As you may have noticed, this column has some math in it a little later, and it’s likely the first time you’ve seen something like that in a newspaper. I’d like to ask that you not let this scare you if you happen to be someone who is inclined to run the other direction when you see lots of big equations. Though the mathematical model is the focus of this column, I will guide you through it and you should be able to get the general idea without having to reference your old math textbooks.

That being said, there is something in common with the 1988 bombing of Pan Am Flight 103 over Scotland, the Sept. 11 attacks, the attempted plane bombing by the shoe bomber Richard Reid and the recent Christmas Day attempt to blow up a flight from Amsterdam to Detroit by Umar Farouk Abdulmutallab that deserves to be addressed.

All of the culprits were Muslims.

This is not a coincidence. It is a direct result of the existence of terrorist organizations within the Islamic faith focused on harming the Great Satan, otherwise known as the United States of America. Since all of the attacks on commercial aircraft in the past 20 years have been committed by Muslim men, logic would say that it would be wise to focus a greater percentage of passenger searches on Muslim men in order to catch these terrorists.

Note that this does not mean that being a Muslim makes you a terrorist or that being a terrorist makes you a Muslim. In the case of terrorist attacks on commercial aircraft, however, there is a correlation between the two.

Unfortunately, you cannot just look at someone and see whether or not they are a Muslim, but you can get a general idea of the part of the world from which they hail. The majority of Muslims come from the same part of the world. Since these are also the places in which the terrorist organizations have the most influence, the easiest, most effective recruiting is going to be done near there.

In the case of the Sept. 11 attacks, 15 attackers were from Saudi Arabia, one from Egypt, two from the United Arab Emirates, and one from Lebanon — all males. These men, as described by the FBI, tend to have dark — brown or black — hair and eyes and an olive complexion.

Since airports have a limited amount of resources — both in terms of security personnel and security equipment — it is necessary to make the most of those resources. Rather than performing searches on random passengers, it would be wiser to perform searches on the people who are more likely to be terrorists. Though airports do some of this, they are not allowed to use race or gender as a factor, as stated by U.S. Code 40127, which says, “An air carrier or foreign air carrier may not subject a person in air transportation to discrimination on the basis of race, color, national origin, religion, sex or ancestry.”

Abdulmutallab, the would-be terrorist on Christmas Day, is Nigerian. His looks don’t fit the stereotypical terrorist example in the strictest sense. This idea leads to one argument against racial profiling that I have often heard, which is that terrorist organizations will simply use people who don’t fit the profile to commit their terrorist acts if racial profiling is instigated.

This is easier said than done. A terrorist who does not fit the profile would be more difficult and costly to find and recruit — and more valuable to lose, known as opportunity cost — so the terrorist groups are predisposed to using those who fit the profile when possible. That’s why 19-of-19 of the Sept. 11 attackers fit the profile description.

It is easy enough to find out how much of an effect racial profiling would actually have on an airport’s ability to catch terrorists, even taking into account the fact that terrorist groups could use people who don’t fit the profile. You just have to set up a mathematical model to show it.

For this model, first assume that this is what is known as a Stackelberg game, where one player — the airport — first chooses the degree of profiling, defined as letting one group of people go unsearched more often than another; then the other player — the terrorist organization — chooses which type of terrorists to use. Also assume that there are only two types of people: Those who fit the profile, known as targets, and those who don’t — known as non-targets. Both types have different costs to recruit and use as a terrorist, and the goal of the terrorist organization is to minimize the cost of a successful terrorist attack — defined by having a terrorist make it through the security check.

Assume that the terrorist organization will send the same number of total terrorists regardless of cost, but the proportion of target to non-target terrorists will change due to the degree of profiling. The goal of the airport is to catch the highest possible fraction of terrorists holding all factors except the degree of racial profiling constant.

Finally, assume that both players have all possible information about the other player, except for the airport, which does not know what target to non-target terrorist ratio will be chosen by the terrorist organization, being that it is dependent on the airport’s chosen degree of racial profiling.

Assuming that the variable cost of a terrorist increases linearly with the proportion of terrorists of that type, the average cost of a successful terrorist attack is given by Equation 1.

This means that the terrorist organization can minimize the cost of a terrorist attack by using Equation 2.

The fraction of terrorists caught by the search is given by Equation 3.

Since we know what the terrorists will choose to do, we can substitute t=c/p into Equation 3, giving Equation 4.

Therefore, we can maximize the number of terrorists caught while holding q, s, are r unchanged, which gives Equation 5.

While this is only a simple model and does not take every possible factor into account, it nonetheless shows that as the cost of non-target to target terrorists increases, so does the optimal amount of racial profiling. The idea to take away from this model is not that there is some magic amount of racial profiling that is easy to calculate and should be used everywhere, but simply that because terrorist organizations are predisposed to using terrorists who fit a certain profile, there exists an amount of racial profiling that allows the most terrorists possible to be caught.

To put this into practice, however, we need to know what the cost ratio is. Since the ratio of the number of target to non-target terrorists used since Sept. 11 is 20-to-1, we will assume for this example that the cost ratio is 20 (based on the fact that t=c/p). That would mean that if 50 percent of passengers are of the target group, the optimal level of racial profiling (p) would be 4.5, meaning that 4.5 times as many non-targets as targets should go unsearched. If 10 percent of passengers are of the target group, the optimal level is 5.4. If only 1 percent are of the target group, then the optimal level is 5.6.

This is not to say that racial profiling should be the only line of defense or the only way we distinguish who is more likely to be a terrorist. This type of model can be used to distinguish between groups of people for any reason, such as whether you bought your ticket that day, which is a method of profiling that is currently being used.

As the numbers show, allowing airports to use racial profiling — politically correct or not — is still an efficient solution.

Blake Hasenmiller is a senior in industrial engineering and economics from DeWitt.