Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

We know a million, a billion, and a trillion are different sizes, but we often don’t appreciate the staggering increases between them. A million seconds from now is just shy of eleven days and fourteen hours. Not so bad. I could wait that long. It’s within two weeks. A billion seconds is over thirty-one years. A trillion seconds from now is after the year 33,700 CE.

The universe has given us only two units of time: the year and the day. Everything else is the creation of humankind to try to make life easier.

A political committee is rarely a good solution to a mathematical problem.

The Julian calendar is too short compared to the orbit. But it is too long compared to the seasons. Bizarrely, the seasons don’t even exactly match the orbital year.

Thankfully, if there’s one thing a pope can do, it’s convince a lot of people to change their behavior for seemingly arbitrary reasons.

But astronomy does give Julius Caesar the last laugh. The unit of a light-year, that is, the distance traveled by light in a year (in a vacuum) is specified using the Julian year of 365.25 days. So we measure our current cosmos using a unit in part defined by an ancient Roman.

In February 2007, six F-22s were flying from Hawaii to Japan when all their systems crashed at once. All navigation systems went offline, the fuel systems went, and even some of the communication systems were out. This was not triggered by an enemy attack or clever sabotage. The aircraft had merely flown over the International Date Line.

When theory lags behind application, there will always be mathematical surprises lying in wait. The important thing is that we learn from these inevitable mistakes and don’t repeat them.

And people are not buying tickets for the expected value; they are buying the permission to dream. Having a non-zero chance of winning a life-changing amount of money allows someone to dream about that version of their life.

My favorite is an ensemble of tests called the diehard package. Sadly, this does not involve throwing the numbers off the Nakatomi Tower or making them crawl through an air vent. But, in my experience, it does help if during the process you yell, “Yippee ki-yay, number-function!”

I think, due to survivor bias, programmers tend to be a sadistic bunch who enjoy frustration.

If a new system is implemented, humans can be very resourceful when finding new ways to make mistakes.