3 is a 0 of multiplicity 2

In a graph, when you touch or cross the x-axis, you can call that point “a zero.”  If whatever you’re drawing crosses the x-axis at “3,” then “3 is a 0.”  And “multiplicity” determines the shape of the thing you’re drawing at that point on the graph: the even numbers are parabolas, odds are dog-legs, and a “one” is a plain old line. “Multiplicity 2” means that at the point your thingy touches the x-axis, it does so in the shape of a parabola.  And although my class hasn’t gotten to this yet, I also know that it’s possible to have imaginary zeros.  I don’t know what you do with imaginary zeros.

Multiplicity has been a favorite word of mine since I was introduced to Bergson and Deleuze.  But I usually use the word in a sloppy way, as in: “we should have a multiplicity of voices represented in the literary canon.”  That’s a terrible thesis.  Bergson (who was a math whiz before he became a philosopher) wrote about both quantitative and qualitative multiplicities in much more precise, interesting ways.

Qualitative multiplicity is found in a singular experience that can’t be juxtaposed against another one.  One of Bergson’s examples is to imagine the stretch and elasticity of an elastic band. “Bergson tells us first to contract the band to a mathematical point, which represents ‘the now’ of our experience. Then, draw it out to make a line growing progressively longer. He warns us not to focus on the line but on the action which traces it”(from the Stanford Encyclopedia of Philosophy).  The duration of the stretch, the inherent tension, the smooth transition from point to line, the experience of it all: these elements contribute to the qualitative value of the multiplicity more than a static image (such as a graph of a trajectory like the one above) can preserve.

So there’s math + philosophy. And also + art: in Findings on Elasticity, editors Hester Aardse and Astrid Alben write, “Elasticity has no inhibitions.  Science has no inhibitions…As science continues to shamelessly stretch knowledge as far as it will go, unburdened by inhibitions, so art, in its limitless ways of expressing human experience, often confronts our inhibitions and suggests where we should put them.”  It’s a wonderful book full of experiments and installations and inventions exploring (it seems to me) the question: How do we authentically record, document, preserve, share, communicate our experience of the qualitative multiplicity of elasticity?

These notions of multiplicity-via-elasticity (math, philosophy, art) relate to the nomadic paths of protest librarians and the (often surprisingly divergent) paths of the libraries’ physical collections of books.  The question is, how do these trajectories represent both quantitative and qualitative multiplicities, and how can they be recorded in a meaningful way.  This is a project to root around in over the summer.

PS: This article about an exhibit called “Design and the Elastic Mind” randomly passed through my Facebook feed just as I posted this entry: Curator Forced to Kill Out-of-Control Bio-Art Exhibit

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.

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.

“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?