April 27, 2010

Numeracy and the news

I recently purchased this book at a charity book sale. Although published in 1995 it remains as relevant as ever, as the quality of our daily newspapers is only ever as good as the mathematical ideas embedded within the stories. It's an informative, humourous, and quick read, at roughly 200 pages. Paulos lays the book out in  the style of a newspaper and each chapter (or article) is just a few pages long. 

While certainly worth a read on your own, here are some of his arguments that really leaped off the pages:

- Many of us, including otherwise sharp journalists, have a "strong disposition to make judgments or evaluations in light of the first thing that comes to mind" (p. 14). This is understood as the availability error, and Paulos advises us to be wary of "facile parallels and analogies" (p. 16). He encourages us to "search for interpretations or associations that undermine the prevailing one that is so temptingly available" (p. 17).

- Due to the interconnectedness of the variables in question that exist within nonlinear dynamic systems, "much economic and political commentary and forecast are fatuous nonsense" (p. 19). Similarly, specific, long-range weather forecasts are "virtually worthless" (p. 24). A key reason for this unreliability is the Butterfly Effect, imperceptible changes in original conditions that lead to considerable deviation.

- Game theory demonstrates that "the conscious randomizing of choices can, if done right, maximize one's effectiveness" [emphasis mine] (p. 30). Hmmm...

- We tend to get correlation and causation confused. The presence of one does not indicate the presence of the other. Just so yo know, "the degree of correlation between two variables depends critically on the range of the variables considered" (p. 65). Moreover, "an understanding of the mathematical notion of  conditional probability is crucial to the proper interpretation of statistics" (p. 135).

- If it helps, Paulos reminds us that "what's critical about a random sample is its absolute size, not its percentage of the population" (137).  


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