Visualizing Numbers Effectively

 

Most people have trouble with numbers. They easily visualize up to twelve. Once beyond 100 numbers kind of blur together. There is a difference between a one in 500 chance of something happening and a one in a million chance, but most people do not really understand it. Or the difference between a million and a billion.

“Making Numbers Count: The Art and Science of Communicating Numbers,” by Chip Heath and Karla Starr, offers a solution to that problem. It presents tools to understand numbers and effectively communicate the meaning of numbers to others. The authors provide a step-by-step process to give readers mastery of numbers using a few simple rules.

Take the difference between a million and a billion. Heath and Starr have readers visualize the difference this way: a million seconds is twelve days; a billion seconds is 32 years.  You suddenly appreciate the scale of the difference. Twelve days is two workweeks linked by a weekend. Thirty-two years? Depending on your age, it could be twice your lifespan, your lifespan, or half your lifespan. Regardless of your yardstick, you know it is a whole lot more than two workweeks linked by a weekend.

Heath and Starr then present the rules used to develop this analogy. Translate everything into understandable concepts, focus on one thing at a time, and use user-friendly numbers. They go beyond this, explaining the strength of analogy, keeping numbers on a human scale, using techniques to convert abstract numbers into concrete concepts, and models to make things understandable. It sounds simple once they break things down.

There are times while reading “Making Numbers Count” you are reminded of Mark Twain’s adage that “there are lies, damn lies, and statistics.” Heath and Starr are open about using their techniques to sway opinion and shape your intellectual battlefield. They show how to make effective emotional appeals using numbers. They also make you aware when these techniques are used on you.

“Making Numbers Count” is written both for people that intuitively grasp numbers and those for whom numbers are an impenetrable barrier. Those comfortable with numbers will find it a tool that allows them to effectively communicate the meaning of numbers to others. Those who preface discussions by stating “I was told there would be no math” will realize “Making Numbers Count” allows them to grasp numbers with a minimum of math. Either way, this book is worth reading.

“Making Numbers Count: The Art and Science of Communicating Numbers,” by Chip Heath and Karla Starr, Avid Reader Press/Simon & Schuster, 2022, 208 pages, $24.00 (Hardcover), $17.75 (Paperback), $13.99 (Ebook)

This review was written by Mark Lardas who writes at Ricochet as Seawriter. Mark Lardas, an engineer, freelance writer, historian, and model-maker, lives in League City, TX. His website is marklardas.com.

Published in Science & Technology
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  1. Skyler Coolidge
    Skyler
    @Skyler

    Seriously?  I guess you can write a book about anything, but this one takes the cake.  Not in a billion seconds would a buy it.  

    • #1
  2. Some Call Me ...Tim Coolidge
    Some Call Me ...Tim
    @SomeCallMeTim

    You were right. The percentage dropped to 78.673%. 

    • #2
  3. DaveSchmidt Coolidge
    DaveSchmidt
    @DaveSchmidt

    Should be required reading for elected officials and their legislative staffs.  

    • #3
  4. Seawriter Contributor
    Seawriter
    @Seawriter

    DaveSchmidt (View Comment):

    Should be required reading for elected officials and their legislative staffs.

    Not necessarily. It might give them ideas.

    • #4
  5. DaveSchmidt Coolidge
    DaveSchmidt
    @DaveSchmidt

    Seawriter (View Comment):

    DaveSchmidt (View Comment):

    Should be required reading for elected officials and their legislative staffs.

    Not necessarily. It might give them ideas.

    Taxpayers? 

    • #5
  6. Seawriter Contributor
    Seawriter
    @Seawriter

    DaveSchmidt (View Comment):

    Seawriter (View Comment):

    DaveSchmidt (View Comment):

    Should be required reading for elected officials and their legislative staffs.

    Not necessarily. It might give them ideas.

    Taxpayers?

    Taxpayers? Mandatory reading.

    • #6
  7. Gary McVey Contributor
    Gary McVey
    @GaryMcVey

    When the Space Shuttle was still being designed and built, the contractors were obligated to estimate realistic rates of failure with loss of crew. They came up with 1/100,000.  Sounds reasonable, right? After all, we use the round-up guesstimate of one in a million airline flights, so estimating that the Shuttle is only one tenth as safe still sounded pretty reassuring. 

    But 1/100,000 actually means we could launch one shuttle a day for the following 274 years before we’d have a statistical likelihood of a catastrophe. Wildly unrealistic, especially now that we know that we had two fatal accidents in 122 launches. 

    • #7
  8. Fake John/Jane Galt Coolidge
    Fake John/Jane Galt
    @FakeJohnJaneGalt

    Gary McVey (View Comment):

    When the Space Shuttle was still being designed and built, the contractors were obligated to estimate realistic rates of failure with loss of crew. They came up with 1/100,000. Sounds reasonable, right? After all, we use the round-up guesstimate of one in a million airline flights, so estimating that the Shuttle is only one tenth as safe still sounded pretty reassuring.

    But 1/100,000 actually means we could launch one shuttle a day for the following 274 years before we’d have a statistical likelihood of a catastrophe. Wildly unrealistic, especially now that we know that we had two fatal accidents in 122 launches.

    Can’t be.  The experts said and the science said.  You do not believe the science as stated by experts?  

     

    • #8
  9. Mad Gerald Coolidge
    Mad Gerald
    @Jose

    DaveSchmidt (View Comment):

    Should be required reading for elected officials and their legislative staffs.

    Those are the knuckle heads deciding to spend millions, billions, or trillions of dollars. There’s a big difference between them but these politicians don’t seem to understand the difference. 

    It’s kind of like if you had 5 in your bank account.  $5 hundred?  $5 million?  If it was your money you would watch it a lot closer.

    • #9
  10. Skyler Coolidge
    Skyler
    @Skyler

    Gary McVey (View Comment):

    When the Space Shuttle was still being designed and built, the contractors were obligated to estimate realistic rates of failure with loss of crew. They came up with 1/100,000. Sounds reasonable, right? After all, we use the round-up guesstimate of one in a million airline flights, so estimating that the Shuttle is only one tenth as safe still sounded pretty reassuring.

    But 1/100,000 actually means we could launch one shuttle a day for the following 274 years before we’d have a statistical likelihood of a catastrophe. Wildly unrealistic, especially now that we know that we had two fatal accidents in 122 launches.

    NASA had become a bloated bureaucracy by then, without its original drive.  Now NASA is a sad reflection in a muddy pond of its former self.   

    • #10
  11. Stina Member
    Stina
    @CM

    When setting punishments for toddlers vs older kids, this plays a big rule in how many minutes of timeout to set.

    A young child’s concept of time is far different from their parent’s. When 1 year is half the life you lived, 10 minutes feels like forever.

    Tactile and manipulative math in early grades is important for similar reasons. It helps with associating numbers with quantity.

    • #11
  12. DaveSchmidt Coolidge
    DaveSchmidt
    @DaveSchmidt

    Skyler (View Comment):

    Gary McVey (View Comment):

    When the Space Shuttle was still being designed and built, the contractors were obligated to estimate realistic rates of failure with loss of crew. They came up with 1/100,000. Sounds reasonable, right? After all, we use the round-up guesstimate of one in a million airline flights, so estimating that the Shuttle is only one tenth as safe still sounded pretty reassuring.

    But 1/100,000 actually means we could launch one shuttle a day for the following 274 years before we’d have a statistical likelihood of a catastrophe. Wildly unrealistic, especially now that we know that we had two fatal accidents in 122 launches.

    NASA had become a bloated bureaucracy by then, without its original drive. Now NASA is a sad reflection in a muddy pond of its former self.

    But the outreach to the Islamic world seems to be on track.  

    • #12
  13. Randy Weivoda Moderator
    Randy Weivoda
    @RandyWeivoda

    People get angry when it rains after a weather forecaster said there is only a 2% chance of rain.  People figure 2 is almost 0, so in their minds the forecast said 0.

    • #13
  14. Doctor Robert Member
    Doctor Robert
    @DoctorRobert

    Gary McVey (View Comment):

    When the Space Shuttle was still being designed and built, the contractors were obligated to estimate realistic rates of failure with loss of crew. They came up with 1/100,000. Sounds reasonable, right? After all, we use the round-up guesstimate of one in a million airline flights, so estimating that the Shuttle is only one tenth as safe still sounded pretty reassuring.

    But 1/100,000 actually means we could launch one shuttle a day for the following 274 years before we’d have a statistical likelihood of a catastrophe. Wildly unrealistic, especially now that we know that we had two fatal accidents in 122 launches.

    This number, 1/100,000, is patently absurd.  To place a shuttle built with new technologies atop a 15-story rocket and propel it into space via a controlled explosion, to spend a day or a week or a month in space where there is no margin for error nor hope for backup, then to have it re-enter the atmosphere while generating temperatures in the thousands of degrees is intuitively and inherently dangerous.  The number 1/100,000 should have been rejected before it was proposed.  Our experience in the Mercury, Gemini and Apollo programs, which killed three crew and nearly killed four or five others, should have made that plain.

    This was not innumeracy, this was rank stupidity.  And anyone accepting such a number was stupid, too.

    • #14
  15. Bartholomew Xerxes Ogilvie, Jr. Coolidge
    Bartholomew Xerxes Ogilvie, Jr.
    @BartholomewXerxesOgilvieJr

    Randy Weivoda (View Comment):

    People get angry when it rains after a weather forecaster said there is only a 2% chance of rain. People figure 2 is almost 0, so in their minds the forecast said 0.

    People tend to forget (or don’t understand in the first place) what probability means. If the weather forecast says there’s an 80% chance of rain, and then it doesn’t rain, that does not actually mean that the forecast was wrong. Indeed, you can’t really judge an individual prediction as right or wrong unless it asserts a 100% (or 0%) probability.

    • #15
  16. Skyler Coolidge
    Skyler
    @Skyler

    Bartholomew Xerxes Ogilvie, Jr. (View Comment):

    Randy Weivoda (View Comment):

    People get angry when it rains after a weather forecaster said there is only a 2% chance of rain. People figure 2 is almost 0, so in their minds the forecast said 0.

    People tend to forget (or don’t understand in the first place) what probability means. If the weather forecast says there’s an 80% chance of rain, and then it doesn’t rain, that does not actually mean that the forecast was wrong. Indeed, you can’t really judge an individual prediction as right or wrong unless it asserts a 100% (or 0%) probability.

    Shhh!   There might be a statistician listening!   Don’t upset their voodoo math. 

    • #16
  17. MarciN Member
    MarciN
    @MarciN

    Randy Weivoda (View Comment):

    People get angry when it rains after a weather forecaster said there is only a 2% chance of rain. People figure 2 is almost 0, so in their minds the forecast said 0.

    When the prediction is that there is a “2 percent chance of rain,” I read that to mean that in similar weather conditions, 2 out of 100 times it actually rains. That’s pretty close to a zero chance of rain.

    All of the weather predictions are made by computers these days. It’s really just simple arithmetic: “In this spot, when these conditions occur, 2 out of 100 times it rains.” At least that’s what I’ve always assumed.

    Is there another way to read that number?

    • #17
  18. Randy Weivoda Moderator
    Randy Weivoda
    @RandyWeivoda

    MarciN (View Comment):

    Randy Weivoda (View Comment):

    People get angry when it rains after a weather forecaster said there is only a 2% chance of rain. People figure 2 is almost 0, so in their minds the forecast said 0.

    When the prediction is that there is a “2 percent chance of rain,” I read that to mean that in similar weather conditions, 2 out of 100 times it actually rains. That’s pretty close to a zero chance of rain.

    All of the weather predictions are made by computers these days. It’s really just simple arithmetic: “In this spot, when these conditions occur, 2 out of 10 times it rains.” At least that’s what I’ve always assumed.

    Is there another way to read that number?

    That is how I figure it, too.

    • #18
  19. Jimmy Carter Member
    Jimmy Carter
    @JimmyCarter

    Randy Weivoda (View Comment):

    MarciN (View Comment):

    Randy Weivoda (View Comment):

    People get angry when it rains after a weather forecaster said there is only a 2% chance of rain. People figure 2 is almost 0, so in their minds the forecast said 0.

    When the prediction is that there is a “2 percent chance of rain,” I read that to mean that in similar weather conditions, 2 out of 100 times it actually rains. That’s pretty close to a zero chance of rain.

    All of the weather predictions are made by computers these days. It’s really just simple arithmetic: “In this spot, when these conditions occur, 2 out of 10 times it rains.” At least that’s what I’ve always assumed.

    Is there another way to read that number?

    That is how I figure it, too.

    Years ago, I saw a weather program that explained the “percent chance of rain” is the expected percentage of viewing area coverage that is expected to get rain. 

    Meaning if the local weather station predicted 10% chance of rain, then They are expecting 10% of that station’s viewers will get rain. 

    • #19
  20. MarciN Member
    MarciN
    @MarciN

    Jimmy Carter (View Comment):

    Randy Weivoda (View Comment):

    MarciN (View Comment):

    Randy Weivoda (View Comment):

    People get angry when it rains after a weather forecaster said there is only a 2% chance of rain. People figure 2 is almost 0, so in their minds the forecast said 0.

    When the prediction is that there is a “2 percent chance of rain,” I read that to mean that in similar weather conditions, 2 out of 100 times it actually rains. That’s pretty close to a zero chance of rain.

    All of the weather predictions are made by computers these days. It’s really just simple arithmetic: “In this spot, when these conditions occur, 2 out of 10 times it rains.” At least that’s what I’ve always assumed.

    Is there another way to read that number?

    That is how I figure it, too.

    Years ago, I saw a weather program that explained the “percent chance of rain” is the expected percentage of viewing area coverage that is expected to get rain.

    Meaning if the local weather station predicted 10% chance of rain, then They are expecting 10% of that station’s viewers will get rain.

    :-)  

     

    • #20
  21. Stina Member
    Stina
    @CM

    Jimmy Carter (View Comment):

    Randy Weivoda (View Comment):

    MarciN (View Comment):

    Randy Weivoda (View Comment):

    People get angry when it rains after a weather forecaster said there is only a 2% chance of rain. People figure 2 is almost 0, so in their minds the forecast said 0.

    When the prediction is that there is a “2 percent chance of rain,” I read that to mean that in similar weather conditions, 2 out of 100 times it actually rains. That’s pretty close to a zero chance of rain.

    All of the weather predictions are made by computers these days. It’s really just simple arithmetic: “In this spot, when these conditions occur, 2 out of 10 times it rains.” At least that’s what I’ve always assumed.

    Is there another way to read that number?

    That is how I figure it, too.

    Years ago, I saw a weather program that explained the “percent chance of rain” is the expected percentage of viewing area coverage that is expected to get rain.

    Meaning if the local weather station predicted 10% chance of rain, then They are expecting 10% of that station’s viewers will get rain.

    That’s nuts.

    • #21
  22. Skyler Coolidge
    Skyler
    @Skyler

    Jimmy Carter (View Comment):

    Randy Weivoda (View Comment):

    MarciN (View Comment):

    Randy Weivoda (View Comment):

    People get angry when it rains after a weather forecaster said there is only a 2% chance of rain. People figure 2 is almost 0, so in their minds the forecast said 0.

    When the prediction is that there is a “2 percent chance of rain,” I read that to mean that in similar weather conditions, 2 out of 100 times it actually rains. That’s pretty close to a zero chance of rain.

    All of the weather predictions are made by computers these days. It’s really just simple arithmetic: “In this spot, when these conditions occur, 2 out of 10 times it rains.” At least that’s what I’ve always assumed.

    Is there another way to read that number?

    That is how I figure it, too.

    Years ago, I saw a weather program that explained the “percent chance of rain” is the expected percentage of viewing area coverage that is expected to get rain.

    Meaning if the local weather station predicted 10% chance of rain, then They are expecting 10% of that station’s viewers will get rain.

    That’s my understanding as well.

    • #22
  23. Fake John/Jane Galt Coolidge
    Fake John/Jane Galt
    @FakeJohnJaneGalt

    Currently the weather predicts a 35% chance I will get water in my house.  My mother in laws is at 54%

    • #23
  24. Some Call Me ...Tim Coolidge
    Some Call Me ...Tim
    @SomeCallMeTim

    Last millennium, when I was in high school, a fellow student in our speech class gave a speech on the movie Jaws. He mentioned that the shark was 26 feet long, which most of us knew. Then he took out a tape measure and showed us how long 26 feet really is.  It made quite an impression.  He got an A. 

    You know, Seawriter, I may just read this book after all.  Keeps your stats up. 

    • #24
  25. Seawriter Contributor
    Seawriter
    @Seawriter

    Some Call Me …Tim (View Comment):

    Last millennium, when I was in high school, a fellow student in our speech class gave a speech on the movie Jaws. He mentioned that the shark was 26 feet long, which most of us knew. Then he took out a tape measure and showed us how long 26 feet really is. It made quite an impression. He got an A.

    You know, Seawriter, I may just read this book after all. Keeps your stats up.

    One example the book had was Grace Hopper showing how far light travels in one millisecond by bringing out a 900ft + piece of wire. It was to show the importance of reducing computational speeds.

    • #25
  26. Percival Thatcher
    Percival
    @Percival

    Seawriter (View Comment):

    Some Call Me …Tim (View Comment):

    Last millennium, when I was in high school, a fellow student in our speech class gave a speech on the movie Jaws. He mentioned that the shark was 26 feet long, which most of us knew. Then he took out a tape measure and showed us how long 26 feet really is. It made quite an impression. He got an A.

    You know, Seawriter, I may just read this book after all. Keeps your stats up.

    One example the book had was Grace Hopper showing how far light travels in one millisecond by bringing out a 900ft + piece of wire. It was to show the importance of reducing computational speeds.

    Adm. Hopper used to hand out a nanosecond’s worth of copper wire – 30cm (11.8 in.).

    • #26
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