Top-Down Learning

And Other Learning Insights

"An idea starts to be interesting when you get scared of taking it to its logical conclusion."

— Nassim Taleb, The Bed of Procrustes


What's the best way to learn new things? I've been thinking about this question for a while now, and I think I finally have some inklings of an answer.

Let's get a few definitions out of the way:

  • Knowledge: Wikipedia tells me that "the definition of knowledge is a matter of ongoing debate among philosophers in the field of epistemology". Fine. For our purposes though, let's think of it as useful information — information that has some kind of utility. Knowing something — as I see it — doesn’t just mean memorizing facts. It means understanding how something is done; being able to use information to solve problems.

  • Learning: The process of acquiring or creating new knowledge.

  • Intelligence: I like Francois Chollet's definition — "The intelligence of a system is a measure of its skill-acquisition efficiency over a scope of tasks with respect to priors, experience, and generalization difficulty." In other words, it's the efficiency of learning.

So then, asking "how can I learn more efficiently?" is the same as asking "how can I become more intelligent?".

I had a few realizations that changed the way I think about learning:

  • First, we do most — if not all — of our thinking by analogy. Old concepts are recombined to form new ones; ideas have sex with each other to create new ideas. This is why it's important to relate what you're learning to something you already know — the more hooks you have in a new idea, the better you'll understand and remember it, and the more new insights it'll lead to. In addition, some concepts have dependencies to other concepts. If you don’t understand something, chances are you need to learn about one of the concept’s dependencies.

  • Second, nothing is inherently difficult. What matters is how information is presented — if something is complicated, chances are it isn’t presented in an elegant way. For example, people used to do math in Roman numerals - ew. Related to this, it seems that Pareto power laws apply to learning as well — you can get 80% of the understanding by spending 20% of the time on something, and you get the other 20% by spending the other 80%.

  • Third, as Kanye said, everything in the world is exactly the same. Recognize and exploit metapatterns. Here’s Stephen Wolfram talking about the same thing.

  • Fourth, and most important, is that top-down learning is better than bottom-up learning.

What do I mean by that last one? Basically, do you start with something general (high level) and go down as deep as you need to go? Or do you start with something specific (low level) and work your way up?

Top-down learning is question / problem oriented. Bottom-up learning is tool / resource oriented — learn the tool, then look for problems to apply it to. Bottom-up learning is, it seems, fundamentally backwards.

For example, there are two ways to learn a web framework — say, ReactJS. You can start with the specific — just take a course on it, because it might be useful one day. Or you can start with the general - there's a problem that needs to be solved, and it's best solved by creating a web app. Okay, then what are the best web frameworks to do that? Go learn the most promising one. This general-to-specific approach is basically how I got into web development. This (extremely oversimplified) picture shows you what I mean:

Elizabeth Van Nostrand has the clearest formulation of this idea that I've seen:

"The method I eventually landed upon involves starting with a question, not a book. If I start with a book and investigate the questions it brings up (you know, like I’ve been doing for the last 3-6 years), the book is controlling which questions get brought up."

Ana Lorena Fabrega hits on a similar point:

Michael Nielsen's explanation of the best way to understand something:

"Often the best way to understand something is to use it, to get comfortable, to play a lot, and to do lots of informal experiments. As you build familiarity you understand why things are the way they are. At that point, you can go back and better understand the meaning of the basics."

Play around with something. Break it. Debug it. Treat the world like your laboratory. Formulate questions and hypotheses. Answer them.

And of course, there's always Tim Urban's blog:

"The way I approach a post like that is I’ll start with the surface of the topic and ask myself what I don’t fully get—I look for those foggy spots in the story where when someone mentions it or it comes up in an article I’m reading, my mind kind of glazes over with a combination of “ugh it’s that icky term again nah go away” and “ew the adults are saying that adult thing again and I’m seven so I don’t actually understand what they’re talking about.” Then I’ll get reading about those foggy spots—but as I clear away fog from the surface, I often find more fog underneath. So then I research that new fog, and again, often come across other fog even further down. My perfectionism kicks in and I end up refusing to stop going down the rabbit hole until I hit the floor."

Another way to look at it: bottom-up learning is the classic mistake of putting the cart before the horse — you're trying to optimize for the metric of reading a book instead of learning what you want to know. Goodhart's Law in action.

So to sum up:

  1. Try to find the clearest formulations of ideas.

  2. Look for connections between new things and things you already know.

  3. Start with a question or with a problem instead of a course, a book or a tool.

We become more intelligent by learning to learn better.


Postscript:
Since publishing, I’ve come across Trishank Kuppusamy’s essay ‘Why universality trumps IQ’, and it complements the ideas expressed here quite nicely. Give it a read!

Postpostscript:
Another helpful essay is ‘How to learn on your own’ by Roger Grosse.


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