How knowledge works

Why everything you know about knowing stuff is wrong. Plus, professional statisticians who can't do statistics, and math vs. cherry pie.

Imagine 2 people, Kyle and Louis. Kyle is a high school senior from a small town in northern Texas. The furthest he’s ever been from home is Dallas, where he goes once a year with his dad to watch a Cowboys game.

Kyle’s friends invite him on a trip to Cancún during spring break.

“Where’s Cancun? Asks Kyle.

“It’s in Mexico.”

“Are you crazy?” says Kyle. “I’m not going to Mexico. I don’t want to get killed!”

Louis, meanwhile, grew up in Paris, France. He traveled extensively in his youth, learned to speak 4 languages fluently, and today works at a big international bank.

Because he spent a lot of time in Mexico during his 20’s, today he works as the bank’s liaison to Mexico. He routinely goes on business trips to Mexico City, Monterrey, and Guadalajara. During those business trips, he and his wife like to spend time off in Oaxaca and in beach towns on the Yucatan Peninsula.

Louis has a lot of Mexican friends who tell him to be careful where he goes. He doesn’t look Mexican, so if he wanders into the wrong area, he could get killed. So Louis takes precautions when he visits Mexico: he doesn’t go out alone at night, and he carries a decoy wallet with him in case he gets mugged.

Kyle and Louis both know the same thing — Mexico is a dangerous country. But they know it in different ways, and at different depths. That’s why Louis feels safe going to Mexico, while Kyle doesn’t.

Everything you know about knowing stuff is wrong

In the Robert Heinlein novel Stranger In A Strange Land, about a human baby born on Mars, raised by Martians, and then taken to Earth, the Martian language has a word called grok. Grok basically translates to “understand something very deeply”. You can know something, but you don’t grok it until you really get it.

That’s how knowledge works in real life, too. People usually view knowledge as a binary thing. Either you know something, or you don’t. But the truth is more nuanced. The truth is that there are different levels of knowledge.

This is why, when you were in school, you found multiple-choice tests way easier than free response tests. Just because you can recognize the right answer when given a list of choices doesn’t mean you can recall the answer from scratch.

This is also why Kyle and Louis can both know the same thing — Mexico is a dangerous country — and respond in opposite ways. Louis knows that Mexico is dangerous and goes to Mexico. Kyle knows that Mexico is dangerous and avoids Mexico.

Why does knowledge work like this? Here are a few reasons.

Professional statisticians who can’t do statistics

The psychologists Daniel Kahneman and Amos Tversky wanted to know if people were good intuitive statisticians. That basically meant whether people automatically think about statistics problems the way that a professional statistician says they should.

So they created a bunch of statistics problems disguised as real-world scenarios. They were baffled: even professional statisticians couldn’t solve their problems.

When professional statisticians looked at Kahneman and Tversky’s problems, they approached them the wrong way, even though they taught lectures and wrote textbooks about how to do them the right way.

Why? My theory is that your brain has different modules. When the statisticians do lectures and write textbooks about statistics, they’re in statistics mode. But when they’re chatting with Kahneman and Tversky, they’re using a completely different part of their brain.

This is one of the major problems with how modern education works. If you’re a 10th grade trigonometry student, you’ll learn about stuff like sines and cosines and tangents and stuff. But let’s imagine that one day, you’re trapped in a triangular room, the walls are closing in on you, and you need to measure the sides of the room in order to escape.

That’s a trigonometry problem. But you probably won’t see it as a trigonometry problem, but your brain isn’t in “trigonometry mode”. It’s in “escaping from being trapped in a room” mode. You probably won’t think to use your protractor and calculator to figure out how to get out.

(Teachers call this transference and it’s one of those dark secrets that educators would rather not talk about. The stuff we learn in a classroom usually doesn’t translate to real life, specifically because we learn it in a classroom and not in real life.)

Why you can’t learn to ride a bike by reading books

Kyle, the Texan high school student from the beginning of this article, took Spanish classes. In his Spanish classes, he read grammar textbooks and memorized lists of vocabulary.

That gave him a lot of conceptual knowledge about how the Spanish language works. But when Kyle visited his local taco truck, that conceptual knowledge was worthless. The dudes in the truck talked so fast that Kyle couldn’t understand them.

Meanwhile, Louis learned Spanish on the street while traveling Mexico in his youth, by actually having conversations with people. He sucked at Spanish at first, and he embarrassed himself every time he tried to order food at a restaurant. But the more he practiced talking in Spanish, the better he got at speaking Spanish.

If you quizzed Kyle and Louis on Spanish grammar rules, Kyle would do better: Louis can’t tell you a lick about Spanish grammar rules. But if you dropped the 2 of them in Mexico City, Kyle wouldn’t understand a thing, and Louis would be able to chat up anybody he wanted to.

Why? Because Louis has muscle memory. His knowledge about how to speak Spanish didn’t come from cramming his head with facts. It came from practicing, over and over again.

Muscle memory

When it comes to learning languages, muscle memory is way more useful than conceptual knowledge. That’s because conceptual knowledge requires your conscious mind, and your conscious mind is way too slow to follow a real life conversation.

The same goes for riding a bike, doing open-heart surgery, and driving a car. Reading books about bikes, heart surgery, and driving cars won’t help you learn. The only way to learn is to practice.

Most skills have a way bigger muscle memory element than we realize. For example, writing. You would think that writing an article like this is mostly about how much stuff you know. The truth is, my ability to explain weird concepts in writing got way better as I wrote more and more of these articles, mostly because my subconscious mind was constantly building muscle memory every time I wrote. (If you don’t believe me, go read some of my earliest articles.)

Math vs. Cherry Pie

Every time legendary physicist Richard Feynman learned a new mathematical formula, he started by proving it.

The other students in his math classes would just memorize the formula, and that would be that. Feynman went a step further. He would play around with the theorem until he understood why it was true.

That gave him a way deeper understanding of his math theorems, which helped him use those math theorems to come up with a bunch of cool physics models.

Richard Feynman understood his math theorems far better than I understand how to bake cherry pie. Last weekend, for the first time in my life, I baked cherry pie. It didn’t come out right because I just blindly followed the recipe.

Because I just blindly followed the recipe, I didn’t understand that I wasn’t supposed to overwork the pie crust, and that I needed to bake off the excess water in the cherry filling. So the crust turned out wrong, and the cherry filling leaked all over the pan. (Now, I do understand that I’m not supposed to overwork the crust, and that I need to bake off the excess water in the cherry filling.)

There are different levels of knowledge. At the most basic levels of knowledge, you know something well enough to recognize it on a multiple-choice test, or parrot the words to it and pretend you understand it. At deeper levels of knowledge, you can build something from scratch, or even modify it.

At the most basic level of knowledge, you just know stuff. If someone asks you about it, you can recite what you know. But you can’t weave what you know into anything else, or use what you know to produce other stuff. (Think about a physics student who memorizes Maxwell’s equations.)

At higher levels of knowledge, you can understand the implications of what you know and apply it to real life stuff. (Think about an engineer who uses Maxwell’s equations to build a computer.)

And at even higher levels, you can use what you know to create something entirely new. (Think about a theoretical physicist who uses Maxwell’s equations to produce new models and theories about how electricity works.)

This is why Picasso said: Learn the rules like a pro so you can break them like an artist.

Hey! Thanks for reading.

My name’s Theo and every Monday I publish an article about whatever was on my mind the week before. Usually about psychology, how the world works, or long-term trends in society.

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