Innumeracy: Mathematical Illiteracy and Its Consequences
You don’t know numbers. Oh you might have gotten through school learning just enough of math to get through tests and graduate. But you don’t know numbers. The majority of us don’t know numbers. We have no idea how probability and statistics work. We really have only a passing knowledge of how numbers really affect our lives.
John Allen Paulos points this out in Innumeracy. This book is not going to teach you math. This book isn’t about that. This book will show you how the population really has no clue about how math works. And Paulos is pretty upset about that.
What this book will do is give you a quick introduction on how probably works. On how statistics work. How we tend to fall into logical fallacies based on our ignorance on how certain concepts like regression to the mean and the law of large numbers work.
Paulos is one of the very few mathematicians that can write clearly and convey complex math problems in a way that is easily understandable. Granted there can only be so much an author can do to simplify how say the probability of a certain combination of dice being rolled. The reader has to meet Paulos half way and really pay attention to the math concepts in the book.
With that being said, everyone could benefit from reading it. Paulos makes a good point half way through the book when commenting on the state of math education. Math teachers more often than not do not know their subject. They aren’t trained in math. And math needs more than just memorizing tables. Math concepts help in logic and problem solving. Remember that cold sweat when you got to the word problems in math class? Paulos makes the point that those are what math really is and should be taught that way. More advanced math is more like word problems than, say, solving a quadratic equation. He does make a joke that maybe math teachers should spend a few weeks teaching graduate math and the professors can switch places and teach middle school math. The kids would benefit greatly form it and the teachers really couldnt’ do much harm to the graduate students. Win-win so to speak.
But this idea that the way math is taught is the underlying problem with why our society, which relies so much on math, does not understand it. This feeds into how we treat statistics (as some kind of lie because Mark Twain’s famous quote) even though statistics, when used properly and done properly, give us the best possible view of probability. Paulos makes the analogy that statistics are to probability as engineering is to physics. One is the applied science (statistics, engineering) the other the theoretical science (probability, physics). It is an apt comparison since we probably know as much about engineering as we do about statistics.
Paulos shows that good statistics have solid methods behind them and when they are reported have the qualifying figures to show the methodology. The best example he uses is the percentage of women that will get breast cancer in, 1987 numbers, 1 in 11 women would develop breast cancer. But when you look at the numbers, this 1 in 11 statistic looses its shock value when you look at how many women 30 years old (1in 1000) 50 years old(1in 500) and 60 to 80 years old (1 in 250). This points out how statistics need some sort of frame in order to interpret them.
Since most people don’t understand how statistics come about they tend to think that statistics are either just made up or manipulated to set forth a personal agenda. At times they are, but good statistics with great methodology are fair representations of reality.
This is the underlying theme of Paulos’s book. He wants people to learn to think critically and know what questions to ask as well as know what to look for when dealing with numbers in real life.
Innumeracy is definitely a book worth picking up.
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