Memorizing sequences

This is the third part in a four-part series on memorizing statistics. Here, we focus on memorizing sequences.

1. 1 Projects/Writing/02 Series/Memorizing/Memorizing numbers (start here)
2. 1 Projects/Writing/02 Series/Memorizing/Memorizing units
3. 1 Projects/Writing/02 Series/Memorizing/Memorizing sequences (you are here)
4. Memorizing sources (to be written)

Throughout the series, we've been building on top of a spaced repetition system (SRS).¹ That's because—whatever the subject matter—memorizing requires repetition, and our drive towards efficiency (read: laziness) means we want to minimize the frequency of repetition. Enter the unreasonably efficient SRS.

With an SRS memorizing becomes a choice. You just deposit a nugget of information in your deck of flashcards, and the information will eventually come to rest in your long-term memory banks. Usually.

Sometimes, getting a bit to stick requires more effort. Such was the case with with numbers (start of this series) and units (part 1) because these types of data interfere. When you attempt to deposit 18.6% in your mental bank, you're liable to withdraw 16.8% or something altogether different.

For numbers, the solution was to use mnemonic techniques like the part 2. These hijack our strong visual machinery to separate numbers out of interference's reach. With units, the solution was to avoid memorizing as much possible. Instead, to develop a physical intuition that would make the units self-evident. And when that fails, to use Major system.

Here with sequences, the difficulty is elsewhere: a sequence presents too much information to recall all at once. Suppose we wanted to memorize the stages of the cement-manufacturing process:²

Cement manufacturing

1. Mining raw materials: limestone, clay, sand, & slate
2. Crushing and grinding hard materials; Stirring of soft materials
3. Blending in right proportions
4. Burning in a kiln to produce "clinker"
5. Grinding the clinker with gypsum

Naïvely, we could put this on the back of a flashcard and write something on the front like, "what are the 5 stages in the manufacturing process of cement"? But flashcards are supposed to be atomic. As cards get larger, the odds that we forget one item increase towards certainty. Big cards are bad.

Fortunately, we have better options.

1. Break it Apart

The first thing we could do is to divide the sequence of 5 stages into 5 different cards:

What is the first stage in the manufacturing process of cement? […]

What is the second stage in the manufacturing process of cement? […]

With simple examples, this may be more than enough. But this approach hides several weaknesses.

First, with a sequence, we often care more about relative order than absolute order. Say I forget whether "clinker" is what goes into the kiln or what comes out of it. I'd have to call to mind stage 4 and stage 5 separately then compare their abstract ordinals to resolve my confusion. Better to skip the labels and learn directly that grinding clinker follows burning in the kiln.

Second, your choice in labels might not be universal. Two different people could disagree about how to classify the stages of cement manufacturing (maybe mining & extraction fall outside of "manufacturing"). A third might expect more granularity in your description.

Finally, reducing a sequence to numbers again risks the interference effect. You might accidentally swap two steps in your head.

2. Use Overlapping Cloze and Images

With a little extra effort, we can get around these problems.

To emphasize relative order over absolute order, use overlapping cloze-deletions (i.e., fill-in-the-blank). Rather than prompt each step in isolation, provide the previous or surrounding steps as context. Check out this Anki plug-in to make overlaps easier.

What is the next stage in cement-manufacturing?

1. …
2. Crushing and grinding hard materials; Stirring of soft materials
3. […]
4. …
5. …

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1. …
2. Crushing and grinding hard materials; Stirring of soft materials
3. Blending in right proportions
4. …
5. …

Better still to shift to images so you can take advantage of your visual and spatial brain powers. Use the Image Occlusion Enhanced plugin (by the same author) for the visual equivalent of cloze-deletions. Hide part of a sequence diagram and prompt yourself to fill it in. Not only is this often easier to memorize, but you avoid the risk of "locking-in" too rigid a sequence: with a picture, you can always add in additional intermediate steps later.

What is the first stage in cement manufacturing? memory pegs

1. Mining raw materials: limestone, clay, sand, & slate³

3. Use Memory Pegs

What if the sequence we're trying to memorize is intractably numerical. Then, how to avoid interference?

Suppose we wanted to memorize the order of the biggest emitters of CO₂ (from WRI 2020). And we have to know the explicit rankings. ⁴

GHG emissions by country

1. 🇨🇳 China: 11.8 GtCO₂e
2. 🇺🇸 USA: 5.77 GtCO₂e
3. 🇮🇳 India: 3.36 GtCO₂e
4. 🇪🇺 EU: 3.20 GtCO₂e
5. 🇷🇺 Russia: 2.46 GtCO₂e
6. 🇮🇩 Indonesia: 2.28 GtCO₂e
7. 🇧🇷 Brazil: 1.39 GtCO₂e
8. 🇯🇵 Japan: 1.24 GtCO₂e
9. 🇮🇷 Iran: 0.882 GtCO₂e
10. 🇰🇷 South Korea: 0.671 GtCO₂e

Now, you could use the technique we explored in (the part 1) to memorize the amount of emissions.

E.g.: to convert 11.8 GtCO2e into letters ("TTF") then into words ("too tough") and make a mental association (China becomes an impassive bouncer). But we care about rankings not absolute terms.

If we try to apply the Major system to the single digits of a (short) list of rankings, the technique breaks down. It's difficult to make sticky words & images when you have only one letter to work with. E.g. 1st -> "T" -> ?, 2nd -> "N" -> ?, etc.

Instead, we're going to use perhaps the simplest mnemonic technique: the memory peg. Ahead of time, we associate an object (a "memory peg") to the ten (or more⁵) numbers we'd like to be able to memorize.

To make it easier, a common choice is to make the initial association by rhyme or sound.

Memory pegs

1. One -> Gun
2. Two -> Shoe
3. Three -> Tree
4. Four -> Door
5. Five -> Hive
6. Six -> Bricks
7. Seven -> Heaven
8. Eight -> Plate
9. Nine -> Wine
10. Ten -> Hen

We actually already saw this technique in Major system, where we created a memory peg for each unit we might want to remember. This is the same idea but for numbers. And it makes sense to use whenever your numbers are single digits. Moreover, you can use this technique in conjunction with the previous techniques.

Then when it comes to memorizing the numbers, we instead make an association with the memory pegs.

E.g.:

1. 🇨🇳 China: I'll leave it to you to make an association between China and guns, violence, genocide. Very difficult.
2. 🇺🇸 USA: How about imagining Trump leading a ritual burning of Nike shoes because of Colin Kaepernick while the QAnon shaman dances over the flames.
3. etc.

When we get past 2 digits to memorize, it's natural to graduate to the part 2. In either case, you'll still want to prompt yourself with flashcards you've made on Anki.

4. Use a Memory Palace

If you need something more powerful, you can use a memory palace (aka "method of loci").

The premise is simple. Visualize a place you know well. Then, mentally fill this location with the items you'd like to memorize. Move through the location (in your mind) and pass the items in the order you'd like to retrieve them. It helps to make the items as grotesque and lewd as you can.

Our brains are highly adept at visual and spatial reasoning. The memory palace hijacks this ability to store potentially incredible amounts of information.⁶ It's the foundation for the strong memories of professional mnemonists and indigenous communities the world over (Kelly 2019).

In my personal experience, I don't end up using the memory palace often because I find it requires too much time compared to the other approaches (at least for simple sequences and non-prose). This is probably more evidence that I am a novice mnemonist than that the memory palace is excessive (professional mnemonists can memorize decks of cards using memory palaces in minutes⁷). With more experience, the time it takes will go down, but the benefits will remain high.

But until we novices get to the level of expert, simpler techniques have more than enough to offer. They bridge the gap and keep us motivated at our growing memories as we develop yet better techniques. (2 Areas/Principles/Laws/Benford's law)

Conclusion

Try it all, and see what works.

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Footnotes

Footnotes

1. Specifically Anki though you can use whatever you want. Point is: I'm assuming familiarity with the idea of an SRS. If that's not the case, return to the Major system. ↩

2. My examples throughout this series remain tied to the climate crisis. As it turns out, cement is responsible for 4-8% of global CO₂ emissions (Britannica 2021). ↩

3. We should probably further split "limestone, clay, sand, & slate" into their own set of flashcards. ↩

4. This example is a bit contrived since rankings change all the time, but the point is to demonstrate a mnemonic technique. ↩

5. Because of 1 Projects/Writing/02 Series/Atomic Workflows's (which states that the leading digit in natural sources of data tends is "1" disproportionately often), it makes sense to come up with memory pegs for all numbers between 0 and 20. Additionally, you can come up with memory pegs for the letters in the alphabet then track orderings by letter. You'll manage up to 26 items (at which point you can safely return to the top and repeat). ↩

6. Using pictures gets us part of the way there, but it still limits us to only 2 dimensions. ↩

7. I haven't mentioned Person-Action-Object (PAO), which is a subtechnique of the memory palace that many professionals use to memorize long sequences of digits and playing cards. Maybe it serves as practice, but I feel PAO is a little too contrived for what we need in real-world memorizing. Knowing the digits of $\pi$ to the thousandth decimal is not going to make you a better conversationalist or debater. ↩