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Guesstimation 2.0: Solving Today's Problems on the Back of a Napkin

Lawrence Weinstein
Publisher: 
Princeton University Press
Publication Date: 
2012
Number of Pages: 
377
Format: 
Paperback
Price: 
19.95
ISBN: 
9780691150802
Category: 
General
[Reviewed by
Dominic Klyve
, on
09/3/2012
]

This book is an immediate successor to the author’s Guesstimation, which was co-authored by John Adam. One gets the sense that after writing Guesstimation, Weinstein had so many other ideas about interesting questions to ask that he could fill a second book — and so he did. Does this make the book feel silly or unnecessary? Not at all. It is a delightful volume; I had a hard time putting it down.

Like the earlier book, this one is a series of interesting questions which sound very difficult to answer, but which can be approximated using a few simple estimates and some clever (though elementary) mathematics. The book has two purposes: actually answering the included problems, and teaching readers to do good estimates of problems like these on their own.

One of the challenges of teaching the art of guesstimation is finding good problems. The main idea behind a book like this, of course, is that once one masters the techniques, one can quickly find approximate answers to any of many different problems. Finding good problems to explain these techniques, though, is trickier. The problems must be:

  1. Comprehensible
  2. Interesting
  3. Have non-obvious answers
  4. Have answers that one can reach via easily estimated qualities
  5. Not require specialized knowledge.

The last requirement, of course, is a bit subjective; in fact, the author assumes a wide variety of background knowledge for the different problems in this book. The first chapter contains problems which could be used directly in a quantitative reasoning class. Others are more challenging, and may be more appropriate for science majors.

One of my favorite features of this book was when a question seems unanswerable the author chooses a criterion for an answer and leads the reader through the solution. Consider, for example, “how far should I walk to recycle an aluminum can?” How could one even go about answering this question? The idea here is that the walk is worthwhile if the value of your time in walking to the recycling bin is less than the value of the energy it would take to make a new can. Estimating this last value seems doable, if tricky — most readers of this column probably share with me a basic ignorance of the process of converting bauxite ore into aluminum. Certainly, though, this is a chemical process, and bonds must be broken. The author reminds us a chemical process we interact with almost daily —batteries! I need only glance at a battery in my junk drawer to see that an AA battery has a 1.5V potential. From this starting point, the author leads us quickly through to an estimate of the energy cost in producing an aluminum can.

By necessity, the reader has to learn a few values in the course of doing the estimates. Some of these were so fascinating that I plan to remember them for some time. I now know, for example, that in interstellar space there is about one hydrogen atom per cubic centimeter. I know how many solar neutrinos pass through my body every second (4 x 1014) and how many interact with my atoms (about 10 per day). I now know that the angular resolution of the human eye is about 10-4 radians, and that when I pay the power company for a kilowatt-hour, I’m getting about four million joules! Did I actually need to know any of these facts? No. Do they enrich my life? Absolutely.

I hope to be able to use many of the tricks I learned in the future. I also hope to teach some of them to students. This would make a great secondary textbook in many classes, ranging from quantitative literacy to a science methods class for future educators. A careful study of this book would certainly improve a student’s ability to take a complicated question, break it down into solvable parts, and assemble the parts to find an answer. Because this is quite close to what I want my students to do when faced with a difficult problem in pure mathematics as well, I consider this to be a very valuable book indeed.


Dominic Klyve is an assistant professor of mathematics and statistics at Central Washington University.

Acknowledgments xi
Preface xiii

1 How to Solve Problems 1

2 General Questions 11

  • 2.1 Who unrolled the toilet paper? 13
  • 2.2 Money height 17
  • 2.3 Blotting out the Sun 19
  • 2.4 Really extra-large popcorn 21
  • 2.5 Building volume 25
  • 2.6 Mass of money 29
  • 2.7 A baseball in a glass of beer 33
  • 2.8 Life on the phone 37
  • 2.9 Money under the bridge 41
  • 2.10 Monkeys and Shakespeare 45
  • 2.11 The titans of siren 49
  • 2.12 Airheads at the movies 53
  • 2.13 Heavy cars and heavier people 55
  • 2.14 Peeing in the pool 59

3 Recycling: What Really Matters? 63

  • 3.1 Water bottles 67
  • 3.2 99 bottles of beer on the wall . . . 71
  • 3.3 Can the aluminum 75
  • 3.4 Paper or plastic? 79
  • 3.5 Paper doesn't grow on trees! 83
  • 3.6 The rain in Spain . . . 87
  • 3.7 Bottom feeders 91
  • 3.8 You light up my life! 95

4 The Five Senses 101

  • 4.1 Don't stare at the Sun 103
  • 4.2 Men of vision 105
  • 4.3 Light a single candle 109
  • 4.4 Oh say can you see? 113
  • 4.5 Bigger eyes 117
  • 4.6 They're watching us! 121
  • 4.7 Beam the energy down, Scotty! 125
  • 4.8 Oh say can you hear? 131
  • 4.9 Heavy loads 135

5 Energy and Work 139

  • 5.1 Power up the stairs 143
  • 5.2 Power workout 145
  • 5.3 Water over the dam 149
  • 5.4 A hard nut to crack 153
  • 5.5 Mousetrap cars 155
  • 5.6 Push hard 159
  • 5.7 Pumping car tires 161
  • 5.8 Pumping bike tires 165
  • 5.9 Atomic bombs and confetti 169

6 Energy and Transportation 173

  • 6.1 Gas-powered humans 177
  • 6.2 Driving across country 181
  • 6.3 Keep on trucking 185
  • 6.4 Keep on biking 189
  • 6.5 Keep on training 193
  • 6.6 Keep on flying 197
  • 6.7 To pee or not to pee 201
  • 6.8 Solar-powered cars 205
  • 6.9 Put a doughnut in your tank 209
  • 6.10 Perk up your car 213
  • 6.11 Don't slow down 217
  • 6.12 Throwing tomatoes 219

7 Heavenly Bodies 223

  • 7.1 Orbiting the Sun 227
  • 7.2 Flying off the Earth 229
  • 7.3 The rings of Earth 233
  • 7.4 It is not in the stars to hold our destiny 237
  • 7.5 Orbiting a neutron star 241
  • 7.6 How high can we jump? 245
  • 7.7 Collapsing Sun 249
  • 7.8 Splitting the Moon 253
  • 7.9 Splitting a smaller moon 257
  • 7.10 Spinning faster and slower 263
  • 7.11 Shrinking Sun 267
  • 7.12 Spinning Earth 271
  • 7.13 The dinosaur killer and the day 273
  • 7.14 The Yellowstone volcano and the day 277
  • 7.15 The orbiting Moon 281
  • 7.16 The shortest day 283

8 Materials 289

  • 8.1 Stronger than spider silk 291
  • 8.2 Beanstalk to orbit 295
  • 8.3 Bolt failure 299
  • 8.4 Making mountains out of molecules 303
  • 8.5 Chopping down a tree 307

9 Radiation 311

  • 9.1 Nuclear neutrinos 315
  • 9.2 Neutrinos and you 319
  • 9.3 Solar neutrinos 323
  • 9.4 Supernovas can be dangerous 327
  • 9.5 Reviving ancient bacteria 331
  • 9.6 Decaying protons 335
  • 9.7 Journey to the center of the galaxy 337

Appendix A

  • Dealing with Large Numbers 341
  • A.1 Large Numbers 341
  • A.2 Precision, Lots of Digits, and Lying 343
  • A.3 Numbers and Units 345

Appendix B

  • Pegs to Hang Things On 347

Bibliography 351
Index 355

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