By the summer of 1563, all of Britain had plunged into chaos over religion and the Reformation.

King Henry VIII broke away from the Catholic church back in the 1530s, sparking a near civil war within the kingdom. Protestants killed Catholics, Catholics killed Protestants, and extreme social tensions lasted for decades.

Universities were at the heart of this conflict; rather than focus on real subjects like science and mathematics, students and professors became radical social activists and turned their schools into ideological echo chambers. Sound familiar?

One of the few students who actually wanted to learn was a Scottish teenager named John Napier; Napier had been enrolled at the University of St. Andrews at the time, but he quickly realized that he would never learn a damn thing in that environment. So he dropped out… and started traveling in search of a real education.

No one quite knows exactly where he went or what he did. But when he returned to Scotland eight years later as a young man, Napier had become an intellectual giant.

You might not have ever heard of him, but John Napier was truly one of the great minds of his era. And modern science owes a tremendous debt to his work… in particular his development of logarithms.

If it’s been a few years since you studied math (or ‘maths’ for my British friends), logarithms are the inverse of exponential functions.

Simple example: we know that 102 (or 10 squared) = 10 x 10 = 100. So, the number 10 raised to the power of 2 equals 100.

The inverse of that is to say that the ‘base 10’ logarithm of 100 = 2. Or in mathematical terms, 100 log10 = 2

Napier devised an entire system of logarithms. And this was actually a tremendous leap forward in mathematics, because logarithms made it so much easier for scientists and researchers to calculate solutions to complex problems.

One of the many important applications to come out of Napier’s work is the concept of ‘logarithmic decay,’ which models many real world phenomena.

The idea behind logarithmic decay is that something declines very, very slowly at first.

But, over a long period of time, the rate of decline becomes faster… and faster… and faster.

If you look at it on a graph, logarithmic decay basically looks like a horizontal line that almost imperceptibly arcs gently downwards. But eventually the arc downward becomes steeper and steeper until it’s practically a vertical line down.

Logarithmic decay is like how Hemingway famously described going bankrupt in The Sun Also Rises-- “Gradually, then suddenly.”

In fact logarithmic decay is a great way to describe social and financial decline. Even the rise and fall of superpowers are often logarithmic in scale. The Kingdom of France in the 1700s infamously fell gradually… then suddenly.