Tonight I spent about five hours baking cupcakes and helping Chipmunk study for his calculus exam. It had been a long time since I'd studied this kind of calculus, and I'd forgotten what a lot of the rules were called, how to maximize the perimeter of a rectangle, and what the mean value theorem was. Some of the things I knew I'd never known very well, like what the hell L'Hopital's Rule was [now I know!!!]

But what I did realize is that math and I are starting to get very comfortable with each other. Sure, I probably got ~50% on my math exam on Tuesday, but when I was explaining all of my mistakes to my co-worker after the test, I realized that math and I had reached this kind of cosmic understanding of one another. I've gotten the "feel" for mathematics. I know the way equations think, and what they look like when you graph them.

It's like that wonderful feeling that English majors get when they read a fine work peppered with subtle classical references and they start "getting" all of them.

Right now we're learning the calculus of variations, which we are using to study functionals. What is a functional? Let me explain it to you this way:

Imagine a slack-line tied between two trees. You would like to "slack-line" across this rope. This rope has a certain stiffness, a certain elasticity, and a certain weight per unit length. All of these factors cause it to hang down in a roughly paraboloid shape. But what IS the shape that it will take? How can you describe it? Can you guess what it will be based only on the forces on the rope? And what if then someone stood on the rope? Could you calculate the shape of the rope as they walk across it? Could you calculate how the rope-shape changed? Could you calculate the path that a person would trace in space as they walked across the line?

YES!

Imagining a graph of a line in two dimensions, you have a group of x's that are transformed by a function to make a group of y values. In the case described above, you have a group of parabola-y-looking functions that describe the shape that the rope could take. They all have to have certain things in order to be a candidate: they have to be fixed at the ends where the rope is tied to the tree, for example. These so-called "admissible" (aka "allowable") functions all yield different values when you input them into a functional, which transforms them into a number, like the potential energy of the rope as it hangs there, or a minimum amount of time it would take for a slack-liner to walk from one end of the rope to the other depending on the path. So a functional is like a function which instead of taking numbers and transforming them into other numbers, takes functions and tells you which shape is the best or the most realistic.

Anyway, the calculation of variations is very powerful, because it lets you tackle ridiculous shapes with very poorly defined boundary conditions.

oh math. I love you. More on math at a later time. I should become a calculus tutor.

I know my calculus... it says u + me = us

If we lived in the same area, I would definitely want you as my calculus tutor.
» Mockiller on 2010-03-25 03:26:51

I literally had a test on your first paragraph yesterday.
» middaymoon on 2010-03-25 07:11:17

my head was spinning until the 2gether lyrics. that makes me sad.
» thaitanic on 2010-03-25 08:54:31

Ahh math would be something powerful to just "get a feel for." It's like having a feel for the way that the world just works.

And by the way, your comment made me so happy and I am THRILLED that you have started jumping rope! Thank you for the uplifting words :)
» The-Muffin-Man on 2010-03-26 09:31:23

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