### October 11, 2011 Happy Birthday, Lewis F. Richardson

(and me!)

Have you ever wondered what “higher mathematics” is used for?

Well, Lewis Richardson (born on this day in 1881) used math to forecast weather—and even to study the causes and prevention of war! Richardson also did pioneering work on fractals as he studied the measurement of coastlines and borders. In addition to being a mathematician, Richardson was a physicist, psychologist, and pacifist.

What, what, and what?

• Pioneer: One who settles land that is far from already established towns and cities. OR one who works in a newly-established area of science, technology, etc.
• Physicist: One who studies the matter, energy, and forces of the universe.
• Psychologist: One who studies human behavior and mental processes.
• Pacifist: One who believes that disputes between nations and peoples can and should be settled without war or violence.

What's up with the weather?

Weather is really hard to accurately predict because there are so many factors that affect it, because the atmosphere is chaotic, and because it takes massive computing power to solve the equations that describe the atmosphere.

Richardson suggested using differential equations to forecast weather—and he was right, that's what we use today—but there were no computers or electronic calculators back then. An attempt he made to predict the weather through equations was really off, because he didn't use what we now call smoothing techniques. However, when a modern analyst applied these techniques to Richardson's work, he found out that Richardson's equations were essentially correct. This is considered a remarkable achievement, since he solved the equations by hand while working for an ambulance service.

Of course, Richardson's technique couldn't work while “computers” and “calculators” still mean a bunch of people sitting around solving equations. By the time human computers solved the equations, the forecast was already long out of date. Even the first computers used in weather forecasting took 24 hours to produce a 24-hour forecast.

Nowadays, we have a lot more data to help make our weather predictions—including satellite data and worldwide instruments—and of course we have huge computers to work on all that data. Still, we can only forecast about 10 to 16 days in the future, and our predictions get less accurate near the end of those forecast periods.

War and Borders and Fractals

In his research about war between neighboring countries, Richardson looked for data about length of borders and coastlines, in an effort to find out if there was a correlation between length of borders and frequency of war. However, he found out that different sources gave very different figures for the length of any particular border. He began to research how people made these measurements, and he found out that the smaller the ruler used to measure a coastline or border, the larger the resulting length. To see why, look at these pictures of measurements of the coastline of the British isle:

This Richardson Effect is now considered one part of the birth of the mathematics of fractals.

For more on coastlines and fractals, go here, here, or here.