My real education as a teenager was:
#1-3 happened despite formal schooling, not because of it, something Paul Graham says here:
This suggests the following conclusion:
1. The things you learn by yourself stick; the things that are “taught” to you do not stick.
The fundamental principle of education is to give students an environment, and tools, where they can make discoveries themselves. This requires space, and time, and autonomy.
Students also need to be able to choose what they learn and how they learn it, something that modern rigid curriculums and prison-like school environments do not permit.
However, I would go farther than this and say:
2. Video games provide a much deeper understanding of most subjects than classical education does.
I play a fair amount of chess (I’m not very good) and one thing you develop after playing a lot of chess is that you start to see “lines of force” on the board, e.g. the force a bishop exerts on an enemy pawn; and start to sense “weak points” in the opponent’s structure in a very physical way, in the way that you can sense the shakiest part of a Jenga tower in the physical world.
This is the classical “scholar’s mate” position. As soon as you move your bishop to c4, you just “feel” that the black f-pawn is under pressure. The force exerted by the white bishop and Queen on the f-pawn can be felt as a weakness in the body of a good chess player.
Developing this touch-based, proprioceptive “sense” of a thing is often key to a really deep understanding of it. When you understand something very well it’s almost as though you can play around with it using all your senses — touch, feeling, space.
Feynman:
“If you can’t see it, it’s hard to explain why—but if you try to hold something up with a ladder, say, and you get the ladder directly under the thing, it’s easy to keep the ladder from sliding out. But if the ladder is leaning way waaaaay out, so that the far end of the ladder is only a very tiny distance from the ground, you’ll find a nearly infinite horizontal force is required to hold the thing up at a very slight angle. Now, all these things you can feel. You don’t have to feel them; you can work them out by making diagrams and calculations, but as problems get more and more difficult, and as you try to understand nature in more and more complicated situations, the more you can guess at, feel, and understand without actually calculating, the much better off you are!”
There are stories of Feynman rolling around on the floor, eyes closed in concentration, simulating physical processes with his body. His biographer, James Gleick, writes:
Intuition was not just visual but also auditory and kinesthetic. Those who watched Feynman in moments of intense concentration came away with a strong, even disturbing sense of the physicality of the process, as thuogh his brain did not stop with the gray matter but extended through every muscle in his body. A Cornell dormitory neighbor opened Feynman’s door to find him rolling about on the floor beside his bed as he worked on a problem....In part the process of scientific visualization is a process of putting onself in nature: in an imagined beam of light, in a relativistic electron.