This morning I spent two hours proving (-1)a = -a. I tell my friends I finally figured it out and they stare at me a moment, narrow their eyes a bit, and say, “But isn’t it obvious?”
That’s the problem. It is obvious. We’ve been raised in a culture wherein elementary math education is spewed to the masses–but it’s all given in bits and bytes of data, none of which is strewn together with any understanding of the processes at work beneath them.
That’s why it took me so long to solve the problem–I kept getting stuck on claims of “This is obvious” and had to turn back to step one–to the rules that govern real numbers, the foundation upon which the world was built.
But figuring it out wasn’t the most amazing thing to happen today.
The most amazing thing was was a strip of shade alongside a building I walk past on my way home from class. I should’ve taken a picture, but I was so amazed I didn’t know what to think and ambled forward with my head tilted back, my mouth hanging open.
Normally my only thankfulness for shade is reprise from the sun, but with the angle that golden orb hung at in the sky above, the shadow the building cast fell not only to the ground, but also through a tree–a tall oak perhaps–right in front of me. Yes, I’ve seen shade-stripes on trees before, but that wasn’t all that amazed me–no, there was more.
This tree, this ancient tree, had branches covered in lush and delicious leaves, each verdant fringe a color all its own. And where the branches fell, intersecting the shadow cast, there was a line–suspended far above the earth–where you could see the glimmering leaves suddenly drop into a dark, hunter green oblivion.
I could trace the line of light and shadow from the ground between my feet, up through air, across the leaves suspended in contrast, and to the top of the building where the sun peeked down upon us.
And it was amazing.
It’s obvious that the light falls where nothing obstructs its path, that shadows have an end and a beginning, that shadows cover the world in hidden edges of light and dark–but shadows are two-dimensional. They land where they land and that’s where they stand as we walk by and stare, as we walk by in ignorance because they’re always there.
Today I saw that shadow in three dimensions, cutting through time and space and reminding me there’s always that unseen edge in the air where light meets darkness, their tryst unseen yet somehow before all our eyes in every moment we stand there, watching, their love bleeding outwards in eternal secrecy.
I met with my professor this morning to discuss a proof I’d written, wondering if my reasoning had been right. He told me there wasn’t anything I had said that wasn’t claiming the entire statement was obvious. I was blind to the machines beneath the numbers, the theory behind the applied symbols dancing across the paper, playing limbo with a division bar and waiting to fall when it becomes too low.
I was blind to the interplay of light and shadow in the air in front of me.
But I was given a glimpse of that furtive sideways glance, a glimpse of the workings beneath the world, those basic facts that erect all of modern science–all of technology and modern life–in a few words that beg the question, “Isn’t it obvious?”
No. It never is.