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.
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.
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?