Saturday, May 25, 2013

Abstract Mechanics

Photo:  Clemens Koppensteiner
Having just completed three and a half months of student teaching, I am slowly returning to a less frazzled and more contemplative state. It has been quite the experience. Despite the strain and frustration that comes standard with the job, I am even more convinced that this avocation is my great purpose in this life and am very much happily anticipating getting off the line with my own classes come this autumn.

That said, there were two questions that were repeatedly asked by my students this semester which induced no end of subtle annoyance:
  1. "Why would anyone want to be a teacher and put themselves through all this every day?"
  2. "Why do I have to learn math anyway? It's hard and confusing and no one ever uses it." 

The first one is more difficult because it's more personal. Suffice to say I've got my reasons, wrapped up in a fairly individual batch of ideals and aspirations and innate abilities and cultural considerations and childhood traumas and the like. I think it's important in the grand scheme of things, I'm fairly good at it, it'll hopefully (finally) make for a life which in retrospect will be at least partly well-spent.

The second part is much more about the world at large and as such requires a lot less of a vision-quest vibe - mostly because if you ever ask this question you've just openly admitted that you're not paying attention to reality.

Humans are mathematical creatures. Back when we had to count how many almonds fell off the trees in Mesopotamia, through everything with the Greeks and Indians and Chinese and Aztecs and everyone, through the development of engineering and commerce, through clay tablets to codexes to abacuses to slide rules to the Cray XK7, humans have betrayed a need to fool with numbers to various ends.

And a lot of that shows up in everyday life. Home improvements? Doing your taxes? Figuring out a budget? Setting up a schedule? Considering a wager in Vegas? Math, math, math, math and math. Maybe not the most advanced stuff, but still dependent on a number of algebraic and statistical patterns.

If you care about cars you can take that idea and compound it repeatedly. Quite honestly, if you have any interest in vehicles of any kind - cars, bicycles, airplanes, container ships - you have exactly zero excuses for not taking math (and by extension physics) very, very seriously.

Think about it: We all have these ideas of Power and Velocity and things spinning around and everything that gets translated into speed. But really, have you ever thought about the complete sequence of events that goes into the process from burning gasoline to burning rubber, and how they all depend on accurate and complementary calculations made by legions of engineers who participate in some great dance of collaboration that produces your car?

Applied math. Photo: jfhweb
Never mind the constant numeric shorthand that goes on in vehicle circles: gear ratios, suspension geometry, torsional rigidity, tire diameters, friction and drag, bore and stroke. (How many hopped-up but undereducated gearhead wannabes even understand what "displacement" is? It's only the core of all American understanding of cars and I've seen some pretty misguided descriptions of the term.) Acceleration and speed shift back and forth through calculus. Proper use of trigonometry is the difference between a car with a frame that handles power and cornering loads capably and one that's an ill-handling unstable hazard.

Yes, I know a big part of what I write about is the search for a kind of human element and a preference for feel over raw numbers, but the need for math isn't really about that. Actually it's still very much there but just directed towards different ends. A really sweet-handling car may not run up a sky-high lateral acceleration result (an extremely interesting and oft-misunderstood test that probably deserves its own column) but instead has a tremendous amount of calculation and consideration done to induce a more intangible result; yes, the steering is that accurate and usable because of the geometry of the rods and linkages and arms, and the car manages to feel that planted because the spring and damping rates are really well-matched, and so on.

If you get into racing - that most romantic and innately human of motoring activities - you're in for an even heavier dose of math. Not only is car setup a steadily developing algorithm of tire pressures and fuel delivery rates and corner weighting but driving itself is applied geometry. The standard textbook for competition drivers is Piero Taruffi's The Technique of Motor Racing, which is little more than a collection of obsessive calculations about cornering from someone who was there at the beginning of racing's math-and-science Enlightenment. Almost sixty years after its publication those calculations have not lost a bit of relevance.

To say that math is important in the world at large is understating things significantly; to say that it's important for cars and bikes and the rest is to miss how it's at the very core of these creations. Indeed, math done correctly makes the human element that much more present in a good vehicle's actions.

So this is definitely one of those for-whom-the-bell-tolls moments: You have to know a good bit of math to really grasp a lot of what goes on in the average car, and it helps to have a healthy respect for the higher-level stuff that went into the design and engineering processes. Hopefully what I'll be teaching will help some of my students better understand all of this, which means that we'll keep this entire idea of enlightened personal transportation going foward into an increasingly complex future.

That's why it's important. And that's also a big part of why I'm doing this.

So go finish your homework already.