Wednesday, December 19, 2012

I forgive you, the Distributive Property


You and the rest of your thuggish triumvirate (I'm talking to you:  Associative, Commutative) with your tough-guy demands for protection money at the start of every math course.  But are you ever around later to help out?  Not much.

Even my favorite math site says you are a holdover from the ill-conceived New Math that sent my generation's minds into free-association, communal living and the redistribution of wealth just in reaction to your bullying.  And I quote:
There are three basic properties of numbers, and your textbook will probably have just a little section on these properties, somewhere near the beginning of the course, and then you'll probably never see them again (until the beginning of the next course). My impression is that covering these properties is a holdover from the "New Math" fiasco of the 1960s. While the topic will start to become relevant in matrix algebra and calculus (and become amazingly important in advanced math, a couple years after calculus), they really don't matter a whole lot now.
Why not? Because every math system you've ever worked with has obeyed these properties! You have never dealt with a system where (a×b)×c did not in fact equal did not equal a×(b×c). Which is why the properties probably seem somewhat pointless to you. Don't worry about their "relevance" for now; just make sure you can keep the properties straight so you can pass the next test.
I have to quote that explanation because no one who is not (1) a math teacher, (2) anal-retentive, and/or (3) otherwise afflicted, really gives a toot about you -- let alone has the foggiest what you really are.  And yet you give undue pain to thousands and are a root cause, I can attest, to the onset of childhood math-hate and lingering math-distress in most American adults.

Last night, YoungSon did battle with you.  And you won, Distributive Property, as you so often do, your Pyrrhic victory.  Probably, you, in all your numeracy, are too illiterate to understand that means you really lost.  Lost your student, lost your chance to illumine him.  Your contender retired moaning how he could never get it, how math was too hard, how his brain was math-stupid.  I'm going to give you the benefit of the doubt that you didn't mean to beat your student, but you are so bumblingly blind about the way most minds learn math that I could almost feel sorry for you if you weren't such a brute about it.

Instead of you, which are useless, I gave YoungSon a walnut.  "So you want to solve for x, right?  Imagine x is the nut, the good part.  Write it over again bolder and focus on that X.  That's the prisoner you're going to break out of prison.  It's the sweet meat of the nut, the part you can digest.  You need to get it free from all its husk and shell without breaking it, though.  So if x is inside parentheses, that's the shell.  The adding and subtracting outside the shell, that's just husk -- it breaks off easily if you roll it underfoot, right? and so you can undo each of those and put the mess over on the other side.  The adding and subtracting inside the shell, though, you can't get rid of until you've cracked open the shell of the parentheses.  And it's the multiplying and dividing outside the parentheses that lock the shell so you have to undo that next.  See?"

And he saw. Metaphorically.  Cognitively.

Which if he is like me, he would never never never see by simple-mindedly graffiti-ing the gang-sign of whichever of the -Tive Brotherhood thinks this step or that is his turf.

So I forgive you in the sense of letting you go, not relying on you any more, not trying to argue or explain you.  As far as I'm concerned, you can stop dooming around, Distributive, with your dystopian take on reality.  Keep away from our neighborhood community, Commutative.  Stop being such a donkey, Associative. If you must, we can try again when we have to face the Matrix and other sci-fi forms of the maths, but I don't need you to make things more difficult than they are, when really what I've got now is not that hard a nut to crack.

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