Memorize First, Understand Later?
Is learning like building a house, or solving a puzzle?
Introduction
I recently listened to a live session with Andy Matuschak and Joe Walker in which Andy takes a look “under the hood” at Joe’s podcast preparation process, asks a number of questions, and provides some useful advice. I really enjoyed it— there’s been some buzz around “tacit-knowledge vidoes” recently, and this was a perfect example.
A bit over a year ago I started taking my memory practice seriously. Over the recent holiday break I was talking with some family and friends about how changing my memory practice has completely revolutionized my learning and by extension, my research. To my dismay, no-one seemed all that interested. It’s not that people are uninterested because they don’t care about learning, I think they’re uninterested simply because they don’t have a memory practice and so they don’t understand its value— it honestly feels like a superpower. But as with any superpower, one has to learn how to control it (c.f. Clark Kent, Smallville seasons 1-10).
Understanding Before Memorization
So it’s safe to say that I am interested in good memory practice. About a year ago I skim-read Andy’s article on “How to write good prompts” and watched one of his live note-taking sessions. I also read Michael Nielsen’s “Augmenting Cognition”, but that basically comprised the extent of what I knew about spaced repetition outside of personal experience. I certainly hadn’t read Piotr Wozniak’s “Twenty rules of formulating knowledge”— in fact, I hadn’t even heard of Piotr Wozniak. But during the interview between Andy and Joe the following excerpt stood out, precisely because it really did not resonate with me:
WALKER: … one rule of thumb I have is I won’t write a prompt on something that I don’t understand.
MATUSCHAK: Yeah. Actually, I learned a lot from Piotr Wozniak’s 20 rules of effective space repetition flashcard writing and his number one suggestion is: understand before you memorize.
“Understand before you memorize.” I mean it sounds right. Wozniak points out that one could plausibly memorize an entire German history textbook without knowing German— claiming “The value of such knowledge is negligible.” I’m not about to suggest you should go and memorize an entire textbook (in any language), but I do want to claim that memorizing things that you don’t understand is not only forgivable, but that it can be helpful for learning.
The Mental Bookmark
Let me emphasize that my comments are based entirely on my own experience, and I do not know whether there is much (if any) research on what I am suggesting here. I would love nothing more than for someone like Andy Matuschak or Michael Nielsen to explain exactly the shortcomings of my claims below.
I have found that memorization before understanding can be helpful because it acts as a mental bookmark. Imagine you are reading a complex book. You might come across a term or concept you don’t understand, but you have a feeling that it’s important for later. Instead of stopping your flow to decipher it immediately (which can be disruptive), you place a physical bookmark (sticky note, book-tab) at that page. You continue reading, trusting that the context will become clearer later. Your memory prompt is like that bookmark, but for your mental landscape. It marks a spot you intend to return to, once you have the appropriate context.
Mental bookmarks are particularly helpful when you encounter a key fact or concept whose understanding hinges on underlying ideas you have not yet grasped. The conventional approach in this case would be to first go and understand the component parts, and then to build up to the target understanding. This “understand-first” approach makes a lot of sense if you think of learning as building. You need to lay a solid foundation of understanding, or anything you build on top will be fragile and unstable.
But sometimes (though not always) learning is less like constructing a building and more like solving a jigsaw puzzle. Imagine trying to assemble a 1000pc jigsaw without seeing the picture on the box. For a long time, you’d just have scattered, seemingly unrelated pieces. In fact, when solving a jigsaw, you often refer back to the box so that you know roughly where each piece goes. In a ‘puzzle’ model of learning, you don’t initially know where all the pieces go, but you begin by getting a sense of the overall picture and then you begin to fill in the pieces.
So what if you did the following?: memorize the very thing you aim to understand first— (that is, create a mental bookmark). In doing this, you recognize that you don’t understand its content yet, but the bookmark contains all of the component pieces that you’re about to go and attempt to understand. If you’re using spaced repetition, the mental bookmark also becomes a scheduled check-in on your knowledge gaps. What I am suggesting here is that sometimes remembering what you want to remember is just as important as understanding it.
And after all, isn’t the whole point of having a memory practice to remember the things that you want to remember?
A Simple Example from Michael Nielsen
Let me give a simple example where memorizing first and understanding later can be helpful. I’ll borrow Michael Nielsen’s example. Suppose you want to memorize the theorem: “a complex normal matrix is always diagonalizable by a unitary matrix.” This might as well read “colorless green ideas sleep furiously” if you’ve never heard the terms “diagonalizable”, “unitary” or “normal” (which turns out to be anything but normal), but the specific content of the theorem is not crucial to the example I am making here.
Nielsen describes how he wrote his Anki cards in two phases. In the first phase, he writes cards that help him understand the proof of the theorem. In the second phase he writes cards to help him push the boundaries on his understanding of the theorem.
I’d like to suggest a phase 0:
{{c1:: a complex normal matrix}} is always {{c2::diagonalizable by a unitary matrix}}.
(For those who don’t know, this is the format for a cloze deletion card in Anki).
And you can actually do this before you begin phase I or phase II or phase XXVII or however you structure your process of understanding. In fact, this can help you orient your phase I— now you know what you don’t know.
And if in two weeks’ time, this card seems like something that is no longer worth understanding, then you should delete it and be done with it! But this is unlikely to happen since the reason you created the memory prompt in the first place was that you knew this was something that you wanted to understand.
Ok, I Lied (and a word of warning)
Although I made it sound like Andy and Joe would disagree with me on this, Joe makes exactly this point in the next breath following the excerpt I quoted earlier:
WALKER: Right. Having said that maybe there’s one little exception to that though which is for definitional things. I might write prompts even if I don’t fully understand all of the contours of the underlying concept. And it’s still helpful because even if I’m slowly, stochastically learning this concept, I’m still picking up the language and it’s making the eventual understanding easier.
YES. This is exactly right. But the conversation moved on immediately after this, and I thought this point deserved some exposition, which is why we’re here.
The beauty of memorizing first is that it can accelerate the learning process. By having the ‘answer’ or the key fact already in your memory before understanding every detail, you create a mental hook for new information to attach to. When you later beginning putting the pieces of the puzzle together, you’re not starting without a picture. That being said, if you simply memorize and never return to these prompts to fill the gaps in your understanding, then Wozniak’s warning about meaningless knowledge becomes valid. The mental bookmark is only useful if you eventually turn the page.
I’m interested to hear whether other people have had this experience too. Please feel free to reach out to me if you have any thoughts on the role of memorization in learning and understanding!
Happy bookmarking,
DJ