Learn by exploration, then by theory
I’ve never been very disciplined on long flights. I always have grand productive plans going in — reading and writing, maybe some coding — but they never pan out. I’ve enjoyed a lot of average blockbusters in uncomfortable seats.
Last month, however, I managed to spend an entire 8 hour flight reading a book. Normally I’m a pretty fickle reader (I’m trying to get better), and on the face of it, this was a pretty dry non-fiction book. But I just couldn’t put it down!
The book was William Zinsser’s On Writing Well. Here’s why it gripped me, and how I think we can have more experiences like this.
“Eureka moments” are the best part of learning something — the feeling of discovering new insights that change how you view things.
You might occasionally mess around on a piano. You figure out how to play “Mary had a Little Lamb”. You start noticing some patterns — certain notes sound nice when played together — but you don’t understand why. You decide to learn Maple Leaf Rag by watching YouTube tutorials. You can eventually press the right keys at the right time, it sometimes even sounds nice. But you still have no idea how or why it works.
One day you decide to try and understand what’s going on. You discover that a whole world of theory exists around music. You learn about chords — this is why some notes sound nice together! You learn about keys — this is why Maple Leaf Rag uses the same few notes! You also discover that people have theorised specifically about learning how to play the piano. It turns out you weren’t the first to wonder why most of the learning seems to happen while you’re asleep.
These concepts are really basic — 7 year olds learn them in music lessons. But to you, they feel profound — they completely change your view of music, and discovering them is incredibly rewarding.
Learning by exploration is like being in a dark room. When you enter, you have no idea what’s in there, how it’s laid out, or even how big it is. You fumble your way around, knocking into things. You occasionally feel out the shape of something, but can’t tell what it is. You start to build up a map of the room in your head, but it’s wholly imprecise and mostly inaccurate.
Learning by theory afterwards is like being guided around the room with a torch. Some things will look familiar — “ah yeah I thought it was something like that!”. Others will take you completely by surprise — “I had no idea that was even there!”. Amazingly, both will be moments of profound insight and both will feel great. You can eventually turn on the lights and see how everything fits together.
Of course, there are other ways to find out what’s in the room.
Studying maths at university involves learning about lots of different concepts. This is the typical format:
- You’re presented with definitions of new concepts.
- You’re presented with a theorem involving these concepts, telling you how they relate to one another.
- You’re presented with a proof — a step by step explanation of why the theorem is true.
For a lot of my degree, I tried to take shortcuts. I’d skim through the definitions, theorems, and proofs, not thinking too hard about them, and hoping I could string them together with a couple of tweaks to complete the assignments. Usually, I couldn’t.
If maths is a room, then this is like looking at a picture to see what’s inside. On the surface, this approach made me feel like I understood the space, but in reality, this understanding was brittle. A picture of the same room from a different angle — what a maths assignment often amounts to — would be enough to throw me off.
The right way to study maths, I’m told, is to first explore the room in the dark.
Read the definitions and theorem. Try and prove it yourself — feel your way around the concepts, explore the logical steps you can take, and see what obstacles you run into. Dissect things — why is this definition meaningful? Why are these conditions necessary? What if we removed one?
Only after this exploration, dive into the theory. Read the proof carefully — each line will illuminate some part of the room, and eventually, you’ll be able to turn on the lights and see how everything comes together.
I didn’t take this approach in my degree, but I’ve tried to in my writing. This is why I was so gripped by that book on the plane — I’d spent some time exploring non-fiction writing (I wrote some blog posts), but On Writing Well was my first foray into non-fiction writing theory. Each page had a new Eureka moment that confirmed my suspicions, fleshed out my hunches, or most often, opened my eyes to insights completely new.
I got a lot from the book. But if I’d read it first before writing anything, I suspect I’d have gotten a lot less. Worse than that, reading it first would have just been no fun. Like reading the plot before watching a film, it would have spoiled the Eureka moments that made the experience so special.
1. Explore first
The “explore-first” approach comes naturally when we’re intrinsically motivated to learn something. Many programmers started out creating web pages for their Neopets guilds. If you don’t find yourself wanting to explore something, then you might be trying to do it for the wrong reasons.
2. Find the right cadence between exploration and theory
In the past, I’ve been guilty of spending too much time in exploration before learning theory, and I’m sure that the opposite applies for many people. If you find yourself stuck in the learning process, it might be worth switching from exploration to theory, or vice versa.
3. Embrace amateur-ship
Most of the low-hanging Eureka moments are concentrated in the early parts of learning, so being a “prolific amateur” — dipping your toes into lots of different fields — is probably very rewarding. (Of course, going deep has its own, different rewards)