The negative wind speed beneath my wings

We had our first test this week.  The last question was a word problem about the amount of pollution in the air based on the speed of the wind.  Somehow, I ended up with a negative wind speed.  Which I know is illogical and impossible (unless I completely misunderstood the LIGO announcement this week).  But the math that I had worked out to arrive at the negative wind speed looked pretty much right to me.  And so, knowing that my answer was absolutely wrong, I wrote it down anyway.  Something is always better than nothing.

It is only this week dawning on me that I might actually fail this course, which has put me into a very fast five-stages-of-grief tailspin.  At the peak of my frustration, I told a friend that I was doing everything I knew how to do, and it wasn’t enough.  She said:

  • “Did you visit your professor during office hours?” No.
  • “Did you seek out tutoring?” No.
  • “Did you find other books to explain the same problem differently?” No.

She pointed out that I was not, in fact, doing everything I knew how to do.  Fellow math students have also suggested that I sit in the tutoring center while doing homework and that I ask around for links to YouTube videos of people working through the steps for given problems.

Honestly?  I HATE THESE IDEAS.  I believed learning math wouldn’t require as much collaboration as learning to write seems to require.  And honestly, the idea of doing math in a vacuum appeals to me. I’m not sure why, when I know how powerful collaboration can be.  For some reason, I want to be inside a black hole with math, where nothing IS something.  Or something like that.  Maybe my answer to this test question was me trying to tell myself as much.  Except I don’t know enough math to have ever orchestrated the negative wind speed answer on purpose.

This week, I need to reassess my goals with this math business.  If this project is going to last longer than a semester, I suppose I need a better plan.  Working in a black hole, as much as I like the idea of it, isn’t going to get me very far.

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.

Radicals in math and politics

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.

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Radical power: defining degrees of freedom (in stats)

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.

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Correlating radical math with radical politics

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.

I’m a math major.

Last semester, I took a statistics class with the excuse that it was job-related.  The truth is, though, deep down I have always been in love with math and ashamed to admit it.  In high school and college, when one is required to make life-long decisions before one really knows what life-long should and could be, I chose the English direction rather than math.  I believed (wrongly) that this was an either/or choice.

But statistics opened a fissure.  Math is everywhere: Borges is all about math.  Badiou is all about math.  Libraries are all about math.  And that’s just the easy-to-list stuff.  So this semester, I formally declared myself a math major at the school where I teach, and I have enrolled in College Algebra.  This is my first math class since 1987*. I have to take another basic skills class after this, then four semesters of calculus, and THEN I can start the “real” math major classes.

I should have probably started with an even more elementary class, but my ego (and checkbook) didn’t want me to.  So only in week two, I am already struggling to keep up.  I am a terrible student.  This is going to be a long journey.

Someone suggested that I blog about it.  I don’t know who will want to read this, how often this topic has been done, or even what I will have to say.  But I think it’s a good idea.  I make my students blog and “reflect.”  So a little practicing of the preaching is in order.  Who knows what this might add up to (<- see what I did there?).

*Except for stats last semester, and a little foray into developmental math a few years ago.