Wednesday, May 28, 2003

Each day is better than the next

Last night I spent alot of time with Anne-Marie; we installed the air conditioner in the guest room (which is where the TV is), worked on plans for some of our art projects (EL-wire lotus flowers for Burning Man), and watched 'Star Trek - Nemesis' (don't bother). Between her job and my sickness, we often go days at a time without really getting to hang out, so this was a great joy.

I just sent off another circuit board design to the board house... I'm an electrical engineer, or rather I guess I was one when I was employed, but now I am just a very well educated hobbyist. I'm doing some research into the things I didn't feel they explained well enough in school... if I go back for a Masters degree, I'll probably have my thesis done before I even start classes.

There is this old 'joke' about a drunk guy who is searching the ground near a streetlamp... someone passing by asked him what he was doing:

Drunk: "I'm looking for my watch."
Other guy: "Where did you lose it?"
Drunk: "Over there in the dark alley..."
Other guy: "So why aren't you looking for it over there?"
Drunk: "There's more light over here."

I feel like most of what I learned in college was 'more light over here' information... not very practical in the long run, but something they could test you on. I spent so much time doing the assigned work that I didn't have time to actually learn anything useful. I once asked a prof about some arcane aspect of what we were studying, and instead of admitting that he didn't know, he admonished me to not waste my time thinking about things that wouldn't be on the exam.

When I was studying electromagnetic field theory, we spent a hell of alot of time doing problems that involved infinite planes, infinitely long wires, and spherical capacitors. Real-world problems are very difficult to do, since anywhere there is a clearly defined edge, the math goes nuts. It's called a non-differentiable point... since alot of the math relies on field components that are either tangent or perpendicular to the surface, a non-differentiable point (which has no clearly defined tangent or perpendicular) gets very messy. So the solution, in academia, is to only choose problems that do not have these messy properties.

A capacitor is usually thought of as two conductive plates, separated by a thin non-conductive material (could be air, or some dielectric material). But plates have edges, and the math gets messy... so the academic solution is to think about spherical capacitors, where one sphere is nested in another, and somehow the charge on the inner sphere is magically accessed without poking any holes in the outer sphere. Clearly this is crap, but in my day I was an expert on spherical capacitors.

I sincerely hope I am never asked to solve a real-world problem in electromagnetic fields... I'm going to look pretty silly when the only tool I have in my mental toolbox is an imaginary and non-realizable academic fiction.

One of the classes I enjoyed the most in school was 'control theory'... how to model physical systems mathematically, and develop a control algorithm to get the system to do what you want it to do. My senior project (627KB PDF) was a flight computer for my university's amateur rocket group, and in a control sense a rocket is a type of inverted pendulum, like when you balance a broom on your hand. I have thought alot about inverted pendulum type problems... they have become the de-facto standard for testing control systems. The Segway is a recent popular example of an inverted pendulum control problem.

So, now, in my copious free time, I have been working on real-world inverted-pendulum control problems... and of course, I am finding that everything I thought I knew turns out to fall into the 'more light over here' class of problems.

At the root of the problem lies the issue of non-linearity, which is the most poorly named property... the class of 'linear' systems (such as the ones we studied in school) is so incomprehensibly small and irrelevant compared to the class of 'non-linear' systems, but they are much easier to solve, so they get most of the attention. It turns out that most real-world problems cannot be directly solved by the methods we were taught in school, which I am sad to say turned out to be a very big surprise for me.

One accepted method for solving these real-world problems is to develop the math right up to the point where the non-linearities block you from proceeding further, and then linearize the equations about some operating point (for instance, the operating point of an inverted pendulum might be an angle of zero degrees from vertical, and an angular momentum of zero). For very small deviations from this operating point, this estimation process works reasonably well... but for larger deviations, it all falls apart.

So anyway, I am applying this process to the projects I am working on, to see where they lead. If nothing else, I gain some knowledge about how the world works, and how little we really know about it.