems. That would help me understand you much better, I think.

    Gotta get off the Internet now--doctor call coming in.

    May not return to this discussion but look forward to seeing you and Kaz at the Poetry Club.

    --Bob

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  26. Hi, Bob.

    I must confess (sinner that I am) that at first I was not going to post your latest (and last) comment because, well…. But I decided to go ahead and post it, because I think it demonstrates, and better than anything I could ever say, that you are not of sound mind.

    Yrs, Gregory

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  27. After re-reading all of these comments it seems we are diverging off the path in many directions. I personally have no problem with anything Gregory said in this blog entry except that he seemed to imply that there was some difference in how math does math and how mathematical poetry does math. Now we get into problems because there are different kinds of mathematical poetry which both Bob and I have tried to delineate even if we call them different things. However, Gregory addresses (at least in this blog entry) what Bob calls "mathematical Poetry" and I call "equational poetry". What I will argue is that equational poetry does math exactly the same as math does math due to mathematical poetry being a field of applied mathematics. There has been some talk of analogy. There is no difference in how math uses analogy and mathematical poetry uses analogy. I am from the camp that claims that at the axiomatic level math is based on metaphor and therefore uses analogy. Even though Gregory doesn't acknowledge this I must say that I really like the poems that he has presented here. I think three of them are wonderful and very unique relative to what I have seen people does with "Arithmetic Poems "

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  28. I must confess that I didn't realize that Gregory was taking about his arithmetic poems such as "to + to = too." These are--by any standards, it seems to me--mathematical poems. What confused me was that Gregory seemed to be defending some kind of poem as mathematical poetry that did not carry out a mathematical operation, as the "to" poem does.

    Warning, One of my two reactions to the Mathematical Graffiti Wall that I plan to read Saturday gets quite involved with Gregory's "to" poem (which I quite like) and with some of our arguments.

    --Bob

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