On July 17, 1981, two walkways supported by common braces collapsed at the Kansas City Hyatt Regency Hotel. A priori, they were well designed but two modifications that would not have caused any incident separately and for which the calculations, added together, caused the death of 114 people. On February 25, 1991, during the Gulf War, a Scud missile hit the barracks of the United States Army in Dhahran (Saudi Arabia) and caused 28 deaths and more than a hundred wounded. The method for counting the time in the Patriot missile defense system accumulated a tiny error that increased the longer it remained on (reached a third of a second), so that it was impossible to intercept a missile flying at 6,000 kilometers by time. The patch computer arrived the day after the Dhahran attack. On January 28, 1986, the Challenger space shuttle exploded during its launch. Seven people died. O-rings (donut-shaped) that joined the sections of the reusable propellant rockets failed, but an error was also found in the system used to check if the propellants maintained a perfect circular section.
These are some of the many examples proposed in the essay Mathematical Pifias, just published by the editorial Crítica, of Matt parker, professor and disseminator who has a YouTube channel of your own. In Mathematical Pifias, all kinds of failures related to mathematical errors in fields such as engineering, statistics, computer science or economics are detailed. And although the subtitle of the book states that "Wrong has never been so much fun", many of the mistakes made have had a more tragic than jocular outcome.
"Our human brains are not wired to be good at math by default," Parker explains in the book's introduction, "the skills that allow us to survive and build communities do not necessarily encompass academic mathematics." However, although he says that "all humans are foolish when it comes to learning academic mathematics," he explains that with enough training it is possible to learn to think mathematically.
And it doesn't just talk about more or less complicated things, like equations, algorithms or derivatives. Also with something easier, such as appreciation of quantities. "As humans, we are not good at judging the size of the high numbers," says Parker in the introduction of Mathematical Pifias. And he puts as an example that for people - “instinctively, humans perceive numbers logarithmically, not linearly” - the difference between one million and one billion (one billion) seems the same as between one billion and one billion (one million of millions). And simply, because each step is a thousand times higher, which does not help to visualize figures such as budgets or the public deficit of a country. In these cases, the expert usually sets the example in seconds. Thus, a million seconds is 11 and a half days, a billion seconds is more than 31 years, and a billion more than 31,000 years. In this way, he believes, the “gap” existing between the dimensions of each number is better visualized.
Precisely, Parker dedicates an entire chapter to the measurement of time, with special attention to the partial solutions given throughout history to establish the calendars, where the expert describes some errors caused by the coexistence of several different in different countries. Like the one committed by the Russian shooting team that arrived a couple of weeks late at the 1908 Olympic Games in London because July 10 for the Russians was July 23 in the United Kingdom. Or that there are confusing historical data, such as the date of the landing of English troops on the Island of Re in 1627, which occurred on July 12 of that year in English historical documents, but on July 22 for the French.
Keeping track of time can be a source of problems even for computer systems. "At 3.14 on Tuesday, January 19, 2038, a large part of our modern microprocessors and computers will stop working," Parker predicts. The reason is that many devices that count and store time and dates in seconds in a binary system (that of zeros and ones that use computers) of 32 bits (which implies a maximum figure of 32 in a row) will deplete your account in more than 68 years (beginning to count by convention since the beginning of the year 1970). Of course, there are already many devices that use a 64-bit system, which gives a period of 292.3 billion years, a margin that gives much more security.
Other times, you don't have to count the time badly for something to fail, just cross an imaginary line on the planet. Thus, in February 2007, six modern F-22 fighter jets flew from Japan to Hawaii when all navigation systems stopped working, in an incident that caused no casualties, but some blushing. Simply, the devices had flown over the international date change line (the 180º meridian) and the computers went crazy. Something easy to explain (except perhaps for flat earthers) but that the engineers did not take into account.
Perhaps the most spectacular are the consequences of engineering errors. Parker dedicates many examples. And the expert blames many of those accidents that sometimes, when engineers force the limits of what is possible, suddenly manifests "a hidden facet of mathematics."
And it illustrates it with the evolution of the bridges from the failures that they encountered. Thus, a bridge collapsed in 1826 in Manchester when a platoon of riflemen crossed it and the infrastructure reached the resonant frequency (this is how they describe contagious vibrations). A railway bridge fell in Chester in 1847 in a completely new way of failing after twisting through the center. The concept of "torsional instability" was already perfectly assumed by engineers when another in Tacoma Narrows collapsed in 1940. The wind, passing underneath, caused a “flaming” effect that was fed back until it was thrown. In a new twist of the problems that appear when innovated, it was news London Millennium Bridge, opened in 2000. It closed only two days later, affected by a "synchronous lateral excitation" caused by pedestrians. That is, the bridge was "involuntarily tuned" for the frequency of one hertz (one cycle per second) and it oscillated laterally when groups of passersby walked at the same pace (not necessarily the passage of rifle soldiers from Manchester 170 years before).
The list of mathematical errors is endless. A lake that empties in 1980 in a few hours due to a triangulation error when drilling 36 centimeters wide in an oil survey. Hundreds of people died because the doors of a theater that suffered a fire in 1903 opened inwards. A man who dies in a hospital after suffering a radiation dose one hundred times higher than he needed due to a configuration failure of the system to verify the device settings ...
But not all cases reported by Parker in his essay are catastrophic. Among the funniest are the most harmless, such as London's Fenchurch Street building with a concave glazed facade that during its construction in 2013 it concentrated a “calcining ray” that scorched everything it touched in its path, although it did not cause victims. OR the Harrier plane that promised in its advertising Pepsi (for not doing his calculations well) if he gathered seven million points and that a citizen judicially claimed to verify that for $ 700,000 he could get a military reactor that the Marines bought for more than 20 million.
However, among harmless scumbags, there is an error of representation of a geometric figure that especially bothered the author of the essay. In 2017 he asked the British Parliament, unsuccessfully, to change as all the signals in the country that indicate the proximity of a football field should be replaced. They represent a ball based on hexagons (as if it were a honeycomb) when that two-dimensional geometric figure can never form a spherical shape (yes a cylinder). More correct would be to do it with a truncated icosahedron based on 20 hexagons and 12 pentagons, the most recognizable form that the old soccer balls traditionally had. The refusal of the British government is a disdain for Parker for the teaching of mathematics.
“This book is a collection of my favorite mathematical mistakes of all time,” explains Parker about his essay, although in general, he clarifies: “We all make mistakes. Continually". And despite the large number of clicks listed in the essay, Parker launches a reassuring message for readers at the end of his book: "We must remember that many things that work perfectly around us do so thanks to mathematics."