I’m about halfway through Eagleton’s book, Hope Without Optimism. Optimism, it seems, is a vacuous, ungrounded belief that everything will be ok. Everything will work out for the best. It’s an attitude and an outlook. And when things don’t work out for the best, they have to be quickly recast as actually the best but we didn’t know it right away (the “what doesn’t kill you makes you stronger” kind of thing). Eagleton is not a fan of optimism. Neither am I.

Hope, on the other hand, requires a lot of work and for the most part, has very little to do with optimism. You can be hopeful without being optimistic. You can hope desperately for something, knowing full well that it likely won’t come to pass. And hope requires that we acknowledge that things might not work out for the best. That doesn’t mean we should quit. Not at all. There is a realism and a drive implied with hope that optimism doesn’t require. Hopeful people hold a certain fidelity to the virtue of hope. The whole idea is to forge ahead in a hopeful way, despite the presence or lack of optimism.

I’ve begun MATH 140 for the second time. So far, the material is familiar and I am passing, but I’m certainly not “acing” this course the way I expected–given that his is my second time through. And, of course, life is again getting in the way in all kinds of wonderful and insidious ways.

However: I will remain hopeful. Not optimistic. But unflaggingly hopeful.

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?

Chapter one of College Algebra: we are learning about square roots. After you square something, you can use a square root to undo the square. They provide reversibility. The number under the root-sign-thingy is the radicand, and the number on the outside is the index. The entire square root expression is called a radical.

Radicals seem to be mostly used for party tricks with negative numbers. “Hey, Pythagoras, watch me square this negative number. POOF. I have a positive number. Where did the negatives go??” Without the negative, you can do practical things like calculate a standard deviation and play with “degrees of freedom.” As long as the squared numbers remain under the safe cover of the radical, they are in a (heterotopic) space where you can add, divide, apply, and make meaning. And the really wondrous part? Not only can you square away negative signs when you don’t want them, and not only can you later conjure them back with your radical-at-the-ready, but you can ALSO bring them back with the new meanings still attached.

A radical in math is related etymologically to a radical in politics. The word means “from the roots, fundamental,” and—most surprising to me—”vital,” as in: “the humour or moisture once thought to be present in all living organisms as a necessary condition of their vitality.” Thus a radical math expression and radical politics both desire to get at the root of a thing, to dig down to the fundamental part that cannot be broken down into anything smaller, to understand the vitality permeating the matter. Imagining radical activists (think Arab Spring or Occupy) camping under the umbrella of the radical sign, it’s only a small step then to disappearing the negatives, functioning from a place of absolute value, and harnessing the inherent vitality of their expression. The power of this expression comes from the quantity of the root, which increases exponentially.

I’m not sure of the value in this comparison, other than to say there it is. In my studies of radical politics, I plan to think more about the disappearing negatives, degrees of freedom, and how meaning is carried back across the threshold of the radical.