How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

An important rule of mathematical hygiene: when you’re field-testing a mathematical method, try computing the same thing several different ways. If you get several different answers, something’s wrong with your method. For example: the 2004 bombings at the Atocha train station in Madrid killed almost 200 people. What would be an equivalently deadly bombing at Grand Central Station? The United States has almost seven times the population of Spain. So if you think of 200 people as 0.0004% of the Spanish population, you find that an equivalent attack would kill 1,300 people in the United States. On the other hand, 200 people is 0.006% of the population of Madrid; scaling up to New York City, which is two and a half times as large, gives you 463 victims. Or should we compare the province of Madrid with the state of New York? That gives you something closer to 600. This multiplicity of conclusions should be a red flag. Something is fishy with the method of proportions.