Note: The legwork for this task was done on Friday, June 22, but I was unable to upload the Praxis until now. This will be important later.
Partial Differential Equations.
I'll endeavour to explain. You see, in calculus, the derivative of a function is used to represent how much that function changes in response to changes in its input (represented by variables in the function). The high-school definition is that the derivative of a function represents the slope of the tangent to a curve at any given point (which is why the derivatives of quadratics are linear, the derivatives of linears are constant, and the derivatives of constants are zero). This tangent can represent a whole host of things, though. Taking the derivative of a function is called "differentiating", and in most cases it's fairly straightforward.
So, a differential equation relates a function to its derivatives of various orders (the derivative of a function is a first-order derivative, the derivative of that
derivative is a second-order derivative, and so on, and so on). They crop up all over the place in science, mostly with regard to deterministic (i.e, not random) relations between quantities (expressed as functions) and their rates of change (expressed by derivatives).
Continuing, a partial derivative is one in which a function with many variables is differentiated with respect to only one of those variables. The other variables are assumed to remain constant for the purposes of the partial derivative. This is opposed to a total derivative, in which all the variables are considered.
a partial differential equation is a differential equation containing functions with multiple variables, which relates them to their partial derivatives. Got that?
This was what my morning was like today. Sitting, rifling through Wikipedia, puzzling through concepts I'd either never heard of, or hadn't heard of since first year D/I Calc classes. Computer Science doesn't do a great job of drilling that stuff into your head; you do your first year calculus classes and then just kind of leave it in the back of your brain until... well, until you get a job and they ask you to bust it all out again.
But at about ten o'clock, something magnificent happened- a package arrived for me. I don't get a lot of mail, so each package- even if I know what is inside- is like a mini-adventure in a box. And I knew what was in this box. Boy, did I.
I'd put in an order for a new Mac at work- I'd just been getting myself situated and "in the groove" of the workplace, as it was- so I needed a computer I could call my own. And it had finally arrived. A shiny new iMac, gleaming under the fluorescent lights like pure, shimmering moonlight given shape.
So, I mean, it was fine
, but I was more digging the box. Unpacking objects is a primal art. The sensation of discovery, of finding out what lies behind the next cardboard flap, is intoxicating. It's the same feeling that made Magellan want to circumnavigate the planet. It's the same feeling that gets scientists into labs each day. The feeling of knowing, instead of imagining.
Computer boxes are so great, Macs especially. They're filled with all kinds of cool stuff. Oddly-shaped bricks of Styrofoam, peripherals all individually packaged in smooth, white cardboard with encouraging messages written on them ("Congratulations. You and your iMac were made for each other"), big sheets of clear plastic to be peeled off of screens- it's a veritable cornucopia of things that just satisfy that part of your brain that likes watching things open up.
By now, it was lunch. I hadn't bothered to clean up the mess I'd made unpacking (what am I, some kind of killjoy?) and so, as I sat down to eat my soup and sandwich, my room was full of boxes, foam, discarded plastic wrappers and stickers of every sort. I ate, surrounded by the detritus of the digital age.
As I packed away my last spoonful of soup, I laid down the cheap aluminum bowl and came to a startling realization- on all sides, lay garbage. Garbage behind, beside- all but in front, where the shiny new iMac sat. I took stock- a few spoons, some plum pits wrapped in saran wrap, the aforementioned aluminum bowl. My human half had no comment.
However, my Player half said "There's a story in there".
And so, I dug, and I found it.
It was about this point where a co-worker sauntered by and happened to notice me intently taking photos of trash sitting on my desk.
"What are you doing?" he said, his voice a wavering cadence of uncertainty, suspicion, and curiosity.
I turned around slowly, trying not to look startled. I fancy I must have looked rather like a cornered animal, giving my best, most intense glare (proven to bruise fruit from thirty yards). But really, I probably just looked like someone who had been working too hard, and whose brain finally buckled under the strain.
"It's my lunch break", I said, without a hint of inflection. "And I'll do what I want".
There was, at this point, a rather loud "CLANK". You can tell, because the camera shook.
The story thus concluded, I paused to think about it's meaning. But, alas, before any profound thoughts could be put to paper, I realized I was at work, and my lunch break was nigh-on over. I hurriedly scooped the trash into the bin, and returned to my partial differential equations.