Imogen I. Morris
“It’s time to let the secret out: Mathematics is not primarily a matter of plugging numbers into formulas and performing rote computations. It is a way of thinking and questioning that may be unfamiliar to many of us, but is available to almost all of us.”From ‘A Mathematician Reads the Newspaper’ by John Allen Paulos
Newspapers and online articles are filled with an attractive, addictive jumble of gossip, headlines, statistics, quotes, tips, life-changing news and celebrities. How do we sort this mess into fact, fiction, or, as I suspect forms the majority, somewhat meaningful half-truths? Making this task harder, is our innate wishful-thinking. As humans, we find it hard to look past our emotions and biases to evaluate articles and arguments in a rational objective way. This is where maths, particularly logic and statistics, can help us. And contrary to common belief, this doesn’t mean we need big calculations, abstraction from reality or number-crunching. Rather, we need to creatively imagine alternative scenarios to encourage a healthy skepticism; we need to puzzle-out mind-boggling statistical paradoxes and we need to use rational-thinking to find a clear path through an otherwise misleading and overcrowded junk-heap of ‘facts’.
In our workshop for the Festival of Creative Learning 2019, we applied a few simple concepts to analyse a selection of print articles and online articles on current news topics. One of the most useful concepts was the difference between good arguments, which are merely those which are reasonable, and valid arguments, which are those that if you believe the assumptions, you have to believe the conclusion. We are more likely to believe an argument is valid if we believe the assumptions and the conclusion. Can you spot which of the following arguments is valid?
- Tidying our houses means that our possessions are easy to find. Therefore tidying our houses makes us feel better.
- Cannibalism is a personal and acceptable choice although it causes harm to people. Therefore it is okay to inflict harm on people.
In the workshop, attendees chose to analyse a varied range of article topics from various sources. The body language of Shamima Begum, the health benefits of pomegranates, a rise in Chinese applications to Scottish universities, antibiotic resistance and a politically-charged article on the SNP investment plan are just a few. Almost universally, we found that the articles appealed to unnamed ‘experts’ for facts, unnamed ‘studies’ for statistics and unnamed ‘critics’ for opinions. Emotionally-charged language such as ‘back-of-a-fag-packet’ or ‘massive ego’ abounded and so did unexplained sciencey-buzzwords e.g. ‘phytochemicals’. The domains of statistics were unspecified. Apparently ‘a quarter of Chinese applications are to Scottish universities’. Is that likely? We believe the author meant ‘out of those to UK universities’. Arguments were never out of a logic textbook, but reconstructing implicit premises and reasoning, we found many that were reasonable. However, particularly the politically charged articles tended to be one-sided, presenting mostly arguments from one side.
Why not have a go at analysing a news article yourself? Here are some tips for conducting a logical and statistics-savvy investigation. Compare your analysis with the way you normally read an article. Do you find that you see flaws in statements that you would usually take on trust?
- Try to determine the thesis of the article. What are the author’s conclusions? What is being argued for and against?
- Is this intended to be one person’s opinion or as an objective news article? Has it been clearly labelled as opinion or fact?
- Search out emotive language. Is it helpful in understanding the feelings of other people, or is it exaggerated and manipulative?
- Look for counterexamples to every conclusion drawn. If they are outlandish, the conclusion is probably reasonable.
- Work out the underlying reasoning behind arguments. Once you have found what you think is the general structure, think again whether the argument is reasonable.
- Look for some reference for every fact (e.g. to a study, expert, book) and evaluate the quality of the reference.
- Do the statistics make sense? Is the value expected or surprising? Sometimes a news article can present the statistic in different ways to make it seem big or small. For example, they could say ‘1000 people in the UK get disease X every year’ which seems like a lot. Or they could say ‘the chances of anyone getting disease X are 0.0015%’ which seems unbelievably small. But in fact, they are equivalent statements! So think of alternative presentations of the statistic before you decide it is large or small.
- Are there any implicit assumptions, including stereotypes or assumptions based on our culture?
- Is the article balanced and fair? Would anyone feel offended by what the article says?
- Is the headline relatively accurate compared to the actual content of the article?
- If there are any photographs, visuals and graphs, do they contradict the content of the article? Are they emotive or do they mislead? Have they been accurately labelled and explained?
If you would like to explore this topic further, here are some of the resources I found inspiring when putting this workshop together.
‘A mathematician reads the newspaper’ by John Allen Paulos
‘Logic’ by Wilfred Hodges
Some interesting resources on using argument technology to analyse an ethical debate:
Collections of spurious correllations:
Guide to logical fallacies with examples of politicians making those fallacies:
BBC podcast on spotting statistical fallacies in the news and understanding statistics in our lives: