Why Anki Works: Part 3
From theory to practice
VII. Atoms Are What You Make Of Them
Consider the following cards for the principal parts of φέρω. Which is the best-designed?
Most veteran SRS gurus will tell you it’s card 4. It gives a single, simple prompt—what’s the aorist passive of φέρω?—and triggers the brain to fetch a single word. When you’re reading Greek, after all, verbs don’t come in nice dictionary-entry sequences—you just see a single form and need to know what it means and what its grammar is doing. Card 4 is an atomized card, and a basic principle of good card architecture is that the memories cards call up should be atomic.
But what exactly do we mean by an “atomic” memory?
The aorist passive (6th principal part) of φέρω is ἠνέχθην. How atomic is ἠνέχθην—really?
As it turns out, there is a lot going on in a Greek word!
By the time you hit the aorist passive in any decent introduction to ancient Greek, all of the details in the diagram above are going to be old hat. You’ll know the alphabet, the accentuation rules, and the rules for the past-tense augment cold. Everything in the above diagram, except maybe the stem/ending boundary, is going to be automatic.
An atomic memory, or a card designed to review one, is not really defined by its size. Chunks are not Unicode codepoints, restricted to such-and-so many bytes.
A chunk is atomic when all the subchunks have solidified and automated.
Let’s return to the riddle at the top of this post: which of the following cards is the best-designed?
It’s none of them—and all of them.
The reason this question is a trick one is that the answer depends on the user and not on the card1. Let’s take a look at card 1. Card 1 is triggering the following prompt-chunk pathway.
Can we store all those forms in a single chunk? We can, but only if the subchunks within have solidified.
And maybe they have! It does sometimes happen that, upon seeing some word or concept, it simply installs itself into your memory; my experience is that after a long enough time studying some subject, you come to recognize a certain mental ding! that tells you that this word or concept, for whatever reason, has finished installing, and will stay there so long as it’s reviewed from time to time.
What happens if we add a card asking for the principal parts of φέρω, and keep flunking it?
This does not mean that a card that prompts you to produce the five remaining principal parts will never come in handy. But it doesn’t make sense to review it yet. Before we can review it, we need to review the subchunks until it solidifies.
I’ve been reading Greek off and on since the age of 12, so my mind is accustomed to absorbing new Greek, and producing a new card for every single weird principal part is usually overkill. My usual go-to is to split the five spares into two chunks: one chunk containing the 2nd (future) and 3rd (aorist active and middle) parts, and a second containing the 4th (perfect active), 5th (perfect middle/passive), and 6th (aorist passive). So we drill down to Card 2.
I got the 4th and 5th okay, but had trouble with the 6th. That’s because the first subchunk is usually the most salient, so your memory trailed off.
When the problem is subchunk failure, review the subchunk. Either card 3 (giving the first five principal parts as a prompt for the sixth) or card 4 (what’s the aorist passive of φέρω?) could work here. Card 3 is probably just fine if you’re well aware that the 6th principal part is always the aorist passive2.
It’s also not necessarily the case that a card 4-type prompt (what’s the aorist passive of ____?) is necessarily pulling up an atomic memory. Some verbs in Greek insert an unpredictable sigma (σ, the ‘s’ sound) before the -θ- of the 6th principal part. This is particularly common in verbs whose dictionary form/headword ends in -έω, whose 6th may alternatively lengthen the final -ɛ- of the stem to -η- —or may not. So we have the following patterns:
The following situation is therefore entirely possible!
It all depends on whether or not the required subchunks have solidified for the learner. In this situation, the principal parts of φέρω have solidified and the whole nine yards can be pulled up as a single chunk. But the 6th principal part of καλέω has not:
Drill down to the subchunk and solidify:
Eventually this subchunk solidifies and merges, as the f in hlifan did in the example in part 2. Solidification entails automation, and before too long we’ll be able to do this:
This is not to say that you should memorize most things as lists (but see the next section). Greek verbs are rather unusual in that they have a large number of stems which often present irregularities, though it’s rare for things to be quite as bad as φέρω (in general, if I see an aorist passive that’s formed from a verb whose headword ends in -έω, I’ll be able to recognize its source regardless of whether it has -έθην, -ήθην or -έσθην).
But, to state the implication clearly: larger chunks are usually more efficient, as long as you can manipulate them to grab useful subchunks out of them. After all, we don’t learn words by learning each letter individually; we learn them as whole units, and only need to dissect them when one of these letters fails, for whatever reason, to land. The same applies to larger chunks.
VIII. A Word on Mnemonics
You may have noticed that I’m two-and-a-half posts into a manifesto on memory and still haven’t mentioned mnemonics. What gives?
It’s not because there’s anything wrong with mnemonics—they’re tremendously useful. Rather, it is only now that we have built a foundation that will allow us to understand why mnemonics work in the first place.
Parentheses, exponentiation, multiplication, division, addition, subtraction is a laundry list. You could learn the order of operations by making clozes for each single operation, but it isn’t a list that’s likely to install quickly or easily.
Please excuse my dear aunt Sally, on the other hand, is far more natural. And, once it’s been installed, we don’t need to remember the laundry list itself. We can simply bring up the quickly-installed high-level chunk and check the operations indexed by the first letter of each word.
Indeed, my suspicion is that in many cases the list is actually faster. It would be interesting to compare the reaction time of, say, people who learned each irregular Greek principal part individidually (as What’s the perfect active of πέμπω?) vs. people who learned them as part of a list (πέμπω, πέμψω, ἔπεμψα, πέπομφα, πέπεμμαι, ἐπέμφθην), with list-dissection to solidify subchunks. My hypothesis is that the latter will beat the former. (If you know of any papers on this question, please feel free to leave a comment).
Memory parlor tricks, such as people who can memorize randomly-shuffled decks of cards, rely on mnemonics because they constitute easily-installed chunks that can be dissected to retrieve arbitrary information that doesn’t install easily. A common strategy is to take each possible pair of two cards (52 * 51 = 2,652) and associate it with a person, place or action, then arrange these in a memory palace. When the order of the deck is retrieved, the memorizer goes through the memory palace in order and converts each shorthand chunk back to the cards it represents.
We can now start to see why the model of the mind as a spreadsheet, implicit or otherwise, can be so misleading: the apparent size of a chunk correlates loosely with, but does not dictate, the burden it places on human memory. The text string ()^*/+- is 7 bytes long, while Please excuse my dear aunt Sally is 32 bytes long. The latter is still much easier to memorize.
IX. Card Architecture, Part I
We are now finally able to really talk about good card architecture.
Recall the basic principle: each card should give a single prompt which precisely fetches a single chunk from memory. That chunk should be as large as necessary, but no larger. If we misjudged our ability to install that chunk, we drill down to the troublesome subchunks and learn them first.
Here’s what an amino acid looks like. Know it for Tuesday’s quiz. Gotcha, we need the whole structure of an amino acid installed in a single chunk by Tuesday. I’ll make a pretty cloze diagram in Figma and learn it that way.
Ugh, that’s a lot. Now what?
Well, what subchunks do we have here? Mr. Smith said that’s a carboxylic acid group on the right. Excellent:
Now we can rewrite the amino acid card:
You color-coded it. Yes, I did. We’ll do the same for that amine group.
Nope, still not landing. Break it up like this.
Glover 1989 says free recall is more effective than cloze deletions. Precocious, aren’t we? We can do that too:
The free recall card is the most effective way to get the structure of an amino acid into your head—once you’ve reached a certain point where the subchunks are safely welded together (at which point you might want to suspend the intermediate cards with clozes and abbreviations). But if we start with the free recall card on day 1, we’re going to keep banging our head against it until we give up and go back to staring at our notebooks. That’s because a successful full-recall of the whole molecule isn’t just an arbitrary sequence of bonds and atoms. Here’s what that amino acid really looks like under the hood:
Chunk 12 is what you drew. But chunks 1-11 are how you got there.
That is why Anki fails—and why it works.
X. Card Architecture, Part II
This section is a bit of a laundry list of personal observations on good card architecture. I should note that I do not profess to have card architecture down to a perfect science.
1. Vocab cards
All information about a word in a foreign language should fit in a single chunk. Let’s do some German.
Remember: the prompt (front of a card) should give only as much information as necessary to fetch the necessary chunk—and no more than that. So: what’s wrong with this basic-and-reversed card?
The problem with this card is that the German prompt gives too much extraneous information. We do not need to know the gender going from German to English, and we don’t really need to know the plural. The German-to-English prompt should really only read Ei.
But we don’t want this:
This card does not force us to fetch the whole chunk. It is only asking us to fetch the headword. We want to fetch the gender and the plural of this word, like this.
My standard vocabulary card has four fields: lemma (headword), category (noun, verb, etc.), gloss (an English gloss), and full form (where we put additional information.)
Here is what this looks like for Ei:
The full form always appears on the back of the card. That means that English-to-German prompts with the gloss and the category (since so many English verbs are homophonous with nouns) to fetch the full form.
German-to-English is a little different. The prompt is the lemma, but this changes to full form when I press enter, along with the category:
This is because I want to fetch the full form every time—I don’t want it fed to me.
But what if we have trouble with plurals or gender? Easy-peasy: just do a cloze:
These cards isolate troublesome subchunks and force them to solidify.
Some words require so much extraneous information that a single vocab card won’t cut it: the principal parts of φέρω are like this and don’t go on the main vocab card for the headword (they’d just add clutter). Weird, idiomatic usages (like which preposition to use with a verb) usually require their own card.
Clozes are also good for compounds, as I’ve noted—especially for prefixed compounds in German or Russian:
We can also use clozes to attack crossed wires. We’ve seen this in Gothic; here’s the Coptic version:
Some details do not lend themselves well to clozes, such as tone or stress/accent placement. In this case, a basic card is usually best:
Note: when you’re drilling down to attack a subchunk that isn’t landing, the rule that of prompts should be spartan goes out the window. You want to feed yourself every other single subchunk to prevent wire-crossing, at least at first. For reasons that aren’t obvious to me, excluding the gloss in a card on accentuation can make remembering the accentuation harder, because your mind starts trying to reach for the meaning as well as the accent placement, and you don’t want it to do that3. Remember, the mind processes one chunk at a time.
On color-coding
The human mind is very, very good at remembering colors—for good reason, since it helps us distinguish ripe fruit from raw, poisonous animals from harmless, and edible plants from weeds. One consequence of this is that, for vocabulary in particular, arbitrary information is best encoded by colors.
For German, Latin, Sanskrit or Greek, this is usually gender:
My experience with Russian and Lithuanian is that gender is generally predictable from the shape of a word, but accent paradigm4 is not. So that’s what it makes sense to use color-coding for.
In Mandarin or Cantonese you’d probably want to use color for tone, since that’s the most common form of arbitrary word-level information (and color is far more memorable than diacritics or tone numbers). Color-coding is also useful in certain clozes; when I use a cloze to remember a certain vowel in a word or ending, I usually use red text for long vowels and the default blue for short ones.
Color-coding would probably be incredibly useful for math, but MathJax (the math package that comes with Anki) won’t do it. You could always use Figma. And as we’ve seen in the amino acid example, we can use color-coding in other subjects where we have lots of fiddly, similar-looking things that we absolutely need to keep separate. (In my [not-terribly-large] chemistry deck, methyl groups are a cyan Me).
For synonyms in the target language, you can always give a gloss like “to kill (not interficiō or caedō)”. If there are too many of these to be practical (as is the case for Latin words for ‘kill’ after a certain point) then you can resign yourself to only doing a one-way target → native recognition card. Just don’t forget that you’ll still need to put the full form of the word on the back and the back only.
This is the end of part 3. In part 4 we will go back to theory and ask ourseves: what is a fact?
This does not mean that all cards are created equal. There is such a thing as objectively atrocious card architecture. I’m simply saying that there isn’t a One True Card Design for any given piece of information.
Native speakers, of course, don’t learn such things in a particular order—ἠνέχθην is simply what happens when the ‘aorist passive’ function operates on φέρω, or rather on the more primordial meaning (we don’t usually think of go when we say I went to the supermarket.) But I reject the idea that it’s always and everywhere bad to learn things like principal parts in an order, particularly because with enough automation and exposure, the brain doesn’t need to hop Mario-like from form to form. (We learn numbers in a certain order, but we don’t have to do a for-loop through a mental array every time we talk about a billion dollars or the 67th annual meeting of the local Rotary club.)
Of course, when operating in the language, you don’t want to be jumping back and forth between the English translation and the target language. It is probably the case that the gloss on such a card is a “training wheel” that can be taken off once it’s been solidified, so that we’re just asking for the accentuation of ghāsa without the gloss.
Imagine, if you’ve taken Latin, that the word stress jumped around as you declined a noun according to the case, as well as an arbitrary category orthagonal to the declension and gender, so that the genitive of equus was equī́, but that of servus was sérvī. This is the system in Russian; in Lithuanian the stress may additionally have one of three pitch contours, though they’re usually predictable from the word, the case ending and the syllable where the accent lands.
I only learn languages dumb people also speak, but i admire your facility demonstrated here! I must admit to scrolling through, though I had a number of comments.
1. Tut means strawberry. I have never heard anyone say mulberry until just now.
2. I have always been good at memorizing, but for me memorization of Songs is nearly instant. I like to learn things by heart through song and will make up my own. Or even a beat.
3. I naturally do a version of spaced repetition where I like to review things.
4. I need a better note taking system.
(No need to respond to any of this, I just had to comment)