On March 11, Japan was hit by an earthquake and tsunami 9.0 in magnitude that killed thousands of people and left many more missing. This disaster created a chain of events that is heavily influencing people’s lives around the world.
The Japanese yen hit an all-time high right after the disaster. This rise in the yen is probably due to Japanese households and investors selling foreign currencies to buy yen after the tsunami. A stronger yen hurts the Japanese economy because consumers abroad have less buying power, making Japanese exports seem more expensive, therefore producing a decline in sales for Japanese manufacturers.
To combat this phenomenon, many nations have joined together in a coalition in hopes of decreasing the volatility of the yen. The nations involved are members of the G7, a group of seven industrialized nations whose finance ministers meet several times a year to discuss economic policy. The members are the United States, France, Germany, Italy, Japan, United Kingdom, and Canada. Through a combined effort, the G7 hopes to facilitate Japan to a faster recovery.
A more pressing issue facing the Japanese government is the potential meltdown of six nuclear reactors in Japan. A nuclear reactor contains water and nuclear fuel that create a controlled reaction that heats the water to 550 degrees Fahrenheit to generate electricity. When a natural disaster occurs, the nuclear reactors are designed to shut down the reaction and backup generators would then pump water into the reactor to cool the fuel. The problem caused by the earthquake and tsunami is that the backup generators do not have enough power to pump water through the reactor. So the fuel rods boil off the water and overheat, causing explosions like the ones at Reactors 1 and 3.
Right now, workers at the plants are pumping seawater into the nuclear reactors to prevent a complete meltdown which would release radioactive substances. Although the reactors seem to have stabilized by the seawater pumping, traces of radioactive iodine have been found in milk from a farm close to the plant in Fukushima as well as in tap water in Tokyo. The half life of radioactive iodine is short but if absorbed, the radioactive iodine may pose health risks to the human body.
Pick up an almanac, the Guinness Book of World Records or any newspaper and write down all the numbers that you find. Most people would expect that the first digits of these numbers would be uniformly distributed from one to nine. However, amazingly, you are likely to find that 30% of these numbers begin with the digit 1!
This unusual phenomenon is known as Benford’s Law, which is not a rigid mathematical law, but more of an observation. Rather than an equal 11% chance of each digit appearing as the first digit in a set of real-world data, the distribution is matches more with a logarithmic scale, with a 30.1% chance that the digit one appears as the first digit of a data point and only a 4.6% chance that the digit nine appears as the first digit of a data point.
There are reasons for Benford’s Law, but here are some logical reasons. If we take a random number and list the numbers less than it, the digit 1 will always appear the most. For example, 40% of the numbers less than 3,000,000 start with the digit 1 and while this percentage gets smaller as the number you choose gets larger, it will at the least equal that of the numbers. Another reason is that the percentage change between numbers gets smaller as you use bigger and bigger numbers. If a stock price was at 100, it would take a 100% increase to get to 200. However, if the stock was at 800, it would only take a 12.5% increase to get to 900. Thus numbers in data tend to stay within the range of numbers that start with one the most often.
Benford’s Law also has some great practical applications. It can be used to show whether a set of real-world data is authentic or not. In fact, it was used to detect fraud in the 2009 Iranian elections, where the data did not quite match up with the distribution given by Benford’s Law. So the next time someone shoves a bunch of statistics at you, don’t just gobble it up. It is simple enough to count the numbers and see whether the data could possibly be authentic.