November 13, 2018
I frequently visit a website called Better Explained where the creator of the site explains various math and computer science concepts. His approach to the whole site is to explain things in a way that people develop an intuition about the concepts. This is in contrast to the way that we learn a lot of things in school, where we are expected to use rote memorization to connect seemingly unconnected topics and equations. I’ve learned multiple ideas from this site that I remember struggling greatly with in high school and college.
I think this is closely related to the idea espoused by Charlie Munger and Farnam Street that you should think of your knowledge as a lattice or scaffolding that you can hang new knowledge on. It’s invariably easier to learn new material when it fits easily into the context created by the rest of your knowledge. If you asked someone who knew nothing about history when Julius Caesar lived, they would have a whole several thousand years to choose from. If they knew the centuries that Rome was a world power, they could narrow down his possible lifetime to something like a thousand years. If they know enough about Roman history to know that he presided over the transition from Republic to Empire, they’d probably be able to place his life within 150 years of when it actually happened, without knowing any specific dates about anything. This is an intuition created by having a scaffolding of more general information on which to hang more specific information.
What’s more, simply memorizing Julius Caesar’s birth and death years doesn’t help you understand anything about the world. Understanding the fall of of Roman Republic and rise of the Roman Empire and Caesar’s role in it can help you form opinions even about modern political happenings. It may not be very relevant most of the time, true, but it’s infinitely more useful than just knowing a bunch of arbitrary dates. It’s intuition about how the world works.
Learning about how the sun’s rays are used as energy by plants and by us, and how that energy changes form as those plants are eaten by us and by animals, and again as we eat the animals is intuition about how the world works. It requires almost no memorization of specific scientific facts, it’s just a story about the journey of energy. As your understanding improves, you can add more specific numbers to the energy absorbed by the plants, animals, and solar panels and their efficiency. If you add to this a general understanding of the energy content of things like wood and coal or how many calories a person burns in a day, you’re able to do back of the envelope calculations about the number of plants or animals needed to feed a city, or the number of solar panels required to replace all of the coal burning plants, or the number of solar panels needed to replace the heat generated by a wood stove. I think most of us expect that you would need to be at least a physics undergrad to know this stuff, but I bet that a determined 10 year old could easily understand this. The math is all basic arithmetic, after all. The trick is in the story telling. Once you know the story of how energy moves, you only need to assign a dozen rough numbers to different parts to do some really powerful calculations, using nothing more than arithmetic!
I think we’d find that most of the world is like this. You can get 90% of the understanding for 10% of the work. Obviously you’re not going to get a job in the Department of Energy with the knowledge from the previous paragraph, but you’d know more about the specifics of how energy moves through the world than most people, and every time you read a news story about this or that hotly contested thing related to the climate or agriculture, you could do your own calculations in your head and decide how credible the story is.
Just like you look like a wizard when you know how to reset your grandparent’s router, many seemingly complicated topics are simply various combinations of a handful of important but basic truths, and you can seem like a wizard by knowing them and being able to reason from those first principles about how the world works.
I’d venture that this sort of intuition is the single most important thing kids can learn about the world. Everything in this world is connected. If they learn how things are connected and how to reason about those connections, it becomes much easier for them to believe that they can actually affect the world. They just need to choose a point and apply leverage. When most people see something like computers or solar panels, they see a black box that just works. When an electrical engineer looks at those things, they see tools that can be manipulated to whatever ends they see fit. We don’t all need to be electrical engineers to have intuitions about how these things work, though we think that we do. How powerful would it be for our children to believe that they can change the world? And not in the inspirational quote sense of being the change they want to see in the world, but in the real, concrete sense of seeing all sorts of complicated things as tools instead of as magic.
We tend to feel like we shouldn’t understand anything that we’re not “qualified” to understand, but that’s not how knowledge works. There’s never been a better time to be a person who needs to learn things. Practically anything you could ever want to learn is available for free online (and a lot of stuff you would never want to learn…). The only problem is where to start, but if we can teach our children to build knowledge scaffoldings for themselves, they can start wherever they want and they’ll just know more and more as time goes by.
We're sharing what we've learned in the course of doing some unconventional things in the hope that we can help others do better and get more out of life.