Quadratics and calligrams

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The curve of the banana is a parabola that can be calculated with the quadratic formula.  More at http://blogs.swa-jkt.com/swa/10326/2012/11/21/quadratic-functions-in-the-real-world/

A month into the semester, and my algebra book has not yet mentioned this critical bit: the two solutions produced by a quadratic equation are actually the points on a graph that a parabola passes through.  Not until ch 3 this week, “Functions and Graphs,” when finally: we have some pictures.  This changes everything.

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A well-known calligram about the Eiffel Tower by Guillaumme Apollinaire. See more at http://www.galleryintell.com/artex/poems-peace-war-guillaume-apollinaire/

Coincidentally, this week my own students and I read the part of Foucault’s The Order of Things where he mentions “the beautiful calligrams dreamed of by Linnaeus” (135).  A calligram is a piece of text written in the shape of the object it describes.  It’s often associated with poetry, but it’s also tied by definition to pictures.

Botanist Carl Linnaeus attempted to use calligrams in his scientific descriptions of plants: “the order of the description, its division into paragraphs, and even its typographical modules, should reproduce the form of the plant itself.  That the printed text, in its variables of form, arrangement, and quantity, should have a vegetable structure” (135).  Linnaeus felt that his classification system would be better represented if he used the lines on the page as both text and image.  The idea of overlaying a mathematical, formulaic grid onto language in order to suss out buried meanings and connections is nothing new.  Centuries later Lacan would try something similar (in my mind, anyway) by creating mathemes: graphic representations of his ideas that you can now buy on tee-shirts.

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“The Treachery of Images,” Magritte  (http://collections.lacma.org/node/239578)

In a separate essay called “This is not a pipe,” Foucault discusses Magritte’s paradoxical painting as another type of calligram “secretly formed, and then carefully undone.”  He writes that calligrams “bring text and image as close as possible to each other,” and usually the calligram erases the binary between: “to show and to name; to figure and to speak; to reproduce and to articulate; to intimate and to signify; to look at and to read.”  In Magritte’s work, says Foucault, through the contradiction and the conflation of the words and image, this is an act of mischief.

The graph of a quadratic equation seems to be a mischievous  variation on the calligram, one that conflates the idea of general and specific, of a formula to be applied universally and of a specific diagram of a particular banana.  Seeing the equation and its result together simultaneously forms and undoes their relationship, at least for the uninitiated (as I am), at which point we are (I am) surprised and delighted to find the correspondence.

And a parting question for those who are already fluent in quadratics (can you say it that way?). I imagine that having both the equation and the graph is a bit redundant, the way Neo sees the Matrix code and the agents simultaneously, so once fluent, does the act of plotting the graph continue to generate any meaning, laughter, or surprise?

Please excuse my dear Aunt Sally: That’s an order.

We have begun working with quadratic equations.  I am failing this miserably, but I think I have discovered the root of the problem:  the Order of Operations.  This is the fundamental set of rules that dictates 5 + 6 x 2 equals 17 and not 22.  I realized last week that when overwhelmed by an equation, I start with the parts that look easy (so I do all the addition first, for example).  The Order of Operations says no, no, no, you can’t do it that way, and it makes my answers non-negotiably wrong.

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Please Excuse My Dear Aunt Sally: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.

Until today, I believed that basic math skills were grounded in axioms (self-evident propositions) and theorems (things capable of being proved).  But in studying up on the Order of Operations, I found that it is a convention.  Granted, it’s a widely accepted, super duper important one.  But at its heart, a convention is simply “an agreement or covenant between parties.”  In other words, I’m failing math because of a spit and a handshake.

If a convention is simply an ongoing agreement to a set of (arbitrary) rules, then the Order of Operations is just math’s grammar, a study of “the relations of words in the sentence, and with the rules for employing these in accordance with established usage.”  My field of writing and composition has largely abandoned the right/wrong binary of grammar in favor of multiple grammars representing marginalized voices.  My biased impression is that basic math has, conversely, tightened its grip on this binary.*

Math and writing used to have multiplicity more in common.  In Hidden Harmonies: The Lives and Times of the Pythagorean Theorem, I read that Babylonian scribes may have “thought of values differently arrived at the way we think of variant spellings: there is no ideal that ‘color’ or ‘colour’ better realizes” (36).  And the authors then write that the algebraic Babylonian culture “was founded on recipes, which are always modified by locality and detail” (41).

I have to tell you, I love the idea that my test answer isn’t wrong–it is simply my shiraz to math’s syrah.  Come on, Aunt Sally. Let’s carve out a little space for my particular dialect of quadratic equation.  We can discuss further over a glass of wine.

*This might be because so much of the homework is done online with inflexible, automated grading systems.  The computer is a harsh mistress.