"We must stop the rebels' offensive, otherwise the whole of Mali will fall into their hands -- creating a threat for Africa and even for Europe," said the French foreign minister, Laurent Fabius.

3) Exporting jihad

The greatest risk of the Mali campaign is that it will actually nurture the very threat that Fabius worries about: serving as a recruiting sergeant for jihadists, to rally the faithful against a "crusader" enemy in Muslim lands. Two jihadist sites -- the Sinam al-Islam Network and al-Minbar Jihadi Media Forum -- have already urged support for fighters in northern Mali, saying, "Rise O servants of Allah, let us set a fire under the feet of the falling French cross."

There is also the danger that extremists among the 5 million Muslims in France, the vast majority of them of North and West African origin, may seek revenge for French intervention. Less than a year ago, French intelligence services moved against militant cells after a young gunman who had traveled to the Pakistani tribal territories shot dead seven people in Toulouse.

President Francois Hollande has already ordered tighter security in public places.

"France is watching individuals who want to go to Afghanistan, Syria and the Sahel," said Interior Minister Manuel Valls. "We're watching those who could return here."

Mali's neighbors could also be drawn in if they support the French intervention. Algeria has gone to great lengths to insulate itself from Mali's turbulence, but Wednesday a militant group known as Qatiba -- led by a veteran Algerian jihadist, Mokhtar Belmokhtar -- attacked a gas installation in eastern Algeria and claimed afterward to be holding dozens of foreigners. The group said the attack was in retaliation for Algeria permitting French overflights as part of its operations in Mali.

For the Algerians, the assault on a critical part of its vital gas industry was a major embarrassment.

Security analysts said another group of militants appear to have attacked a Malian town from neighboring Mauritania.

Thirty thousand French citizens live in West Africa; eight are already held by Islamist extremists. Senegal has stepped up security in the capital, Dakar, especially in locations frequented by foreigners. And a former U.S. ambassador in Nigeria, John Campbell, writes on the Council on Foreign Relations website that many Nigerians believe the local group Boko Haram has developed links with AQIM.

"If such links do exist on meaningful terms, it would seem likely that Boko Haram will escalate their attacks in northern Nigeria in solidarity with its Islamic brothers," he writes.

4) The soul of Islam

Twelve years ago, Mali was one of six developing nations invited to attend the G8 summit in Italy, and was seen as a beacon of civilian rule and stability in Africa. After chronic instability in the years after independence, it achieved a peaceful transfer of power from one democratically elected president to the next in 2002. (The presidential election set for April 2012 never took place in the aftermath of the coup.) It had a thriving press and lively radio stations. Women had a role in public life. Indeed, in 2011 the prime minister was a woman.

Despite their country's poverty and frequent food shortages, Malians had a reputation for moderation and tolerance, and a rich history as one of the intellectual centers of Islam.

Most Malians are of the Sufi tradition -- a mystical interpretation of Islam that includes a reverence for saints and is despised by puritanical Sunnis.

The city of Timbuktu (sometimes called the city of 333 saints) was a religious and educational center in the 15th and 16th centuries, and its libraries had priceless collections of Islamic documents and books. Its tombs and mosques comprise a UNESCO World Heritage Site, and attracted scholars and tourists from all over the world.

Ansar Dine set about destroying those tombs, insisting they were idolatrous. Throughout the past few months, there have been reports of Malians' shock at seeing public floggings and amputations in areas controlled by militant groups. Radio stations were ordered to stop playing music and instead broadcast verses from the Koran.

UNESCO's secretary general, Irina Bokova, said last July, "The attack on Timbuktu's cultural heritage is an attack against this history and the values it carries -- values of tolerance, exchange and living together, which lie at the heart of Islam. It is an attack against the physical evidence that peace and dialogue is possible."

Mali's glorious musical tradition derived from poets known as griots, highly influential teachers and guides. From this background has blossomed an extraordinary succession of world-class musicians (Ali Farka Toure, Tinariwen, kora player Toumani Diabate and the Super Rail Band to name just a few) who have won fans as diverse as Jimmy Page and Ry Cooder.

So as much as it is a military and political battle, the struggle for Mali's future is also cultural and religious. It pits a tolerant Islamic tradition -- which celebrates music and in which women have a public life -- with an ascetic interpretation that bans music, forbids education of girls and destroys ancient tombs and shrines as "idolatrous."

5) A humanitarian crisis

Hundreds of thousands of Malians are now either refugees in camps outside the country or internally displaced. Most are dangerously prone to malnutrition and disease. There are at least 150,000 refugees now in neighboring countries. More than 50,000 live in one camp alone in Mauritania, where Doctors Without Borders has found chronic rates of malnutrition among children. Malaria and diarrhea are killing infants.

"It is hard to say when the refugees will be able to return home, but many have already suffered as a result of this crisis," said Karl Nawezi, head of the non-governmental organization's operations in Mauritania.

"The influx of refugees is far from over," he said. And many families are tempted to leave the relative safety of the camps because they are herders who need to return to their animals.

Additionally, some 200,000 Malians have fled south to escape the Islamists. Even today, they are still arriving in towns like Segou as the battle lines to the north shift in the sands.