AAAS: Nice figures plus other vital statistics

February 15, 2002

This year's AAAS conference covers everything from geometry jokes to science on the box, the atrocities of September 11 and bioterrorism.

John Allen Paulos is a man with a mission. It is one that, if successful, could transform the way many of us think. He wants to take the mystique out of mathematics.

Long viewed as an abstract and difficult subject, maths is in need of a drastic change of image, particularly in the United Kingdom where there is concern over a shortage of maths teachers in schools and the knock-on effects on universities - some are having to provide extra maths coaching to their science students. Paulos, professor of mathematics at Temple University in Philadelphia, and author of a number of bestselling books, including Innumeracy and A Mathematician Reads the Newspaper , believes part of the problem is the many misconceptions people have about the subject.

He cites five because it is "a nice number". "The first and most pernicious," he says, "is that mathematics is nothing more than computation. The truth is that in many areas of the subject, mathematics has as much to do with computation as writing has to do with typing. Algorithms, rules and drill are certainly not unimportant, but our mathematical problems result more from insufficient exposure to mathematics as a way of thinking and a set of intricately connected higher-level skills than from an inability to compute."

The second is that maths is a completely hierarchical subject, building from arithmetic and algebra to more complex analysis. Paulos says this is not necessarily so and that, although there is a cumulative aspect to some parts of maths, sophisticated notions can be explained to people with little mathematical background. Once when discussing this at a talk, he was asked what "comes after" advanced calculus. He says his questioner was "a bit nonplussed when I responded 'serious gum disease'."

Third is the view that story-telling is not an effective educational tool in mathematics. Paulos, who briefly majored in philosophy and English as an undergraduate, says he has always appreciated how "stories, parables, vignettes and sometimes even jokes help to put formal mathematics into context, illustrate its limitations and emphasise what should be a truism: that numbers and statistics always require interpretation". Several of his books deal with the interplay between words and numbers, a recent column focuses on mathematical metaphors and a new volume explains how maths is rooted in metaphors, not divine inspiration.

The fourth misconception is that only a select few can understand maths. "Almost everybody can develop a workable understanding of numbers and probabilities, of relationships and arguments, of graphs and rates of change and of the ubiquitous role these notions play in everyday life," Paulos says.

Last, there is a romantic view that maths limits freedom, that "numbers numb one to the big questions, to the grandeur of waterfalls and sunsets". Paulos believes that "too many people cling to the usually unarticulated belief that one must choose between life and love on the one hand and numbers and details on the other".

He could add that mathematicians are seen as strange humourless eccentrics, a view that his own work has certainly bucked. His writing is bursting with humour: indeed he has written extensively on the subject of humour, drawing parallels between the formal structure of jokes, mathematical notions of logic and geometry.

Paulos has written extensively on the kind of problems misconceptions about maths lead to. The most obvious is the statistical illiteracy of many journalists, the very people charged with explaining the ever-expanding number of complex issues we face today.

From genetically modified food to MMR paranoia, we are surrounded by statistics, and unless we can understand what they mean, we might as well be floundering in the dark, says Paulos, citing the US presidential election of 2000 - "an examination of the tiny difference between Gore and Bush in the official vote totals, especially given the crude Florida election apparatus, would have shown it to be statistically meaningless. Distinguishing between the two men was a bit like measuring bacteria with a yardstick," he says.

Other recent examples include "fuzzy economics, the phony menace of shark attacks, the frequency of medical errors, the infrequency of the disease-of-the-month, college ratings and the use of weasel words such as 'may' and 'linked'".

He goes on: "Overblown health scares remain ubiquitous, as do stories about miracles and conspiracies, as do political and economic spin doctors. In a million and seventeen different ways, misperceptions about probability and risk are quite apparent wherever we turn."

Paulos is doing his bit to try to improve journalistic standards, but it is an uphill struggle. As an adjunct professor at the prestigious Columbia School of Journalism, he is heading a course on numbers in the news.

"Columbia hopes it will become a national model," he says, adding that he is not so optimistic.

He wants to see journalists use "the same scepticism they bring to most other subjects" when they encounter statistics and numbers. "They may question a person's motives, but all he has to do is provide a few statistics and their eyes glaze over and they acquiesce to whatever is being said."

Part of the problem is the type of people drawn to journalism. "Simple statistics are not that difficult, but, often, people attracted to journalism are those who hated science and maths. They are people who like to tell a good story, which can mean ignoring things that get in the way of that story."

Some issues, such as climate change, are so complicated that they are more a matter of opinion. Paulos's advice to journalists is that they should report all sides and give some sense of perspective and not just a list of anecdotes. For instance, they should mention if there is a general consensus about a particular subject, such as the fact that most scientists agree that global warming exists. He is against what he calls "phoney balancing", such as when an astrologer's views are given equal weight to an astronomer's. "Astrology is clearly nonsense," he says. Journalists also need to point out where statistics are coming from. "Unless you know that, there is no way to evaluate it. There is a nebulous borderland between maths, psychology and public policy that needs to be further explored. People need to know what the motivations behind different suppliers of statistics are, whether they are the government or a pressure group. It would help if schools pointed out how figures are manipulated, if they taught people to think critically about numbers and about good mental hygiene.

"One aspect of what I do," says Paulos, a self-confessed newspaper addict, "is to mathematically deconstruct news stories. It needs re-doing continually. It is like taking out the garbage. It keeps collecting. It would be helpful if newspapers had ombudsmen and if one of their jobs was to ask if articles make sense on a surface level and whether they are the right measure. To the standard litany of journalistic questions - what, who, where, when and how - could be added 'how likely'. Journalists should be truth tellers."

He is fairly optimistic that mathematical literacy is improving, despite "the stunning innumeracy of so many (including those in high places)". "There is a greater awareness of the importance of numbers, probability, logic and mathematics generally than there was ten years ago," he says, citing the success of recent biographies of mathematicians Paul Erdos, Ramanujan and John Nash, films with a mathematical theme such as Good Will Hunting , Pi and A Beautiful Mind (about Nash), plays such as Copenhagen and Proof and books on cryptography, Fermat's last theorem and chaos. Moreover, "we are even more awash in numbers, percentages, rates, probabilities and statistics of all sorts than we were then, and their importance is obvious to more of us".

But what about his own efforts to improve statistical literacy? He says modestly that the feedback he gets is positive, but that his readers are "a biased sample of the population".

"I'd like to claim that my books and columns have helped lessen innumeracy and pique popular interest in mathematics but, being numerate, I know that correlation does not necessarily mean causation and I can take credit for only 0.3952 per cent of the improvement in our collective mathematical savvy. (I might be wrong about that last figure.) Alas, however, almost any major news event serves as a reminder of how far we have to go."

Whether he is right to be so negative about his own efforts, his books have done what many might consider impossible - pushing maths right up there with Jackie Collins and Harry Potter.

Mandy Garner John Allen Paulos is speaking at the Science and Society symposium, "Show me the data! Wanted: more accuracy in media reporting", on February 15.

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