Imagine a land where bombs explode almost daily and children are killed by terrorists without conscience. On one side we find a people who suffered through the horror of slave-labor death camps; on the other side a people who suffered through a terrible war -- which they began when what they felt was their property was seized from them -- a terrible defeat and (for them) a terrible occupation. Now imagine those same peoples 15 years later, living side by side, peacefully.

This sounds like a pipe dream: The Middle East could never be this way, we think. But we do not need to imagine this land.

We are living in it.

One century after America's Civil War, the descendants of slaves daily faced the twin terrors of homicide and arson. Yet only 15 years after the rise of the Rev. Martin Luther King Jr., the back of segregation and neo-Confederate violence had been broken.

Can Palestinians likewise mount a successful, nonviolent movement toward peaceful co-existence with their former adversaries? In short, can history repeat itself?

How expensive would it be for us if it did not? America spends an estimated $3 billion a year in support of Israel. This support is justified because Israel is a democracy and our main ally in the region. Yet we also spend $2 billion supporting Israel's nondemocratic neighbor, Egypt. Billions more have been spent maintaining bases in Saudi Arabia, Kuwait and now Iraq. We justify these expenditures by surrendering to the serpentine excuses of realpolitik: We need the support of key figures and families in the region, we say, and so we have to work with them. Just as we once said of the Dixiecrats and other segregationist politicians in the American South.

We can transform this paradigm, as we did then, and at little cost to ourselves. We can utilize the experience of the civil rights movement -- which Secretary of State Condoleezza Rice knows all too well (her childhood friend was killed by an improvised explosive device in segregated Birmingham) -- to assist Palestinians in their stride toward peace. What we need is a Muslim Martin Luther King.

Many believe that leaders are born, not made, but programs to cultivate leadership and promote good will among men have been used successfully for generations. Oxford's Rhodes Scholarship is one such example. Its idea is to bring the best and brightest from the British Commonwealth (and beyond) to build strong ties among English-speaking peoples, and stronger ties to England. Founder Cecil Rhodes, pirate though he was, wished for there to be "an understanding between the three great powers" -- America, Britain and Germany -- that "will render war impossible."

What we recommend is a sister program for the Middle East. One could hold a competition for the 30 best young orators in the Palestinian diaspora. (King first gained prominence at age 26, and the Rhodes Scholarship is only for men and women under that age.) Send them to an American institution such as Stanford University, where they could study for the doctorate under Professor Clayborne Carson, director of the Martin Luther King Jr. Papers Project and historian of the civil rights movement and the Student Non-Violent Coordinating Committee. Then, after they have spent several years studying the African American experience with special courses and lecturers, focusing especially on the efficacy of nonviolent direct action, send them back to their native lands.

This is no program of indoctrination. Indeed, it would be detrimental if American spy organizations were to infiltrate or interfere with the King scholars in any way: the scholars would lose all credibility at home. Just as King spoke out against Southern injustice (and American injustice in Vietnam), the King scholars must be free to criticize America and, it is to be expected, the occupation. They would not be able to lead the Arab street otherwise.

By bringing young leaders from the region, we would avoid disasters like the U.S. Army's flirtation with mathematician Ahmed Chalabi, a man who had no real roots in Iraq, but whom America still wished to enthrone as a new shah. The Chalabi experiment blew up in America's face like a roadside bomb.

The King scholarship program might cost only $2 million per year -- an endowment of perhaps $20 million could put it on its feet indefinitely. And, coupled with the application of "soft power," the export of American culture -- notably, hip-hop music, which serves both as a mechanism for promoting intercultural understanding and as a nonviolent channel for youthful aggression -- one could reasonably expect to see the flower of peace bloom in the desert of despair.

Two specific aspects of the civil rights movement would be most effective in resolving the Israeli-Palestinian conflict: first, the proper utilization of legal instruments as a way to wage a nonviolent campaign; second, the utilization of mosques to mobilize a nonviolent grassroots struggle. Mosques in the West Bank and Gaza can be used to promote peace over violence and terrorism, and the African American experience can teach Palestinians how to do this.

In "The Trial" by Franz Kafka, at one point two men stand outside a gate. One seeks to enter; the other seeks to prevent him from entering. Both men wait there for their entire lives. Though one is guard and the other the one guarded, both men are prisoners.

In game theory, the branch of mathematics made famous by "A Beautiful Mind," there is a paradox called the Prisoners' Dilemma. Each of two prisoners may believe it is in his best interests to harm the other, but one can mathematically prove that both men would be better off if they cooperated. A King scholars program might help us resolve the prisoners' dilemma that is the Middle East.

This is a utopian dream, perhaps. But another man dreamed, once, and we all know what became of that man's dream.

We are living it.

Does the conflict in Iraq amount to a civil war? In many ways, the public debate over this question is largely political. Calling Iraq a "civil war" implies yet another failure for the Bush administration and adds force to the question of whether U.S. troops still have a constructive role to play.

Politics aside, however, the definition of civil war is not arbitrary. For some -- and perhaps especially Americans -- the term brings to mind all-out historical conflicts along the lines of the U.S. or Spanish civil wars. According to this notion, there will not be civil war in Iraq until we see mass mobilization of sectarian communities behind more or less conventional armies.

But a more standard definition is common today:

1) Civil war refers to a violent conflict between organized groups within a country that are fighting over control of the government, one side's separatist goals, or some divisive government policy.

By this measure, the war in Iraq has been a civil war not simply since the escalation of internecine killings following the bombing of a Shiite shrine in Samarra in February, but at least since the United States handed over formal control to an interim Iraqi government in June 2004.

Here's why: Although the insurgents target the U.S. military, they are also fighting the Shiite-dominated Iraqi government and killing large numbers of Iraqis. There is little reason to believe that if the United States were suddenly to withdraw its forces, they would not continue their battle to control or shape the government.

Political scientists who study civil war have proposed various refinements to this rough definition to deal with borderline cases. One issue concerns how much killing has to occur -- and at what rate.

2) For a conflict to qualify as a civil war, most academics use the threshold of 1,000 dead, which leads to the inclusion of a good number of low-intensity rural insurgencies.

Current estimates suggest that more than 25,000 Iraqis have been killed in fighting since the U.S.-led invasion in March 2003 -- a level and rate of killing that is comparable to numerous other conflicts that are commonly described as civil wars, such as those in Lebanon (1975-1990) and Sri Lanka (beginning in 1983).

The organization -- or rather, disorganization -- of the warring communities in Iraq means that a large-scale conventional conflict along the lines of the U.S. Civil War is unlikely to develop. More probable is a gradual escalation of the current "dirty war" between neighborhood militias that have loose ties to national political factions and are fighting almost as much within sectarian lines as across them.

This is roughly what happened in Lebanon and at a lower level in Turkish cities in the late 1970s. Ethnic cleansing will occur not as a systematic, centrally directed campaign (as in Bosnia), but as a result of people moving to escape danger.

And there's another twist to the terminology:

3) If the conflict in Iraq becomes purely a matter of violence between Sunni and Shiite communities driven by revenge and hatred rather than by political goals, many political scientists would say that it is something other than civil war.

Almost no one, for example, calls the Hindu-Muslim violence in India a civil war.

A civil war has to involve attempts to grab power at the center of government or in a given region, or to use violence to change some major government policy.

In Iraq's case, however, the vacuum of power at the center means that communal violence will inevitably be tied to struggles for political power and control.

A final complication concerns the nature of international involvement. Some argue, for example, that the war in Bosnia should be seen as an interstate war rather than a civil war, since the Bosnian Serb forces were armed and directed largely by Belgrade. Post-Mobutu violence in Congo is often termed a civil war, even though fighters have been closely tied to armies from neighboring states.

4) A conflict may be both a civil and an interstate war at the same time.

The Vietnam War, for instance, clearly comprised both a civil war in the South and an interstate war involving the North, the South and the United States.

Iraq may be moving in this direction. The United States and Britain are already openly involved, and such neighboring countries as Iran and Syria are more covertly involved. Not that it matters to the people dying there, but the next debate here may turn on whether what is already a civil war in Iraq should be viewed as an interstate war as well.

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.

Before attacking Iraq in March 2003, the United States told the world that Saddam Hussein had reconstituted his nuclear weapons program in defiance of the United Nations. That claim, used to justify the war, was based on assessments provided by the United States intelligence community. But as everyone now knows, those assessments were wrong. So Jeffrey T. Richelson's history of American nuclear intelligence, including our attempts to learn about Iraq's nuclear program, could hardly be more timely.

In "Spying on the Bomb," Richelson, the author of several books on American intelligence, has brought together a huge amount of information about Washington's efforts to track the nuclear weapons projects of other countries. He examines the nuclear projects of Nazi Germany, the Soviet Union, China, France, Israel, India, South Africa, Taiwan, Libya, Pakistan, Iran and North Korea, as well as Iraq. Through interviews and declassified documents as well as secondary works, he sets out briefly what we currently know about those projects and compares that with assessments of the time.

This may sound like heavy going, but Richelson writes with admirable clarity. And along the way he has fascinating stories to tell: about plans to assassinate the German physicist Werner Heisenberg during World War II; about discussions in the Kennedy and Johnson administrations on the possibility of attacking Chinese nuclear installations; about Indian measures to evade the gaze of American reconnaissance satellites; and about the bureaucratic infighting over the estimates on Iraq.

The United States has put an enormous effort into gathering information about the nuclear projects of other countries. After World War II it equipped aircraft with special filters to pick up radioactive debris from nuclear tests for isotopic analysis. It created a network of stations around the world to register the seismic effects of nuclear explosions. Most important, in 1960 it began to launch reconnaissance satellites that could take detailed photographs of nuclear sites in the Soviet Union and China. Richelson occasionally speculates about the role of communications intercepts and of spies, but these appear from his account to have been much less important than the other methods of collecting information.

Through these means the United States has gathered a vast quantity of data, sometimes to surprising effect. Intelligence played a crucial role in the cold war, for instance, by reducing uncertainty about Soviet nuclear forces. Alongside such successes, however, there have been failures. One notable example concerned the first Soviet test, which took place in August 1949, much sooner than the C.I.A. had predicted. Another was the failure to detect Indian preparations for tests in May 1998, even though at an earlier time the United States, with the help of satellite intelligence, had managed to learn about preparations the Indians were making and to head off their tests.

But the most serious failure of all was in Iraq in 2003, because in no other case did the intelligence assessments serve as justification for the use of military force. The information needed for avoiding political surprise is one thing. That needed for preventive war is quite another, if only because of the consequences of making a mistake.

Beyond making the uncontroversial recommendation that "aggressive and inventive intelligence collection and analysis" should continue, Richelson draws no general conclusions. That is a pity, because his rich material points to issues that cry out for further analysis. He suggests in one or two cases that failures sprang from the mind-set of the intelligence community, but he does not elaborate on this point. He has little to say about relations between policy makers and the intelligence community, even though the quality of intelligence and the use made of it depend heavily on that relationship.

His focus is no less narrow in his discussion of foreign nuclear projects. He concentrates on the programs themselves, paying very little attention to their political context. Does that reflect a technological bias in nuclear intelligence? Would, for example, the prewar assessment of Iraqi nuclear capabilities have been more accurate if it had paid more attention to the broader political and economic circumstances of Hussein's regime?

The task of intelligence has become more complex than it was during the cold war. A single dominant nuclear opponent has now been replaced by a number of nuclear states, along with states and stateless terrorists that are aiming to get their hands on nuclear weapons. Meanwhile, the technology needed for producing nuclear weapons has become easier to acquire.

Many critics believe the recent performance of the intelligence community shows it has not responded adequately to this new situation. Richelson does not have much to say on this question; nor does he discuss the likely impact of the current reforms, initiated in response to the Iraq war, on the quality of intelligence. His reticence may imply that he does not think reform is necessary. Still, it is disappointing that he does not draw on his historical survey to discuss whether new approaches are needed for dealing with nuclear threats, and, if so, what those new approaches might be.