Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

An error of 0.000095 percent may not feel like much; it is only off by one part in a million. And when the time value is small, the error is also small. But the problem with a percentage error is that, as the value gets bigger, the error grows with it. The longer the Patriot system was running, the larger the time value became and the bigger the error accumulated was. When the Scud missile was launched that day, the Patriot system near the target had been on for about a hundred continuous hours, roughly 360,000 seconds. That’s about a third of a million seconds. So the error was about a third of a second. A third of second does not feel very long until you’re tracking a missile going 3,800 mph. In a third of a second a Scud missile can move almost 2,000 feet. It is very hard to track and intercept something that is a third of a mile away from where you expect it to be. The Patriot system was unable to stop the Scud missile, and it hit the US base, killing twenty-eight soldiers and injuring about a hundred other people.