Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

my favorite method of comparing big numbers to time. 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.

Today’s world is built on mathematics: computer programming, finance, engineering . . . it’s all just math in different guises.

The human brain is an amazing calculation device, but it has evolved to make judgment calls and to estimate outcomes. We are approximation machines. Math, however, can get straight to the correct answer. It can tease out the exact point where things flip from being right to being wrong, from being correct to being incorrect, from being safe to being disastrous.

Computers just blindly follow the rules they are given and do the logical thing, with no regard for what may be the reasonable thing.

Humans are very suspicious of round numbers. We are used to data being messy and not very neat. We take round numbers as a sign of rounded data.

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

people will inevitably make mistakes a certain percentage of the time. The pragmatic approach is to acknowledge this and build a system robust enough to filter mistakes out before they become disasters. 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.

In general, it’s amazing what you can prove if you’re prepared to ignore enough data.

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

Being an engineer, or working on any important mathematics, is a terrifying job.

It can be a tragedy when a mathematician makes a mistake that causes a disaster, but that does not mean we can do without mathematics. We need engineers designing bridges, despite the pressure that comes with it.