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 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.

Several models have been proposed for the dose-response function and the incubation period distribution for human inhalation anthrax. These models give very different predictions for the severity of a hypothetical bioterror attack, when an attack might be detected from clinical cases, the efficacy of medical intervention and the requirements for decontamination. Using data from the 1979 accidental atmospheric release of anthrax in Sverdlovsk, Russia, and limited nonhuman primate data, this paper eliminates two of the contending models and derives parameters for the other two, thereby narrowing the range of models that accurately predict the effects of human inhalation anthrax. Dose-response functions that exhibit a threshold for infectivity are contraindicated by the Sverdlovsk data. Dose-dependent incubation period distributions explain the 10-day median incubation period observed at Sverdlovsk and the 1- to 5-day incubation period observed in nonhuman primate experiments.

Part I of this article looks at the American institution of legal controls on the executive branch and their subsequent erosion post-9/11. It explores three changes incorporated in the USA PATRIOT Act: alterations to the Foreign Intelligence Surveillance Act; the introduction of Delayed Notice Search Warrants; and the expansion of National Security Letters. Outside of this legislation, the weakening of the Attorney General guidelines

increased the FBI's ability to collect information. The article highlights the Department of Defense's ("DOD") movement into the domestic surveillance realm. It discusses a number of operations both inside and outside the DOD, such as TALON, Echelon, Carnivore, Magic Lantern, TIPS, and the use of watch lists. Part I concludes with a discussion of the data mining efforts underway. The article argues that Total Information Awareness, ADVISE, and other projects catapult surveillance into another realm. Moreover, while any one program, such as the NSA initiative, may be considered on narrow grounds, the sheer breadth of current powers raises important concerns.

Part II notes that, until recently, no laws governed police and intelligence service information-gathering authorities in the UK. Extraordinary stop and search powers for terrorist-related offences, and warrants for police interference with property provided exceptions. But physical searches of property conducted by the intelligence services, the interception of communications by law enforcement and intelligence agencies, the use of covert surveillance or "electronic bugs," and the running of covert human intelligence sources operated under the legislative and judicial radars. Beginning in the mid-1980s, the European Court began to raise objections to the lack of safeguards and statutory framework. But each time the Court handed down a significant finding against the United Kingdom, the state responded not just by, at least on the surface, meeting the demands of the European Convention of Human Rights, but, it appears, by expanding executive surveillance authorities. Moreover, the warrant system introduced retained control within the executive branch. Not subject to judicial review, the standard applied is reasonable suspicion--considerably less robust than probable cause. Like the United States, Britain draws on new technologies; the country leads the world in its use of public surveillance systems.

Having laid out legal developments on both sides of the Atlantic, Part III moves to policy concerns: it begins by briefly exploring the substantive, political, legal, social, and economic risks posed by such measures. It then considers six approaches that would help to mitigate the risks. First is the possibility of creating a property right in personal information. The second centers on the regulation of access, transfer, use, and retention of data. Such efforts would satisfy demands for accountability and transparency in both the public and private sector. A third possibility centers on scaling back the existing powers of the state. Fourth, both countries may contemplate placing limits on what constitutes national security. Fifth, alternative safeguards and oversight structures deserve attention - such as reporting requirements, random audits, the creation of ombudspersons, the insertion of the judiciary, and (in the UK) allowing intercepted communications to be used as evidence. Sixth, preventing countries from introducing ever greater powers of surveillance under the claim that they are only temporary in nature would force legislatures to consider the long-term impact of provisions beyond the immediate terrorist threat.

In his State of the Union address in January, President Bush stressed the importance of improving math education. He proposed to "train 70,000 high school teachers to lead advanced placement courses in math and science, bring 30,000 math and science professionals to teach in classrooms, and give early help to students who struggle with math."

But where will these teachers come from? And will the training of teachers be sufficient to increase the number of students choosing math and science careers? And why does all this matter?

Because mathematics is the foundation of the natural sciences. It is no coincidence that Isaac Newton, the man who formulated the law of gravitational attraction that revolutionized our understanding of the universe, was also the man who popularized the calculus. And the natural sciences, however pure, are what give us airplanes, cable TV and the Internet.

In the 2003 Program for International Student Assessment, a test that measures math literacy, American 15-year-olds performed worse than their peers in 23 countries, as well as those in Hong Kong. It's not hard to see why. According to the National Council of Teachers of Mathematics, 40 percent of the nation's middle school math teachers do not have the equivalent of an undergraduate minor in math. The average starting salary of a teacher is only $30,000, whereas the average starting salary for a recent college graduate in computer science or engineering is $50,000.

Short of following the British, who have proposed paying experienced math teachers more than $100,000, with a guaranteed minimum of $70,000, where will we find a way to attract the thousands of teachers George Bush wants?

New York State initiated an innovative program to bring teachers from Jamaica for two or four years to teach in New York schools. Jamaica, a developing nation where one U.S. dollar equals 65 Jamaican dollars, is nonetheless a stable, English-speaking nation with an unbroken democratic tradition; it stands poised to beat the United States in establishing the world's first Institute for Mathematical Methods in Counterterrorism. When teachers for the New York program were recruited on the campus of the University of the West Indies, recruiters found more experienced math and science teachers than they ever dreamed they would.

But you can have all the teachers in the world and still not inspire kids to learn math. My friend Autumn e-mailed me about her nephew, Joshua: "He's upset because he's asked several of the math teachers why math is important or what are certain formulas used for -- there has to be a use, correct?"

Autumn told her nephew about my work in counterterrorism and for the television crime drama "Numb3rs." Autumn reported, "He's told his math teachers about you as well, and about the show 'Numb3rs.' He's informing them that through something called lattice theory you are managing to fight terrorists -- all with math."

Mathematics is art, and should be appreciated for its beauty, not simply for its utility. But we cannot expect 11 year-olds to cherish totally order-disconnected topological spaces as much as professional mathematicians do.

As I first proposed in January 2005, television shows like "Numb3rs" (or "Medium") -- where the main characters are mathematicians -- could work with the National Council of Teachers of Mathematics to show kids how math is really used; the council and Texas Instruments are now working together to use "Numb3rs" to promote math literacy in schools.

Another way to inspire kids is to relate mathematics to something they see every day. In order to excite students and draw funding to his school, school superintendent Ronald Ross of Roosevelt, N.Y., has begun looking into the idea of creating a curriculum involving math and counterterrorism. What kinds of topics would students learn?

The opening line of the Oscar-winning movie "A Beautiful Mind" is "Mathematicians won the war." During World War II, the mathematics underlying cryptography played an important role in military planning. Winston Churchill admired Alan Turing, the mathematician who had mastered the German codes, recognizing him as the man who had perhaps made the single greatest individual contribution to defeating Hitler.

At Los Alamos, the lab that built the atomic bomb, Cliff Joslyn uses lattice theory to mine data drawn from thousands of reports of terrorist-related activity to discover patterns and relationships that were previously in shadow.

Lattice theoretical methods developed at MIT tell us the probability that we have disabled a terrorist cell, based on how many men we have taken out and what rank they hold in the organization. Lauren McGough, a Massachusetts high school student, tested the accuracy of this model by getting her classmates to pretend they were terrorists, passing orders down a fictitious chain of command, essentially confirming what the theory predicts.

High school students could learn algebra, trigonometry, calculus and logic while also learning concrete applications involving homeland security. No longer would students yawn and ask, "What is math good for?" Beauty could defeat both terror and boredom.

Whatever you may think of the State of the Union address, when it comes to supporting math education, we should all see pi to pi. President Bush is correct when he says that mathematics education in America must improve if the United States is to stay economically competitive, but the stakes are much higher than that. During the Cold War, the United States would not have tolerated a military gap between itself and its adversaries. Yet today, with 61 percent of all U.S. doctorates in math going to foreigners (15 percent to Chinese), we readily accept a "math gap."

Dollar for dollar, the best defense against our adversaries' weapons of mass destruction may be our allies in the Americas, armed with weapons of math instruction.

Improving math education is not merely a smart idea. It is a matter of national security. Algebra is one revolutionary Islamic concept we cannot afford to neglect or ignore.