You won’t get smarter by drilling IQ tests or playing the violin. Dual n-back probably won’t improve your working memory. But you can remember anything you choose to with spaced repetition.

Spaced repetition is, by far, the most effective cognitive hack I’ve used. It used to be that I’d read a book and afterwards remember almost nothing. Sometimes I’d take Kindle highlights, or notes, but never review them. And I hoped that though I could not necessarily name what I recalled (because whose memory has an index?) that somehow the important information was woven into my knowledge, tacitly. This is mostly a cope.

I love learning, and spaced repetition has helped me become extremely good at it. But it took a long time to become effective at it. There’s a lot of advice on the Internet on how to do it effectively, most of which is phrased in terms of very general principles, but very few concrete examples. But what people struggle with is: how do I turn this specific, concrete piece of information into a set of flashcards?

This post describes the rules I use to write effective flashcards, with as many examples as I could reasonably find.

Contents

1. Overview of Spaced Repetition
2. Limiting Factors
   1. Habit Formation
   2. Card-Writing Skills
3. Words of Encouragement
4. Rules
   1. Rule: Understand First
   2. Rule: Be Honest
   3. Rule: Keep It Fun
   4. Rule: Repeat Yourself
   5. Rule: Organize by Source
   6. Rule: Write Atomic Flashcards
   7. Rule: Write Two-Way Questions
   8. Rule: Ask Questions in Multiple Ways
   9. Rule: Concept Graphs
   10. Rule: Cache Your Insights
   11. Rule: Learning Hierarchies
   12. Rule: Learning Sequences
5. Examples
   1. Example: Magma Formation
   2. Example: Plate Tectonics
   3. Example: Neural Cells
   4. Example: Neuron Types
   5. Example: Vector Spaces
   6. Example: Parity Group
   7. Example: Logical Consequence
   8. Example: Periodization
   9. Example: Rational Numbers
   10. Example: Regular Expressions
   11. Example: Voltage
   12. Example: Isomers
   13. Example: Months of the Year
   14. Example: Powers of Two
   15. Example: Rilke
   16. Example: Pharmacology
   17. Example: Misc. Examples
6. Scripts
   1. Sequence Script
   2. Poetry Script
7. Software
8. Prior Art
9. Conclusion

Overview of Spaced Repetition

The idea is mechanically very simple: as you learn things, you write flashcards, which are question/answer pairs. Then you review them: you look at the question, recall the answer, and turn the card over to see the answer. Then you grade yourself: did you recall correctly or incorrectly?

If you keep recalling correctly, the review interval grows longer; if you get it wrong, the interval gets shorter.

Some people use paper cards, most people use software such as Anki, because the algorithm schedules reviews efficiently, so you don’t over-review material. Unless you have a paper fetish, just use software.

Limiting Factors

If you’re so smart, why aren’t you rich? Or: if spaced repetition is so effective, why doesn’t everyone do it? Why isn’t it as common as drinking coffee?

There are two main limiting factors to effective spaced repetition.

Habit Formation

For spaced repetition to be useful, it has to be a habit. I drill flashcards every day as part of my morning routine. But habit formation is difficult, doubly so for people who have ADHD or are low in conscientiousness.

The reason you have to do it every day is that the spaced repetition algorithm schedules the reviews for you, freeing you from having to do that manually. But you don’t know what cards are due in a given day until you open the app. And if you skip a day, those cards pile up and are due the next day.

A common failure mode (and I did this more than once, before I got the hang of it) is to use Anki for two weeks, then drop it, and pick it back up six months later only to find you have 600 cards due for review. This is not encouraging, and it defeats the point of spaced repetition, which is to review the cards on the intervals the algorithm chooses.

I don’t have much advice in this area, except that if you have persistent problems with conscientiousness, untreated ADHD etc. you should address that first.

Card-Writing Skills

Writing effective flashcards is a skill that took me a while to acquire. Many of the cards I wrote in the first four or six months of using spaced repetition consistently turned out pretty much useless, and this can be frustrating. The main reason to write this post was to communicate the lessons I learnt so you can jump in to using spaced repetition effectively from the start.

One reason this can be frustrating is you’ll often remember a flashcard for the first few weeks of it (when you’re seeing it with high frequency), but after a couple of months, you start failing it. It didn’t take root in your long term memory, because it was poorly written in some way. And this long feedback cycle means it takes time to acquire these skills through trial and error.

Words of Encouragement

Learning is an automatic, instinctual process. It’s a fundamental feature of intelligence. It’s a testament to how bad schooling is that people think they have to have a special kind of brain to learn effectively, and that the idea of learning triggers aversion in people. Remember the words of Feynman: “what one fool can do, another can”.

Rules

Here are my rules for effective spaced repetition.

The rules are sorted by applicability (but not necessarily importance), with the more general ones first, and most specific ones last.

Because many of the examples involve multiple rules at the same time, I decided to list the examples separately from the list of rules.

Rule: Understand First

Don’t try to memorize what you don’t understand. The concepts should be clear in your head before you try to commit them to memory. “Clear” can be a fuzzy thing. What I tend to do is: dig, expand, and clarify the text until I’m comfortable I have a good grasp of this region of the concept graph, and then write the flashcards.

Often, when reading a book, you can’t write the flashcards exactly as you read the text, because further information can clarify or tie together important concepts. It can be useful to keep a scratchpad where you write tentative flashcard text as you read a chapter, and at the end you organize and re-organize your scratchpad until you can commit it to flashcards.

Rule: Be Honest

The software doesn’t know whether you recalled something correctly or not. You are only accountable to yourself. If you recalled something wrong, or not quite right, err on the side of caution and mark it forgotten.

Rule: Keep It Fun

This is crucial to maintaining the habit. If reviewing flashcards feels like a chore, you will become averse to doing it.

I used to frequently have this problem. I solved it in a few ways:

1. Having a diverse knowledge base you’re drilling helps, so you are not bored by going through the same topic for a long time. Typically, spaced repetition software will shuffle the cards, so that if you’re drilling all the cards across all decks, you will be surprised often.
2. A common source of frustration is cards that are too long to recall quickly, and thus feel like a chore. Break big cards down into smaller cards. It feels good to be able to fly through the cards quickly.
3. Cards that are difficult to recall are very frustrating. I solved this by applying the rules described in this post.

Rule: Repeat Yourself

Memory is frequency times volume. Individual cards should be extremely brief, but your deck as a whole can be as repetitive as you want.

Rule: Organize by Source

Organize content by source, not topic.

The reason is you’ll often bring in information from multiple sources: multiple textbooks, plus Wikipedia, plus lecture notes, etc. Each one of these sources likely has a different way of organizing knowledge.

Don’t waste time trying to find the perfect ontology.

Make a deck for each source. In the case of textbooks, make a sub-deck for each chapter. In the case of math textbooks, possibly make a sub-sub-deck in each chapter to put theorem cards.

This also makes it easier to keep track of how far along you got into a text.

Rule: Write Atomic Flashcards

Cards should be short. They should refer to as little information as possible. They should be like chemical bonds, linking individual atoms of knowledge.

This is the most important thing. By far the worst failure mode is to put too much in a flashcard.

There’s two reasons for this rule:

1. Larger cards are harder to remember.
2. It’s harder to objectively grade yourself: when you reveal the answer, you might have got some things right and some things wrong. If you click forget, you will be over-reviewing the parts you already know. If you click remembered, you will under-review the parts you forgot.

There is one exception to this: you can have big cards if you also have smaller cards that add up to the same information. You can think of the larger card as testing that you can collate the information from the smaller cards.

Rule: Write Two-Way Questions

When possible, ask questions in two directions.

Whenever you have a term with a definition, the obvious thing to do is to ask for the definition from the term, e.g.:

Q: What is the order of a group?

A: The cardinality of its underlying set.

But you can also ask for the term from the definition, e.g.:

Q: What is the term for the cardinality of a group?

A: The group’s order.

When you have some notation, like $\mathbb{R}$ for the real numbers, or $\dim V$ for the dimension of a vector space, the natural thing to ask is what the notation means.

Q: What does $\mathbb{R}$ stand for?

A: The set of real numbers.

You can also ask the question backwards:

Q: What is the notation for the set of real numbers?

A: $\mathbb{R}$

Rule: Ask Questions in Multiple Ways

Ask questions in multiple ways. Ask for formal and informal definitions of terms. Ask for the formal and informal statements of a theorem. Ask questions forwards and backwards. Add contextual questions: “what is the intutition for [concept]?”. Add questions that link different concepts across your knowledge graph.

The more interlinked your knowledge graph is, the better.

Rule: Concept Graphs

It can help to visualize the concepts you’re acquiring as being like a graph, where each node represents a discrete concept having certain properties, and the edges in the graphs are questions which get you from one concept to another.

Rule: Cache Your Insights

When studying, you will often infer new knowledge that is not explicitly written down in the text by thinking about what you’ve just read. After verifying that your inference is actually true, it can be helpful to “cache your insight”—to make a flashcard for that new discovered piece of knowledge.

Rule: Learning Hierarchies

A lot of knowledge is hierarchical, of the form “Foo can be either A, B, or C”, or, dually, “A is a kind of Foo”. By analogy to OOP: these concepts are joined by superclass and subclass relations.

The idea is to ask questons in the top down direction (“What are the subclasses of Foo?”) and the bottom-up direction (“What is Bar a subclass of?”).

This ties into keeping flashcards atomic. Even when some information is not hierarchical, intrinsically, breaking down large flashcards into smaller flashcards is fundamentally building a hierarchy of flashcards.

Rule: Learning Sequences

In general, to learn a sequence $(A_1, \dots, A_n)$, you want to generate the following flashcards for each $i \in [1,n]$:

You might also want:

1. A test card: a flashcard asking you to recite the sequence from beginning to end.
2. A cloze sequence: flashcard with a cloze deletion for each element in the sequence, to fill in the blank given the context.

The sequence script can generate these for you.

How thorough you want to be depends on the nature of the information. Most of the time I use a cloze card and a test card.

Another type of card you might use (I use this to memorize poems) is a card that gives you some context (the previous one or two items in the sequence) and asks you to fill in the blank. For example, if you wanted to learn the sequence (A, B, C, D), you might have these flashcards:

The poetry script can generate these for you.

Examples

Many of these examples are overkill: we collect a lot more flashcards than the subject deserves. But this is to illustrate the general rules. With experience, you can learn how many questions a particular topic requires, and different volumes of your knowledge graph will be more or less interlinked.

Example: Magma Formation

From my geology notes:

Let’s break this down hierarchically. We want to memorize three things:

1. What magma is.
2. How it forms.
3. Where it forms.

First, the definition:

Second, we want to know how magma forms. A common mistake here would be to put the magma-forming processes and their explanations in the same flashcard. Rather, to keep each card as small as possible, we want to separate the list of processes from their definitions.

So we first as for a list of mechanisms:

And then we ask for an explanation of each. We don’t really need to ask why adding temperature melts rock:

Third: where magma is found. Again, we separate the list from the details:

Then we ask for details. For each place where magma forms, we ask both which processes are involved, and what the full causal explanation is. We also ask the question backward: which places involve a given process.

We can visualize the resulting knowledge graph like this:

Example: Plate Tectonics

Here’s the information:

Applying the rule that cards should be two-way, we want two flashcards for the term ‘plate boundary’.

For the different types of plate boundary, we only ask the question in the top-down direction (we don’t need to ask “what kind of thing is a transform boundary?”, since the name kind of gives it away):

For each kind of plate boundary, we also ask the question in two ways:

Graphically, here’s how the questions link the concepts in the knowledge graph:

Example: Neural Cells

Visually:

We first write the top-down questions:

And the bottom-up questions. We don’t ask these when the answers are obvious: “what are microglia/macroglia a kind of” has an obvious answer.

Example: Neuron Types

This is a brief example about keeping cards short and using hierarchies to break things down.

From my neuroscience notes:

Let’s start by doing this the wrong way, by loading too much information into one card.

Let’s first break this down by separating terms from definitions:

Now we ask the questions in the backward direction: from the definition to the term:

Example: Vector Spaces

Here’s what we want to learn:

We have to break this down. Severely. We will do this step by step.

First, we have to separate the informal (intuitive) and formal definitions:

We add one brief question about notation (you may choose to skip this one, it’s an example):

Now we ask about the signatures of the operations:

Next, we ask for the axioms:

Finally, we ask what each axiom means:

Graphically, you can try visualizing the flashcards and their relationships like this:

If you want to be extra thorough, you can also write the backwards questions:

Example: Parity Group

We can turn this into the following flashcards:

Example: Logical Consequence

From my notes on logic:

We begin with the most basic question:

Then we ask questions specifically about semantic consequence:

And then about syntactic consequence:

Example: Periodization

Timelines are a great example of how breaking information down hierarchically can help you learn long sequences. Sometimes the breakdown is already done for us.

We want to learn the following things:

1. What the geologic time scale is.
2. How it divides the Earth’s history.
3. The four eons.

Let’s begin with the simplest flashcards, the definition of the GTS:

The subdivisions form a sequence, from oldest to most recent: eon, era, period, epoch. So let’s feed it into the sequence script. Here’s the input:

Geologic Time Units
Eon
Era
Period
Epoch

Running cat units.txt | ./sequence.py > units.csv and importing units.csv into Mochi, we get these flashcards:

You probably don’t need all of these. You can probably get away with just these:

Now, since this is a concept hierarchy, we also ask the “what is” questions.

And, since units have a duration, we ask what for the duration. We do this forwards and backwards:

Now, the four eons. These form a sequence, we don’t do the whole sequence script thing again, since you have probably, again, just use these:

We also ask when each eon began and ended, forwards and backwards:

Example: Rational Numbers

Let’s commit this to spaced repetition:

Let’s visualize the concept graph as we build up the flashcards. We start with the central node, the concept of the rational numbers:

Then we add a notation node, linked by two forward and backwards questions:

Formal as well as informal definitions:

And a final note on notation: what the $\mathbb{Q}$ stands for:

Example: Regular Expressions

This is an example about asking questions in two ways.

These cards go from a concept to a regex:

In addition to the above, add cards that go from the regex to the concept:

Example: Voltage

This is an example of asking questions in different ways

The idea here is:

1. We first ask for the definition of voltage in terms of both electric potential and work.
2. We also ask what is the term for each definition.

Which gives us the following flashcards:

Example: Isomers

This is fairly straightforward: we have to learn a hierarchy of definitions. We’ll divide this into two tasks:

1. First, definitions. Ask questions from the term to the definition and from the definition to the term.
2. Second, hierarchy: ask about subtypes and supertypes.

So let’s begin with the definitions. First we ask the questions in the forward direction:

And now the definitions, in the backward direction:

We left some information out, to keep the cards atomic, now we have to ask questions to recall that information:

Now we move on to the hierarchy, which connects these concepts. We first ask the questions in the downward direction, from parent to child:

And now in the upward direction:

And, finally, the examples:

Question	Answer
What kind of isomer is this?	A cis isomer.
What kind of isomer is this?	A trans isomer.

Example: Months of the Year

Suppose you want to memorize:

The index-to-element flashcards:

The element-to-index flashcards:

The successor flashcards:

And the predecessor flashcards:

Example: Powers of Two

Let’s memorize the first sixteen powers of two:

The forward cards ask for the power:

While the backwards cards ask for the exponent from the power:

Finally, I have a test card that asks me to recall the entire sequence in order.

Example: Rilke

Let’s memorize this poem:

You could run this through the sequence script, but that seems a bit cold and mechanical. We’ll use the poetry script instead, which shows us two lines of context and asks us to complete the next line. The generated flashcards are:

And so on. You get the pattern.

Example: Pharmacology

This will be an example of caching your insights. From this text, we can deduce more things:

1. A high value of $K_d$ means the drug has a low affinity for the binding sites, because it takes a higher concentration to reach the same amount of binding.
2. A low value of $K_d$ means the drug has a high affinity for the binding sites, because it takes a lower concentration to reach the same occupancy.

And from the above two facts we can also conclude:

1. $K_d$ is inversely proportional to binding affinity.

From this, we can start asking the questions:

Visually:

Example: Misc. Examples

Given:

US Treasury bonds are called treasuries.

You can write the following forward-backward cards:

Given:

The derivative of $\sin x$ is $\cos x$.

You can ask for both the derivative and the antiderivative:

Scripts

A lot of these rules would be impossible to apply if we had to write all the flashcards by hand: it would simply be too tiresome. Fortunately we have automation.

I put up the scripts I use in this repository. These are largely based on Gwern’s scripts.

Sequence Script

The sequence.py script generates flashcards for learning a sequence, according to the principles in Rule: Learning Sequences.

Given a file greek.txt as input:

Greek Alphabet
Alpha
Beta
Gamma

We can run cat greek.txt | ./sequence.py > cards.csv, and this will generate the following:

Plus the cloze card:

Poetry Script

The poetry.py script generates flashcards where you are given two lines of a poem and have to recall the next line. For an example of using this, see here.

Software

Most people use Anki. It’s open source, has lots of plugins, and has a free card sync service. This is the default choice.

I use Mochi. It has a much nicer UI than Anki, which helps in maintaining the habit because it’s more pleasant to use. It also supports cloze deletion for images out of the box, as opposed to relying on a plugin.

The only Anki feature I care about that Mochi lacks is note types. Anki’s note types let you generate multiple cards from the same structured information. For example, you could have a “Chemical Element” note type with fields like “Name”, “Symbol”, “Atomic Number”, and card templates like:

So from one note (“Hafnium”, “Hf”, “72”) you automatically derive four flashcards. And if you edit the note data, all the cards get updated. Mochi lacks this feature, in practice it’s not terrible, and you can get most of the way there with cloze deletions.

Prior Art

The most cited resource on writing flashcards is a classic 1999 article by Piotr Woźniak, creator of SuperMemo. The article is Effective learning: twenty rules of formulating knowledge and I endorse most of it. Let me reiterate the important parts:

1. Understand before memorizing: the concepts have to be clear in your head before you try to commit them to memory. “Clarity” is a fuzzy thing, but what I do is dig, expand, clarify until I feel comfortable formulating knowledge.
2. Cards should be atomic, and should refer to the smallest possible conceptual units.
3. Avoid trying to memorize long sequences.
4. Avoid trying to memorize big unordered sets of things.
5. Keep the wording simple.
6. Redundancy is good. Do repeat yourself!

Conclusion

I hope that you will find these rules and examples useful. Now go pick up a textbook and learn something useful.