How to Learn Complicated Things

In the First World War, both sides had the problem of trying to take the other side's territory at a time in history when defensive technology was far superior to offensive technology. An enormous amount of effort (lives in this case) was made to take very small pieces of land - progress which was often reversed weeks later in a counter-attack. This was part of their 'bite-and-hold' strategy - focus relentlessly on taking small amounts of ground, and secure it before moving on to make the next small piece of progress.

It didn't work then, and you shouldn't adopt the same mindset when solving problems now.

I am talking, in this case, about a particular kind of problem - learning and understanding complicated, conceptually difficult things. If you're a student, or a professional in a technical field, or even if you just have any sort of curiosity about the world around you at all, this is a problem you will encounter a lot - and how effectively and efficiently you can do this underpins almost all other kinds of success.

What does the 'bite-and-hold' approach to learning things mean in the context of learning things, and why is it wrong? It means finding some resource - be it a textbook, online tutorial, explanatory article, or whatever - and working through it, section by section, not moving on to the next section or resource until the one before it has been fully understood. This intuitively seems like the best approach, as moving onto the the next section when you haven't fully understood the current one feels like a bit of a waste.

The problem is that this takes ages, because sometimes people's explanations of things often just aren't fully understandable. You get 80% of the value and understanding you will get from the text on the first read-through, and every subsequent read-through offers very diminishing returns.

Instead, you should move lightly and quickly through the resource, without worrying too much about not understanding what you are reading. If something doesn't make sense from the explanation on the page, or if you are completely lost - don't stress about it. Just keep going, extract what you can, and don't worry about not quite getting what the author is trying to say. At the end, when there will be inevitably be many things you don't understand about what you have just read, write those things down, in full sentences, as questions - and then move on to the next section/book/article/whatever.

The reason this is so much better comes down to a fundamental fact about human beings. With very few exceptions, people are not good at explaining things. A concept or idea can be very clear in a person's head, but when the time comes to transmit that understanding to someone else's brain by trying to write it down in words, it becomes garbled and corrupted. It doesn't matter how intelligent the person trying to explain it is. In fact in my experience, very intelligent people are the worst at being able to explain things, because they fundamentally cannot conceptualise or remember what it is like not to understand the thing they are trying to explain to me.

(Indeed, generally the best people at explaining concepts are people who only recently came to understand the concept themselves - not only will they still be excited about it, but more importantly they will still be able to remember what it is like not to understand it.)

And because of this, you need to read multiple explanations of a concept by many different people, before your brain will begin to synthesise its own understanding of the concept. A single readthrough of many different explanations of something is far, far better at conveying the concept than reading a single person's explanation over and over again, convinced that you're just reading it wrong and that surely they wouldn't write an explanation that didn't make sense or was incomplete. Well they would, and they have, because like everyone, like me, and probably you, they aren't very good at explaining things, because almost no one really is.

While it may sound obvious that you need multiple resources to understand something, that's not the core advice here - the core advice is: use multiple resources, but move through them lightly without worrying if you don't understand something, or if they progressively lose you as you get further into it.

Even knowing this, there can be a certain amount of pseudo-anxiety as you do this - worrying that you somehow should be understanding what you are reading, worrying that you are wasting your time, that if you don't understand it from this explanation you never will, etc. Let it go - the failing is theirs, not yours.

To take a totally "hypothetical" example, suppose you were midway through a computational PhD which, in its second half, involved a lot of machine learning, and suppose you had no experience with this and had to learn about it. You might approach this by starting with the mathematical building blocks - linear algebra, probability, calculus etc. - in depth, before moving onto learning about machine learning. You might spend huge amounts of time on these subjects - subjects which people are notoriously bad at explaining properly (in my experience) - wasting time determined to understand what this one chapter in this one textbook in this one branch of Mathematics means, while your hypothetical PhD ticks away week by week and you are far from where you need to be. Or, alternatively, you might eventually give up on the idea of firmly understanding one building block before moving on, blitz through multiple textbooks and tutorials in a short space of time, and make vastly more progress in one month than you had in the previous twelve. Eventually you would read enough different explanations of it that something would click. I imagine.

Ultimately, the approach you take to learning something determines how quickly you become competent enough to actually start doing useful things, which in turn determines the total number of those useful things you will ever be able to do. Don't waste your time reading the same chapter over and over again, and above all remember - if you don't understand what they have written, the blame is more theirs than yours.