[What's the difference between a million and a billion? Can you feel it?]

 

Consider this thought experiment designed to help people understand the difference between “a million” and “a billion.” You and a friend each enter a lottery with several large prizes. But there’s a catch: If you win, you must spend $50,000 of your prize money each day until it runs out. You win a million dollars. Your friend wins a billion. How long does it take each of you to spend your lottery windfall? As a millionaire, your encounter with runaway consumerism is surprisingly short. You go bust after a mere 20 days. If you win on Thanksgiving, you’re out of money more than a week before Christmas. (Sorry, Cousin Ana, the lottery money ran out before we bought your present, but we did get you the Orange Crush umbrella!) For your billionaire friend, resources would hold out a tad longer. He or she would have a full-time job spending $50,000 a day for… 55 years. Approximately two generations. Almost 14 presidential terms. One wait to hear your name called at the DMV. 1 billion—1,000,000,000—is a number.

 

We might think we understand it because it’s right there, in black and white, but it has so many zeros that our brains fog up. It’s just “lots.” When we see how much larger it is than a million, it comes as a surprise.

 

The U.S. government has a 5 A Day campaign that’s designed to encourage kids to eat five servings of fruits and vegetables a day. McDonald’s alone outspends this campaign by a ratio of 350 to 1.

 

We know the fast-food companies have big ad budgets, we know that they outspend healthy messages, but 20 times more, 143 times more, 350 times more? What’s the big deal?

 

The higher numbers get, the less sensitive we get to them, a phenomenon psychologists have labeled “psychophysical numbing.” Moving on the number scale from 10 to 20 feels significant. But moving an equal distance from 340 to 350, even though it’s the same increase, we feel nothing… that’s “numbing.”

 

McDonald’s alone outspends the 5 A Day campaign by 350 to 1.

 

watching McDonald’s commercials, they spend 1 minute on 5 A Day.

 

If a child sees a McDonald’s commercial every single day, it would take them almost a year to see just one commercial about 5 A Day.

 

Calendar time is easier to feel than number counts.

 

97.5% of the world’s water is salinated. Of the 2.5% that’s fresh, over 99% is trapped in glaciers and snowfields. In total, only .025% of the water on the globe is actually drinkable by humans and animals.

 

Imagine a gallon jug filled with water with three ice cubes next to it. All of the water in the jug is salt water. The ice cubes are the only fresh water, and humans can only drink the drops that are melting off of each.

 

The largest volcano in the solar system, Olympus Mons on Mars, is about 300,000 square kilometers in area and about 22 kilometers (14 miles) tall.

 

The largest volcano in the solar system, Olympus Mons on Mars, covers an area as big as Arizona or Italy. It’s so tall that if you tried to fly over it during a normal cross-country plane flight, you’d crash into it halfway up the slope.

 

A very small percentage of Fortune 500 CEOs are women.

 

Among Fortune 500 CEOs, there are more men named James than there are women.

 

 

34% of White applicants and 14% of Black applicants without records received callbacks, compared to 17% and 5% with records.

 

White job applicants who had served jail time for a felony were more likely to receive a callback than were Black applicants with impeccable records.

 

Throughout the first 18 years of his career in the NBA, LeBron James scored over 35,000 points. Throughout the first 18 years of his career in the NBA, LeBron James scored

 

There are about 400 million civilian-owned firearms in the United States.

 

There are about 330 million citizens in the United States, and more than 400 million firearms… or enough for every man, woman, and child to own 1, and still have around 70 million firearms left over.

 

In Bangladesh, millions survive on pennies a day. With little access to banks, they’re forced

to pay outrageous interest rates (100% a year or more) whenever they need to access money.

 

Muhammad Yunus—an economics professor in Bangladesh—scoured the streets of a village to locate every resident who worked with moneylenders. In total, those 42 villagers were borrowing $27. Using just his paycheck as a professor, he loaned the 42 villagers the sums they would normally borrow from the moneylenders. One woman, who wove beautiful bamboo stools, borrowed 22 cents from Yunus for her day’s materials. Freed of the outrageous interest her moneylender charged her for her 1-day loan, she was able to take home more than the 2 cents a day she had made in the past and still have enough to pay Yunus back in short order. From there, she used the surplus to improve her family’s nutrition and housing, and her children’s schooling. This story happened over and over for the villagers to whom Yunus loaned money. The repayment rate was 100%.

 

The U.S. national debt is $27 trillion.

 

The U.S. national debt is $27 trillion—$82,000 per citizen.

 

Our median customer is 32 years old, married, with kids; and 93% of our customers work a full-time job. Our typical customer has 1.7 children (with 1.3 under the age of five). Her top 3 reasons for buying our product are 1) convenience, 2) familiar flavor, and 3) “not as bad” nutritionally as many of our competitors.

 

Our prototypical customer is a 32-year-old mom stopping by the store on the way home from work after picking her kids up from daycare. She is going down the aisles with a 2-year-old in the cart and a 4-year-old walking beside her. She has to grab the box she wants for dinner without the 4-year-old unloading the shelf closest to him. And when she tries to read the ingredients in fine print, the 2-year-old is slapping the box out of her hand. After considering our prototypical customer, we recommend simplifying the package design, so people can locate their favorite flavor faster, and increasing the font size of our nutritional information.

 

learned that lesson the hard way when his company tried to introduce a third-pound burger at the same price as the McDonald’s quarter-pounder. More than half the customers thought they were being ripped off. “Why should we pay the same amount for less meat?” they said.

 

The value of the new A&W burger depended on consumers comparing two fractions: 1/3 and 1/4. But fractions are difficult for everyone because they’re parts of things as opposed to whole objects. We like to count things, and fractions don’t equal “things.” So, we jump to the closest available whole numbers. 4 is bigger than 3, so we mistakenly infer that a 1/4-pounder is a bigger burger than a 1/3-pounder.

 

Rule #1. Simpler Is Better: Round with Enthusiasm.

 

5/11 is about half. 217 is about 200.

 

Rule #2. Concrete Is Better: Use Whole Numbers to Describe Whole Objects, Not Decimals, Fractions, or Percentages.

 

For numbers less than 1, you can use a method we call “counting in baskets” to make things start to show up as whole numbers. If you find that .2% of people have a certain trait, use a basket size of at least 500, maybe 1,000, to make them show up as real people. “1 out of 500” or “2 out of 1,000” makes these abstract percentages into real things.

 

Make the baskets as small as you can while retaining the wholeness of whole numbers. If 2/3rds or .67 or 67% of people didn’t like the new flavor, then make them feel like people in a room. “2 out of 3 people thought cheesy marshmallow was “disgusting.” Going up to 67 out of 100 would dilute understanding.

 

But if you need to bring in multiple stats, you don’t want to mix basket sizes. You want a basket small enough that it feels real and doesn’t make your audience do math, but large enough that multiple stats are directly comparable. 1 in 6 people thought cheesy marshmallow flavor was intriguing, while 4 in 6 thought it was disgusting (note that we changed the basket size above s...

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George A. Miller’s “Magical Number 7” has an expansion module, under certain conditions. We can load around 7 coherent “units” into our mental working space, but depending on our learning and expertise, those units may vary in size.

 

If we counted each atom in a human body, which elements would be the most common? Consider some alternative ways of expressing this:

 

Hydrogen 62% Oxygen 24% Carbon 13% Nitrogen 1.1% Other

 

For every 10 atoms in your body, 6 are hydrogen, 3 oxygen, 1 carbon. All the other elements are much less common.

 

40% of U.S. adults do not always wash their hands after using the bathroom at home.

 

2 out of every 5 people you shake hands with may not have washed their hands between using the toilet and touching your hands.

 

If you want to help people understand quickly, define your new concept in terms of something your audience already knows.

 

As you search, favor objects that only need a simple multiplier. 4 koalas or 72 pistachios are tougher to work with than simple multipliers such as 2 or half. In the research, people understood and recalled number translations best when the multiplier was 1. For example, “social distance is about the length of a tatami mat” (if you’re Japanese) or “almost the length of an adult cassowary” (if you’re from Australia), or “approximately an adult gator” (if you don’t need your ankles).

 

In 2020, the global video games market reached $180 billion. By comparison, in the movie business, world box office revenues were $42 billion in 2019 (pre-COVID), while world music revenues were $22 billion.

 

Hopper pressed her engineers to streamline their code. (In wartime, a fraction of a second can separate life from death.) During lectures, she would hold up a bundle of wire cut to the length that electricity traveled in a microsecond, or 1 one-millionth of a second. It was 984 feet long. She said, “I sometimes think we ought to hang one [of these bundles] over every programmer’s desk, or around their neck, so they know what they’re throwing away when they throw away microseconds.”

 

Imagine if Earth’s 7.7 billion people were shrunk to a village of 100: » 26 villagers would be children (14 years old or younger). 5 villagers would come from North America, 8 from Latin America, 10 from Europe, 17 from Africa, and 60 from Asia. » 31 would be Christians, 24 Muslims, 15 Hindus, and 7 Buddhists. 7 villagers would represent every other religion, and 16 wouldn’t identify with a religion. » 7 people would speak English as a first language, and another 20 would speak it as a second. 14 villagers would be illiterate; 7 would have a college degree. » 29 people would be overweight, and 10 would be going hungry.

 

A million seconds is 12 days. A billion is 1,000 times greater than 1,000,000. A billion seconds is 32 years.

 

Our development team of 100 engineers drinks a lot of coffee… Equipping each floor with new coffee stations would cost $15,000, plus additional ongoing fees for supplies and maintenance. At 10 minutes a day per person traveling down to the break room for coffee and back, our engineering department spends 80 hours a week getting caffeine. New coffee makers would pay for themselves within weeks; afterward, they’d make money for the company. Our current system acts as if we’ve hired 2 full-time engineers just to walk back and forth from their offices to the break room, and their hall banter isn’t even close to West Wing quality.

 

There are a little more than 50 million people in England, and around 50 deaths each day via accidental causes (slipping in the tub; being swept away in a flooding river; falling from a ladder). The daily risk of dying there in an accident is roughly 1 in a million. Your risk of dying unexpectedly in England on any given day is the same as your odds of having to guess which date someone is thinking of between 500 BC and August 1, 2200.

 

Odds of winning Powerball: 1 in 292,201,338 Imagine having to guess which second of a day someone is thinking of—any date, hour, minute, and second from the time they’re born to the time they turn 9. If you match, you win the lottery prize. The jackpot is yours. All you have to do is think of the resident of the United States whose name is written down over there on that folded piece of paper. (Hint: they are older than the age of 10.)

 

In 2016, the $148 million allocated to the National Endowment for the Arts accounted for .004% of the federal budget expenditures ($3.9 trillion). Suppose we eliminated it in response to criticism? Trying to balance the budget by eliminating the NEA would be like editing a 90,000-word novel by eliminating 4 words.

 

A single M&M has 4 calories. In order to burn off the calories in a single M&M, you’d have to walk 2 flights of stairs.

 

Statistical translation: We had 600 deaths per 1,000 troops. Nightingale’s translation: “We had, in the first seven months of the Crimean campaign… from disease alone, a rate of mortality which exceeds that of the Great Plague of London.”

 

In army hospitals, 25–35-year-old British soldiers in peacetime had mortality rates of around 19 per 1,000, compared with 11 per 1,000 in London hospitals. Nightingale’s translation: “It is as criminal to have a mortality of… 19… per 1,000 in the Line, Artillery and Guards in England, when that of Civil life is only 11 per 1,000, as it would be to take 1,100 men per annum out upon Salisbury Plain and shoot them.”

 

We are losing 1,100 men per year to preventable causes! Nightingale’s translation: “We hear with horror of the loss of 400 men onboard the Birkenhead by carelessness at sea; but what should we feel if we were told that 1,100 men are annually doomed to death in our Army at home by causes which might be prevented?”

 

One historian wrote an article on Florence Nightingale called “The Compassionate Statistician” and made the case that she never forgot the horror of men suffering in the hospital. She felt a connection to those soldiers for the rest of her life.

 

So all you have to do is find some comparison that already carries the emotion you need, and use your numbers to justify why the emotion ought to transfer.

 

More interesting from the standpoint of understanding emotion are situations where we are dealing with super-superlatives, which we call “incomparables.” These incomparables are the biggest and the best… and second place is not even close. When we have such a figure, we should emphasize it—indeed it would seem hard to miss the opportunity.

 

This analysis of the top 11 rivers eliminates any question of what river is the biggest or which one should make us feel the most awe. Note that we did this by adding up the erstwhile competitors and showing that the Amazon was yet bigger.

 

For another example of this principle in the realm of automobiles, consider Tesla, a company that investors believe has so much potential to revolutionize the industry that its market cap in 2021 was greater than that of its next few automotive competitors combined (including GM, Ford, Toyota, Honda, and VW). See how the translations above phrase these astonishing leads in concrete terms and left out the math? For a real super-superlative, we should be able to establish its dominance without any (visible) numbers at all.

 

In terms of economic prowess, California leads all the other 49 states in GDP. If California were a free-standing country, it would be the 5th-largest economy in the world.

 

In comparing California to a country, we use a technique we call category jumping—comparing something to an entirely different class of competitors, in the case of California comparing a state to nations.

 

In 2020, Apple was at one point valued at over $2 trillion. Imagine Apple as a country, with its shareholders as citizens and its citizens’ sole source of wealth their Apple stock. The total wealth of Apple would still be ahead of 150/171 countries, including Norway, South Africa, Thailand, and Saudi Arabia.

 

Livestock are responsible for 14.5% of global greenhouse-gas emissions. “If cows were a country,” they would be the third-highest producer of greenhouse emissions among all nations. They produce more emissions than Saudi Arabia or Australia or India, “and surpass every country in the European Union combined. They lag behind only China and America.” (Based on Steven Chu.)

 

Every gun that is made, every warship launched, every rocket fired signifies, in the final sense, a theft from those who hunger and are not fed, those who are cold and are not clothed. This world in arms is not spending money alone. It is spending the sweat of its laborers, the genius of its scientists, the hopes of its children. The cost of one modern heavy bomber is this: a modern brick school in more than 30 cities. It is 2 electric power plants, each serving a town of 60,000 population. It is 2 fine, fully equipped hospitals. It is some 50 miles of concrete highway. We pay for a single fighter plane with a half-million bushels of wheat. We pay for a single destroyer with new homes that could have housed more than 8,000 people… This is not a way of life at all, in any true sense. Under the cloud of threatening war, it is humanity hanging from a cross of iron. 

 

The dry statistic: A 12-oz. serving of Ocean Spray Cran-Apple juice has 44 grams of sugar, or 11 teaspoons. The translation: Drinking a 12-oz. serving of Ocean Spray Cran-Apple juice is the sugar equivalent of 3 glazed donuts from Krispy Kreme… plus 4 sugar cubes.

 

In the United States every year, nearly 270,000 patients die from sepsis. Kaiser Permanente in Northern California recently developed a protocol that reduces sepsis deaths by 55%! If it were rolled out to every hospital in the U.S. it would save 147,000 lives per year. That’s more lives saved than saving each year every woman with breast cancer and every man with prostate cancer… combined!

 

There’s a 20% chance of experiencing a mental illness in a given year, and a 50% chance of being diagnosed with a mental illness in your lifetime. To a group sitting at a conference table: Say, “For every 5 people, 1 of you will be diagnosed with a mental illness this year. At some point in your lifetime, either you or the person across from you will be diagnosed with a mental illness.”

 

Average earnings in Kenya are about $7,000 per year (compared with $68,000 in the United States). Kenyans spend about 50% of their income on food. If you spent the same portion of your weekly income on food as Kenyans do, 7 days of eating would cost you $650 for dishes like cornmeal porridge and potato pea mash. How easily could you pay your other bills if food sucked up that much of your resources?

 

Jeff Bezos is worth $198 billion. Let’s imagine if each step of a staircase represents $100,000 in the bank. Most people, including 1 in 2 Americans and 89% of the world, can’t even step onto the first step of the staircase because they have less. After 4 steps, we’ve lost over 75% of Americans. Fewer than 1 in 10 people will ever reach the 10th step: a million dollars. Now put on your most comfortable hiking shoes. You’d have to climb for almost 3 hours before reaching the net worth of a billionaire. After spending 9 hours a day climbing steps for 2 months, you’d have Ironman-level quads as you finally reach the wealth of Jeff Bezos.

 

The current operating system for programming industrial robots is from 1969. You want to convince people that that is ludicrously out of date… As people enter the meeting room, play music from 1969. During your discussion section, say: “We call those ‘classic’ rock and roll songs. Do you want your tech to be classic?” To the music soundtrack, add visuals: Show ads for cars from 1969, clock radios, a computer, rotary-dial telephones, television sets with big dials. Serve them a TV dinner with Baked Alaska for dessert. Remind them: “If you miss an episode of a TV show, you may never see it again.”

 

Or if she were teaching a less athletic class, she could select two students to stand at opposite ends of the classroom and assign a third student to walk between them, spooling the thread around them as the class continued. It would take around five minutes—long enough for the point to sink in. From “a microsecond,” to a concrete piece of wire, to actually having to travel that length of wire, each level of translation makes the statistic easier to understand and harder to ignore.

 

A batter has roughly a quarter of a second—250 milliseconds—to decide whether to swing at a pitch, and even less time (150 milliseconds) to take the swing. Clap your hands as quickly as you can for just one second. Most people can clap 4 or 5 times. Suppose you can clap 4 times a second. A major league batter has only 1 of those claps to decide whether to swing at a pitch. By the time you’ve clapped twice, the play is over.

 

The U.S. Congress is 73% male and frequently passes legislation that affects the lives of women. If you have a large group, select a subgroup of 3 women and 1 man. Have them vote on issues that only affect the men in the group.

 

Odds of winning Powerball: 1 in 292,201,338 Imagine having to guess which date someone is thinking of—any date between January 1 in the year 0001 (1 A.D.) and September 18 in the year 2667. If you match, you win the lottery prize. Just as they are about to hand you your check, they reveal that the fine print on your ticket requires passing one more hurdle. There are 300 identical envelopes on the wall. If you don’t pick the one that holds your check, you receive nothing.

 

59% of Americans said that growing trade ties between countries are “very good” or “somewhat good.” Zakaria, citing a Pew survey: “Thumping majorities everywhere said that growing trade ties between countries are ‘very good’ or ‘somewhat good’—91% in China, 85% in Germany, 88% in Bulgaria, 87% in South Africa, 93% in Kenya and so on. Of the 47 countries surveyed, the one that came in dead last was… America, at 59%. “The only country within 10 points of us was Egypt.”

 

Modern humans first appeared 200,000 years ago—a very recent addition to the universe. The Big Bang occurred an estimated 13.8 billion years ago. Suppose the history of the universe spanned the 24 hours of a single day. The Big Bang happens precisely at midnight. For a long time, nothing happens. 12 hours pass, then 16. At about 4:10 p.m., our sun comes to life in the midst of a cloud of dust and the planets start forming around it. 5 minutes later, the Earth appears and starts to cool. Single-celled life appears on Earth by 5:30 p.m. Vertebrates don’t arrive until late that evening at 11:09 p.m. Dinosaurs and the first mammals appear around 11:37 p.m. T. rex shows up at 11:52, with 8 minutes left in the day, but disappears when an asteroid hits a minute later. The entire history of humankind doesn’t even take up the final second.