by David Salsburg
Dr. Salsburg's remarkable book focuses not on statistics, but on the mathematicians who shaped the statistical world in which science and social science now functions. It's clear throughout the book how much the author admires the brilliant and the generous pioneers of this field, though he also includes stories of arrogance and dismissive attitudes. He often writes eloquently about his encounters with exemplary texts from mathematicians of the past. His far-ranging anecdotes and references (even including a mathematical poem from the 1500s) introduce real men and women and share stories of their relationships with each other.
There is no record of anyone getting angry at Samuel W. Wilks. He approached everyone he dealt with, whether a new graduate student or a four-star general of the army, with the same informal air. He was nothing but an old Texas farm boy, he would imply, and he knew he had a lot to learn, but he wondered if...What followed this would be a carefully reasoned analysis of the problem at hand.There is also a chapter devoted to a few of the many noteworthy women in mathematics and statistics.
Early in the book, he talks about the difficulties in conducting scientific experiments. For example, classroom students may be asked to calculate the gravity constant but find their calculations vary widely from the published 9.8 meters per seconds squared. Teachers may say it's merely mis-measurement or sloppy techniques, but in fact, that's exactly what happens in every experiment. Scientists repeat an experiment hundreds of times and their measurements are never exact. Plotted all together, they show a distribution. (Even so, let's hope the scientists have less mis-measurement and sloppy techniques in general than the high school students.)
The results of individual experiments are random, in the sense that they are unpredictable. The statistical models of distributions, however, enable us to describe the mathematical nature of that randomness.The style is often humorous.
The reader may recall those terrible moments in high school algebra when the book shifted into word problems...Imagine a word problem where nobody knows how to turn it into a formula, where some of the information is redundant and should not be used, where crucial information is often missing, and where there is no similar example worked out earlier in the textbook. This is what happens when one tries to apply statistical models to real-life problems.There are lots of descriptions of the real-life work of mathematicians which may be of interest to a student considering studying math in college or as a career.
It is better to do mathematics on a chalkboard than on a piece of paper because chalk is easier to erase, and mathematical research is always filled with mistakes. Very few mathematicians can work alone. If you are a mathematician, you need to talk about what you are doing. You need to expose your new ideas to the criticism of others. It is so easy to make mistakes or to include hidden assumptions that you do not see, but that are obvious to them.There are also many examples from real-life, seemingly pulled from our newspaper headlines of economics, sociology, psychology, and health and nutrition. This book provides a useful background for those of us who must sift through all the information thrown at us, giving a basic explanation of what studies may actually show and where they may fall short.
Despite his high praise, he raises interesting questions about the future of statistical practices. I found this discussion particularly interesting as I was also reading Small Is Still Beautiful with its critique of our economic models and indices, many based on the pioneering world of statisticians highlighted in The Lady Tasting Tea. At the end of the book, he asks three questions and answers them in surprising ways:
- Can statistical models be used to make decisions?
- What is the meaning of probability when applied to real life?
- Do people really understand probability?
In logic, there is a clear difference between a proposition that is true and one that is false. But probability introduces the idea that some propositions are probably or almost true. That little bit of resulting unsureness blocks our ability to apply the cold exactness of material implication in dealing with cause and effect.I'm considering assigning this book to my high schoolers in their senior year. I do think it's probably best suited to students who are focused on math, science, or are considering research as a career. Even with few formulas and math explained in words, there are some complicated ideas in the text and lack-luster students may find it more troublesome than enjoyable. For those who are truly intrigued, there is an extensive annotated bibliography, some delightful footnotes, and a helpful timeline.
I have received nothing in exchange for this review. I checked this book out from our library. All opinions are my own. Links to Amazon are affiliate links.
