Memorizing units

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

  1. Memorizing numbers (start here)
  2. Memorizing units (you are here)
  3. 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 themselvesβ€”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).

SymbolNameDimension
s\text{s}secondtime
m\text{m}meterlength
kg\text{kg}kilogrammass
A\text{A}ampereelectric current
K\text{K}kelvinthermodynamic temperature
mol\text{mol}moleamount of a substance
cd\text{cd}candelaluminous intensity

Derived Units

SymbolNameDimensionEquivalents
Hz\text{Hz}hertzfrequency1/s1/\text{s}
N\text{N}newtonforce, weightkgβ‹…m/s2\text{kg}\cdot\text{m}/\text{s}^2
Pa\text{Pa}pascalpressure, stressN/m2\text{N}/\text{m}^2
J\text{J}jouleenergy, work, heatNβ‹…m\text{N}\cdot\text{m}, Cβ‹…V\text{C}\cdot\text{V}
W\text{W}wattpowerJ/s\text{J}/\text{s}
C\text{C}coulombelectric chargesβ‹…A\text{s}\cdot\text{A}, Fβ‹…VF\cdot V
V\text{V}voltvoltage, electric potential differencecc

and more. . . .

Unit Prefixes

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

SymbolNameValue
yyocto10βˆ’2410^{-24}
zzepto10βˆ’2110^{-21}
aatto10βˆ’1810^{-18}
ffemto10βˆ’1510^{-15}
ppico10βˆ’1210^{-12}
nnano10βˆ’910^{-9}
ΞΌmicro10βˆ’610^{-6}
mmilli10βˆ’310^{-3}
ccenti10βˆ’210^{-2}
ddeci10βˆ’110^{-1}
10010^{0}
dadeca10110^{1}
hhecto10210^{2}
kkilo10310^{3}
Mmega10610^{6}
Ggiga10910^{9}
Ttera101210^{12}
Ppeta101510^{15}
Eexa101810^{18}
Zzetta102110^{21}
Yyotta102410^{24}

πŸ’± 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.

πŸ” 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.

β™Ÿ 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.

πŸ‘€ 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. πŸ”’ Use the Major system to convert the number into a concrete object. (4.19 -> "red top")
  2. πŸ“ Use physical intuition to identify the relevant dimensions. ("electricity consumption" -> "power")
  3. πŸ—ƒ 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. β™Ÿ Memorize the unit prefix with a memory peg. (tera- -> "globe (terra)")
  5. πŸ”— 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 ")

πŸ’‘ 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. ↩