Under the paving of the Zocalo there is a lake bed, and under that, the island city of Tenochtitlan. The Aztecs founded it in the fourteenth century on a swampy island in Lake Texcoco, linked it to the shore with causeways and filled the lake with floating gardens, and when Hernan Cortes arrived in 1519 he found a city larger and cleaner than any in Spain. After the conquest in 1521 the Spaniards drained the lake, built their cathedral on the ruins and began a new capital, and the result is the layered centre we see today. The Metropolitan Cathedral, a huge, ponderous baroque pile that took nearly three centuries to finish, leans noticeably, because the ground beneath it is soft clay, and engineers have spent decades trying to stop it sinking unevenly.
The great square itself, one of the largest in the world, is flanked by the National Palace, where Diego Rivera's murals sweep across the stairwell with a rich account of Mexican history, and by the offices of the old city. Just behind the cathedral, the excavated foundations of the Templo Mayor, the main temple of the Aztecs, lie exposed, a rough grey stack of stone with serpent heads. The area is a World Heritage site along with Xochimilco, together recording how the capital grew from a lake city into a colonial centre.
For a rider, the centre of Mexico City is a stress test, and the honest answer is not to take the bike in. Traffic is dense, the roads are cobbled in places, potholes and speed bumps appear without warning, and the city sits at 2,240 metres, so engines run thin and cars crawl. There are restrictions on older vehicles on certain days under a programme called Hoy No Circula, and parking in the centre is scarce. Leave the bike somewhere secure on the edge, or use the metro, which is cheap, fast and busy.
Outside the city, the ride changes completely. The roads east to Puebla pass between the volcanoes Popocatepetl and Iztaccihuatl, and the climb to Paso de Cortes, at about 3,600 metres, is a classic, cold and misty. Fuel is easy everywhere in the metropolis. Eat tacos al pastor, tamales and a bowl of pozole, and take your time. In the early morning, before the crowds, the Zocalo has a hushed scale that is worth seeing.