How to think well and understand things

notes on independent learning

Buy my new book! My mom says it’s great

My favorite pastime is trying to understand things. Give me a textbook and I will gladly spend months bathing in the ideas, diagrams, and explanations therein, soaking up all the knowledge I can squeeze into my little sponge brain. I want to answer the big questions and uncover the workings of the world, and I don’t want to be thwarted by concepts that are difficult to understand.

The notes below are motivated by the question of “how to get better at understanding”, or how to learn a new subject independently (something which I’ve done here and there). In the process, we will begin to touch on the more general question of how to think well.

Pay attention to when you do or don’t understand something

The Radiance of Attention by Luc Tuymans

When I was doing my first programming internship, I was pretty bad, not just because I didn’t know much, but because I wasn’t aware of how much I didn’t know. I spent a lot of time fumbling around an unfamiliar codebase and struggling to figure out what a JavaScript Promise is. I was clueless about how clueless I was, and unsure where to start.

If you’re trying to learn something new, especially in a technical field, you will find yourself in a similar position. Say you’re trying to read a paper about how Learning induces long-term potentiation in the hippocampus and you have no idea what any of those words mean. The challenge is in figuring out how you can get from point A, your current mental state where the paper (and the title) is inscrutable, to point B, some future mental state where the paper is totally intelligible to you.

This is like being plopped into a foreign country and trying to learn the language on your own. One approach is to break things down into manageable pieces and understand those first. Make a list of all the words or phrases you don’t understand and look them up. (And every time you find a new word you don’t know, add it to your list and repeat.) So “learning induces long-term potentiation in the hippocampus” becomes:

• “Learning” ← pretty straightforward

• “induces” ← this is just another word for “causes” or “brings about”

• “long-term potentiation” ← this just means that the connection between neurons becomes stronger

• “hippocampus” ← this is a region of the brain that we believe to be responsible for memory

Done! Learning things causes your neurons to form stronger connections in a specific part of the brain.

It’s not always this easy—sometimes there will be so many new concepts that you need to step back and do more background reading first. But there is a simple meta-level skill here, and that is to keep asking: What are the things I do and don’t understand? At what point in the chain of reasoning did I get lost? What do I need to figure out next to make progress? You want to be relentless in identifying your conceptual blockers and pushing past the confusion.

What does it even mean to “understand” something? We don’t have an answer that everyone agrees on. But here’s a guess: it has something to do with your mind entering an isomorphic (read: structurally similar) state to the mind of someone else who does understand it, and perhaps both of your minds are isomorphic to the idea in question.

That’s great, but how can you check if you’ve achieved this? By seeking feedback in as many forms as possible. Play around with the idea, re-explain it to yourself, ask yourself why the concept or theory is in this particular shape rather than another shape. What are the implications of the theory? What does it leave unresolved? Share all of these thoughts with others and see whether it makes sense to them.

Understand how we got here

The Discussion by Eduoard Vuillard

We want to be aware of when we understand what our counterpart is saying (our “counterpart” can be a person, a paper, a book…), but it’s also important to understand why they landed at this conclusion in the first place.

Let’s divide the space of things you’re trying to learn (say you want to learn basic neuroscience) into the what and the why. The what is the content of our models and theories. “The brain is made up of 85 billion neurons which communicate via electrical spikes and neurotransmitters.” That’s useful to know. But if you’re serious about understanding, you also want to know: why do we conclude that there are 85 billion neurons and that they communicate via spikes and neurotransmitters? The answer lies in a long history of experiments, proposals, and disagreements. Or basically: fights and makeups between neuroscientists. The history is important—not so much who said what, but what was said and why, how we changed our beliefs over time.

From Constance Reid’s biography of the mathematician David Hilbert:

Hilbert had no patience with mathematical lectures which filled the students with facts but did not teach them how to frame a problem and solve it. He often used to tell them that “a perfect formulation of a problem is already half its solution.”

The final answer is only part of the picture. When you know the trail of experiments and arguments that led us here, you start to build an intuition for how to solve future problems. Why do we believe the hippocampus is responsible for memory? Why is the software architected in this way versus another? It’s even better if you can “reproduce” this trail yourself—write out your own proof for the theorem, implement your own version of the algorithm, design your own hypothetical experiment.

Seek flexibility over correctness

How Little She Really Understands Herself by Haddon Sundblom

For a few years I was engrossed in philosophy and science out of a rabid desire to find the Truth. Truth is great, it’s something we should all strive towards. But once you develop an emotional attachment to it and pin your whole identity on having found it, you enter an intellectual well that’s very hard to climb out of. This mental rigidity is bad, not just for further intellectual progress, but also for your mental health.¹

Where does consciousness come from? Everyone has a different opinion: it comes from self-reference, or from social interaction, or having a world-model, or it’s inherent to reality. Where is memory stored? Most neuroscientists think it’s in the connections between neurons, while a few think it’s in the individual neurons themselves. When grappling with big questions we haven’t answered yet, you need the mental flexibility to “take on” different perspectives and see the merits and flaws of each.

But even when you’ve found the answer, you need to remain flexible. In the late 1800’s, the leading physicists were convinced that physics was over—Newtonian mechanics reigned supreme, and we just needed to sort out a few small details. Physicist Albert A. Michelson said at the time: “Our future discoveries must be looked for in the sixth place of decimals.” And then of course Einstein and others came on the scene and turned everything upside down, proposing that time is not absolute, space is curved, and there is a multitude of universes. To mitigate our tendency to cling to one view, we need to constantly expose ourselves to different schools of thought and attempt to understand them even when we think they’re probably wrong.

Not having a singular Truth² to cling onto is inherently unpleasant, but there are ways to keep our clinging in check. If understanding is contorting your mind to be isomorphic to someone else’s, the holy grail is to be able to contort quickly between various frames of thinking, to see how something that seems absurd on its face might actually be the next world-changing insight. Maybe in the mental gymnastics you’ll discover something new.

Thanks to James, Matt, and my brother for helpful notes on earlier drafts of this piece.

1. In a recent paper, Robin Carhart-Harris and others propose a new unifying framework for mental illness based on the concept of “stuckness”:

Robin Carhart-Harris @RCarhartHarris

The view proposes that the core feature of mental illness is a learned ‘stuckness’ to thinking & behaving. Examples = getting stuck on despairing thoughts in depression, triggering fears in anxiety disorders, self-critical thought in eating disorders 🧵 2/7

While being stuck on a philosophical or scientific idea is not as extreme as stuckness in despairing or anxious thoughts, I think there’s a similar process at play. See also, Michael Ashcroft’s Getting unstuck – physically and philosophically.

2. I’m avoiding the bigger question here of whether “objective truth exists” and what form it might take. My current stance is something roughly along the lines of: there is an objective world, but the mere existence of an objective world does not imply the existence of propositional truths about it. See this tweet and the accompanying discussion:

Jake Orthwein @JakeOrthwein

@reason_wit_me @DorfGinger But you say that because the world exists objectively (independently of us), there must be objective truths about it. Does this follow? Truth is a property of statements/propositions/representations. That the world *exists* does not determine what properties such things can have.

In particular, the notion that reality can be described by perfectly precise propositions seems dubious to me right now, given the inherent nebulosity of all objects and categories. This need not lead to futility about our ability to do science and make progress—those are both still possible. This is inspired by David Chapman’s work which I’m still wrapping my head around.