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."

North Korea is poised to flight test a ballistic missile that may have intercontinental range -- an action the Bush administration declares would be provocative. Others have called for sanctions if the flight test occurs, the use of U.S. ballistic-missile defenses to intercept the missile in flight or a pre-emptive attack against the missile-launch site. But is this missile test a red line that, if crossed, seriously threatens U.S. security and, hence, warrants strong action? The simple answer is "No."

In thinking about this test, one must not lose sight of two paramount goals: rolling back North Korea's nuclear weapons program and the eventual peaceful reunification of North and South Korea. Ballistic missiles constitute a serious threat to the U.S. homeland only when armed with nuclear warheads and they are only one delivery means for such weapons. In this sense, ballistic missiles are of secondary concern. By most estimates, North Korea has sufficient nuclear material for a few nuclear explosive devices, but whether they can design a nuclear weapon that satisfies the size, weight and delivery constraints associated with intercontinental-range ballistic missiles is far from obvious.

If North Korea tests a three-stage version of the Taepodong-2 missile, it will likely attempt to put a satellite into orbit, just as it did in 1998 when it failed to place a satellite into orbit with the smaller Taepodong-1 missile. North Korea has a sovereign right to launch satellites, or to test ballistic missiles for that matter. International protocol requires launch notification and restrictions on air and marine traffic for reasons of range safety -- steps North Korea failed to take in 1998 -- but no international agreement bars this test. True, North Korea agreed to a unilateral moratorium on ballistic missile flight tests in 1999, pending further talks with the United States regarding North Korea's missile program, but the Bush administration refused to join these talks. North Korea leader Kim Jong Il reaffirmed this flight test moratorium in the 2002 Pyongyang Declaration signed with Japan, but this document is not a legally binding commitment.

If successful, this flight test would demonstrate that North Korea can produce rockets large enough to carry payloads intercontinental distances. However, this does not translate into an immediate threat because North Korea has not demonstrated that it can build a nuclear warhead that is small enough to fit on top of a Taepodong-2 missile and that can survive re-entry into the atmosphere after flying intercontinental distances.

Given vastly superior U.S. conventional and nuclear forces, deterrence should dissuade North Korea from ever using such missiles, except for saber rattling, or worse selling nuclear weapons or nuclear material abroad (this is a serious red line). Kim Jong Il may be a ruthless totalitarian leader, with little regard for the welfare of his people, but he is not suicidal.

More important, these missiles would be highly vulnerable to pre-emptive attack in the midst of a crisis, which is when pre-emption makes sense, because these missiles are large and easy to detect, they are not mobile, and they take many hours, if not days, to erect in a vertical position and fuel -- precisely the activity that generated this concern.

On the other hand, U.S. sanctions against North Korea in the wake of a test flight could backfire. They would likely cause rifts with other friendly parties to the Six Party talks aimed at eliminating North Korea's nuclear weapons, especially China. U.S. national missile defenses may not be within range, depending on the flight trajectory, to intercept this flight test. If this unproven U.S. missile defense were to fail and North Korea's flight test succeed, the Bush administration would be embarrassed, and Kim Jong Il triumphant. And, pre-emptive attack against the test facility would be a unilateral act of war at a time when U.S. unilateralism has hurt more than helped U.S. vital interests. South Korea would adamantly oppose such adventurism because Seoul is vulnerable to retribution, being within artillery range of the Demilitarized Zone.

So, what should the United States do on the eve of this flight test? Nothing, beyond expressing its dismay that North Korea appears to favor conflict over cooperation.

A Taepodong-2 flight test allows the United States to learn more about this missile than North Korea, given the concentration of technical intelligence assets in the area, which would help resolve the question of whether this missile, in fact, constitutes a serious threat to the U.S. homeland. In addition, such a test would isolate North Korea further and reinvigorate the Six Party Talks by encouraging South Korea, China, Japan, Russia and the United States to overcome their differences and create a united front to persuade North Korea to renounce its nuclear weapon program, which is the real threat.

Stepping back, U.S. leaders should see that North Korea is a mouse and the United States the elephant. Contrary to popular mythology, elephants are not, and should not be, afraid of mice.

In 1979, anthrax was accidentally released in the city of Sverdlovsk (pop. 1,200,000) in the former Soviet Union, infecting about 80 to 100 people and killing at least 70. Russian officials claimed at the time that tainted meat sold on the black market was responsible; American officials argued that a nearby biological weapons facility released the killer spores. In the early 1990s, Harvard researchers visited the city to piece together the epidemiology of the outbreak. Their investigation, published in Science magazine in 1994, concluded that the Soviet cover story was false.

Now, physicist Dean A. Wilkening, director of the science program at Stanford's Center for International Security and Cooperation (CISAC), has revisited this Cold War tragedy and used its real-world data to improve our ability to model the medical effects of inhalational anthrax. This, in turn, allows him to model more accurately hypothetical scenarios such as the release of a kilogram of aerosolized anthrax in Washington, D.C., today.

The models researchers have used in such thought experiments "predict very different outcomes," says Wilkening, whose work to better understand the human effects of inhalational anthrax was supported by grants from the John D. and Catherine T. MacArthur Foundation and the Carnegie Corporation. Using real-world data from the Sverdlovsk outbreak and from limited nonhuman primate experiments, he was able to eliminate two of four theoretical models currently used in "what if?" scenarios that inform bioterrorism policies ranging from how much medicine we should have on hand in the Strategic National Stockpile to how rigorous post-attack decontamination efforts need to be. He reports his findings in the May 1 issue of Proceedings of the National Academy of Sciences.

"To date, researchers haven't paid enough attention to which model they use," Wilkening says. "Different models can give predictions that vary by a factor of 10 or more, so it matters which model one uses for predicting the human effects of inhalational anthrax." Wilkening aims to anchor models on the best available data and provide realistic models that the bioterrorism community can employ in policy studies.

The Sverdlovsk outbreak is "a sort of natural experiment," he says. "It's a tragic incident, but it also is a very valuable source of scientific data that one can use to distinguish between the four models currently in use." The upshot of his analysis is that two of the models currently in use are not accurate for predicting the human response to inhalational anthrax.

Insufficient data is available to resolve which of the remaining two models he examined is most accurate. That answer will have to await further data from costly nonhuman primate experiments, should they ever be performed (none are planned). "We have to use both [models] right now, or use them as bounding cases," he advises.

Wilkening explored four policy issues that illustrate the consequences of choosing different models: 1) calculating how many anthrax-exposed people would become infected and how many would die; 2) assessing if decontamination would be needed; 3) determining how soon exposed people would show symptoms and how soon doctors would recognize those symptoms as anthrax; and 4) calculating how soon exposed people need to receive antibiotics to avoid contracting the disease.

"To figure out what happens in a bioterrorist event, you need to know two basic properties about the pathogen you're dealing with," Wilkening says. One is the dose-response curve, which determines the likelihood of becoming infected at different exposure levels--the higher the dose of anthrax you get, the higher the probability that you will become infected. The dose at which 50 percent of an exposed population becomes infected, called the ID50, is around 10,000 spores. The other basic property is the incubation-period distribution, or the time the pathogen takes to grow in the body before symptoms first appear.

Wilkening's study brought dose-dependence to a debate over how long the incubation period is for inhalational anthrax. Published data from vaccine efficacy tests in which nonhuman primates were challenged with high doses of anthrax--up to a million spores--indicate an incubation period of one to five days. Data from Sverdlovsk, which exposed people to low doses probably on the order of 1 to 10 spores, indicate a longer incubation period, about 10 days. Whereas previous authors have debated whether nonhuman primate experiments or the Sverdlovsk data should be used to determine the incubation period for inhalational anthrax in humans, Wilkening demonstrates that both estimates are correct, with the difference between them being due to the dose dependence of the incubation period and the very different doses received in each case.

"If you are exposed to a higher dose, there is a much higher chance that an anthrax spore will germinate quickly, thus leading to a shorter incubation period," he says. "Sverdlovsk was a low-dose exposure event and, consequently, one would expect anthrax spore germination to take a longer time, thus leading to a longer incubation period."

Truth and consequences

Russian officials confiscated the medical records of the Sverdlovsk victims and have so far refused to release details of what happened on April 2, 1979. "It would be nice to know exactly what happened, because that would allow us to model the event more accurately," Wilkening says.

Nevertheless, based on weather and other data from the day of the event, scientists think that around 2 p.m. spores, or dormant cells that revive under the right conditions, were released from a military facility, and the Bacillus anthracis spores spread up to 5 kilometers downwind. People breathed in the spores, which geminated and incubated in the body for between four to 40 days before people began to feel ill or show signs of illness such as sore throat, coughing, pains, aches and runny nose--the same symptoms as flu--that indicated they had entered what doctors call the prodromal phase. Within four days, people passed the point of no return, called the fulminant phase, in which toxins from the bacteria had built up to such an extent that people went into shock and died.

It's impossible to save those who've entered the fulminant phase and difficult to save those who've entered the prodromal phase. But if people can start treatment after exposure but before symptoms appear, there's a good chance that they will survive--a conclusion Wilkening draws from work by colleagues at Stanford's Center for Health Policy. Treatment primarily consists of antibiotics such as ciprofloxacin, doxycycline or penicillin. While a vaccine to prevent anthrax exists, it is not yet available for the general public but would be made available to people exposed to anthrax, according to the Centers for Disease Control and Prevention website.

In his study, Wilkening ruled out two of the four models because they either did not fit the Sverdlovsk data or the nonhuman primate data, or both. "There are two models that people have used that should no longer be used to predict fatalities, models B and C." (The four models used in his analysis are labeled A-D for convenience.)

Using the two remaining models A and D, he predicted that a hypothetical attack releasing 1 kilogram of anthrax spores in Washington, D.C., would infect between 4,000 and 50,000 people, most of whom would die if not treated quickly with antibiotics. The difference of a factor of 10, Wilkening points out, is "an uncertainty with which we must live for the time being until better data can resolve which of the models A or D is more accurate."

Regarding decontamination efforts, the higher the probability of becoming infected at low exposure levels, the greater the need for effective decontamination, especially for indoor environments. Spores "by nature are hardy," Wilkening says. In the soil, out of the way of sunlight, they can last for a decade. "Residual contamination can be a very serious problem in the wake of an attack," Wilkening says. "Unfortunately, both models A and D predict that residual surface contamination from anthrax spores will be a problem. Consequently, we need to come up with effective indoor decontamination strategies."

Analysts such as Professor Lawrence Wein of the Graduate School of Business are considering the issue. Last year, he assessed decontamination and concluded cleaning buildings to make them safe to reoccupy was a billion-dollar proposition.

In addition, the four models make very different predictions about when symptoms would occur. The day after exposure, they predict between 10 and 1,000 people feeling sick, with more people getting sick in the viable versus discredited models.

"In terms of detecting the outbreak rapidly, this is a good thing because it says that doctors could recognize it [sooner]," Wilkening says.

In terms of treating people before they reach the prodromal phase, however, this is a bad thing because people become sick quicker. Wilkening's analysis may help policymakers reassess how fast antibiotics need to reach people. His best model says administering antibiotics by day three saves 90 percent of exposed people. "Today we cannot meet the three-day requirement," he warns.

North Korea's nuclear facility at Yongbyon, which had been "frozen" under international inspection since 1994, was reactivated this January for the production of plutonium. Just last week the North Koreans announced that they intended to use the resulting plutonium to make nuclear weapons, which only confirmed what we always believed.

If it keeps on its present course, North Korea will probably have six to eight nuclear weapons by the end of the year, will possibly have conducted a nuclear test and may have begun deployment of some of these weapons, targeted against Japan and South Korea. By next year, it could be in serial production of nuclear weapons, building perhaps five to 10 per year.

This is a nightmare scenario, but it is a reasonable extrapolation from what we know and from what the North Koreans have announced. The administration to this point has refused to negotiate with North Korea, instead calling on the countries in the region to deal with the problem. The strategy underlying this approach is not clear, but the consequences are all too clear. It has allowed the North in the past six months to move from canned fuel rods to plutonium and, in a few more months, to nuclear weapons. And the consequences could extend well beyond the region. Given North Korea's desperate economic condition, we should expect it to sell some of the products of its nuclear program, just as it did with its missile program. If that happens, a nuclear bomb could end up in an American city. The administration has suggested that it would interdict such transfers. But a nuclear bomb can be made with a sphere of plutonium the size of a soccer ball. It is wishful thinking to believe we could prevent a package that size from being smuggled out of North Korea.

How did we get into this mess?

For several decades North Korea has aspired to have nuclear weapons. During that period successive administrations have, through a combination of threats and inducements, curtailed their program but never their aspirations. In the late 1980s the first Bush administration saw the potential danger and persuaded the Soviet Union to pressure North Korea to join the nuclear Non-Proliferation Treaty and subject its nuclear facilities to international inspection. The North Koreans complied, but they stalled long enough to give them time to make and store enough plutonium for one or two nuclear bombs before the inspectors arrived.

Shortly after the Clinton administration took office, they tried again. As spent fuel was being taken from the nuclear reactor at Yongbyon, the North Koreans ejected the inspectors and began preparations for reprocessing. This would have given them enough plutonium for five or six additional nuclear bombs. President Clinton considered this sufficiently dangerous that he declared reprocessing a "red line." In response, I had the Joint Chiefs prepare a plan to use military force if necessary to prevent this outcome. When Kim Il Sung offered to negotiate the issue, Clinton responded that he would negotiate only if the North Koreans froze all activity at Yongbyon during the negotiation. In the end, military force was not necessary. The agreement that ended this crisis was far from perfect, but in its absence North Korea could today have 50 to 100 nuclear weapons.

But the North Koreans never gave up their desire for nuclear weapons. Even as they complied with the freeze at Yongbyon, they covertly started a second nuclear program at a different location. American intelligence discovered signs of this program and last fall confronted the North Koreans, who did not dispute the charge. The administration responded by stopping fuel oil deliveries called for under the old agreement, to which the North Koreans responded by reopening Yongbyon and racing to get nuclear weapons.

There are three basic approaches for dealing with this dangerous situation. The administration can continue to refuse to negotiate, "outsourcing" this problem to the concerned regional powers. This approach appears to be based on the hope that the regional powers will be able to prevail on North Korea to stop its nuclear program. But hope is not a strategy. If their hopes are not realized and North Korea continues on its present course, it will soon have a significant nuclear arsenal. And while the regional powers could play a role in resolving this crisis, they are unlikely to succeed in the absence of a clear American negotiating strategy in which they can participate.

A second alternative is to put economic pressure on North Korea and hope for "regime change." Or the United States could take military action to bring this change about. But while the regime may one day collapse, with or without economic pressure, there is no reason to believe that it will happen in time - the nuclear threat is imminent. Taking military action to force a timely regime change could result in a conflict comparable to the first Korean War, with casualties that would shock the world.

The third alternative is to undertake serious negotiations with the North Koreans to determine if there is a way to stop their nuclear program short of war. The administration is clearly reluctant to negotiate with the North Koreans, calling them loathsome and cheaters. It is easy to be sympathetic with this position; indeed, the only reason for considering negotiation with North Korea is that the other alternatives are so terrible. The administration, seeing the danger, has said that it "would not tolerate" a North Korean nuclear arsenal. The North Koreans responded to this declaration by accelerating their program. The conflict between our views and their actions is a formula for drifting into war. It is imperative that we stop that drift, and the only clear way of doing that is by negotiating.

Any negotiations with the North Koreans are likely to be difficult and protracted, so they should be predicated on a prior agreement that North Korea will freeze its nuclear activities during the negotiations. For negotiations to have a chance of success, they would need to have a positive dimension, making it clear to North Korea that forgoing nuclear weapons could lead it to a safe and positive future. But they would also need a negative or coercive dimension, both to induce North Korea to take the right path and to give us and our allies more credible options if diplomacy should fail. President Kennedy said it best: "We should never negotiate from fear, but we should never fear to negotiate."

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.