 What can mathematics tell us about refugees? For generations, Americans have supported immigrants, those looking for better lives for themselves and their families. In fact, we're a nation of immigrants. Less than one percent of our population is pure Native American, and one child in nine is the first in their family to be born in the United States. While some people hate and fear immigrants, most Americans accept and support them and see their presence as a reflection of American values. When famine threatened millions of Irish with starvation, many came to America to raise families in a new land. Their children became industrialists, entertainers, judges, soldiers, and presidents. During the same period, millions of others left Germany and their descendants became prominent Americans. Yes, even this guy. When anti-Semitism threatened their lives, many Jews left Europe and some came to America. Albert Einstein, Leo Zillard, and Eugene Vigner helped persuade the US government to begin the Manhattan Project. Other refugees, like Enrico Fermi and Hans Bethe, worked on the Manhattan Project, and after the war, John von Neumann and Edvard Teller played critical roles in the development of America's nuclear arsenal, and descendants of refugees, like Hyman Rickover, helped America win the Cold War. As long as there is war, as long as there is intolerance, as long as there is poverty, as long as there is fear, and as long as America is a better place to live than the rest of the world, there will be people who want to move here. Why should we let them? There are two types of immigrants, economic migrants, who are looking for opportunities to make money, and refugees, who are looking for any place they can survive. Kalina Cortez, now at the Bush School of Government and Public Service at Texas A&M University, studied how the different types of immigrants fared. She found that within 10 years of their arrival, refugees earn more, work more, and speak better English than economic migrants. Cortez's study is based on a statistical analysis, and many people deride the value of statistics. Mark Twain rather famously opined that there are three types of lies, lies, damned lies, and statistics. But the reality is that statistics doesn't lie, people do, and most often they lie by omitting key factors. And the thing to remember is that meaningful statistics can't be reduced to the 140 characters of a tweet. Meaningful statistics can't be posterized as an internet meme. Meaningful statistics can't be reduced to a 10-second sound bite. One important piece of information is known as the standard deviation. And this comes about as follows. Suppose you have a machine that produces something, for example, bars. We could set the machine to produce bars of a certain length and run the machine. But because of manufacturing irregularities, not all bars will be exactly one meter in length. What we'll find is that some bars are shorter, and some bars are longer. Now suppose we have a second machine, which can also be set to different lengths. We'll go to where we can't see the lengths that the machines are set to and run both machines. And the question we have to ask is, were both machines set to the same length, or were they set to different lengths? As a general rule, if the difference between the average bar length is greater than three standard deviations, it's probable that the two machines were set to different average lengths. Cortez found that the annual earnings of newly arrived refugees was 12 standard deviations below those of economic migrants. But within 10 years, the annual earnings of refugees had surpassed those of economic migrants by 50 standard deviations. In both cases, the differences are large enough to conclude that there is a real difference in the annual earnings. But why? One possibility is that refugees became more skilled in English. Cortez found that the percentage of those with poor English skills was about the same for economic migrants and for refugees. But within 10 years of their arrival, the refugees had improved their English skills considerably. This greater assimilation of refugees into American culture made it easier for them to ascend farther up the economic ladder. Refugees are more likely to take a class to improve their English language skills. This in turn means that they can make greater and more profound contributions to this country. In other words, these refugees are very much their own ancestors who came to this country seeking a better life. And in return, they make America great through their service, devotion, and sacrifice. 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