George Habash, a militant and former secretary-general of the Popular Front for the Liberation of Palestine, once characterized terrorism as a "thinking man's game." Using mathematics, researchers at Stanford University's Center for International Security and Cooperation (CISAC) have made fighting terrorism a thinking man's game as well.

CISAC affiliate Lawrence M. Wein of the Graduate School of Business and CISAC Science Fellow Jonathan Farley are both applying mathematical models to homeland security problems, such as preventing a nuclear detonation in a major U.S. city and determining whether terrorist cells have likely been disrupted.

Wein, who teaches operations classes about different business processes used to deliver goods and services, has focused his research on bioterrorism and border issues. He has performed, he says, the first mathematical analyses of hypothetical botulism poisoning, anthrax outbreaks and smallpox infections.

"One overriding theme of my work is that all these homeland security problems are operations problems," said Wein, the Paul E. Holden Professor of Management Science. "Just as McDonald's needs to get hamburgers out in a rapid and defect-free manner, so too does the government have to get vaccines and antibiotics out and test the borders for nuclear weapons or terrorists in a rapid and defect-free manner."

In collaboration with Stephen Flynn of the Council on Foreign Relations, a nonpartisan research center, Wein recently has conducted research to improve security at U.S. borders and ports. Port security has received significant attention recently owing to the furor over Dubai Ports World's bid to manage six terminals at major U.S. harbors. The aim of Wein and Flynn's work is to prevent terrorists from bringing into the country a nuclear weaponbe it an atomic bomb or a so-called "dirty bomb," or conventional explosive packed with radioactive waste.

"Of all the problems I've studied, this is the most important because the worst-case terrorist scenario is a nuclear weapon going off in a major U.S. city and also it is the one the government has dropped the ball on the most," Wein said. "They have done a very poor job."

Instead of using the existing approach, where U.S. Customs actively inspects a minority of containers based on information from a specialized tracking system designed to identify suspicious containers, Wein and Flynn have recommended the government use a multi-layer, passive screening system for every container entering the country. Under their system, Customs would photograph a shipping container's exterior, screen for radioactive material and collect gamma-ray images of the container's contents. If terrorists shielded a bomb with a heavy metal such as lead to hide it from radiation detectors, gamma-ray imaging would allow inspectors to see the shielding and flag the container for inspection. Wein and Flynn believe this whole process would cost about $7 per container.

"Right now about maybe 6 percent of the containers are deemed suspicious and they will go through some testing and the other 94 percent of the containers just waltz right into the country without an inspector laying an eye on them," Wein said. "What we're proposing to do is 100 percent passive testing."

Wein's earlier work addressed a different threat: bioterrorism. In 2005, Wein revealed the nation's milk supply was vulnerable--a terrorist could potentially poison 100,000 gallons of milk by sneaking a few grams of botulinum into a milk tanker. Although the government and dairy industry have collaborated to intensify the heat pasteurization formula for milk, Wein is still pushing for additional botulinum testing, which he says would cost less than 1 percent of the cost of milk.

Wein also has used math to study smallpox outbreaks, the U.S. fingerprint identification system and U.S.-Mexico border security issues. Wein's congressional testimony on the fingerprint identification system in 2004 led to a switch from a two-finger system to a 10-finger system. His 2003 research on anthrax attacks resulted in a Washington, D.C., pilot program to use the U.S. Postal Service to distribute antibiotics throughout the capital after an outbreak. Seattle is now testing a similar program.

"In Washington, D.C., now, if there is a large-scale anthrax attack, postal workers will be the first to get their Cipro and, on a voluntary basis, they will go door-to-door distributing antibiotics," Wein said.

He said the common thread throughout his research is queuing theory, or the mathematical study of waiting lines, but he also draws upon mathematical epidemiology for his smallpox studies; air dispersion models for the anthrax model; supply chain management for the milk study; probability theory for the fingerprint identification system; and models for nuclear transport and detection for his work with containers.

From tainted lactose to lattice structures

While Wein is working on improving the government's counterterrorism systems, Jonathan Farley is working to figure out when terrorist organizations have been effectively disrupted. His mathematical model is designed to help law enforcement decide how to act once they have captured or killed a terrorist or a number of terrorists in a cell.

A professor at the University of the West Indies who will chair the Department of Mathematics and Computer Science there next year, Farley is on a one-year science fellowship at CISAC. In 2003, he co-founded Phoenix Mathematical Systems Modeling Inc., a company that develops mathematical solutions to homeland security problems.

He is using lattice theory--a branch of mathematics that deals with ordered sets--to determine the probability a terrorist cell has been disrupted once some of its members have been captured or killed.

"Law enforcement has to make decisions about what resources they should allocate to target different cells," Farley said. "The model should provide them with a more rational basis for allocating their scarce resources. ... It will inform you when you're making decisions about how much time and effort and how much money you're going to spend going after a particular cell."

While at Stanford, Farley hopes to unearth the perfect structure, mathematically speaking, for a terrorist cell--or in other words, a cell structure that is most resistant to the loss of members.

"If it's possible to determine the structure of an ideal terrorist cell, you can focus on a much smaller number of possibilities, because it makes more sense to assume the adversary is going to be smart rather than stupid," Farley said.

Farley has suggested it is possible Al-Qaida and other terrorist organizations already may have figured out the perfect structure for a terror cell by trial and error.

"I don't expect Osama bin Laden to be reading lattice theory in his caves in Afghanistan," said Farley. "But if it follows from the mathematics, perhaps heuristically, the terrorists will have come to the same conclusion--that this is the best way to structure a terrorist cell."

Although Farley acknowledges his model is not a panacea for terrorism, he hopes it will help reduce guesswork that might be involved in pursuing terrorists.

"It's not that I think mathematics can solve all of these problems," Farley said. "Because it can't. But it's better to use rational means to make decisions rather than guesswork."

John B. Stafford is a science-writing intern at Stanford News Service.

Noah Feldman

In looking at the brewing civil war between the two groups in Iraq, it's easy to assume that the cause is ancient hatred. Nothing could be further from the truth. For the overwhelming majority of Iraqi history, Sunnis and Shi'ites have lived peacefully side by side, and numerous Iraqis are the children of mixed marriages. Instead we are witnessing in Iraq what occurs when government collapses and there is no state around capable of guaranteeing personal security.

What do you do when your family is in peril and you cannot turn to the government for protection? The answer is that you will take security wherever you can get it. You need to find some group that will be capable of keeping you safe, and that group had better be one that can count on your loyalty just as you can count on its protection. If you are a member of my ethnic, racial or religious group, then we share at least some basic bond, which may be enough to ensure our loyalty to one another. I need some assurance that you will have my back, and identity is better than nothing.

Sunnis and Shi'ites may find themselves joining militias or supporting denomination-based political parties even if they are not particularly pious and would much prefer not to. Something similar happened in the former Yugoslavia when its government collapsed with the fall of communism and nothing replaced it. Ethnic activists - call them identity entrepreneurs - will always form the core of the new militia. These radicals will emphasize symbols, like al-Askari mosque that was blown up last week in Iraq, and hope that followers will react by strengthening their commitments to the group itself.

Is it possible to break the cycle of violence that gets under way when identity groups move toward civil war? One answer is for an outside force to impose a solution. The killing did not stop in Bosnia or Kosovo until Western powers showed they were willing to bomb. But this approach is not viable in Iraq, where U.S. bombs came first and civil strife has followed. Instead the only way out of the violence is for Iraqis to realize that they have more to gain by negotiating a settlement between their groups than they do by allowing a full-blown brothers' war to break out.

Vali Nasr Author The Shia Revival (forthcoming)

What lies at the heart of the sectarian violence in Iraq is not so much religious dispute as it is a very secular competition for power and prominence in the new Iraq. Iraq is not all that different from Northern Ireland or Bosnia, where religion paraded as ethnicity and became a vehicle for communal rivalries. In the vacuum of power left by the fall of Saddam Hussein, the game of numbers has favored Shi'as, who are 60% of the population. It is for this reason that they wholeheartedly embraced democracy. Disgruntled Sunnis, on the other hand, vested their fortunes in boycott and violence, hoping that as spoilers, they would gain leverage in negotiating over the future.

Few in the West recognized the depth of either the Shi'a anger at the Saddam regime or the Sunni rage born of loss of power. There is a strong sense of Iraqi identity among both Shi'as and Sunnis, but as strong allegiance to sect and ethnicity in every election has shown, a shared notion of what Iraqi identity means and how each community sees the future of Iraq is fast disappearing. As happened in Bosnia, in Iraq mixed marriages and shared memory of coexistence will not be enough to stop internecine violence.

Shi'as embraced the political process that the U.S. set in place in 2003 in the hope that it would guarantee their security and serve their interests. There is indication now that many Shi'as are having second thoughts. Already overstretched in facing the Sunni insurgency, the U.S. can hardly afford losing the Shi'a as well. If tensions escalate to a full-blown civil war, Iran, Saudi Arabia, Jordan and Syria may all join the war to protect their co-sectarians and to scramble for pieces of a failed Iraq.

Pulling Iraq back from the brink will be difficult. Building a strong central government and an effective security force will help. The challenge is to get them up and running before events on the ground pass a point of no return.

James D. Fearon

By any reasonable definition, there has been a civil war in progress in Iraq at least since the Coalition Provisional Authority formally handed over authority to the Iraqis in 2004. A civil war is a violent conflict within a country fought between organized groups seeking to compel a major change in government policies or to take control of the center or a region. The insurgents in Iraq target the U.S. military, but they are also fighting against the Shi'ite-dominated Iraqi government and killing large numbers of Iraqis. There is little reason to think that if the U.S. suddenly withdrew, the insurgents would not continue to fight to control or shape the government.

When we hear talk about incipient civil war in Iraq, the fear is of an escalation of the current insurgency into a much bigger war. Analysts may have in mind something like the U.S. Civil War, with Sunni and Shi'ite armies fighting each other across well-defined fronts. Or they may imagine a sudden spasm of massive communal conflict and ethnic cleansing along the lines of Bosnia or Rwanda. Neither scenario is all that likely, although bouts of violent ethnic cleansing are certainly possible in a few parts of the country, especially Kirkuk.

My guess would be that as the insurgency continues to create insecurity, sectarian militias will continue to grow in power and influence. They will increasingly supply local security, but in the form of protection rackets that extort as they protect. They will clash with each other over territory and control of revenue sources. Since the Sunnis remain highly disorganized, some of these local fights may initially be intra-Shi'ite. But in the absence of effective political incorporation and protection from national police and army units - which are heavily infiltrated by Shi'ite militias - Sunnis will gradually form a patchwork of militias. Neighborhood-by-neighborhood conflict and violence will increase. Think Lebanon.

Juan Cole

If you look at the ethnic conflicts and street demonstrations during Iraq's modern history, it is remarkable how few have involved Shi'ites fighting Sunnis. During the colonial era, Iraqis were united by their opposition to the British occupation. Sunni and Shi'ite tribes cooperated in rebelling against British rule, and were only put down with a bombing campaign in 1920 that killed 9,000. In 1941 mobs targeted Iraq's small Jewish population; Jews had been a valued part of the Iraqi national fabric but were accused, unfairly, of being pro-colonial. After World War II, much of the violence in Iraq was fueled by issues of class. In 1948 slum dwellers and railway and oil workers revolted against a government treaty with Britain. In 1959, Arab nationalists assassinated Communist Party members, while mobs in Mosul and Kirkuk attacked and killed rich businessmen and landowners.

Iraqi Muslims have not all along been severely divided by religious sect. There have been many instances of strong cooperation between Sunnis and Shi'ites. Other social divides have led to mob violence in the past, but Iraqis have overcome them to re-establish national unity. It remains to be seen whether they can accomplish this feat again.

Since the controversy over cartoons of the Prophet Muhammad erupted, Europe's leaders have shown remarkable--and uncharacteristic--courage under fire. Refusing to apologize for the alleged slight to religious Muslims, a chorus of Continental voices has instead risen to the cartoons' defense, citing freedom of expression as the very essence of liberty, democracy and the European Way.

Unfortunately, free speech is about the weakest card in Europe's hand these days. An Austrian court's conviction and sentencing of the British historian David Irving to three years imprisonment for Holocaust denial is merely the most recent footnote to European hypocrisy on freedom of expression over the past decade.

The European Convention on Human Rights, which legally binds all EU states and supersedes domestic law, explicitly guarantees "the right to freedom of expression" including "the freedom to hold opinions and to receive and impart information and ideas without interference by public authority."

This provision is in keeping not only with the U.S. Bill of Rights, but with the central instruments of international human rights law to which Europe and America claim adherence. Yet Europe's interpretation of free expression has diverged markedly from America's broad deference to First Amendment freedoms of speech, assembly and religion.

American courts have upheld the publication of false, even racist materials, the right of neo-Nazis to rally in Jewish neighborhoods, and the objections of some citizens to the Pledge of Allegiance and to school dress codes on religious grounds.

European governments, on the other hand, have consistently trampled analogous rights, outlawing publication of hate speech, trade in Nazi paraphernalia, and the wearing of distinctive religious clothing, to name but a few recent examples.

According to the Austrian court that convicted him on Monday, David Irving's offense was to have "denied, grossly played down, approved, or tried to excuse" the Holocaust in print or other media, in violation of a 1992 statute. Although he has not been tried at home in Britain, Irving was convicted and fined in Germany in 1995 for "inciting race hatred."

At best, Irving is a monumentally terrible historian, who, only after publishing dozens of books on World War II, read the notes of the Holocaust mastermind Adolf Eichmann and came around to admitting that the Nazi genocide might actually have occurred. At worst, he is an artless but unrepentant bigot, on the model of America's David Duke or Austria's own Jörg Haider, but without any independent political power.

Why, then, is Irving's Holocaust denial, like other minority and extremist views in European society, of such great concern to lawmakers? If European governments want to guard against the repetition of genocide, they should actively educate their citizens in tolerance and respect for different cultures and beliefs, not gag those who express conflicting ideas.

Europe's suppression of free speech is guaranteed to spawn and incubate precisely the kind of bigotry and sectarian violence it is intended to prevent. Hounded for the unthinkable crime of publishing false history, David Irving appears almost heroic as he stands up to censorship, fines and imprisonment, making him a kind of martyr for neo-fascist groups.

Likewise, suppression of young Muslims' rights to dress or worship as their religion requires lends government sanction to already widespread anti- Muslim attitudes. This official xenophobia in turn breeds simmering resentment that has already exploded into mass violence and been manipulated by radical Islamists to recruit willing terrorist agents from within European society.

While European leaders should be praised for their belated conversion to the cause of free speech, outraged Muslims around the world are right to allege a double standard. Until Europe consistently respects its own guarantees of free expression, and actively promotes tolerance instead of clumsily stifling dissent, its brave rhetoric will ring disappointingly false.