Problem Solving

Remember those word problems in elementary and junior high math?

If Tommy rides his bike at ten miles an hour and the store is four kilometers away, How much change would he get from a twenty dollar bill if he bought four dozen eggs at $2.95 a dozen? And how in the world would he get them back home safely?

We universally hated those problems. It's too bad because they probably represented the few, if only, chances to do any real problem solving in school. School was, and probably still is, cognitive oriented. How many facts can you cram into your head for just long enough to spew it out on the next exam? Our whole focus of education is wrong. Sure, there is some basic stuff that everyone should know about our history, culture, our bodies, etc, that could probably be summed up in a few good sized text books, or less. But apparently, even this isn't happening. Ever see those polls that say 57% of seniors in high school can't find the Pacific Ocean on a map? That stuff is mind boggling. Or current events, one poll the other day said something like 45% of adults don't know who Karl Rove is. He's probably only the second most important man in the US political scene today (I wonder if they know who number one is?). I guess we all have gaps and holes in our cognitive domain, but boy, some people must have holes you could drive a semi through. So, if the cognitive gaps are this bad, it doesn't leave much hope for the problem solving realm.

The sad part is that problem solving is really fun! It's curiosity with power tools. Sometimes I think the main object of school is to kill a child's curiosity about the world. We explain curiosity away by putting labels on it. "Teacher, what makes the moon go around the earth?" Answer "That's gravity, Bobbie". Well, that one's done, what's next? I was in college physics before I really knew what made the moon go around the earth. No kidding, and I was a chemistry major and lifelong science buff. Oh, sure, I could talk about the attractive forces, I could even regurgitate an equation if I had to, but I didn't really know in any meaningful sense. It happened like this: One day I was sitting in the huge physics lecture hall, bored out of my skull, thinking "why can't they make more left handed desks in these places". In the background was a voice that was talking about orbital motion and falling bodies. Now, all my life before this very instant, I was fascinated and disturbed by the fact that orbiting bodies had just the right amount of momentum to keep them perfectly balanced against the attractive force of the body they were orbiting. I guess I thought it was because if they didn't, they would either fly off into space or crash into the larger body (which is largely true), thus, only these perfect matches would last. All the physics majors out there are giggling now, but I really didn't know.

So, here I am half listening to the professor, and thinking again about this perfect match problem for the upteenth time. And then something magical happened. The words "falling body" triggered a brilliant flash of intuition. He didn't explain it for me, but he provided the key piece to the puzzle. I was so excited, I was almost dizzy, I wanted to scream "THEY ORBIT BECAUSE THEY ARE FALLING BODIES!!!!" There is no perfect match. ANY body that approaches or FALLS toward a larger body can play out one of three scenerios depending on it's speed and mass relative to the larger body. If it is high, it's path will be curved but it will first fall and then escape, just passing by it. If it is too slow, it's path will be curved enough so that it falls and crashes into the larger body. But for everything in between, it is captured by the gravity of the larger body but its fall never reaches the larger body, it continues to FALL forever in an elliptical orbit. So the moon, the earth and all the other planets are still falling bodies. Falling bodies that are just barely captured will have enormous elliptical orbits, slowing down at fartherest extent of their orbit, nearly about to escape, but can't quite make it, so they slowly turn back toward the larger body gaining a lot speed as they swing just past it on the return trip, but not close enough to crash into it. If you slowed them down, remember the retro rockets Scotty, they would still fall, but their orbit would bcome smaller. There would be a continual sucession of smaller and smaller orbits as you slowed the object down more and more until they did crash.

So, I know a lot of you are saying big deal. But my problems aren't your problems. Each of us has 'falling body' problems wandering around in our psyche, nagging, aching to have an answer. Sometimes, maybe even most times, we aren't even truly aware of the nature of the problem, we only know the nagging feeling. These are problems that cognitve learning usually can't answer because we just haven't been taught the process or the beauty of problem solving. Cognitive learning provides the fundamental stuff from which we can build theories, and it is from theories that we attempt to solve problems.

Why didn't the curiosity get beaten out me? That's a good question. Part of the answer is that I was a 'goody two shoes' in school. All the teachers said on my report cards "If I only had a classroom full of little Brent's". It was disgusting. Unlike a lot of other bright children that act out on their boredom with school, I turned it inward. I wondered about stuff. The reason I wasn't a trouble maker was that I was inside my head most of the time, both in school and out. I had my own little realm going on in there that didn't depend on real world much, or at least the social world. I can remember quite clearly when I must have been about seven or eight, looking at an electric motor. I can still see that motor. I was thinking, how in the world can something like that work? It just a case with a bunch of wires inside that you plug into the wall. Now I bet that is still the extent of understanding of fully half of the adult population in the US. But it bugged me. So, I did something about it. I went to library. Those were different days, I use to take the bus by myself at the age of five and go into town and to the library and the movies, and nobody even thought anything about it. And there I got books on electric motors, how they worked and how to build them. I had a little work shop in the basement and started building simple motors from dowls, thread spools, wire, and copper tubing for a commutator, it ran on six volt lamp batteries my father used to bring home from work for me. From building a simple motor, I got to learn how they worked. Later, I got a reputation as the kid who knew how everything worked. Maybe I couldn't understand or explain the fine details, but I could tell you how a car, or the refrigerator or the TV worked. The other kids would try to stump me, but they couldn't.

I guess that set a pattern for my life. It has been a source of immense pleasure and also painful frustration, mostly in school and college, where the real meaning of what you are supposed to be learning isn't important. Especially math, but that's the subject of another post. Then later, I too, became a teacher, and I tried to teach this awe and wonder of knowing how the world works. I put a priority on this aspect over the cognitive realm, so of course I was fired. Public school and I were just too combustible a mixture. I have continued to teach over the years, but only when I could do it my way, and it in little ways, usually in one to one situations, but I have taught adult college classes too, using these same principles.

Thus it is that I approach bonsai the same way. I reject the cookbook approach. I want to know why I have to root prune when the plant is dormant. I try to incorporate plant physiology into teaching bonsai, so that you gain the power to solve your own problems. These are extremely powerful tools. If you know how plants grow, then you can manipulate them and predict the outcome of your actions, whether you have read about it or not. The parable in the bible is so true: If you give a man a fish, you feed him for a day, but if you teach him how to fish, you feed him forever.