You might think you have a phone number, but you don’t really. It’s not a number: you’re not going to perform any mathematical operations on it, and if it starts with a zero then things will go wrong if you do what you would normally do with a number that starts with zero, ie omit it. For this reason, as the “standup mathematician” Matt Parker explains with amusing pedantry, he would really rather we call them “phone digits”.
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This is an innocent example of our general fuzziness about maths, where intuitions can go drastically awry. “As humans,” Parker notes for example, “we are not good at judging the size of large numbers.” A million seconds, he points out, is less than two weeks, but a billion seconds is 31 years. And even the mathematics of professionals can fail in critical situations, if our models of how things behave are incomplete. Before the Tacoma Narrows bridge in Washington State collapsed after twisting like a ribbon in the wind, no one had foreseen that kind of “flutter” feedback loop. No one imagined, either, that a single exercise class on one floor could make a whole skyscraper shake, as one did in South Korea in 2011. (The song playing, Snap’s “The Power”, encouraged people to jump up and down at a tempo that matched a resonant frequency of the building.) There may well remain other principles yet to be discovered as we make everything bigger and longer.
In the meantime, engineers continue to make mistakes as elementary as confusing units of measurement. Parker tells the alarming story, for instance, of a passenger jet on which both engines failed midflight because the fuel had been weighed in pounds rather than kilograms. (Luckily, the pilot was able to fly the plane down like a glider and land safely.) Famously, too, a Martian probe burned up in the atmosphere because one piece of software was using imperial units while the rest was expecting metric.
On one passenger jet both engines failed midflight because the fuel had been weighed in pounds rather than kilograms
While such examples come with serious lessons about ways to make systems more tolerant of user failure (because users will always fail), Parker is consistently very funny. His chapter on geometrical errors reports with pride that he started a petition for the UK government to replace all football signs – which show an impossible football made entirely out of hexagons – with the mathematically correct figure, comprising 20 hexagons and 12 pentagons. He will teach you to look carefully at any PR image that involves a set of interlocking gears, because chances are the whole mechanism would not be able to move at all. Of one such picture featuring Lego people placed inside such a fatally stationary arrangement of cogs, he writes: “The longer I think about it, the more I’m convinced that this does actually make a great analogy for workplace teamwork.” There are, too, highly entertaining discussions about probability, rounding errors, randomness, correlation, and other concepts we commonly get wrong unless we think really hard.
Fair warning is here given, too, of another Y2K-style bug that is due to hit in 2038. To keep time, computer clocks are all silently counting the seconds since 1970: Parker is the sort of person, he happily tells us, who went out on a boozy night with his mates in 2009 “to celebrate 1,234,567,890 seconds having passed”. Unfortunately, the computers were only given a 32-digit binary address to keep the total number in, and it will run out of space in 19 years, shutting the computers down, unless the problem is fixed. Parker is, of course, the kind of person who knows that the original Y2K bug really was a huge danger: “Through a massive effort, almost everything was updated. But a disaster averted does not mean it was never a threat in the first place.”
Computers, indeed, are a rich source of examples of when maths goes wrong. Databases, Parker points out, are only as good as the data entered into them, and bad data can be worse than none at all. Most pragmatically, he points to a multitude of real-world threats created by the widespread habit of using Microsoft’s Excel software as an ersatz database, rather than as a simple spreadsheet manager. A lot of cell biologists use Excel, he reports, which tends to cause problems because there are genes called MARCH5 and SEP15. Type those into Excel and it will helpfully translate them into dates.
It would be easy to blame poor Excel for such garbling – except that, as Parker insists, people really shouldn’t be using it that way in the first place. Here, as so very often in all walks of modern life, the most appropriate response is the old IT support engineer’s sarcastic acronym, PEBCAK: problem exists between chair and keyboard.
• Humble Pi: A Comedy of Maths Errors by Matt Parker is published by Allen Lane (£20). To order a copy go to guardianbookshop.com. Free UK p&p on all online orders over £15.