This is some of the comments to one of Geof Huth’s blog post reviewing Bob Grumman’s new book, really a chapbook, entitled A Preliminary Taxonomy of Poetry
Geof said, “Mathematical poems add mathematical features that visualize the poetry, so I consider them visual poems, and to have a category for flowchart poetry assumes that process symbols are textual and thus not visual. I'd argue, again, that they are not orthodox text, so these poems are also visual poems.
Also, Bob's definition remains indefensible: "poetry that uses mathematical symbols that actually carry out mathematical operations." These mathematical operations are not actual; they are apparent. That is a big different. Duck cannot be divided by yellow in any mathematical way, though it could in a metaphoric way that has nothing to do with math directly.”
I am going to have to take exception to both of you on a couple of things. First I will start with you and the top paragraph. Unfortunately I have never seen a definition of Visual Poetry that everyone agrees upon. Yet I will have to say that I like what I understand to be Karl Kempton and Karl Young’s definition of: “Visual Poetry is a Poetry that has to be seen” This is such a simple yet powerful definition that seems to me to be true in every case of vizpo that I have seen. With that being said, There are what I would consider pure mathematical poems whereby they can be understood by reading them alone. An example would be, “Love is equal to the limit of 1 over ‘x’ as ‘x’ approaches zero”. This mathematical poem can be understood perfectly without seeing it therefore it would not be visual poetry.
In the next paragraph above Bob states that, " These mathematical operations are not actual; they are apparent. That is a big different.”
I will argue that these operations are actual and they work the same as any equation in applied mathematics. The ‘variable’ or we can say ‘concept’ or ‘word’ in any mathematical poem can be substituted with a number that represents the value of the variable/concept/word/term. The ‘word’ can be substituted with a multitude of numbers just like in the equation ‘x’ equals ‘y’ squared whereby x can equal anything and y will equal whatever x is squared. The thing to focus on is that the words have value or magnitude and they have mathematical relationship to each other. This means the words in a mathematical poem can be substituted with a number and the words or concepts along with their mathematical syntax within the equation provides the units or “unit meaning”. To make this clear let’s look at the equation from physics d=vt or distance is equal to the velocity multiplied by time. If you look at velocity you get units of miles per hour. If you look at time you get the units hours and when you divide the unit ‘miles per hour’ by ‘hour’ you simple get the unit ‘miles’. And ‘miles’ is the unit for distance. Notice we did not talk a bit about numbers, yet, those variables can all be replaced with numbers and it is important to note, the units will remain. Mathematical poetry is the same however the units are created within the poem itself. Unfortunately all the mathematical poets I know are not addressing this issue and thus are missing the boat by thinking that mathematical poems don’t do math.
In your next example where Duck is divided by yellow you say that you cannot divide it in any mathematical way. This is not true you can divide it, however, it is pretty much meaningless gibberish at worse and a wild metaphor at best. The bottom line is that Duck divided by yellow is not anymore incoherent than much of Gertrude Stein’s work.
Endwar (Andrew Russ) wrote:
On mathematical poetry and mathematics: I’m not sure I agree completely with anyone here. It seems to me that in a mathematical poem one sees a mathematical operation with words (usually) operating in a metaphorical way (thus the poetry enters). That said, the mathematical operations involved are usually well-defined for numbers, but not for various words and concepts. “3+1=2” is something everyone (is taught to) agrees on in a literal way, and it follows from the definitions of each number and the signs “+” and “=”. The statement "candy cane + child = happiness" is also probably pretty generally understood, but not with the same level of definiteness (or definition, as per the previous sentence) as the numerical example earlier. You could write "candy cane + child = obesity", which would probably also be understood, but because of the metaphorical nature of the math, you can’t conclude (via the law of substitution) that “happiness = obesity” (though some may point out the phrase “fat, dumb, and happy”, which could then lead us to conclude “happiness = obesity = stupidity” . . . You can see, then where the multiple meanings of words (bifurcations of meaning, to throw in another mathematical metaphor popular in some at one time trendy lit-crit circles)) can lead.)
I would argue that a mathematical poem is a statement that represents a mathematical operation on the words involved, but which isn’t necessarily one that can be checked the way mathematical statements with numbers can be. I will even go one step further and assert that one can create a mathematical poem that is mathematically wrong but which still makes a metaphorical point. I have done this using matrix multiplication – a 2x2 matrix times a 2x1 vector is set equal to a 3x1 vector. That’s not something you can do with real number (or even imaginary number) math, but I think it works as a poem.
Written mathematics is inherently visual, not verbal: I can grant Bob’s point that “3-1=2” is visually not interesting, and furthermore it hardly matters what font is used. It does matter a bit what numbers are used – roman numerals will say “III-I=II”, and binary says “11-1=10”, and ternary says “10-1=2”, which are all the same numerically. But it becomes evident for large numbers that roman numerals are unwieldy for calculating, and we are used to the decimal number system, so the non-decimal numbers need cumbersome subscripts or context to be read as intended. I would argue, though, that the real test of whether we have something verbal versus something visual is whether the statement can be read aloud. Again “Three minus one equals two,” is pretty straightforward, but that is merely because of the simplicity of the expression. Try reading, say, a passage out of the middle of J.D. Jackson’s Classical Electrodynamics or any other graduate physics or mathematics text, and it will be immediately obvious why these equations aren’t written out in words and why mathematicians and scientists do nearly all their professional discussions with slides or in the presence of a blackboard. And even if one does manage to put the text purely into words read aloud, you will find nobody in the audience who will understand what has been said who hasn’t at least written down some equations or a drawing as a guide. One of the most tedious reading experiences I had was a few pages out of an algebra text written by Leonhard Euler, who felt it was necessary to write down an equation and then repeat the equation in words, such as:
The kinetic energy is equal to half the product of the mass and the square of the velocity.” This continues for page after page.
If you’re still not convinced, show me how to do read calculus aloud and make it intelligible. Two pages minimum.
Because the visual representation is integral to the intelligible communication of all but the simplest mathematics, I would argue that mathematics is inherently visual language, and that by extension, mathematical poetry is also inherently visual poetry. The visual poem may still not depend on which font is used (though I have examples where that is the case as well), but it still can’t be read aloud and have the same meaning, because it will not then register as mathematical.
Kaz wrote in response to Endwar:
That is an interesting argument however, you seem to be making a distinction between the existence of a math equation which doesn’t have to be seen (like your Euler example) and then the distinction of performing the mathematical operations which have to been seen. (or at least I will agree that I would have extreme difficulty working out equations with out seeing them). Yet, since you can have math equations in verbal form (you just can’t work them out) it seems that math does not have to be in visual form and therefore not necessarily ‘exclusively’ visual. Or this begs the question what is math? Is it the performing of mathematical expressions or is it the expression itself? Or a mathematical Platonist would claim that math is an inherent object in nature … Gee why did I have to drag the Platonists into this – go ahead and slap me and forget that I said that.
Bob Grumman wrote:
Thanks for all the comments, endwar. I’ll get to all of them, I hope. Right now, just some thoughts in response to your comments about mathematical poetry.
I don’t care whether a poem can be read aloud or not. Mathematics is written in text just as ordinary verbal material is. Text printed standardly is effectively not visual, as far as I’m concerned: it’s symbolic. So a purely mathematical poem, in my definition, would be expressed in verbal and mathematical symbols.
On further thought, it seems to me all mathematics can be read out loud. So what if one needs to see it on the page to understand it? That would be true of many linguexclusive poems, too. Even relatively simple ones. I’ve almost never understood poems I was unfamiliar with when read at poetry readings.
As for the child and candy cane, I like your reasoning, but it now seems to me you have simple shown that “candy cane + child = happiness” and “candy cane + child = obesity” are both incorrect! They should be “candy cane + child = happiness + X” and “candy cane + child = obesity +Y.” And “happiness – obesity + X – Y.”
* * * * * * *
By the way, I love this discussion of mathematical poetry. I suddenly wondered, though, if there’s a subject fewer people in the world would be interested in.
One futher note: even if we admitted that difficult math must be seen to be understood, that would not make “candy cane + child – X = happiness” a visual poem since that particular poem would not have to be seen to be understood. That said, I can’t wait for the first mathematical poem based on mathematics you have to see on the page to understand.
As far as this Candy Cane analogy goes. I think that in both cases multiplication works better than addition. That said, I would imagine that people would relate to the following best.
Candy cane + childhood = happiness
Candy Cane x childhood = obesity
I am going to ignore the two equations above and rewrite them as multiplication problems with coefficients. The bottom-line is asking what numerical values you assign to these variables or words:
1(Candy Cane) multiplied by 100000(Childhood) equals 1(happiness)
1000(Candy Cane) multiplied by 1(Childhood) equal 1(Obesity)
Bob said, “Text printed standardly is effectively not visual, as far as I'm concerned: it's symbolic”
Gee Bob, if symbols are not visual then what are they? … verbal descriptions of symbols are just that ‘descriptions’ they are not the symbol.
Here you make an excellent point that language is just as difficult to understand when listened to as large mathematical equations Thus making a stronger case that pure mathematical poetry is not visual poetry or possibly making the case that all poetry is visual:
“On further thought, it seems to me all mathematics can be read out loud. So what if one needs to see it on the page to understand it? That would be true of many linguexclusive poems, too. Even relatively simple ones. I've almost never understood poems I was unfamiliar with when read at poetry readings.”
Instead of the definition of Visual poetry being – Poetry that has to be seen then state it as such: “Visual poetry is poetry that cannot be verbalized.”
Bob said on his blog:
This is, I believe, the first time I’ve accepted that the operations are metaphorical, as Gregory St. Thomasino tried to convince me six months or so ago. My trouble (still) is that the operations seem actual to me–the sun really does multiply a field to get flowers!
Kaz said as a comment to Bob’s Blog:
There is a bit of a disconnect here. All mathematics is based in metaphor not just mathematical poetry. The problem Gregory had was that he was trying to delineate mathematical poetry from pure mathematics by claiming that mathematical poetry works by analogy and Pure mathematics doesn’t.
If you read George Lakoff’s book “Where mathematics comes from” then you will come to realize that all mathematics is based in metaphor. Not just mathematical poetry.