I’m still mulling over spaced repetition and why there seem to be such stark dividing lines between people who love it and those who feel “meh” about it.
Don’t get me wrong, spaced repetition is absolutely a useful tool. There just seems to be something missing in the conversations around it. Besides the issue of probabilities, I think there is also an issue with the context of both the things we aim to memorize and the context of the models that are popular on the internet.
Basically, there is no context.
Spaced Repetition: A Recap 🐝
First, let’s revisit the well-known models of spaced repetition.
There was a guy named Hermann Ebbinghaus who ran some memorization experiments on himself – for science! He tested himself by memorizing random strings of letters and found that he would forget them at a rate that has now been dubbed the forgetting curve, which looks like this:
Spaced repetition is a sort of algorithm or predictive model that tells us when we should next test ourselves on some fact so we don’t forget it. This is represented in the following graph by the flattening of the forgetting curve:
When I was steeped in language learning, an ideal use-case for spaced repetition, I read up about all of this. I was reluctant to allocate time for managing a spaced repetition software on top of my studies but I eventually did and used the behemoth flashcard machine, Anki. It paid off and the tool completely revolutionized my study; I could remember much more than I could have without it.
But once my main priority in life was no longer language acquisition, the habit of spaced repetition usage also fell in priority. Why? If the results are so stellar why wouldn’t one rush to flashcard-arize their entire life? Well, there are a few practical reasons: Where is all my brain-manual data going? Do I have the time to manage all those pesky flashcards? But I think there’s another deeper reason why I, and others, don’t tend to invest time into this practice on the regular. (Besides the probability problem)
Since covid19 got us all thinking about bats, why not have them illustrate the details for us?
Manners of Locating 🐝
Bats navigate their surroundings via echo location, especially at night: They build a mental picture of their surroundings based on the echoes they hear from their own squeaks. They rely on these mental pictures for navigation and to find tasty insect food.
Now, say we are the bats. Pertinent facts or details are the tasty insects we seek. Each squeak is some form of recall. The fading of the sound waves we rely on for navigation are dictated by the forgetting curve and the various elements of the sound wave correspond to various attributes of recall such as number of connections to relevant material, personal connection, context, etc.
Flash - Beam 🐝
Say we are studying a foreign language. If we study with flashcards and spaced repetition, we might write a word on one side and its definition on the other, and test ourselves in both directions to ensure we can both recognize the word and recall it when we want to use it ourselves. With the aforementioned mental model, a flashcard review might look like this:
It’s a narrowly focused beam, likely a single factoid devoid of context. It’s very “bright”, as you are probably going to retest yourself in a single study session until you have solidified the target connection. Since you’re performing recall with spaced repetition, the consistency is strong and long-lived – you are intentionally staving off the forgetting curve after all.
Since the size of this beam is so small, it would take a really, really long time to find any insects in a large area. It would be helpful if we could expand the size and scope of our echo location beam and use more various types of squeaks to cover more ground and receive more kinds of information. (Which is exactly what bats actually do, by the way)
Cloze - Ray 🐝
In the Anki world, people try to do this by utilizing a type of flashcard called “clozes”. Say we’re still studying language: On the front of a flashcard you write the word on the front, but instead of the definition on the back you write a sentence the word might be used in with the word itself removed. So, if we’re trying to memorize “echo location”, the opposing side of the flashcard might read “__ ____ is a navigational technique that bats use to navigate the dark.”
This type of flashcard is popular because it is trying to address the context-less-ness of flashcard systems that use spaced repetition. By using a cloze instead of a definition, you are implicitly solidifying some of the word’s contextual features like what other words are commonly used with the target word (called collocations), proper grammar usage, perhaps some cultural or situational awareness, and sometimes even connotation.
With this type of flashcard, our echo location “beam” starts to look like a “ray”:
Since we’re picking up some minimal context the “ray” is a bit wider, but only by a bit, and we potentially lose a bit of clarity since we are connecting the word to an immediate context as opposed to its direct definition. The rest of our squeak is about the same in “brightness” and consistency since we’re using the same system and technique to reaffirm this memory.
But this is still rather small. Remember, we are just tiny bats searching for even tinier bugs. How do we know the general area we are in even has any bugs? What if there is a hive across the map? How do we find it? How do we even know that we should be looking for it?1
Read - Sweep 🐝
I’ve been seeing this quote on the internet lately that “CEOs read a book a week”. I don’t know how reliable this is, but I decided to give it a go this year. Contrasted with my previous language learning experience, it is a vastly different feeling that reminds me of the aforementioned variable squeak we’re looking for. Say we read a new book for the first time once:
The scope is much larger and wider. We might call it a “sweep” of an area. It’s much less bright because we’re essentially scanning a bunch of information whose datapoints we won’t necessarily remember completely the first time through. The consistency is more variable since we may resonate more strongly certain portions of a book, have more relatable knowledge, or have more or less direct experience with the subject-matter.
Something else really interesting happens when you use multiple “sweeps” (or read multiple books) in close enough succession before the “sweep” completely dissipates (or the forgetting curve completely flattens): Reoccurring information starts to stand out on its own.2 At least, that is my experience.
And since you have now experienced said factoid (or seen some bug) from multiple angles, you can start to accumulate some depth of the target: Instead of building a clear 2-dimensional image of a bug you can start to build a steadily-increasing-in-resolution-3D understanding, since each sweep is presenting information from slightly different perspectives.3 I think this is in part what people are referencing when they talk about learning “deeply”.
This “sweep” analogy also fits nicely with some note-taking-related advice I’ve heard floating around which fits under the umbrella: “Do not write what can be referenced”. Just keep a reference to where relevant information is stored. Focus less on high resolution upfront, sweep more area, build a high resolution understanding over time with the benefit of added perspective.
All types of beams’n’sweeps have their uses, but they will provide vastly different benefits and drawbacks in our insect-fact hunt. As the bat gets closer to an insect, it makes a lot of sense to use the finer “beams” mentioned before to zero-in on those buggy bites. Once we have figured out what information will be useful, it might make sense to drill it into our minds.4 The trick is learning how to use all of these skills effectively and to know when to use them.
Searching In Darkness 🐝
For me, this mental model provides a backdrop that fills some contextual holes left by popular models of spaced repetition. You can read a list in the footnotes, but the most important is this:
Navigating unknown territory requires specific skills not exercised by memorization and spaced repetition.
As humans, we desire immediate, assured answers. This alone can lead us astray, but what’s worse is that we are suffering from our successes: We have unravelled so many mysteries of the world that for most of our day-to-day questions there does exist some “correct” answer. Further, the body of knowledge humanity has built is so vast that even if you spent an entire lifetime just memorizing it all you probably wouldn’t even memorize a fraction of it. I think modern public education reflects this: School has become a place we go to memorize the “correct” answers that have been accumulated. Our educational institutions have come to embody a pathos of knowledge memorization instead of an ethos of knowledge discovery. So, when it feels like we have all the answers to our questions, the tool that best helps drill answers into our heads seems like the one tool to rule them all.
I think we have been in this mindset for so long that we have forgotten that we evolved in a world where much of what was going on around us was a complete and total mystery. We need reminders that our mental maps may be wrong. As was plainly evident as a bat, alternating between tool types to navigate our environment is a crucial ability that we got to exercise in the dark. If we want to instill creativity and foster the capacity for making novel discoveries in our youth, we cannot afford to force them to just memorize all the knowledge we have accumulated. We need to deliberately provide environments for young learners where they can tinker and experiment. We somehow need to give them places to be where they are not faced with “correct” answers, even if “correct” answers exist. We need to foster and provide exercise for the muscles that are required for navigating the unknown.
It is imperative that we do not forget that the search for truth in the midst of a complicated reality is not too dissimilar to making our way through the dark.
Appendix - More Mental Model Takeaways 🐝
- “Memorizing” is not necessarily the goal. The surroundings around our bat represent all the other things we could “know” or memorize. We don’t necessarily need to be able to see the entire map, or to know everything, to accomplish our goals or find tasty treats.
- There are downsides to over-relying on precision tools. Spaced repetition is a tool that allows us to make our memory intentional and it can be difficult to see any negative aspects of having more choice. But even if you can echo locate very precisely in one corner of the map, how do you know you are or are not in an insect-starved section of the map? How would you be able to discover, in a reasonable amount of time, a flourishing insect nest somewhere else?
- Be aware of your surroundings. Whether it’s your field of study or work, or flying through mountainous terrain, you need to stay cognizent of what the landscape is telling you in order to make meaningful progress toward those tantalizing targets. Your perfect vision of that specific coordinate won’t help much if you end up flying right into a tree.
- What can be known is incomprehensibly vast and complex. Each insect represents some pertinent fact just in relation to what you’re aiming for. In order to find them, there are countless obstacles to be overcome, landscapes to be navigated, predators to evade…It can feel exhausting addressing so many issues just for one critter, but that is all part of the package that is bat-life.
- Doing is data dense. You have to try lots and lots of different tools and techniques in order to build a general mental map. As the flashcard, cloze, and reading examples show, you learn a lot more about the terrain by expanding the amount of exposure in doing than by studying single contextual-less facts.
It is also interesting to point out the similarity to “stochastic gradient descent”, which is also a problem about solving for an ideal target value when faced with potential local values that look good, but aren’t the best on the map. ↩
There are some useful resources that help determine when precisely to use spaced repetition here, here, and here. In essence, be sure to put some effort into determing “when” and “how” to use spaced repetition in conjunction to other forms of practice and learning. ↩