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John Allen Paulos

April 28, 2020

We can readily understand many of the implications of illiteracy - but what about a widespread unfamiliarity with mathematics? Now that most of use have a smartphone calculator in our pocket, do we really need to have an intuitive grasp of mathematical concepts? In Innumeracy, John Allen Paulos explores the growing problem of mathematical illiteracy and its consequences.

The book is filled with 'brain teasers' - scenarios which look straightforward, but can be deceptive if not analyzed properly. You will find nuggets of information on calculating probabilities, rigging card games, conducting polls, debunking pseudoscience, and interpreting statistics. These are both entertaining and educational. For example:

When the leaders of eight Western countries get together for the important business of a summit meeting - having their joint picture taken - there are 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320 different ways in which they can be lined up. Why?

Out of these 40,320 different ways, in how many would President Reagan and Prime Minister Thatcher be standing next to each other? To answer this, assume that Reagan and Thatcher are placed in a large burlap bag. These seven entities (the six remaining leaders and the bag) can be lined up in 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040 ways (invoking the multiplication principle once again).

This number must then be multiplied by two since, once Reagan and Thatcher are removed from the bag, we have a choice as to which one of the two adjacently placed leaders should be placed first. There are thus 10,080 ways for the leaders to line up in which Reagan and Thatcher are standing next to each other.

Hence, if the leaders were randomly lined up, the probability that these two would be standing next to each other is 10,080/40,320 = 1/4.

Innumeracy by John Allen Paulos, pg.

Following along, you can calculate combinations of Mozart waltzes, potential poker hands, and the probability that your lungs contain a molecule that was part of Julius Caesar's last breath. You'll learn to decipher stock market scams, calculate distributions of birthdays in a random crowd, and choose a potential spouse the 'statistical way.'

The back cover claims that "Innumeracy lets us know what we're missing, and how we can do something about it." It certainly delivers on the first part of the promise - however, I found the second to be a little under-represented. To be clear, throughout the book each example of what not to do was followed by an example of what to do - how to properly calculate this probability, or conduct that survey - and perhaps these tactical suggestions meet the author's promise. However, I would have appreciated more data-driven suggestions on what to do about the problem at large. At times, the book also felt rather like a rant, and could have used more structure.

In the conclusion, Paulos mentions that although he is certainly "distressed by a society which depends so completely on mathematics and science and yet seems so indifferent to the innumeracy and scientific illiteracy of so many of its citizens…" the book was not motivated by anger. Instead, he explains, "The desire to arouse a sense of numerical proportion and an appreciation for the irreducibly probabilistic nature of life - this, rather than anger, was the primary motivation for the book."

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