|"Solve for E,"|
Courtesy Aaron Parecki
An absence greater than zero,
The square root of negative one,
An unimaginable number,
From this there is no sum.
You see, there is no zero greater than zero; the square root of negative one is an imaginary number, therefore, impossible to imagine...like life without someone who has always been there. And once that person is taken away, they cannot be added back.
As for my hero and stand-in dad Pythagoras, an amazing theorem, which actually makes rearranging furniture in my poky old house a lot easier, is named after him. Seriously, it's like the universe's gift to people who live in small spaces.
A2 + B2 = C2.
In some sort of myth I created for myself, Pythagoras was accused of hubris for demonstrating that the geometry of the universe was imperfect: if a2 + b2 = 2.16666 repeating...what the hell? There is no precision in that! Hence, "Pyth" and his school had to disperse, and he most likely died of starvation hiding in a cave. Except records of the time indicate he died of natural causes at the age of 75 in his hometown after having served as something akin to mayor. Still, it's a good story.
But back to imaginary numbers.
Multiply a positive real number by itself, and you get a positive result. Multiply a negative real number by itself, and you get...a positive result. So the square root of both positive and negative numbers is always positive. But electrical engineers and physicists need negative square roots. I could discuss the position of a particle in space...and snowplows...but I wouldn't know what the hell I was talking about. I think the gist is imaginary numbers make solving equations more elegant in the way that the colon (as used in writing and not pooping...although...sometimes writing is pooping) replaces a whole lot of words.
I know a lot about math.
And if you are willing to look up my second-grade teacher and explain that to her...for me...I would gladly stand behind you, peer around your shoulder, and nod my head, with my lips pursed, in complete allegiance.
Because I still can't subtract. Twelve minus eight? I use my fingers because I can't remember.
I'd like to believe this has something to do with my philosophical embrace of optimism: it is simply against my nature to negate.
The truth is, it's because of a blue crayon.
Also, I'm not philosophically optimistic. I could theoretically subtract some people from this earth for their actions and/or ideology if it weren't illegal (and against my conscience...because I do have one), and that doesn't really indicate an optimistic bent.
But back to the blue crayon.
We learned to add in first grade, we learned to subtract in second grade, we learned to multiply in third grade, and we learned to divide in fourth grade...all the while "practicing" the skills we had previously learned via worksheets filled with numbers that became increasingly longer. We had calculators in the 70s; I can only guess my teachers thought they were a passing fad. But, even as young as I was, I completely understood the concept of "work smarter, not harder" and wondered, really, what the point of all the worksheets was. I'm an educator, and I still consider all that busy work a weak attempt at scaffolding.
My second grade teacher, let's call her Ms. Break-It (which is actually an awesome play on her real last name...but I'm protecting "the innocent"), decided to try something new.
A million bad ideas have been born out of a desire for novelty, so this was not the first of its kind: we would grade our own subtraction worksheets...with the crayon color of our choice. I will never see a pedagogical value in having 2nd graders score their own work, but maybe I missed something in one of my education courses. Whatever. Black has always been, will always be, my favorite color, but it was not an option...the little weasel, a chubby boy with a handsome face and dirty blond hair, who turned me in probably got to it first. Blue was the next best thing.
We all completed the same worksheet, so Ms. Break-It could call out the correct answers. We, using the crayon-color-of-not-my-choice, marked our incorrect answers. We had been instructed not to erase. On problem number 5,678, I noticed my numeral two looked like a "Z." Because my brain is so big, I was anticipating algebra before I even knew what it was; I could not let the "Z" stand because we were subtracting, not "solving for." I used my bla...I mean...blue crayon to make the "Z" more clearly into a two. Then I realized I had "corrected" a correct answer...Ms. Break-It would be confused...she would take points off a problem I had triumphantly and with great effort gotten right!
Goddamit, I tried to erase the crayon without erasing my answer, which is physically impossible, but I irrationally held on to the belief it could be done.
And then the weasel pointed at me and shouted, "She's erasing! She's erasing!"
I remember being called to Ms. Break-It's desk and everything goes blank after that.
Flash forward and Ms. Break-It offers us this crumb of wisdom: "Little boys are better at math and science, and little girls are better at writing and art." I guess that was supposed to make me feel better. I don't know. I wasn't the only girl in the class; there were quite a few of us...I'm guessing we made up 54% of the students? So why Ms. Break-It felt the need to proffer her newly gleaned knowledge, I'm not exactly sure.
But I was a precocious child. I remember "teaching" my mom about socialism with a chalkboard and drawings in the dining room of our home...how hard it must have been for her to hold back the laughter every time I said, "the means of reproduction." But I got it: our work is our life. To value some work as worth more than other work seemed unfair to me. The ditch digger makes clean running water possible, without which there would be no surgeons and CEOs. (Full disclosure: these lectures were prepared with the aim of increasing my allowance.)
I also knew that I couldn't name a single famous woman author or artist sitting in that classroom on that day. Every artist and writer I knew about was a man (Michelangelo, Shakespeare, KISS). And I wanted to raise my hand and ask, "If that's true, if little girls are better at art and writing, where are all the women artists and authors? I want to know about them," but I didn't know how to ask that question.
At that time, the only famous women I knew were models and actresses, and I can't even remember who they were. There was no Sally Ride, no Hillary Clinton, no Alice Walker, no Tina Fey, no Madonna, no etc. There were only a few women, like Madame Curie (Mrs. Curie), who seemed to pop up in history and then fade away as some sort of anomalous event.
So, yes, my first brush with patriarchy came when I was seven or eight years old, and, while I didn't have a name for it, I understood its message: "Women have never accomplished very much." And I figured I wouldn't either...especially since I could not fucking subtract. (Sorry, Mom.)
"Can't subtract." I feel certain this was written on my 2nd-grade report card, and I have allowed it to characterize me for 40 years of my life.
"Can't subtract." I was revising a 50-page grant a few weeks ago and I ran into a table that basically showed we intended to increase the rate of X by 10% each year over five years. I looked at it and looked at and looked at it: "That's 50%." I did the math: "We're going to increase the rate of X from 57% to 93%? That's going to be challenging. Actually, I don't think that's possible." So I knocked it down by half, still challenging but at least do-able. As I finished revising the table it dawned on me: I recognized a statistical conundrum, and I solved it. With math.
"Can't subtract." The one thing I would never say to my daughter, the thing my dad would have told me wasn't true, the thing I've said to myself a million times, is the one thing I haven't said so far, and I'm not going to say it.
Instead, I'll say, "I'm good at math. I may need my fingers to subtract, but I know how to do it."
And to all the daughters out there I didn't have...don't ever let someone else define you or what you can do.