Mathematics and the News

 

 

John Allen Paulos. A Mathematician Reads the Newspaper (1995) I bought this book because I’d read Paulos’s Innumeracy, a seminal book that I think every teacher should read. This book extends one of his themes, that the media are a prime source of innumeracy, and so tend to distort and misinform. Each section corresponds to a section of the paper, News, Sports, the Arts, etc. The misuse or misreporting of statistics features in all sections, but the unwarranted surprise at coincidences, and confidence in economic and sports forecasts, together come a close second.
     Once again, Paulos muses on the vagaries of voting. Every voting system ever attempted has produced results that annoy a large section, sometimes even the majority, of voters. If he were to write today, he would note the vacuousness of political polling, which always produces more or less misleading results.
     But mathematics is about patterns and processes, so even the society section, with its reports about charity balls, the doings of famous people, etc, gives opportunity for mathematical musing about relationship networks, and the interconnectedness of our social circles, which Facebook et al have made more obvious than ever in the 25 years since Paulos wrote the book.
     This was a re-read, I enjoyed the book, but not as much as Innumeracy. ***

     Update 2020 08 13: Percentages are real problem.
     One of the most common errors is to report a percentage change without reporting the base rate. For example, "XYZ increases the cancer of some obscure organ  by 150%". True, it increases the rate from 1 per 100,000 per year to 3 per 100,000 per year.
     Another egregious error is to confuse percentage points with percentages. Thus, "Unemployment rate increases 2 %". Yup, it rose  from 5% to 7%, which is an increase of 2/5, or 40%.

   Update 2020 12 22: Raw numbers vs Rates: How to misreport covid-19

     Every day now we hear the number of new cases and deaths from covid-19. Almost never the rates. For example, Ontario reported some 2100 new cases the other day, while Alberta reported about 1800. But Ontario has roughly three times the population of Alberta, so the rate in Alberta is about three times higher.

     The mistake is to treat every jurisdiction equally, which hardly ever makes sense. The same error shows up when reporting miscellaneous numbers about cities and towns. Such as crime rates. Small towns naturally have fewer crimes, but related to population, the crime rates are usually higher than in the large cities.

     Related to time, the rates are of course lower. Hence the pained astonishment when a neighbour murders his family. This suggests that we pay more attention to events along our individual time-lines, and less to events within the communtiy at large. Our preception biases mislead us.

     Rule of thumb: Do The Arithmetic! Always calculate the rates.