If you’ve been to med school, read Gwern1 religiously, or gotten deep into language-learning world, chances are good that you’ve run across Anki. Anki is a spaced-repetition system (SRS) that makes retaining and studying material far, far more efficient than it used to be.
There are dozens of introductions to what Anki does and how it works that Google will fetch for you. Everything I’m about to write assumes that you’re familiar with spaced repetition as a general concept and some general idea of its history (e.g. the Leitner box), a wheel I’m not interested in reinventing—the Wikipedia article has a good overview; Gwern’s article on the subject is a classic for those who prefer something a little less dry. If the term “spaced-repetition system” is an entirely new one for you, go read up before moving forward.
This post is, on its face, about Anki and how it works, drawing on my experience using myself as a guinea pig over a period of over a year and more than 160,000 cards.
Many of the illustrative examples are from foreign-language cards, because that’s what I’ve used Anki most intensely for.
But, dear reader, this post series is not really about Anki at all—it is about the human mind, and how it learns and stores information. It is, above all, about things I wish I’d realized, or been shown, well before the final pieces snapped into place for me at the age of 27.
I. The Brain is Not A Spreadsheet
The human mind is very likely the most complicated structure known to science. Given this, and given how little is still known about how it works, it is unsurprising that we grope for metaphors when trying to think about how it operates, in the same way that Enlightenment philosophers compared the universe to clockwork, or the way the popular imagination compares the electrons of an atom to planets rotating around the star. When the territory is simply too complicated to make an accurate map of, find a map of something else that you can actually read.
The trouble with the human mind is that the metaphor we’ve landed on for thinking about how it operates is that of an Excel spreadsheet.
I do not mean to say that education schools tell their charges that the mind works exactly like an Excel spreadsheet and that this model of the brain is consciously perpetuated by sinister boneheads2. Everyone knows that you can’t just write factoids directly to memory (unless you’re John von Neumann or Solomon Shereshevsky), which is why I seem to be tilting against a strawman; “the brain is a spreadsheet” is an obviously daft proposition on its face.
My point here is a bit more nuanced. We know the brain is not a spreadsheet, but we don’t have a better metaphor for how it learns or remembers things3, and so when we try to learn—or, worse, try to teach kids how to learn—we act as if it is one.
Here’s a list of important ions for the chemistry quiz, along with their charges. I forgot acetate. That’s a long one, C₂H₃O₂⁻; try staring at it a little while longer and maybe it’ll write itself to your memory, in cell B76 in the sheet named ‘tenth-grade chem class’. I was staring at Katie’s new ponytail instead. Here’s your C; you can get a B with a retake.
In other words: if the “brain as spreadsheet” metaphor were being consciously peddled, what would be different?
This is not to say that staring at the formula for acetate, or writing it over and over, or even making a flashcard of it and putting it in a Leitner box, or even making an Anki card out of it, cannot work eventually. It’s called spaced repetition, after all.
However, it’s inefficient—and painful after a certain amount of time. The reason is that all of the options above lie along a continuum of efficiency for processing knowledge the wrong way. Staring at the formula is about as inefficient as it gets. Writing it over and over is a bit more effective. Making a flashcard and reviewing it whenever Mom yells at you to study chemistry is a bit more so. Putting that flashcard in a Leitner box and reviewing it on a set schedule will be even better than that, and Anki can make the review process automatic for you without having to shuffle pieces of paper around.
But the problem with all of these approaches is that they’re trying to write the entry “acetate” into a mental spreadsheet cell that doesn’t exist as such.
II. The Brain is Lazy
So why is education—whether inside or outside of school—so reliant on the spreadsheet metaphor (even if it’s implicit rather than explicit)?
Primarily, I think, it’s because it seems intuitively correct. We do have a large number of facts and concepts in our head that we can fetch out of our memory at a moment’s notice, much like looking something up in a spreadsheet. And we’ve all seen people who can just rattle off whole poems or speeches at the drop of a hat, as if they’re able to store the whole spiel in a single cell. We hold these truths to be self-evident, that all men are created equal, that they are… And the student of Latin or Greek will fondly or not-so-fondly recall having to learn the “principal parts” of verbs by heart as a single mental entry4. Easy enough with the regular and mostly-regular ones:
amō, amāre, amāvī, amātum ‘I love, to love, I loved, (having been) loved’
dūcō, dūcere, dūxī, ductum ‘I lead, to lead, I led, (having been) led’
λύω, λύσω, ἔλυσα, λέλυκα, λέλυμαι, ἐλύθην ‘I loosen, I will loosen, I loosened, I have loosened, I have been loosened, I was loosened’5
But then you get to the nasty little irregular verbs:
ferō, ferre, tulī, lātum ‘I bring, to bring, I brought, (having been) brought’
φέρω, οἴσω, ἤνεγκον, ἐνήνοχα, ἐνήνεγμαι, ἠνέχθην ‘I bring, I will bring, I brought, I have brought, I have been brought, I was brought’6
Great, I heard spaced repetition can really help us with this. Let’s go!
Uh, hmm, that’s one of the weird ones. The stem ends in a liquid so it’s probably gonna have a contract future. OK, φέρω, φερῶ…oh wait no, it’s φέρω, οἴσω. Hmm wasn’t the aorist something weird? With a nu, maybe? ἔνεξα, that sounds…about right…? OK, and then…uhhh πέφορα, πέφερμαι, ἐφέρθην. Sure, why not.
Dammit.
Does this sound familiar?
Here’s what you actually stuffed into your brain:
Every time you try to review “principal parts of φέρω”, your brain tries to fetch a single “cell” with all six principal parts in it. The most salient thing about it is the first principal part, φέρω itself. Indeed, that’s how it’s indexed.
Then things get tricky.
You eventually remembered that the future (2nd principal part) οἴσω is totally unrelated to the headword, but only after rooting around in there—you started by inventing a fake future **φερῶ, which is what you’d expect the future to be if φέρω were regular. The aorist (3rd principal part) is out of left field yet again, and you vaguely remembered the shape of the stem, but defaulted to something that sounded “regular”. Then you totally blanked on the fourth, fifth and sixth and invented forms that sounded about right from the headword.
That’s because the brain is lazy. It indexed this information by the most salient sub-piece, which was the headword, φέρω. Everything else is treated as a footnote. The first footnote is fetchable, and you can remember the vague shape of the second footnote and would probably recognize the correct form if you saw it while reading, but the rest—poof.
Why doesn’t this problem arise with λύω? Since λύω is the regular verb in Greek, the one that gets trotted out in the paradigm charts, the only thing you really need to index is the headword. So long as you know the general rules for forming the other principal parts—you add a sigma to get the future, the augument plus a sigma to get the aorist, reduplication to get the perfect—you can produce them on the fly. That is because those rules are small, simple chunks.
III. Cells vs. Chunks
Factoids—times tables, principal parts of verbs, the president of France—aren’t stored in cells, per se. They are stored in chunks. Both “cells” and “chunks” are metaphors, of course, but there’s a key distinction: chunks are recursive and can—indeed, almost always do—contain other chunks.
Here is another Figma diagram showing how this works with λύω (we’ll only do the first four principal parts—more than that would add too much clutter).
Solid blue boxes are actual chunks that you have to store, as information, in your head. The dashed boxes you get for free. They don’t have to be memorized separately.
Here, on the other hand, is what this looks like for φέρω:
I think I’m going to go learn Arabic instead, at least that’ll get me good job security with the government. No, wait, hold on.
When I say chunks are recursive, I really do mean recursive. Let’s take a look at somebody who’s got the whole shebang in their head.
Wait, I can’t store that whole chunk in my head, chunks are just cells, you’re lying to me.
Zoom in.
Huh, okay, I suppose if you know most of the rules the 5th and 6th pretty much are fairly straightforward once you know the 4th. Correct—
Wait, we never learned the 6th principal part. That’s the aorist passive.
I never learned the Greek alphabet. What is that letter that looks like an O wearing a belt. Glad you asked.
Chunks can be arbitrarily large. But the big ones—the ones that store the Gettysburg Address, the first 500 digits of pi, the exact order of the 46th deck of cards on the table in front of you at the world memory championships—all break down into smaller and smaller and smaller chunks, all the way down to letters and numbers. The letter t is, itself, a chunk. (There are two of them in the word Gettysburg).
Part 1 is already too long for email. Continue on to some of the ramifications of this model in Part 2.
In fairness, Gwern appears to prefer Mnemosyne. I use Anki—it’s the most flexible and intuitive SRS I’ve come across—but, as we’ll see, the exact choice doesn’t matter very much.
Though I wouldn’t put it past them—I am aware of a motivational speaker who makes very good money travelling to private schools across the country giving presentations about how girls’ brains work like a ball of rubber bands.
Maybe there’s a better metaphor we can use for the brain as a whole, but trying to come up with one isn’t the point here.
To explain for those poor souls who never took Latin or Greek: the “principal parts” of a verb are all the forms you need to know for that verb to conjugate it in its entirety. In Latin, for example, you need to know the present tense (amō) and the present infinitive (amāre); these together give you the present stem (am-) and the conjugation class (1st), which lets you create and recognize all the forms of that verb in the present, future and imperfect. You also need to know the perfect active (amāvī) and perfect passive participle (amātum). Most Latin verbs have four principal parts; Greek verbs normally have six.
Approximately lǘō, lǘsō, élüsa, lélüka, lélümai, elǘthēn, where ü is pronounced as in German, the acute accents (é) mark the stressed syllable and the long marks (ē) mark a long vowel.
Approximately phérō, oísō, ḗnenkon, enḗnokha, enḗnegmai, ēnékhthēn.