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.

Iran has climbed to No. 1 on the Washington crisis hit parade. The question of how to stop Iran's nuclear program has unleashed a torrent of punditry. Advocates of diplomacy and a military strike spar on television and in op-ed pages.

Iran's nuclear ambitions deserve our attention. But even by the most alarmist estimates, Iran is years away from being able to build a nuclear warhead.

Meanwhile, over in Northeast Asia, North Korea now has enough fissile material for five to seven weapons and is quietly churning out enough plutonium to build at least one warhead a year, according to rough intelligence estimates. More ominously, work is moving ahead on a new reactor that could potentially produce enough separated plutonium for up to 10 weapons a year.

Somehow this danger prompts no sense of urgency in Washington. After a promising breakthrough last September, the six-party talks to halt the program have lapsed into a stalemate that is close to total collapse.

The Bush administration seems unconcerned. Diplomacy has ground to a halt. The North Koreans refuse to return to the six-party talks. The White House has barred its chief negotiator from talking directly with them, despite Pyongyang's desire to meet and the urging of our six-party partners.

Administration officials have recently floated a report that they are considering a new initiative to negotiate a peace treaty with North Korea. This is a smoke-screen to conceal an empty North Korea policy. According to administration officials, the peace treaty idea has been kicking around for months without going anywhere. South Korean officials tell me that they have been waiting, so far in vain, for any serious detailed discussion of this proposal.

It is the president himself who opposes direct negotiations with Pyongyang, over anything, including a peace treaty. He sees direct talks with North Korea or Iran as an act of weakness. "Somehow,'' he said last month, "the world ends up turning the tables on us.''

In reality, the administration is content to pursue a strategy of going after North Korean counterfeit currency and production of amphetamines and cigarettes, hoping to cut off the flow of funds from these activities. According to administration officials, Under Secretary of State Robert Joseph, the driving force behind this policy, gleefully talks about ``turning out the lights'' in Pyongyang.

Administration officials claim they are drying up slush funds that North Korean dictator Kim Jong Il uses to buy the loyalty of his subordinates. Some even suggest this could trigger a coup against Kim, with the Chinese pulling the strings.

But American intelligence experts who monitor North Korea closely see little evidence to support the conclusion that North Korea is being brought to its knees. Even if the measures are drawing blood, it is self-delusional to believe that this will bring down a regime that has already proven it is willing to starve its own population to stay in power.

The administration seems intent as well on pressing China and South Korea to curb their trade and investment with the North. The administration's special envoy on human rights in North Korea, Jay Lefkowitz, seems to spend most of his time attacking the South for setting up an industrial park in Kaesong in the North. He portrays it as exploiting slave labor. The South Koreans defend it as a vehicle to bring capitalism into the communist North.

The Bush administration's combination of attempted coercion and diplomatic freeze has only two visible effects so far.

First, it lends credence to North Korean claims that the United States, contrary to the joint statement issued last September, is still intent on overthrowing their regime.

Second, it undermines gains made by allowing chief envoy Christopher Hill to hold direct talks with his North Korean counterparts. That demonstrated a flexibility and confidence that disarmed critics, particularly in South Korea, and isolated the North. It strengthened coordination with China and South Korea, the two players with the most leverage over the North.

Now officials in both those capitals again question American readiness to seriously negotiate. Beijing and Seoul are even more convinced that pushing market reforms is the only route to bring the North to give up its nuclear option. Next month former South Korean President Kim Dae Jung will revisit his historic summit with the North Korean leader in 2000.

This growing gap with our allies and partners is deadly. Even if we wanted to opt for coercion, the United States can't do so alone. For that reason, it is urgent that the United States regains the diplomatic upper hand.