After the terrorist attack on San Francisco, the Department of Homeland Security ramps up security and surveillance in hopes of catching the people responsible, but instead only manage to inconvenience, detain, and even seriously harm innocent civilians. Marcus explains that the problem with the DHS system is that they're looking for something too rare in too large a population, resulting in a very large number of false positives.

What Marcus is describing is referred to in statistics as a Type I error - that is, we reject the null hypothesis (the assumption that nothing is abnormal) when the null hypothesis is actually true. In this case, the null hypothesis is "not a terrorist", and there's enough suspicious data, the null hypothesis is rejected in favor of flagging the person for investigation. Marcus claims that in order to look for rare things, you need a test that only rejects the null hypothesis at the same rate at which the thing we're testing for - in this case, terrorists - actually occur. The problem is, there's also Type II errors. While Type I errors are caused by being too cautious, Type II errors occur when our test "misses" the thing we are actually looking for. When determining how "tough" a test should be, we need to decide how to balance these two risks.

Marcus is advocating for making the system less broad, therefore reducing false positives. However, this increases the risk for false negatives as well. So, which is worse: a false positive or a false negative? That's a question of expected value, which is based off the probability of a result and its consequences. In this case, the result at one end of the spectrum is the terrorists are caught because of this system, but many innocent people are subject to surveillance and searching. On the other end is that no one is caught because they slip through a timid test, and more people are hurt as a result. Clearly, this can easily turn into a much more complicated debate on the values of time, trust, privacy, and life, so I won't try to determine what the correct balance is myself. Although it's easy to describe some aspects of this conflict with numbers, as Marcus did, it just isn't that simple.