Cairo has been the largest city in Africa and the Middle East ever since the Mongols wasted Imperial Baghdad in 1258. Acknowledged as Umm Dunya or " Mother of the World " by medieval Arabs, and as Great Cairo by nineteenth-century Europeans, it remains, in Jan Morris's words, "one of the half-dozen supercapitals - capitals that are bigger than themselves or their countries the focus of a whole culture, an ideology or a historical moment". As Egypt has been a prize for conquerors from Alexander the Great to Rommel, so Cairo has been a fulcrum of power in the Arab world from the Crusades unto the present day. The ulema of its thousand-year-old Al-Azhar Mosque (for centuries the foremost centre of Islamic intellectual life) remains the ultimate religious authority for millions of Sunni Muslims, from Jakarta to Birmingham. Wherever Arabic is spoken, Cairo's cultural magnetism is felt. Every strand of Egyptian society knits and unravels in this febrile megalopolis.

Egyptians have two names for the city, one ancient and popular, the other Islamic and official. The foremost is Masr , meaning both the capital and the land of Egypt - an ur-city that endlessly renews itself and dominates the nation, an idea rooted in pharaonic civilization. (For Egyptians abroad, "Masr" refers to their homeland; within its borders it means the capital.) Whereas Masr is timeless, the city's other name, Al-Qahira (The Conqueror), is linked to an event: the Fatimid conquest that made this the capital of an Islamic empire stretching from the Atlantic to the Hindu Kush. The name is rarely used in everyday speech.

Both archetypes still resonate and in monumental terms are symbolized by two dramatic landmarks : the Pyramids of Giza at the edge of the Western Desert and the great Mosque of Mohammed Ali - the modernizer of Islamic Egypt - which broods atop the Citadel. Between these two monuments sprawls a vast city, the colour of sand and ashes, of diverse worlds and time zones, and gross inequities. All is subsumed into an organism that somehow thrives in the terminal ward: medieval slums and Art Deco suburbs, garbage-pickers and marbled malls, donkey carts and limos, piousness and "the oaths of men exaggerating in the name of God". Cairo lives by its own contradictions.

This is a city, as Morris put it, "almost overwhelmed by its own fertility". Its population is today estimated at around eighteen million and is swollen by a further million commuters from the Delta and a thousand new migrants every day. Today, one third of Cairene households lack running water; a quarter of them have no sewers, either. Up to three million people reside in squatted cemeteries - the famous Cities of the Dead . The amount of green space per citizen has been calculated at thirteen square centimetres, not enough to cover a child's palm. Whereas earlier travellers noted that Cairo's air smelt "like hot bricks", visitors now find throat-rasping air pollution , chiefly caused by traffic. Cairo out-pollutes LA every day of the week: breathing the atmosphere downtown is reputedly akin to smoking thirty cigarettes a day.

Cairo's genius is to humanize these inescapable realities with social rituals . The rarity of public violence owes less to the armed police on every corner than to the dowshah. When conflicts arise crowds gather, restrain both parties, encourage them to rant, sympathize with their grievances and then finally urge: " Maalesh, maalesh " (Let it be forgiven). Everyday life is sweetened by flowery gestures and salutations; misfortunes evoke thanks for Allah's dispensation (after all, things could be worse!). Even the poorest can be respected for piety; in the mosque, millionaire and beggar kneel side by side.

Extended-family values and neighbourly intervention prevail throughout the baladi quarters or urban villages where millions of first- and second-generation rural migrants live, whilst arcane structures underpin life in Islamic Cairo. On a city-wide basis, the colonial distinction between "native quarters" and ifrangi (foreign) districts has given way to a dynamic stasis between rich and poor, westernization and traditionalism, complacency and desperation. The city's tolerance has recently been further strained by natural and man-made calamities. In October 1992, up to a thousand people died in an earthquake , when shoddily built high-rises and hovels collapsed across the city. Its image took a worse battering abroad after the shooting of seventeen Greek tourists in 1996 and the firebombing of a German tour bus a year later - although the tourists now seem to be making a cautious return. Every year its polarities intensify, safety margins narrow and statistics make gloomier reading. The abyss beckons in prognoses of future trends , yet Cairo confounds doom sayers by dancing on the edge.