It’s not getting there,
I am looking out a motel window. It is raining. If I hold my head still the frame doesn't change but I am aware that the leaves in the trees across the street are moving and that rings are coming and going on the puddles as the raindrops hit. My brain does the differentiation, the time-lapse photography, the video recording. I'm not aware of all that. I am only aware of movement, of change, in the leaves and the puddles. They are alive.
I recently watched a video of an interview with Elon Musk, the man behind PayPal, Tesla, and SpaceX. He was asked how he learned rocket science. He thought for a second or two, and answered with a complete absence of irony. He said he read a lot of books on the subject. He said he sought out and hired many people who had experience in the field. He said together they worked on and solved many problems.
Then he paused, and said, You know, that's how I hire people.
How so? asked the interviewer.
Elon Musk said he would ask the candidate to describe some difficult problem he or she had solved. He said someone who had worked the problem through could discuss it to any depth; those who were on the periphery or along for the ride could not.
Check out this wonderful short video from Sal Khan: You Can Learn Anything. Knowing something is not a state. It is a history of struggle and failure. It is experience in the most alive sense of the word.
I recently met a young man new to teaching. His field is transportation, and has years of experience, much of it driving big rigs. I asked him how he was enjoying teaching. I love it, he said. But sometimes I go home frustrated. How so? I asked. Well, he said hesitantly, some of the teachers, they're good people, but they went from grade school to high school to teachers college and then right into the classroom. They've never been anywhere but a classroom.
We were both silent for a while. I thought about how that applies to my trade, flying airplanes. About the pilot shortage that is upon us. About how a lot can be learned in the classroom and on the internet (look at the Khan Academy!) and in simulators and even in airplanes. But something is missing: the struggle and failure of flying a real airplane in real weather and wind.
How can I even speak of failure in the same breath as flying?
Because I had the luxury of learning by doing and stumbling and failing under the guidance of vastly more experienced captains who had flown Sabres or Starfighters or Clunks. I was an apprentice. I learned from masters of the trade. Their lessons stayed with me because we solved problems together. I learned judgment. I learned to respect the airplane's limits and my own. I learned that sometimes you just don't go.
I also thought of how the world changes. I thought of how I flew the fly-by-wire Airbus for nine years and even instructed on it. It was a state-of-the-art machine. And yet we never did a GPS approach. They weren't ready yet in 2004. Now I have been retired for a decade and I am seventy years old, I am flying mostly GPS approaches. These approaches did not exist when I was flying the line.
When I was a First Officer on the DC-8 in 1979, INS had just replaced the Navigators. INS (and later, IRS) imitates the human body, specifically the semi-circular canals in our ears. They are miniature accelerometers (one in each of three axes) and among other things they help us to walk upright. INS uses the Calculus and integrates acceleration: what is the sum of all these accelerations over time? GPS does the opposite: with its ability to rapidly calculate positions to within a few meters, it goes the other way with Calculus: differentiation. It asks, if I look at how my position has changed over time, what does that say about my velocity? About my acceleration?
In essence, navigation is describing dS/dt.
What does all that have to do with learning?
Well, learning is change of ideas. Remember the video, You Can Learn Anything? “Because the most beautiful, complex concepts in the whole universe are built on basic ideas that anyone can learn; anyone, anywhere, can understand.”
Learning is change. Change of mindset, change of assumptions, changes in your idea of yourself. It is a journey of struggle. It is navigation. It is hard work.
But the destination is not static. It is a moving, living thing: the apprehension of a beautiful concept. It becomes a beautiful tool you can now use to bring your talents to bear on the problems facing humanity. It is joy.
What does all that say about teaching?
How shall we teach? How shall we pass on what we know?
How shall we learn as a people, a civilization, a species? Will each generation have to learn anew how to rub two dry sticks together? Or will Galileo read Aristotle, and Newton read Galileo, and Einstein adapt Newton to the scale of the galaxy?
That is not for me to say. But having in small measure experienced the joy of understanding and the joy of helping others understand, and having experienced the joy of change in myself over years and decades, I will not willingly let it go.