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:
Have non-obvious answers
Have answers that one can reach via easily estimated qualities
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.