I’ve been a fan of Justin Skycak’s work for several years. While his style sometimes tastes a little too optimized for social media, the core insights are correct. A brief summary of his philosophy could be:
- Most people are capable of learning to do great things
- The ability to do great things depends on “upskilling”
- “Upskilling” is most efficiently accomplished through retrieval practice and problem-solving He has a lot more to say about productivity, being motivated, and avoiding common learning traps, but I want to focus on “upskilling” and what that looks like for different domains.
Justin works mostly with highly hierarchical knowledge, namely, mathematics and coding. “Hierarchical” means that each piece of knowledge, if it is not axiomatic, depends on prerequisite knowledge. For example, understanding multiplication depends on understanding addition, and understanding logarithms depends on understanding exponents. Math Academy, the company Justin works for, sells math tutoring that takes advantage of the hierarchical nature of mathematics. Their system infers which prerequisites a student needs to strengthen based on a spaced repetition algorithm. This approach works incredibly well for learners who use it correctly. I endorse their product wholeheartedly (and I hope that one day their price will come down so that a mathematics subscription is cheaper than a Netflix subscription).
Unfortunately, most domains of human knowledge are non-hierarchical. In math, it’s relatively easy to define what prerequisite knowledge is for a concept to be learned. It’s also relatively easy to come up with practice problems in mathematics. Furthermore, math problems are extremely verifiable — it’s easy to check whether the learner’s answer is right or wrong.
Let’s contrast practice problems in mathematics a practice problem in neuroscience — maybe something like “design an experiment to determine which human genes are responsible for sensing changes in temperature.” First of all, this hypothetical practice problem has limited verifiability. Instead of being binary right or wrong, the experiment you design will give you some information about the world, with limitations based on the methods you choose to use. For example, different model organisms (cultured cells, worms, flies, or mice) will have different tools available to manipulate the system, with varying degrees of control. Typically, there is a trade-off between the amount of control you have (typically higher for simpler systems) and the likelihood that the findings will generalize to humans, which is usually the system you are trying to understand. Second, the “most correct” answer may depend on context, like how big your budget is for the experiment, and how much time you have. Third, the solution space for this problem is fundamentally different than the solution space for a math problem. Math problems usually define their own solution space. For example, solving a quadratic equation means finding real (or complex) values of a variable that solve an equation. Just by looking at a math problem, you typically are able to figure out the general form that the solution will have. This is not the case for problems in non-hierarchical, poorly-structure domains.
While Math Academy doesn’t have a product for learning anything besides math, some of Justin’s writings still point in the right direction for how to learn non-hierarchical domains. He identifies that most learning happens by doing and producing. Many people have written about the value of writing for improving clarity of thought. I think that much of the usefulness of writing comes from how it substitutes for retrieval practice and problem-solving in non-hierarchical domains. Even though you can’t write down a knowledge graph, the process of thinking and writing strengthens connections between related concepts and helps to identify areas that are weak.
For me, this is a call to repentance. I do a lot of spaced repetition practice, but I do very little to sharpen my skills in non-hierarchical domains. If I’m not producing something, there’s no proof that I’ve learned anything. The effectiveness of my study will largely be determined by what fraction of my study is spent producing, either through spaced repetition, solving practice problems, writing, or some other generative activity.