He is a writer and speaker on mathematics and the importance of mathematical literacy. He argues for scientific notation being a clearer way to work with larger numbers. The ability to put numbers large and small in the correct context is key to understanding them in an intelligent way. Probability and Coincidence.
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I hoped the book would be an in-depth look at where innumeracy stems from and how to prevent it. He mentions standard things like poor math education, psychological blocks like "math anxiety", and popular misconceptions that math is just cold spiritless arithmetic. He does propose a few solutions here and there, like getting more non-mathematicians writing about math and highlighting the warmth and passion of the subject to get rid of negative stereotypes But I do really like his idea of placing more emphasis on estimation in schools, and especially that people should build personal mental libraries of collections of things for every power of 10 up to at least a trillion.
In other words, you should be able to visualize how many is a thousand of something vs a million of something vs a trillion of something.
For example, the stadium in our town seats 1, people; a wall nearby has 10, bricks; etc. It would be handy for people to be able to judge for themselves whether or not a number cited in the newspaper is realistic. Another cool idea is his logarithmic risk scale or safety scale. If only 1 in 5 million US kids is kidnapped each year, the safety index is a much higher 6. If newspapers and TV started to use this kind of scale, it would be an easier way for people to compare the relative risk of various activities.
So the fact that this has occasionally happened to you or someone you know should not be surprising in the least. The author goes on to bash more pseudoscience in detail; I agree with him but doubt that anybody who believes that stuff in the first place is going to be convinced otherwise by something as simple as facts and math.
Anyway, reasonable people often believe total crap too. It cracks me up that, at one point, phrenological exams were commonly a precondition of employment in big corporations!
That only applies to the ratio - the absolute difference between number of heads and number of tails is NOT guaranteed to approach zero. So if Harry is betting heads and Tom is betting tails, and after the first tosses Harry just happens to be ahead 60 to 40, Harry is likely to stay ahead for a long time.
Another good section is about reward and punishment. This is called regression to the mean. And indeed it makes sense that this kind of play is exactly what you do when solving math problems or coming up with proofs. See, Katie?
John Allen Paulos
These consequences - confused personal decisions, muddled governmental policies, even an increased susceptibility to pseudoscience - are not as visible as are those of illiteracy or general cultural ignorance. Unlike the latter failings, however, innumeracy often afflicts intelligent, well-educated people, the kind of people who can understand the most complicated of legal discussions, the most nuanced of emotional interchanges, but whose eyes glaze over at the mere mention of a number or a probability. Topics addressed include stock scams, parapsychological claims, medical testing, insurance frauds, sports records, sex discrimination, coincidences and chance encounters. Reviews "To combat [innumeracy] John Allen Paulos has concocted the perfect vaccine: this book, which is in many ways better than an entire high school math eductation! Our society would be unimaginably different if the average person truly understood the ideas in this marvelous and important book. It is probably hopelessly optimistic to dream this way, but I hope that Innumeracy might help launch a revolution in math education that would do for innumeracy what Sabin and Salk did for polio.
Innumeracy: Mathematical Illiteracy and Its Consequences
Innumeracy PDF by John Allen Paulos