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.