If you choose the latter, and turn up at said airport, your person and possessions will soon be packed tightly into a taxi that defies most known principles of mechanics. The driver will pick the right beat of the complex choreography that constitutes traffic here. Imagine large lumps of steel being hurled at high speed in seemingly random directions on a surface better suited to tanks than to clapped-out Toyotas, then remember you are enclosed in one of them. Welcome to Mexico City.
At the point when a tram, a truck and Tristar are about to converge on your taxi, you could start to feel breathless from both fear and the high altitude. But hold on tight, and your anxieties will evaporate.
Mexico City turns out to possess a calm and civilised soul, which rewards those with the modicum of courage required to seek it out. Imagine a slightly bedraggled version of Paris, and you are nearly there. Handsome, low-rise apartment buildings mingle with glamourous flourishes by 19th-century architects and the odd eruption of Mexico Moderno brashness.
The archaic street layout reflects the fact that the Spanish imposed their capital upon an ancient Aztec site, and furthermore one which straddles a geological fault line. Eleven years ago the earth shrugged a little, and at least 8,000 citizens died. Perhaps this was a final murmur of revenge from Moctezuma, whose palace lies buried beneath the present Palacio Nacional. Traces of the original have been eradicated by an edifice that shows up all the eccentricities inherent in Mexico. The ruling junta - which Mario Vargas Llosa called "the perfect dictatorship" -rejoices in the contrary name of the Institutional Revolutionary Party. A bewildering nation indeed.
Tourists are allowed to delve into the heart of Mexico, and tour the Palacio Nacional for free. It resembles a promising but not perfect hand at poker: a scarlet-tinged frontage of solid Baroque, topped by Twenties triumphalism that belongs to a quite different suit. Inside, you are instantly diminished by the size and power of Diego Rivera's murals. Mexico's history, from civilisation through subjugation to revolution, wraps itself tortuously around a grand staircase.
After this instant briefing in the intrigues of colonialism, descend to a central square that rivals the airport in area. The Plaza Mayor has been the city's main meeting-place for a millennium or more. Across it, the state, in the form of the Palacio Nacional, faces off against the Church. Mimicking the desecration of the Aztec palace, the cathedral was built above the site of the temple. (Or rather, the sites. The ancient calendar was based on a cycle of 52 years, and at the end of each cycle a new temple was built.) Hernn Cortes and his fellow conquistadores destroyed the Aztecs with grotesque ease. Some of the architecture of conquest was borrowed from the vanquished civilisation - for example the pyramidical references in the cathedral - but mostly they set about constructing a city in the image of Europe.
That they succeeded is most evident along the Paseo de la Reforma. The broadest and grandest of avenues slices arrogantly across the city, depositing elegant edifices along the way. It unravels in Chapultepec Park, a flourish of green that marks the western extent of the city centre. And here you find one of the finest museums in the world.
Three historical strands are entwined here. The first is that the indigenous cultures of Mexico were not wholly eradicated by the conquistadores. Descendants of the survivors can be found in communities scattered around the country; soon their numbers will exceed pre-Conquest levels. The second is that the boundaries of modern Mexico comprise an arbitrary geographical creation of the Spanish colonialists: citizens of Tijuana (see below) have much more in common with Californian just across the state line than with the Mayan people of Chiapas (opposite). The third is that the Sixties saw an assertion of Mexicanidad, as the country clawed its way into the polite society of established nations. The double climaxes were the Olympics of 1968 and the World Cup of 1970, but the most lasting token is the extraordinary National Anthropological Museum.
Forget the Internet; Mexico invented a network for exploring cultural cross-references 30 years ago, and housed it in (still) dramatic halls that sprout out of the parkland. Everything that could be salvaged from the Conquest has been assembled here, from the tablets used to calculate the Aztec calendar to the dazzling images of the Mayans. The descriptions are almost exclusively in Spanish, but English-speaking guides are on hand to help explain the repository of national heritage.
"Heritage" seems too awkward and tawdry a word to describe the collection. Its main effect is to make you want to leave town straight away and see some of the original sites. Fortunately, the most striking of all is close to Mexico City (and getting nearer all the time, as the suburbs advance). Teotihuacn is 30 miles north east of the museum. As you struggle free of the shanty settlements, there is no hint that you are about to encounter the greatest historical site in North America.
You will, if you were paying attention at the museum, have learnt that Teotihuacn means "the place where men become gods". The first Mesoamerican civilisation planned that this transition should take place in suitably heavenly surroundings. So 21 centuries ago, the Avenue of Dead was laid out. The approach is encumbered by souvenir vendors, but once free of them you can walk through a petrified city of awesome proportions. Much of the fabric of this once-noble place lies ruined on either side of the thoroughfare, whose name is horribly appropriate. Teotihuacn had expired by the eighth century, abandoned in favour of the lower altitude and better water supplies on the present site of Mexico City. But time has had only the the most superficial effect so far on the miraculous Pyramid of the Sun and its smaller, younger sibling, the Pyramid of the Moon.
Before you come down to earth, take a deep breath. Mostly, Mexico City hides in a volcanic hollow beneath a blanket of smog - hence the smouldering glow that greets incoming planes. Humanity can become too intense. Since 1970, the number of people living in Mexico has exactly doubled - to 96 million. From your experience of the Distrito Federal (capital area), you would be forgiven for thinking that the increase has taken place entirely within the ambiguous city limits. Today, Mexico City has perhaps 25 million citizens. Tomorrow, 3,000 more citizens will join them, as the capital hurtles towards the demographic equivalent of terminal velocity. Get there soon, before the city reaches its inevitable conclusion.