"This is a Capacitor"

In college I took a Physics II course. I had been looking forward to that class since early High School. It was basically an introduction to circuits. I was eager to learn about resisters and capacitors and voltage and how circuits were built and designed. I thought I'd gain some knowledge that I'd be able to use in everyday life.

You wont be surprised to hear that I didn't gain any of that kind of knowledge. Sadly, I doubt I retained any knowledge from that course whatsoever. In truth, I barely made it through! Of course, it was one of those classes where a 60% test score can set the curve...

Anyway, there was one lesson in that class that I will never forget. The professor started class and turned to the board and said,
"This is a capacitor."

Then he wrote "C=Q/V" on the black board.

Yep, those 3 letters and 2 symbols are definitely a capacitor...

Now, maybe its just me, but when someone says "This is a capacitor," I sort of expect to glance up and see him holding one, or displaying a picture of one. I don't expect to see an equation. We never talked about what a capacitor DID, or why you might NEED one. In fact, it wasn't until I had a phone conversation with my dad that I learned a capacitor "stored charge". And I'm not even going to get into the fact that C=Q/V describes capacitance, which is a measurable quantity, and not a capacitor which is a physical device...

So what lesson did I learn from this? Different people learn and think in different ways. I'm a practical applied type of learner. That is, I need to understand and not just memorize. Thus giving me an equation or showing me a graph just isn't quite enough. I need to see steps and logic and explanation. In other words, I have to start from something I know and build up.

Other people certainly aren't this way. I've known lots of people who could simply see an equation and understand. I've known other people who could see an equation and then spit back and pass the class, but maybe not understand.

Fortunately for me, my learning style works great for computer science. Unfortunately for me, it's not how Math is taught. And only rarely how Physics is taught.

I've always believed that calculus and physics should be taught hand in hand. After all, the majority of calculus was developed trying to solve problems in physics. Add in a dash of History and you've got a thoroughly engrossing class in my opinion. But anyone who's been through college knows that isn't how its done most places.

Instead physics is taught with algebra, because the kids don't know calculus, even if they've taken it. And that means you have to memorize and spit back more equations for more circumstances. If it was calculus the number of equations would drop and the amount of logic to handle different circumstance would rise. Great for me! But again, not how its typically done.

Given all this, I guess I can't really blame my Physics II teacher. He was just teaching the way he thinks. Turns out a lot of people think and learn that way just fine. Even the Wikipedia article on Capacitance is written in much the same way. Of course, Wikipedia makes a distinction between a Capacitor and Capacitance and does a great job of describing Capacitors in English...

Still, I've never been convinced that people who were able to learn the equation and solve the "word problems" and ace the tests really understood any of it. Some of them did. But most of them? I find it hard to believe.

I have to end this by pointing out that there are certain topics to which my style of thinking and learning just doesn't help. Things like Quantum physics, for example. Where no matter how you look at it, you can't reduce it to common sense. In these circumstances you have to settle for memorizing the "way things are". Chemistry is like this. And yes, lots of Physics is like this too. But I still claim that after you've internalized the "way things are", you can start to reason logically about it.

Polishing the Golden Shovel

My senior year of High School I took AP English. I hated that class, but I have to admit I did learn a little about writing. One thing I learned was you got a higher grade if you included your own insight and opinions into your "book review" type papers.

My junior year of College I took History of Aviation to fulfill the last of my History credit requirements. It was a horrible class. The material was interesting, and the books we used were decent, but our professor was… well, boring. And the tests and assignments were simply a waste of time. It was quite literally like going back to freshman year of High School with "chapter summary" 1 page papers in 5 paragraphs due every week.

I can’t recall exactly what grades I got on the first few papers, B- or C comes to mind though. The professor had underlined roughly half of my essay (not to indicate anything, I think she was just one of those people who underlines as they read so they don’t loose their place...). Then she’d scrawled, "more examples" or something to that effect on the top. I was kind of peeved. I’d read the material, and I thought that was obvious given the content of my "essay." And like I’d learned in AP English in High School, I’d added in a lot of my own personal take on what the reading had taught me and how it applied to whatever idiotic prompt we’d been given that week. That was clearly not what the professor was looking for.

It took me a few papers to finally realize that this was a class where it didn’t matter what I was learning, or how well I was writing. This was a class where I had to figure out what the professor wanted to see in those papers. It didn’t matter if what she wanted to see made sense, or was good or bad, or furthered my education... It only mattered that she wanted to see it.

So I developed a method for writing those papers. I would look at the prompt we’d been given. Then I’d skim through the material we were supposed to read. When I found a sentence or paragraph that applied to the prompt somehow, I’d underline it and add a mark at the top of the page so I could find it again. When I’d finished skimming the material, I’d go back through and find everything I’d underlined. I’d summarize the sentence and put the page number. Then I would number each quotation 1-n in an order that would sensibly answer the prompt. Finally I’d write my paper. The introduction would restate the prompt. The rest of the paper would be direct quotes (or sometimes paraphrased quotes, always referenced) with transitions between them. The conclusion would restate the prompt. Each of my little 1 page essays would include about 8 to 12 quotes.

Let me drive that home. I literally wrote NOTHING except to transition between quotations. I’m not overstating this, that’s all I did. And while I think I did a decent job masking it with my transitions, it was still quite obvious.

I got As on every paper for the rest of the semester.

My dad once taught me a term which summarizes what I was doing here wonderfully. When I would tell him about some stupid paper I had to write he would say, "Polish your golden shovel!" This referring to all the Bull Shit you’re about to shovel into your paper and attempt to masquerade as golden writing.

Of course, usually when you’re putting your golden shovel to work it’s not as blatant as my History of Aviation story. In fact, in normal use it’s a very valuable skill to have. Sometimes you have to sharpen the saw, and other times you have to polish the golden shovel.

Connect4

In college I took an AI class. For the most part I was pretty disappointed in it. I wanted to learn about techniques to make computers learn (Neural Networks and Evolutionary Computation and so forth) but intro to AI is mostly just A* and Alpha Beta search. Given, those are clever algorithms, but at their core they're just brute force, so I didn't find it all that interesting.

However, our final project in the class was to develop a program to play Connect 4. The class broke into teams of 4-6 people. Then we had a big tournament between all the teams to see who's connect 4 program would win. Our professor gave us a heuristic to start us off which she told us wasn't very good. We were supposed to develop our own heuristic and then any kind of UI (or not) that we wanted.

Heuristics are pretty boring. Basically you just spend a lot of time trying to figure out how to decide, given a certain board state, if the board is good or bad. So you do all the work of figuring out the game, code it into a heuristic, and the computer just brute forces its way through all possible game moves trusting that your heuristic is smart enough to tell what is good and bad.

My team didn't really want to work on the Heuristic. Instead the majority of them went off and created a pretty sweet OpenGL UI where the Connect 4 board would spin around and the pieces would fly off the stack and into the board...

We just used the Heuristic our professor had given us, but a friend and I optimized the crap (memory usage) out of our Alpha Beta search, board state representation, and heuristic evaluation. Because our alpha beta routine was so much faster than the other teams' we were able to search about 2 levels deeper into the game tree.

We tied for first place.

Even though our Heuristic wasn't supposed to be very good, the fact that our search algorithm was so much more efficient meant we looked further ahead than everyone else and that was all it took.

At the time, we also had access to a room full of computers. We considered creating a client/server program to use all those computers to evaluate the game tree in parallel but after we did the math we realized that adding 12 more computers would only get us one level further down the tree because the number of nodes in each level of the tree doubles. We didn't think one more level was worth the effort, so we didn't bother.