Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

Humans instinctively perceive numbers logarithmically, not linearly. A young child or someone who has not been indoctrinated by education will place three halfway between one and nine.

When we are operating beyond intuition, we can do the most interesting things, but this is also where we are at our most vulnerable.

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.

Allowing for the two types of year (leap and normal), and the seven possible days a year can start on, there are only fourteen calendars to choose from.

This is a common theme in human progress. We make things beyond what we understand, as we always have done. Steam engines worked before we had a theory of thermodynamics; vaccines were developed before we knew how the immune system works; aircraft continue to fly to this day, despite the many gaps in our understanding of aerodynamics. 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.

We’ve evolved to jump to probabilistic conclusions that give us the greatest chance of survival, not the most accurate result. In my imaginary cartoon version of human evolution, the false positives of assuming there is a danger when there isn’t are usually not punished as severely as when a human underestimates a risk and gets eaten. The selection pressure is not on accuracy. Wrong and alive is evolutionarily better than correct and dead.

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 September 2016 the BBC news reported that both the US and China had signed up to the Paris Agreement on climate change, summarizing the agreement like this: “countries agreed to cut emissions enough to keep the global average rise in temperatures below 2°C (36°F).”

an example of “survivor bias.” It’s like a manager throwing half the applications for a job into the bin at random because they don’t want to hire any unlucky people. Just because something survives does not mean it is significant.

lot of nostalgia about how things were manufactured better in the past comes down to survivor bias.

The numbers produced by statistics are the start of finding the answer, not the end. It takes a bit of common sense and clever insight to go from the statistics to the actual answer.

A random sequence can be defined as any sequence that is equal to or shorter than any description of it.

Mathematicians aren’t people who find math easy; they’re people who enjoy how hard it is.”