NEWS that AT&T, Verizon and BellSouth gave customer records to the National Security Agency has set off a heated debate over the intricacies of espionage law. But legal or not, this sort of spying program probably isn't worth infringing our civil liberties for -- because it's very unlikely that the type of information one can glean from it will help us win the war on terrorism.

If the program is along the lines described by USA Today -- with the security agency receiving complete lists of who called whom from each of the phone companies -- the object is probably to collect data and draw a chart, with dots or "nodes" representing individuals and lines between nodes if one person has called another.

Mathematicians who work with pictures like this are called graph theorists, and there is an entire academic field, social network analysis, that tries to determine information about a group from such a chart, like who the key players are or who the cell leaders might be.

But without additional data, its reach is limited: as any mathematician will admit, even when you know everyone in the graph is a terrorist, it doesn't directly portray information about the order or hierarchy of the cell. Social network researchers look instead for graph features like "centrality": they try to identify nodes that are connected to a lot of other nodes, like spokes around the hub of a bicycle wheel.

But this isn't as helpful as you might imagine. First, the "central player" -- the person with the most spokes -- might not be as important as the hub metaphor suggests. For example, Jafar Adibi, an information scientist at the University of Southern California, analyzed e-mail traffic among Enron employees before the company collapsed. He found that if you naïvely analyzed the resulting graph, you could conclude that one of the "central" players was Ken Lay's ... secretary.

And even if you manage to eliminate all the "central players," you may well still leave enough lesser players that the cell retains a complete chain of command capable of carrying out a devastating terrorist attack.

In addition, the National Security Agency's entire spying program seems to be based on a false assumption: that you can work out who might be a terrorist based on calling patterns. While I agree that anyone calling 1-800-ALQAEDA is probably a terrorist, in less obvious situations guilt by association is not just bad law, it's bad mathematics, for two reasons.

The simplest reason is that we're all connected. Not in the Haight-Ashbury/Timothy Leary/late-period Beatles kind of way, but in the sense of the Kevin Bacon game. The sociologist Stanley Milgram made this clear in the 1960's when he took pairs of people unknown to each other, separated by a continent, and asked one of the pair to send a package to the other -- but only by passing the package to a person he knew, who could then send the package only to someone he knew, and so on. On average, it took only six mailings -- the famous six degrees of separation -- for the package to reach its intended destination.

Looked at this way, President Bush is only a few steps away from Osama bin Laden (in the 1970's he ran a company partly financed by the American representative for one of the Qaeda leader's brothers). And terrorist hermits like the Unabomber are connected to only a very few people. So much for finding the guilty by association.

A second problem with the spy agency's apparent methodology lies in the way terrorist groups operate and what scientists call the "strength of weak ties." As the military scientist Robert Spulak has described it to me, you might not see your college roommate for 10 years, but if he were to call you up and ask to stay in your apartment, you'd let him. This is the principle under which sleeper cells operate: there is no communication for years. Thus for the most dangerous threats, the links between nodes that the agency is looking for simply might not exist.

If our intelligence agencies are determined to use mathematics in rooting out terrorists, they may consider a profiling technique called formal concept analysis, a branch of lattice theory. The idea, in a nutshell, is that people who share many of the same characteristics are grouped together as one node, and links between nodes in this picture -- called a "concept lattice" -- indicate that all the members of a certain subgroup, with certain attributes, must also have other attributes.

For formal concept analysis to be helpful, you need much more than phone records. For instance, you might group together people based on what cafes, bookstores and mosques they visit, and then find out that all the people who go to a certain cafe also attend the same mosque (but maybe not vice versa).

While researchers at Los Alamos National Laboratory have used this tool to sift through hundreds of terrorism-related reports -- and find connections that human analysts could not have found easily -- it's still dangerous to rely on the math.

This is because, as Kennedy and Lincoln assassination buffs know, two people can be a lot alike without being the same person. Even if there is only a 1 in 150 million chance that someone might share the profile of a terrorist suspect, it still means that, in a country the size of the United States, two people might share that profile. One might be a terrorist, or he might be Cat Stevens.

This isn't to say that mathematicians are useless in fighting terrorism. In September 2004  10 months before the bombing of the London Underground -- Gordon Woo, a mathematician and risk-assessment consultant, gave a speech warning that London was a hotbed of jihadist radicalism. But Dr. Woo didn't anticipate violence just using math; he also used his knowledge of London neighborhoods. That's what law enforcement should have been doing then and should be doing now: using some common sense and knowledge of terrorists, not playing math games.

Math is just a tool. Used wisely, math can indeed help in warfare: consider the Battle of Britain, won in part by breaking the German codes. But use it unwisely -- as seems to be the case here -- and your approval ratings might just hit a new all-time low.

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.

This study, conducted by the faculty and research fellows of the Combating Terrorism Center (CTC) at West Point, serves multiple purposes, the most important of which is contributing to the depth of knowledge about the al-Qa'ida movement. Evidence supporting the conclusions and recommendations provided in this report is drawn from a collection of newly-released al-Qa'ida documents captured during recent operations in support of the Global War on Terror and maintained in the Department of Defense's Harmony database. In the text of these documents, readers will see how explicit al-Qa'ida has been in its internal discussions covering a range of organizational issues, particularly regarding the internal structure and functioning of the movement as well as with tensions that emerged within the leadership.

In the first part of the report, we provide a theoretical framework, drawing on scholarly approaches including organization and agency theory, to predict where we should expect terrorist groups to face their greatest challenges in conducting operations. The framework is informed as much as possible by the captured documents, and provides a foundation upon which scholars can build as more of these documents are declassified and released to the public.

Our analysis stresses that, by their nature, terrorist organizations such as al-Qa'ida face difficulties in almost any operational environment, particularly in terms of maintaining situational awareness, controlling the use of violence to achieve specified political ends, and of course, preventing local authorities from degrading the group's capabilities. But they also face problems common to other types of organizations, including private firms, political parties, and traditional insurgencies. For example, political and ideological leaders--the principals--must delegate certain duties to middlemen or low-level operatives, their agents. However, differences in personal preferences between the leadership and their operatives in areas such as finances and tactics make this difficult and give rise to classic agency problems.

Agency problems created by the divergent preferences among terrorist group members present operational challenges for these organizations, challenges which can be exploited as part of a comprehensive counterterrorism strategy. Thus, the theoretical framework described in this report helps us identify where and under what conditions organizations can expect the greatest challenges in pursuing their goals and interests. Understanding a terrorist organization's internal challenges and vulnerabilities is key to developing effective--and efficient--responses to the threats they pose and to degrade these groups' ability to kill. The captured al Qa'ida documents contribute significantly to this type of understanding.

Our analysis emphasizes that effective strategies to combat threats posed by al-Qa'ida will create and exacerbate schisms within its membership. Members have different goals and objectives, and preferred strategies for achieving these ends. Preferences and commitment level vary across specific roles performed within the organization and among sub-group leaders. Defining and exploiting existing fissures within al-Qa'ida as a broadly defined organization must reflect this intra-organizational variation in preferences and commitment in order to efficiently bring all available resources to bear in degrading its potential threat. While capture-kill options may be most effective for certain individuals--e.g., operational commanders--we identify a number of non-lethal prescriptions that take into account differences in al-Qa'ida members' preferences and commitment to the cause. Many of our prescriptions are intended to induce debilitating agency problems that increase existing organizational dysfunction and reduce al-Qa'ida's potential for political impact.

To achieve long-term success in degrading the broader movement driving terrorist violence, however, the CTC believes the United States must begin aggressively digesting the body of work that comprises jihadi macro-strategy. We therefore also seek to apply our model to the ideological dimension of al-Qa'ida revealed in numerous instances in these documents, the goal being to identify ways to facilitate the ideational collapse of this body of thought. The included documents provide insights into the points of strategic dissonance and intersection among senior leaders that must be better understood in order to be exploited.

In sum, this theoretically informed analysis, along with assessments of the individual captured documents themselves, contributes to existing bodies of research on al-Qa'ida. It provides several tools for identifying and exacerbating existing fissures as well as locating new insertion points for counterterrorism operations. It presents an analytical model that we hope lays the foundation for a more intellectually informed approach to counterterrorism. And perhaps, most importantly, this assessment demonstrates the integral role that scholars can play in understanding the nature of this movement and in generating smarter, more effective ways to impede its growth and nurture the means for its eventual disintegration.

The Bush administration's response to the September 11 attacks has rendered more urgent Al Qaeda's stated objective to eject the United States from the Middle East. The aim here is not to evaluate the direction of the war on terrorism, but to explore why Al Qaeda has been so unsuccessful in capitalizing on its political violence. The article begins with the premise that terrorism is a communication strategy. It contends that Al Qaeda's policy failures are due to its inability to convince Bush that it would refrain from attacking Americans if the United States moderated its Middle East policies. Borrowing from the literature in political psychology and perception and misperception in international relations, the article offers several explanations for Al Qaeda's ineffectiveness in getting this message across. The article concludes by deriving general observations about the limitations of terrorism as a form of political communication.

Scholars attribute conventional violence in a nuclear South Asia to a phenomenon known as the "stability/instability paradox." According to this paradox, the risk of nuclear war makes it unlikely that conventional conflict will escalate to the nuclear level, thereby making conventional conflict more likely. Although this phenomenon encouraged U.S.-Soviet violence during the Cold War, it does not explain the dynamics of the ongoing conflict between India and Pakistan. Recent violence has seen Pakistan or its proxies launching limited attacks on Indian territory, and India refusing to retaliate in kind. The stability/instability paradox would not predict such behavior. A low probability of conventional war escalating to the nuclear level would reduce the ability of Pakistan's nuclear weapons to deter an Indian conventional attack. Because Pakistan is conventionally weaker than India, this would discourage Pakistani aggression and encourage robust Indian conventional retaliation against Pakistani provocations. Pakistani boldness and Indian restraint have actually resulted from instability in the strategic environment. A full-scale Indo-Pakistani conventional conflict would create a significant risk of nuclear escalation. This danger enables Pakistan to launch limited attacks on India while deterring all out Indian conventional retaliation and attracting international attention to the two countries' dispute over Kashmir. Unlike in Cold War Europe, in contemporary South Asia nuclear danger facilitates, rather than impedes, conventional conflict.

United Nations Secretary-General Kofi Annan created the High-Level Panel on Threats, Challenges, and Change in September 2003 with SIIS and CISAC senior fellow Stephen J. Stedman as its research director to identify the major global threats and generate new ideas about policies and institutions to enable the U.N. to be effective in the 21st century.

The panel issued a four-part report, A More Secure World: Our Shared Responsibility, in December 2004.

PART ONE: The panel identifies six types of threats of greatest global concern: war between states; violence within states; poverty, infectious disease, and environmental degradation; nuclear, chemical, biological, and radiological weapons; terrorism; and transnational crime. A collective security system must take all member states' threats seriously and deal with them equitably.

PART TWO: In prescribing policies to prevent threats from spreading or worsening, the report emphasizes development as the first line of defense. Combating poverty and infectious disease, the panel argues, will save millions of lives and strengthen states' capacity to deter terrorism, crime, and proliferation of nuclear and biological weapons. The report also urges the U.N. to improve its capacity for preventive diplomacy and mediation and to forge a counterterrorism strategy.

PART THREE: The report reiterates the U.N.'s recognition of states' right to self-defense, but also suggests that the Security Council should consider stepping in more often to exercise its preventive authority. Peacekeeping, peace enforcement, and peace building are vital to global security, and developed nations should do more to transform their armies into units suitable for peace operations. Post-conflict peace building should be a core function of the U.N.

PART FOUR: The report prescribes revitalization of the Security Council and the General Assembly, and creation of a new Peacebuilding Commission. On the Security Council, the report provides two options for achieving reforms: one would appoint new permanent members, and the other would establish new long-term, renewable seats. Neither option creates any new vetoes.