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.

     

The state of corona virus knowledge as of today (May 3, 2020)

SARS-CoV-2 (the virus) and covid -19 (the illness)

Here’s what “we” know and don’t know as of 2020-05-01. “We” are the people who’ve collected and interpreted the data. “We know” means the data strongly support the conclusion. “We don’t know” means there are insufficient data to draw a conclusion. Compiled from reports in science news magazines, media reports, and Q & A sessions with experts.-WEK

A)    We know: Some people are infected with the virus but don’t get sick.
    We don’t know: how many.

B)    We know that the effects of the virus range from zero to death; and mild to lethal complications.
    We don’t know: Why the virus has such a wide range of effects.

C)    We know: there is a time between infection and symptoms during which a person will be infectious.
    We don’t know: the actual range of both time and severity of this infectious state.

D)    We know: that people who’ve been infected will have anti-bodies in their blood;
    We don’t know: whether the presence of antibodies gives immunity, nor what degree  of immunity, nor how long such immunity might last.

E)    We know: there will be second wave of infection, and probably a third and fourth one,
    We don’t know: how bad these subsequent waves will be.

F)    We know: that some of the economic and social effects will be permanent.
    We don’t know: which effects, nor how these effects might change over time, nor what  the knock-on effects will be.

G)    We know: covid-19 will become another infectious disease that will take its yearly toll.
    We don’t know: when that will happen, nor how common or lethal covid-19 will be.

H)    We know: that some anti-viral treatments show some activity against SARS-CoV-2.
    We don’t know: whether that activity will be good enough for effective tretament.

I)    We know: effective treatments and a vaccine will reduce the danger of covid-19 to that of the flu.
    We don’t know: which treatments will be effective.
    We don’t know: whether a vaccine is possible, and if possible, how well it is likely to work.

J)    We know: the counter-measures have reduced infection rates.
    We don’t know: how effective those counter measures actually were.

K)    We know: that a combination of dry cough and high fever, with some other signs such as difficulty breathing, indicate covid-19. But only a test can confirm the diagnosis.
    We don’t know: what other signs and symptoms may be indicators of covid-19.

Update 2020 05 04: UK doctors have observed covid-19 patients with low and extremely low blood oxygen levels, but without the usual distress. Another puzzle.