Nobel laureate in physics and father of the "atomic age," Enrico Fermi was also a gifted guesser. Rather than tackle complex problems head-on, Fermi would break them apart into tiny, simpler chunks, then compose these chunks to get back at the whole. It's a strategy we have much to learn from.

This process is perhaps best reflected in the paradox that bears Fermi's name. At a lunch in 1950, he raised the following question to his audience: where is everybody? (The extraterrestrials, that is.) Fermi followed with a characteristic calculation that anticipated the Drake equation:

Even with moderate guesses for the later parameters, the sheer number of stars led Fermi to conclude that "we ought to have been visited long ago and many times over" (Jones 1985). Hence the paradox.

Fermi understood that the more guesses he fit into his break-down, the more reliable his final answer would be. That's because as long as your errors are unbiased, they will tend to balance each other out. Guess a little too much over here, a little too much over there, and your answer will come out in the reasonable middle.¹ ^dc6a5a

Thus Fermi was able to estimate the energy of a nuclear blast from the movement of a floating piece of paper and the number of piano tuners in Chicago without turning to yellow pages. He wouldn't get the exact figure, but he could expect a reasonable order-of-magnitude (power of ten) estimate.

Like the paradox, these kinds of back-of-the-envelope questions are now known as Fermi questions. It's worth learning how to solve Fermi questions. First, because you'll hone your bullshit detector for the statistics garbage floating around cyberspace and dinner tables. Next, because practice with Fermi questions weaponizes your internal store of facts (see 1 Projects/Writing/02 Series/Memorizing/Memorizing numbers and 1 Projects/Writing/02 Series/Memorizing/Memorizing units). You'll be able to construct quantitative arguments on the fly that grant your reasoning a significant credibility boost.

Now I hate to give a cop-out answer, but the best way to learn how to solve Fermi questions is to solve Fermi questions. Keep an eye out and a notepad handy. If you're desperate for more structured practice, you can check out the book, Guesstimation, by Lawrence Weinstein and John A. Adam, which has dozens of excellent examples. But, really, everyday debates should present enough opportunities for practice.

That said, one thing you can do which really will help is to memorize reference figures and statistics. So that you can collapse a few of your guesses onto certainties to make your conclusions all the more likely. Check out the Anki deck I made for learning units for a previous article.

---

Footnotes

Footnotes

1. For this to work, your guesses should have similar, not-too-large error margins. This is why we can't really judge Fermi's claim of omnipresent aliens. Who knows what the chance is of a planet bearing life? Or of a species developing intelligence? Escaping the dark ages? Circumventing anti-vax-climate-change-denying-nuclear-war-hawks? ↩

This is the second part in a four-part series on memorizing statistics.

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

Previously, we covered memorizing numbers such as dates, rates, and percentages with the Major system and Anki. But numbers are only a small part of the equation: with real-world statistics, the units matter as much as the digits themselves—especially when we're interested in actually using statistics.

❌ Don't Memorize the Units

Dimensions and units

First, we have to make a distinction between dimensions and units. Dimensions are the underlying physical variables (e.g. length, time, energy, power). Units are reference scales to measure and compare the underlying variables (e.g. meters for length, seconds for time, joules for energy, watts for power).

Whenever you can, avoid explicitly memorizing the dimensions. Instead, derive these by physical intuition. After all, the first rule of memorizing is to understand first. If you really understand what a statistic means, the dimensions should explain themselves.

Let's return to the example of climate-crisis statistics. If you're talking about global emissions, you know the dimensions are of mass: emissions are material, and matter is measured in mass¹. But if you're talking about the energy consumption of a country, you'll need to use dimensions of energy. And if you're judging the production capacity of a new power station, you're interested in power (energy per time).

So too, we'd like to avoid explicitly memorizing units when possible. But this is harder to do because for every dimension there are a dozen alternative units: kilometers and miles, short tons, metric tons, and long tons, Kelvin, Celsius, Rankine, and Fahrenheit, etc.

Our saving grace is the international system (SI from the French système international) of units. If we know that a statistic obeys the SI conventions, there's only one option for every unit. Distance has to be measured in meters, mass in kilograms, temperature in Kelvin. Then, all we have to explicitly memorize is the particular unit prefix (e.g. kilo-, mega-, giga-).

So the easiest thing to do is to convert every statistic you'd like to memorize to SI units before storing them in your spaced repetition system. You'll have to memorize what the SI units are, but you only have to memorize this once for easier memorizing always. It'll also help to know common conversion factors so you can transform these statistics back to whatever other units you later desire.

🌐 SI units

So I've thrown together an Anki deck to help you learn the most common SI units. You can find it here. As always, before you jump in, make sure you have some overview of what the units actually mean (e.g., read their wikis).

Base Units

There are 6 "base units." These are the units whose values are set by actual physical measurements. The rest of the units are "derived" from these base units, 22 of which have special names (typically after notable physicists and chemists). The rest have self-explanatory names (e.g., meter per second and joule per Kelvin).

Symbol	Name	Dimension
$\text{s}$	second	time
$\text{m}$	meter	length
$\text{kg}$	kilogram	mass
$\text{A}$	ampere	electric current
$\text{K}$	kelvin	thermodynamic temperature
$\text{mol}$	mole	amount of a substance
$\text{cd}$	candela	luminous intensity

Derived Units

Symbol	Name	Dimension	Equivalents
$\text{Hz}$	hertz	frequency	$1/\text{s}$
$\text{N}$	newton	force, weight	$\text{kg}\cdot\text{m}/\text{s}^2$
$\text{Pa}$	pascal	pressure, stress	$\text{N}/\text{m}^2$
$\text{J}$	joule	energy, work, heat	$\text{N}\cdot\text{m}$, $\text{C}\cdot\text{V}$
$\text{W}$	watt	power	$\text{J}/\text{s}$
$\text{C}$	coulomb	electric charge	$\text{s}\cdot\text{A}$, $F\cdot V$
$\text{V}$	volt	voltage, electric potential difference	$c$

and more. . . .

Unit Prefixes

I've also included a subdeck to help you memorize the meanings of the standard prefixes.

Symbol	Name	Value
y	yocto	$10^{-24}$
z	zepto	$10^{-21}$
a	atto	$10^{-18}$
f	femto	$10^{-15}$
p	pico	$10^{-12}$
n	nano	$10^{-9}$
μ	micro	$10^{-6}$
m	milli	$10^{-3}$
c	centi	$10^{-2}$
d	deci	$10^{-1}$
		$10^{0}$
da	deca	$10^{1}$
h	hecto	$10^{2}$
k	kilo	$10^{3}$
M	mega	$10^{6}$
G	giga	$10^{9}$
T	tera	$10^{12}$
P	peta	$10^{15}$
E	exa	$10^{18}$
Z	zetta	$10^{21}$
Y	yotta	$10^{24}$

💱 Conversions

Of course, you'll sometimes have to convert to non-SI units. For car speeds kilometers per hour can be more useful than meters per second. And a stubborn fraction of the world continues to cling to the imperial system. So I've added in a subdeck of common conversion factors.

🏔 Reference Objects

Finally, I've added a subdeck that includes reference objects to help you build intuition for different scales of magnitude (e.g. the land-area of Manhattan versus New York State vs Earth, etc.). These reference values may seem arbitrary, but they'll help make the different units and unit-prefix pairings way more tangible.

♟ Memory Pegs

Still, sometimes we'll want to explicitly associate a number to units. Especially when we want to memorize a statistic in its original non-SI formulation. Maybe because the convention in a particular discipline is non-SI. Astronomers prefer light-years and parsecs over petameters for good reason: they former are more practical.

For example, suppose I were trying to memorize that the total electricity end-use of the US in 2019 was 4.19 terawatt-hours (EIA 2020).

In the last chapter, we saw how we might memorize "4.19." 4, 1, and 9 become the consonants r, d/t, and p/b. Then, we compose these into, for example, "red top" (eliding the d-t), and we imagine a spinning red top. Easy.

But it won't be enough just to memorize 4.19 or even 4.19 + "tera" so long as there's an ambiguity between tera-joules and tera-watt-hours. We need an explicit link between the quantity "4.19", the prefix "tera-," and the unit "watt-hours."

The difficulty is that every one of these items is abstract, and our brains have a hard time memorizing abstract objects. That's where the power lies in a trick like the Major system: we turn the abstract and difficult-to-remember into a concrete and much-easier-to-remember "red top."

Memory pegs are similar. But instead of inventing a new object every time we encounter a new item, we choose the associations ahead of time (usually by rhyme or word similarity). It's useful when the set of objects to memorize is bounded (such as our system of units).

For example, "joule" sounds like "jewel," so my memory peg for "joule" could be some grossly large pink jewel. Meanwhile, "watt" makes me think of "Watson," so my peg could be the duo Sherlock Holmes and Dr. Watson. "Tera" makes me think of "terra," the planet we live on. Finally, "hour" becomes "whore" (or some more PG alternative if it's parents reading this).

Putting it all together, 4.19 Terawatt-hours becomes Dr. Watson and a whore balancing on a globe balancing on a spinning red top (raunchiness makes for great memory).

To help you along, I've added a field for memory pegs in the Anki decks I provided above. I filled in my own choice of memory pegs both for the units and the unit prefixes. These might work for you or not, so I recommend you first go through the deck and swap out any pegs you don't like (remember to always personalize your notes). When intuition is not enough, it's memory pegs that will help you recall the units and prefixes for any given statistic.

👀 Conclusion

With the right combination of physical intuition and memory pegs, you have everything you need to memorize numbers and units. Combining the first two chapters, we have a strategy that looks something like this:

1. 🔢 Use the Major system to convert the number into a concrete object. (4.19 -> "red top")
2. 📏 Use physical intuition to identify the relevant dimensions. ("electricity consumption" -> "power")
3. 🗃 Retrieve the possible units corresponding to these dimensions from memory. If there are multiple options (e.g. joules and kilowatt-hours), use a memory peg to distinguish between the options. If there aren't, you can leave the units implicit. (watt-hours -> "Watson + whore")
4. ♟ Memorize the unit prefix with a memory peg. (tera- -> "globe (terra)")
5. 🔗 Visualize an association between the number-derived object and the unit-derived memory peg(s). ("Dr. Watson and a whore balancing on a globe balancing on a spinning red top ")

💡 Bonus: Developing Physical Intuition

But how to develop the physical intuition you need to make memorizing units automatic? It's a chicken-and-egg problem: you don't develop the intuition until you regularly use the units, but you can't use the units until you have intuition for using them.

So put a stop to the decision paralysis and start by learning the units. In a future post, we'll tackle how to put your newly-memorized statistics to good use in the kinds of back-of-the-envelope calculations that can make or break debate.

---

Footnotes

Footnotes

1. Okay, so actually this gets more complicated. First, you could measure emissions in moles (number of particles), but mass is more practical. Also, you have to qualify your units of emissions by the type of greenhouse gas (GHG) (e.g. CO2, CH4, N20) because every GHG has a different global warming potential (i.e. how much a gram of material increases warming). So if you want to compare them against one another, you have to convert the gases to a baseline (usually, gigatons of CO2-equivalents). But then every one of these compounds has a different half-life. So you have to specify the time-period over which you're comparing global warming potentials. And you end up with something like gigatons CO2-equivalents-100-years (gTC02e100). Complicated. ↩

For most of us, numbers are difficult to memorize. Even with a spaced repetition system like Anki.

Biological determinism 2 Areas/Principles/Laws/Weber-Fechner law#Corollary

This difficulty may be a relic of our evolutionary history: relative number mattered more than absolute number—mass mattered more than count. Fortunately, humans have a way of subverting biological fatalism. Over the past millennia, we've developed mnemonic tricks that make it easier to memorize all kinds of facts—numbers and statistics included.

2 Areas/Principles/Laws/Why memorize (Pt. 1)

Because there is a real value to memorizing numbers, statistics, and facts more generally. In debate, quantities ground the conversation in reality; they prevent you and your opponent from floating off into hypotheticals. With the right restraint, a large factual memory can improve your impartiality: you discuss facts rather than beliefs. And the very presence of such a memory can grant you credibility. Memory matters.

In this article, I'm going to break down how to memorize numbers using the Major system. In follow-ups, we'll cover how to memorize units, orders, and sources. Together, you'll have all you need to memorize general statistics.

In particular, I'm interested in integrating these techniques with my spaced repetition workflow. So that memorizing statistics is no one-off thing but part of continual practice.

🎳 Interference

In practice, the more relevant obstacle to memorizing numbers is not evolutionary history but interference: numbers compete with one other for mental bandwidth. And numbers "interfere" more intensely than do words. You probably have a harder time separating 43%/34% and 1367/1376 than cat/mat and dog/god. We don't have the same semantic horse-power pulling apart numbers as we do words.

It gets even harder to memorize when you're dealing with statistics, where you also care to memorize units and sources. Good luck keeping apart acronyms like the UNHCR, UNHRC, and UNCHR (that's the United Nations high commissioner for refugees, human rights council, and commission on human rights, respectively).

GHG emissions breakdown

GHG

🌎 An Example: the Climate Crisis

Because we're interested in memorizing for the real world, let's use a real-world example to memorize.

I'd like to contribute in the fight against climate crisis. To begin, I'd like a better understanding of where exactly our emissions come from. So I am going to commit a whole bunch of climate statistics to memory.

According to the World Resources Institute Climate Watch report (2020) (henceforth, WRI 2020), we produced 49.4 billion tons of CO2-equivalents in 2016 with an uncertainty of about 10%.

Significant figures and error

1 Projects/Writing/02 Series/General/Fermi questions To share an estimate without a measure of its uncertainty or spread is statistical sacrilege. But in less formal settings, we can usually get away with it. That's because the important point is usually the order of magnitude—to know we produced about 50 GtCO2e but not 5 or 500. (If your statistic has error bars greater than an order of magnitude, look for a new statistic.)

The best way to emphasize the relevant order of magnitude is to reduce the number of digits you report. With an uncertainty of 10%, saying "50GtCO2e" is most honest representation.

But sometimes, it can can be advantageous to over-report the digits: "49.38" carries more rhetorical emphasis than "about 50." With the right timing, pulling out all the digits can overwhelm the opponent. But don't do this too often because it is misleading and can be outright pretentious. It's also dangerous because if your opponent requests the error bars, you will end up looking the fool. So judge wisely.

🔢 1-2 Digits Major system

The WRI divides global emissions into 4 top-level sectors (in order of decreasing magnitude):

1. ⚡️ Energy (electricity, heat, and transport): 73.2%
2. 🚜 Agriculture, forestry, and other land-use (AFOLU): 18.4%
3. 🏭 Industry (cement, ammonia, plastics, and other chemicals): 5.2%
4. 🗑 Waste: 3.2%

The principle behind the major system is to associate a unique consonant sound or related set of consonant sounds with each digit. Then, we can read the digits like an abjad by converting numbers into words and words back into numbers.

A Possible Mapping

Number	Consonant
0	s, z, soft c
1	t, d
2	n, ng
3	m
4	r
5	l
6	sh, ch, j
7	k, hard c, hard g, hard ch, q, qu
8	f, v, th, dh
9	p, b

For our example:

1. ⚡️ Energy: 73.2% -> KMN
2. 🚜 AFOLU: 18.4% -> TFR
3. 🏭 Industry: 5.2% -> LN
4. 🗑 Waste: 3.2% -> MN

With a little practice, we get better at turning these into words (the more concrete, the better):

• KMN -> Camion, Come on, Caiman
• TFR -> Tover (Dutch for "magic"), To throw, taffrail (dropping the l)
• LN -> Lion, lan, lawn, lane
• MN -> Money, moan, man

Now, all we have to do is memorize a pairing between two much less abstract objects. For energy and "caiman", I might imagine a radioactively-glowing alligatorid puffing black smoke from its orifices. For AFOLU and "tover" (magic), I visualize a magician converting a large John Deere Tractor into a puff of smoke (actions are more memorable). For industry and "lion," it's a lion trapped in cement, struggling to free itself while it's buried alive in fertilizer (emotional imagery works even better). For waste and money, the Joker burns his large pile of cash.

And it's these pairings that I'll put in my Anki (and if I have the time I'll add or even draw a picture for extra stickiness).

With a little practice, you'll soon get better and faster at this entire process. At the next layer of resolution, we go through the same process

1. 🏭 Energy use in industry: 24.2% -> NRN -> Neuron
2. 🚗 Transport: 16.2% -> DCHN -> Dejeune (from Fr. for "breakfast")
3. 🏘 Energy use in buildings: 17.5% -> TKL -> Tackle
4. 🎉 Unallocated fuel combustion: 7.8% -> KF -> Keef
5. 🌋 Fugitive emissions from energy production: 5.8% -> LF -> Love
6. 🚜 🎣 Energy in Agriculture & Fishing: 1.7% -> DK -> Dock

I'll leave the final images to you.

Special symbols

There's more to numbers than the numerals. There are decimals, percentage signs, ranges, and powers. Without these, how would you know whether "lion" is 52 or 5.2 and "money" 32 or 3.2. Usually, context suffices. Take decimals: if you understand the physical origins of emissions, you'll know that energy production operates at a much larger scale than emissions from cement and ammonia production or from anaerobic respiration in oxygen-poor landfills. But when you need more help, you can use specific memory pegs for these special characters. E.g.: a decimal might become a laser pointer. To make numbers even more memorable, imagine a super-powerful laser slicing the remaining objects in half.

This is a starting point for memorizing 2 or more digits. But it may be slightly overkill for memorizing single digits (as with order of a sequence of elements). And it doesn't help us memorize the units (which are subject to the same problems of interference as digits). Nor sources (with a flurry of names and organizational initialisms). So stay tuned, for the follow-ups.

Atomic SRS

Almost everything there is to say about how to make cards has already been said. See Peter Wozniak's 20 rules of formulating knowledge for general tips, Michael Nielsen's long post on using Anki, and Gabriel Wyner's Fluent Forever for language-learning tips.

Instead of saying what has already been said, I'll make a few comments about how to begin with an SRS. How to apply the idea of "atomic workflows" to building up an SRS practice.

I've been using Anki for a long time, so I may not be the best reference for starting an SRS practice. But——I did fall out of the habit for most of 2019, and having to relearn the routines gave me a few ideas that might be useful to real newcomers.

Habits of an SRS

The atomic workflows process begins by identifying the basic habits that build up a workflow, reducing that set to the most essential subset, then reducing those habits to their fundamental actions.

An SRS workflow comprises three habits:

1. 🔄 Reviewing cards (once a day)
2. 📥 Gathering content (continuously)
3. 🏷 Making new cards (once or twice a week)

Of these, the first is the most important to long-term memorization, and it's where we'll start.

Reviewing Cards

And a Note on Using Other People's Decks

At some point, you'll hear the advice to avoid using other people's flashcard decks. It's good advice: when you create your own cards, they're more personal and ultimately easier to learn. But you can break the rule when the deck is predominantly visual and when its cards are totally irreducible.

The most obvious examples of acceptable deck-stealing are in subjects like geography (e.g., countries and capitals, US states and capitals, German provinces) anatomy (e.g., bones, muscles), and occasionally history (e.g. US presidents, art history, Egyptian gods).

Cards to steal

But do not use other people's decks for subjects like languages (where other people's definitions and translations mislead) or science and history if you still lack the big-picture understanding (let me point out that Wozniak's very first rule is to understand before you memorize). Otherwise, the cards won't fit you.

Besides the risk of impersonal cards, another risk in using other people's decks is that their cards are simply bad. The cards may demand too much information, provide too little imagery, or end up irrelevant. So tread carefully and refer back to the 20 rules.

Cards to avoid stealing

How are you going to know that I meant "hood" with this picture and not "hoody" or "shady" or "delinquent." Probably not a great card of mine, but how are you ever to guess that I prefer this answer over "to provide early evidence of oxygen and carbon dioxide" or "to provide evidence of photosynthesis and respiration." And you won't know any of these broader implications if this card is your only exposure to the subject.

Still, for the newcomer I recommend starting with a shared deck that meets the "obviously appropriate" criteria above.

Choose a fixed moment of your day (for me it's the last part of my morning routine) to build the habit of a daily review session. Don't worry about raising the number of cards you introduce per day—just keep the review short enough that you're able to it consistently.

Tip: except for foreign languages, group all of your cards together under one parent deck. This way you'll train a memory resilient across different contexts.

Avoid languages and avoid making your own cards. Whatever your end-goal, there's almost certainly some bit of trivia you'll find amusing enough as detour. Build the habit first because the daily review is the most important part of the practice.

Falling behind: If you stop reviewing your cards for only a few weeks, you can rack up hundreds or even thousands of backlogged cards. To recover use the same principle as you would when first starting: cap the number of cards you review per day so you focus on consistency over flux.

Making Cards

Next in importance after reviewing cards is making cards (so you can start to learn more than just geography and anatomy). I put aside one hour a week for Italian and one hour a week for general information. You probably won't need more than this.

So you're ready to start making cards. First, familiarize yourself with Wozniak's 20 rules. Then, establish a fixed moment every week (maybe right before or after a weekly review) for making cards. For the time being, keep it simple. Restrict yourself to the following note types: basic, basic and reversed, and cloze deletions.

As for gathering content, choose an easy subject. Something that lends itself to lists. E.g.: vocabulary in your native language, local bird species, or notable political/royal figures.

Basic provides a question and answer Basic and reversed is useful for word-pairs to train both active and passive memory. Cloze deletions are useful for smaller items in sentences (also for grammar in a language).

Don't play around with creating your own note templates until you're intimately familiar with these basic types. And if you do want to explore this avenue, finish reading the Anki documentation first. More often than not, you won't need anything fancier. If you want to learn a language, this is the stage to start dabbling with Gabriel Wyner's strategies in Fluent Forever (and, if you're interested, he's built a new app that might be worth looking into).

Example from Gabriel Wyner's Arabic pronunciation trainer.

Gathering Content

With GTD, you need an inbox where you write down your thoughts before expanding them into tasks then moving them to their relevant horizons. With the Zettelkasten, you take fleeting notes before converting them to permanent notes. So too, with an SRS practice, you need a place to gather questions before converting them to cards in your weekly card-making session.

The easiest starting point is the unassuming list. For example, with physical books I use a post-it as a bookmark that I fill with new vocabulary. With Italian I return to a list of Kindle highlights from my reading and to a separate list of feedback from my weekly speaking practice. With research articles I use variants of the Cornell note-taking method: the questions in the side column immediately translate to questions in Anki.

Consider my examples as illustrations not prescriptions because this habit offers the most flexibility of the three. So use trial and error, and see what sticks.

My next step is to migrate to keeping these lists in Obsidian. Then, to incorporate the Obsidian to Anki plugin. Indeed, the similarity between all these workflows points to a possible unification, but that will have to wait until a future post.

Conclusion

To adopt an SRS workflow, begin by cheating: steal another person's deck to build your daily review habit. Only then move on to making your own cards. Start with simple note types and expand from there. As for gathering content, use simple lists.

In the future, we'll explore fancier integrations with other workflows (GTD and the Zettelkasten), so stay posted.