Timely reunion panel hosted by Stanford president John Hennessy, moderated by Stanford alum Ted Koppel, and featuring Bill Perry and George Shultz.

The final decade of the 20th century was a time of great optimism. The fall of the Iron Curtain ushered in a new era of democracy and freedom for millions. The expansion of the European Union promised to open borders to trade and opportunity. The technology revolutions of the 1990s promised to bridge cultural gaps and unite diverse people.

Yet, in the first decade of the 21st century, this optimism has faded in the face of myriad threats: the menace of terrorism and nuclear proliferation, the danger of virulent pandemics, the global dependence on oil from volatile regions, and the far-reaching and often unsettling implications of an interconnected planet.

In such uneasy times, is it safe to feel safe? What is the way forward in the midst of these challenges? What will it take? What is Stanford doing to help address these issues?

Panelists

John L. Hennessy, Stanford President and Bing Presidential Professor

Jean-Pierre Garnier, MBA '74, CEO, GlaxoSmithKline

The Hon. Anthony M. Kennedy, '58, Supreme Court Justice

William J. Perry, '49, MS '50, former Secretary of Defense, Berberian Professor in the School of Engineering

Dr. Lucy Shapiro, Ludwig Professor of developmental biology and cancer researcher

George P. Shultz, former Secretary of State, Ford Distinguished Fellow, Hoover Institution

Jerry Yang, '90, MS '90, co-founder, Yahoo!

The National Security Agency is a riddle wrapped in a mystery inside a code. Secrets lie within. Located in Fort Meade, Md., it dwarfs the CIA. Its budget is black, unknown. And, most disturbing of all, it is the world's largest employer of mathematicians.

One of its secrets, recently revealed, is that it's monitoring millions of phone calls to learn just who was calling whom. (Technically, only telephone numbers are being recorded, but you don't have to be Q from James Bond to get a name from a number.) This information was being used to determine who might be a terrorist.

Legal or not, the spying program isn't worth violating our civil liberties for. The information one can glean will hardly help us win the war on terror.

With the NSA data, you can draw a picture with nodes or dots representing individuals, and lines between nodes if one person has called another. Mathematicians who work with pictures like this are called graph theorists. The field of social network analysis deals with trying to determine information about a group from such a graph, such as who the key players are or who the cell leaders might be.

But even when you know everyone in the graph is a terrorist, graphs don't contain information about the order or hierarchy of the cell. 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. Monterey Naval Postgraduate School researcher Ted Lewis, in his textbook "Critical Infrastructure Protection," defines a critical node to be such a central hub.

There are two problems. First, the central player might not be as important as the hub metaphor suggests. Jafar Adibi of the University of Southern California looked at e-mail traffic between Enron employees before Enron collapsed, and drew the graph. He found that if you naively analyzed the graph, you could mistakenly conclude that one of the central players was CEO Ken Lay's ... secretary. But that wasn't the person who ran the company into the ground.

Second, as the journal Studies in Conflict and Terrorism reported in 2003, you can kill all the central players in a terrorist cell and still leave the cell with a complete chain of command -- still capable of carrying out a devastating attack.

Expert Kathleen Carley of Carnegie Mellon was able to correctly predict -- twice -- who would take over Hamas when its leaders were assassinated, and her analysis used detailed information about the individuals in the organization, not just what anonymous nodes were linked with what. The moral is that the graph theory approach is inadequate. For useful results, it's important to utilize the lattice theory approach, which takes into account order and hierarchy.

The other questionable aspect of the NSA spying program is that it seeks to work out who might be a terrorist based on their calling patterns. While I agree that anyone calling 1 (800) AL-QAEDA is probably a terrorist, guilt by association is not just bad law, it's bad mathematics, for three 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. Sociologist Stanley Milgram took individuals unknown to each other, separated by a continent, and asked one person to send a package to the other -- but only by sending the package to an individual he or she knew, who could then only send the package to someone he knew, and so on. While Milgram's interpretation of the results has since been questioned, the conclusion that emerged is that it took only six mailings, on average, for each package to reach its intended destination.

For example, President Bush is only three steps away from Osama bin Laden. And terrorist hermits like the Unabomber might be connected only to very few people. So much for guilt by association.

The second reason the NSA methodology is flawed is the concept "strength of weak ties," made famous by Stanford sociologist Mark Granovetter. Robert Spulak of the Joint Special Operations University puts it this way: 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. The links between nodes that the NSA is looking for simply might not exist for the real threats.

Formal concept analysis, a branch of lattice theory, helps rectify this situation. Individuals 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 instance, you might group together people based on what cafés, bookstores and mosques they attend, 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 this tool has in fact been used by researchers at Los Alamos National Laboratory to sift through hundreds of terrorism-related reports, it's still dangerous to rely on the math.

The NSA data mining is flawed because, as Kennedy and Lincoln 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 is just minding his own business. The other is Cat Stevens.

This isn't to say mathematicians are useless. In September 2004 -- 10 months before the July 7 bombing of the London Underground -- mathematician Gordon Woo warned that London was a hotbed of jihadist radicalism. But Woo, who works for the Bay Area company Risk Management Solutions, didn't anticipate the bombings using math. He used his knowledge and experience of London, especially the Wood Green area. That's what law enforcement officials should be doing.

As for tracking terrorist financing, it may already be too late. The terrorism of the future, according to mathematician Stefan Schmidt of the Technical University in Dresden, Germany, may be the terrorism of the futures -- when bombs explode, the stock market drops. Schmidt wants to quantify the impact on the market of a terrorist incident. The only people who know when a bomb will explode are the terrorists. By playing the market, they may already have obtained as much money as they need -- in perfectly legitimate ways -- thus stifling Treasury Department efforts to cut off the source of their funding.

Math is just a tool. Used wisely, math can indeed help win the Battle of Britain (by breaking the German codes). But used unwisely -- as seems to be the case in the NSA telephone caper -- your approval rating might just hit an all-time low.

It's been said that World War I was the chemists' war and World War II the physicists' war, but that World War III is destined to be the mathematicians' war.

With the gravest threat to U.S. security now posed by rogue terrorists who simultaneously hold a grudge and have access to weapons of mass destruction, some of this country's prime human calculators are on the case.

Combatting terrorism not with mortars and missiles but with mathematical models, they intend to prove this theorem: There literally is safety in numbers.

In their vanguard is an amiable Stanford University professor who, by devoting himself to the application of math principles to doomsday scenarios, is beginning to acquire the nickname "Dr. Doom." The attacks of Sept. 11 inspired mathematician Lawrence Wein to channel his expertise into some of the most compelling questions of our time.

He has ciphered the risks of our "woefully inadequate" inspection of container ships, assessed the effectiveness of border-control fingerprint checks to spot terrorists, and performed what may well be the first math analyses of hypothetical botulism, anthrax and smallpox contaminations.

Recall the agitation last year over warnings that the nation's milk supply was vulnerable, based on the calculation that one terrorist with a few grams of botulinum could contaminate a tanker and potentially poison 100,000 gallons of milk? That's just one of many tidings of comfort and joy brought to you by Wein.

Another such upper is that just about 6 percent of containers shipped into U.S. ports will be categorized as suspicious and subjected to tests for a nuclear device, based on a system that relies largely on reporting by the shipper. The rest, Wein noted, "just waltz right into the country without an inspector laying an eye on them."

At Stanford's Graduate School of Business, he teaches a core course in operations, and he says the parallels are strikingly similar: Just as McDonald's needs a well-designed distribution system to get its hamburgers out quickly, so the government needs a well-designed distribution system to get vaccines and antibiotics to citizens who might sicken or die from a bioterror attack. In math lingo, some of these computations rest on "queueing theory" -- the notion that a lot of needy people must line up behind a limited number of distributors.

And what do we do after crunching millions of numbers to arrive at specific prescriptions? Wein has taken on the role of necessary nag to a torpid federal bureaucracy and recalcitrant industries.

In fact, the feds scrambled to try to suppress publication of his damning milk study as a threat to national security -- an argument the journal Proceedings of the National Academy of Sciences rejected before publishing the work.

These days, Wein regularly testifies at congressional hearings, addresses scientific forums and pens op-ed pieces in national newspapers about precisely what the government should be doing -- and where it is falling short.

"I believe my work demonstrates that numbers really matter, and we need to pay attention to what they tell us," said Wein, a critic of the federal government's homeland security failures in key areas, particularly at the ports. "I really don't bring my own personal political views into this -- I would be just as critical of the federal bureaucracy if a Democrat were in the White House.

"Bureaucracy just isn't designed to respond nimbly."

On the other hand, politicians are eager to do something, anything, that might thwart a terror attack or save lives. But in an information vacuum, that makes them easy prey for entrepreneurs hawking all kinds of safety gadgets.

So, much of Wein's math analysis goes beyond documenting threats to assess the most effective, cost-efficient remedies.

Take the milk scare, for example. Wein urged the government to mandate that milk tanks and trucks be locked, that two people be present when it is transferred along each part of the supply chain, and that milk truck drivers use a 15 minute test to detect any toxins. The estimated cost of all this: 2 cents per gallon.

Some other experts disputed Wein's assumptions, and dairy industry groups insisted they already had taken extra steps such as raising pasteurization temperatures to secure the milk supply. They dismissed the scenarios Wein described as "highly unlikely or impossible."

To avoid being victimized by a radioactive device aboard a tanker -- otherwise known as a "poor man's missile" -- he and colleague Stephen Flynn of the Council on Foreign Relations advocate using techniques such as gamma-ray imaging to screen 100 percent of containers. They calculate the cost at $7 per container.

Some of Wein's calculations have translated into real reform.

In 2004, he presented to the White House his findings that the system of collecting only two fingerprints from incoming foreign visitors ran a high risk of missing terrorists because so many prints turned out to be of poor quality. His solution was simple: Take prints from all 10 digits. The government adopted it.

His 2003 research into the most effective response to an anthrax attack prompted pilot programs that are now testing his finding that the best way to widely distribute antibiotics would be by mail carriers, who already go door to door.

Albert Einstein once observed: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

And sure enough, one of the impediments to fighting terrorists with mathematics is the paucity of hard data.

An anthrax scenario illustrates the point. Estimates of fatalities per kilogram of poisonous agent released vary from a low of zero to a high of 660,000. That's because of variables: the dose required to cause infection, the percentage of people who survive infection, the degree of aerosol dispersion, the density of the population, the environmental stability of the agent and the effectiveness of a public health system response.

As Wein acknowledges, "It's not like we can do massive clinical trials on this."

The trail of what-ifs is so convoluted that in 2002 the National Academy of Sciences cited "an irreducible uncertainly of several orders of magnitude in the number of people who will be infected in an open-air release."

This makes some experts suspicious of anybody's calculations, even from a researcher with a pedigree like Wein's.

"With so much uncertainly surrounding the outcome of a bioweapons attack, it does not make sense to plan extensive biodefense programs when more-certain public threats, particularly those involving nuclear weapons, require attention," argued Allison Macfarlane, research associate in the Science, Technology and Global Security Working Group at MIT.

But Wein is undeterred, and is busy on new assessments. Yet he insists his work has not impaired his ability to sleep soundly.

"People really are much more likely to suffer from cancer than a terrorist attack, but that doesn't merit the same attention," he said. "We should do what makes sense to protect ourselves from both."

The nuclear regime in place since the Nonproliferation Treaty (NPT) took effect in 1970 is broken and needs to be fixed, the world's highest-ranking nuclear official told a half-full Memorial Auditorium in a wide-ranging lecture about the future of nuclear energy and weapons yesterday afternoon.

"We have a dysfunctional system -- system that cannot endure," said Mohamed ElBaradei, the director general of the International Atomic Energy Agency (IAEA). "We're reaching the fork in the road. Events in the last few years have made it clear that we need to change course."

The big news from ElBaradei's speech was his support for American entreaties to Iran. But the 2005 Nobel Peace Prize recipient also commented on North Korea, India, Pakistan, Iraq, terrorism, disarmament and the future of nuclear energy.

He said there are probably eight current nuclear states, excluding North Korea. He worried aloud that countries which can currently produce nuclear energy peacefully are only six months away from developing nuclear weapons for military purposes.

"Acquiring the technology to enrich uranium or reprocess uranium basically is the key to develop nuclear weapons as we have seen in Asia and Iran," he said. "They are virtually weapons states because in six months time if they decide for security reasons to develop their own weapon, they are there."

Iraq

While not a household name, ElBaradei was a prominent figure in the news as the lead weapons inspector in Iraq during the run-up to the 2003 American invasion. He said at the time that he could not find evidence of Iraqi weapons of mass destruction, but he would not conclude that there were no weapons in the country or that Saddam Hussein did not have a program.

ElBaradei asked for more time to complete inspections, but the Bush administration declined his request and decided to invade. The U.S. never found the nuclear and biological material that some had promised existed.

"Luckily...well I'm not sure luckily...we were proven right that there was no nuclear or any weapon of mass destruction in Iraq," he said. "But I hope that all of us have learned from the Iraq experience that we cannot just jump the gun. You have to be absolutely sure of the facts."

India

ElBaradei surprised observers when he supported the U.S. agreement with India earlier this year, which allowed the country to continue developing nuclear weapons and energy. He said the agreement with India did not endorse its proliferation activities but was indicative of the kind of outside-the-box thinking the international community needs when considering the spread of nuclear weapons and material.

"The end result is India coming closer and working with the rest of the world," he said. "It is not a perfect agreement, but it has a lot of advantages. From the safety, security and nonproliferation perspective, I see that agreement as a win-win situation."

Pakistan

Pakistan developed nuclear weapons as a response to India. Some have criticized Pakistan for its poor stewardship and control of the bomb, pointing out that weapons were almost fired during a skirmish over the disputed Kashmir region.

AQ Kahn, a senior nuclear scientist who helped Pakistan join the exclusive nuclear club, was caught selling compact discs and other information about bombs to several other countries.

"How much damage was done in the process we don't know," ElBaradei said.

The release of this nuclear material demonstrates the need for a "more robust verification system," he said, adding that Pakistan has come closer to the international community in recent years.

North Korea

Kim Jong Il expelled all IAEA inspectors in Dec. 2002, withdrew from the NPT in Jan. 2003 and announced in February 2005 that his military had a nuclear deterrent.

"North Korea is still a major problem," ElBaradei said. "We don't talk about it enough, but North Korea is declaring right now that they have a nuclear weapon. And the longer that they continue to be in that status, the more it is accepted in the collective conscious. This would be terrible because it will have a lot of negative ramifications in South Korea and Japan."

ElBaradei said ongoing negotiations are an important development but more needs to be done.

"What we see with the current six-party talks should have taken place years ago," he said.

Nuclear Proliferation

ElBaradei stressed that he understands the value of nuclear power, which produces much of the developed world's energy. Reducing its use would create more dependence on greenhouse gas-creating fossil fuels, he said.

"We need to use nuclear energy responsibly to maximize benefit and minimize risk," he said.

He said his "number one nightmare scenario" is a terrorist group acquiring nuclear technology since terrorists are not deterred by the possibility of reprisal.

In the post-Cold War world, ElBaradei said he could see no justification for the U.S. and Russia to maintain their nuclear arsenals on ready alert to fire with thirty minutes notice. He called on America to lead by example and continue to disarm its nuclear stockpile.

"Rather than pass judgment, I'd definitely like to say the U.S. should do more in leading by example in terms of nuclear disarmament," he said.

In September 2005, ElBaradei was reappointed to a third term as director general of IAEA. The United States had considered holding up his nomination but dropped its objections under pressure from European allies, who admire the former law professor from New York University.

Diplomat to the Core

The Egyptian native's sometimes broken English was interspersed with self-corrections and careful legalese nuance. ElBaradei answered questions posed by Political Science Prof. Scott Sagan, the director of the Center for International Security and Cooperation.

When Sagan made bold pronouncements about different country's nuclear activities, including the United States' "colossal failure" when North Korea violated the NPT, ElBaradei seemed careful not to point fingers, play the blame game or make enemies. Nonetheless, for a senior United Nations official, his speech was notably blunt.

"There's no international public servant whose integrity and work I admire more than yours," Sagan told ElBaradei.

Accompanied by his wife, ElBaradei spent the day at the University visiting with faculty and students. He spoke at a lunch sponsored by the Freeman Spogli Institute for International Studies and traveled to Sagan's home for a dinner with invited guests. He left the area at 8:30 p.m.

Today, the Senate Intelligence Committee will begin questioning Air Force Gen. Michael Hayden, nominated to be director of the Central Intelligence Agency, about the National Security Agency's collection of U.S. citizens' telephone records.

The scrutiny of the NSA is deserved, but the Senate and the American public may be missing a broader and more disturbing development. For the first time since the Civil War, the United States has been designated a military theater of operations. The Department of Defense -- which includes the NSA -- is focusing its vast resources on the homeland. And it is taking an unprecedented role in domestic spying.

It may be legal. But it circumvents three decades of efforts by Congress to restrict government surveillance of Americans under the guise of national security. And it represents a profound shift in the role of the military operating inside the United States. What's at stake here is the erosion of the principle, embedded in the 1878 Posse Comitatus Act, that the U.S. military not be used for domestic law enforcement.

When the administration declared the United States to be a theater of military operations in 2002, it created a U.S. Northern Command, which set up intelligence centers in Colorado and Texas to analyze the domestic threat. But these are not the military's only domestic intelligence efforts. According to the Congressional Research Service, the Pentagon controls "a substantial portion" of U.S. national intelligence assets, the traditional turf of the FBI and CIA.

In 2003, Congress created the job of undersecretary of Defense for intelligence to oversee the department's many intelligence bodies -- including a new entity called Counterintelligence Field Activity, or CIFA.

CIFA was ordered to maintain a "domestic law-enforcement database" on "potential terrorist threats" to U.S. military installations, and it began collecting information on U.S. citizens.

In 2005, a presidential commission suggested that CIFA, set up as a clearinghouse for information, be empowered to conduct domestic investigations into crimes such as treason, espionage and terrorism. Astoundingly, the commission declared that such an expansion of military powers would not require congressional approval; a presidential order and Pentagon directive would suffice. One Defense Department program feeding information to CIFA is TALON (Threat and Local Observation Notice), which is supposed to obtain data from "concerned citizens and military members regarding suspicious incidents" that could herald terrorist attacks. But the military appears to have interpreted its mandate broadly. A TALON report was filed on a protest against "war profiteering" by Halliburton, Newsweek reported. The protesters alleged the defense contractor overcharged for food for U.S. troops in Iraq.

Counterintelligence reports were also filed on New York University's OUTlaw, a decades-old organization of openly gay law students. "The term 'outlaw' is a backhanded way of saying it's all right to commit possible violence," concluded one misguided military investigator in a document obtained last month under the Freedom of Information Act." NBC reported that about four dozen TALON database entries on "suspicious incidents" were not about terrorism but about opposition to the Iraq war and military recruiting.

These misguided military forays into domestic surveillance harken back to Vietnam War-era abuses. This time, they are the result of a much broader intelligence-gathering effort by the military on U.S. soil. President Bush said last week, "We're not mining or trolling through the personal lives of millions of innocent Americans." But a 2004 survey by the General Accounting Office found 199 data-mining operations that collect information ranging from credit-card statements to medical records. The Defense Department had five programs on intelligence and counterterrorism.

The Defense Intelligence Agency, created in 1961 to provide foreign military intelligence, now uses "Verity K2" software to scan U.S. intelligence files and the Internet "to identify foreign terrorists or Americans connected to foreign terrorism activity," and "Inxight Smart Discovery" software to help identify patterns in databases. CIFA has reportedly contracted with Computer Sciences Corp. to buy identity-masking software, which could allow it to create fake websites and monitor legitimate U.S. sites without leaving clues that it had been there. The National Geospatial-Intelligence Agency is collecting data from 133 U.S. cities; intelligence sources told the Los Angeles Times that, when collection is completed, the agency would be able to identify occupants in each house, their nationality and even their political affiliation.

In 2002, the Defense Department launched the granddaddy of all data-mining efforts, Total Information Awareness, to trawl through all government and commercial databases available worldwide. In 2003, concerned about privacy implications, Congress cut its funding. But many of the projects simply transferred to other Defense Department agencies. Two of the most important, the Information Awareness Prototype System and Genoa II, moved to NSA headquarters.

The Pentagon argues that its monitoring of U.S. citizens is legal. "Contrary to popular belief, there is no absolute ban on intelligence" agencies collecting information on Americans or disseminating it, says a memo by Robert Noonan, deputy chief of staff for intelligence. Military intelligence agents can receive any information "from anyone, any time," Noonan wrote.

Throughout U.S. history, we have struggled to balance security concerns with the protection of individual rights, and a thick body of law regulates domestic law enforcement agencies' behavior. Congress should think twice before it lets the behemoth Defense Department into domestic law enforcement.

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 naively 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.