Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

To be fair, that is an overestimate, because some of the letters in a UK postcode describe the geographic area. The “GU” in my example is for the Guildford area; “SW” and “E” are the southwest and east parts of London respectively. If the UK wanted to really max out its postcode format by allowing all letters and digits in any positions of two groups of three or four symbols each, then there would be 2,980,015,017,984. Enough for one unique code for each patch of ground of about thirty square centimeters. I think that’s a great idea. When I do my online grocery shopping, I could give each thing I’m ordering the delivery address of the exact cupboard it needs to end up in.

But because phone numbers, historically, needed to be memorized, there has been pressure to keep them short. Thus there are not enough of them to throw away, so phone numbers get recycled; when you cancel a phone contract, your number is not deleted: it’s given to someone else. The chance of a number directly linked to your personal information eventually being reallocated to someone is a definite security risk.

On January 17, 1987, in Yakima Valley Memorial Hospital in Washington (now Virginia Mason Memorial), a patient was due to receive eighty-six rads from a Therac-25 machine

Instead of eighty-six rads, the patient may have received around 8,000 to 10,000 rads. He died in April that year from complications because of this radiation overdose.

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.

Even more depressing is the fact that the US Army knew about this problem and, on February 16, 1991, it had released a new version of the software to fix it. As this would take a while to distribute to all the Patriot systems, a message was also sent out to warn Patriot users not to let the system run continuously for long periods of time. But what constituted a “long period of time” was not specified. As well as the mathematical problems, those twenty-eight deaths were also the result of poorly fixed code and the lack of a message simply saying to restart once a day. The software fix arrived at the base in Dhahran on February 26. The day after the missile attack.

In September 1997, the cruiser USS Yorktown lost all power because its computer control system tried to divide by zero. It was being used by the navy to test their Smart Ship project: putting computers running Windows on warships to automate part of the ship’s running and reduce the crew by around 10 percent. Given that it left the ship floating dead in the water for over two hours, it certainly succeeded in giving the crew some time off.

A change below the precision of the original number is meaningless.

Changing the clocks at the beginning and end of daylight saving time can cause people a lot of stress. Forget about it, and you’ll either show up at work an hour early and embarrassed or an hour late and fired. I actually look forward to the clocks going back, because of that extra hour of sleep. Except I don’t squander it right away: I save it up for a few days, until I really need it. I’ve seriously considered taking an hour off every Friday night, when it will barely be noticed, and spending it on Mondays: sleeping in for an extra hour.

on the Monday after the clocks go forward there is a 24 percent increase in heart attacks. Daylight saving time is literally killing people.

It seems the clocks going forward and depriving people of sleep did cause extra heart attacks, but only in people who would have had a heart attack at some point anyway.

It is our nature to want to blame a human when things go wrong. But individual human errors are unavoidable. Simply telling people not to make any mistakes is a naive way to try to avoid accidents and disasters.

it acknowledges that people will inevitably make mistakes a certain percentage of the time.

When a disaster occurs, it is a system-wide failure, and it may not be fair to find a single human to take the blame.

If humans are going to continue to engineer things beyond what we can perceive, then we need to also use the same intelligence to build systems that allow them to be used and maintained by actual humans. Or, to put it another way, if the bolts are too similar to tell apart, write the product number on them.

Fahrenheit proposed the scale that bears his name in 1724, and the zero point was based on a frigorific mixture. If “frigorific” has not instantly become your new favorite word, you’re cold and dead inside.

A frigorific mixture is a pile of chemical substances that will always stabilize to the same temperature, so it makes for a good reference point. In this case, if you give ammonium chloride, water, and ice a good stir, they will end up at 0°F. If you mix just water and ice, it will be 32°F, and the far less frigorific mixture of human blood (while still inside a healthy human) was 96°F (since redefined to 98.6°F). While these were Fahrenheit’s original reference points, the modern Fahrenheit scale has since been adjusted and is now pinned to water freezing at 32°F and boiling at 212°F. Frigorific!

Goldacre has since started the AllTrials campaign to get all drug-trial data, future and past, released. Check out his book Bad Pharma for more details.

an exercise in showing that correlation does not mean causation.

And, of course, some correlations happen to be completely random. If enough data sets are compared, sooner or later there will be two that match almost perfectly completely by accident. There is even a Spurious Correlations website, which can search through publicly available data and find matches for you. I did a quick check against the number of people in the United States who obtained a PhD in mathematics. Between 1999 and 2009, the number of math doctorates awarded had an 87 percent correlation with the “Number of people who tripped over their own two feet and died.” (Provided without comment.)

No computer can be random unaided: computers are built to follow instructions exactly; processors are built to predictably do the correct thing every time. Making a computer do something unexpected is a difficult feat. You can’t have a line of code saying do something random and get a truly random number without a specialized component being attached to the computer.

If something goes wrong browsing the web, many people know that error 404 means the site could not be found. Actually, any website error like this starting with a 4 means the fault was at the user’s end (like 403: trying to access a forbidden page), and codes starting with a 5 are the fault of the server. Error code 503 means the server was unavailable; 507 means its storage is too full.