This was life beyond roads, mostly without running water or electricity. The people there farmed as their ancestors had for centuries, without machines and using animals and their own strong backs to break up the soil.

A second lagoon was above the scattered farms, a third even higher, past a ridge lost in clouds. When some children saw us hiking past, they ran from their houses to meet us. They wanted to sell us handmade necklaces, bracelets and hatbands. But they also wanted to show us their puppies and talk. We asked where they went to school. They didn’t, they said cheerfully. School was too far away.

Finally it was time to go to Cuzco where the cathedral and neighboring Iglesia de la Compañio compete to see which has the grander facade. Their colonial splendor ranks with the great churches of Europe and covers two sides of the main plaza. Two-story buildings with ornately carved balconies flank the other sides.

As former center of the Inca empire, Cuzco celebrates its builders in ways both large and small. Its biggest statue is a towering image of Pachacutec, the leader who founded the city and transformed the Incas from a relatively small tribe to rulers of an area stretching nearly 2,500 miles from Ecuador to central Chile. A giant face of the Inca sun god tops the biggest fountain. Across from the post office, another sun god emblem crowns a block-long mural telling the history of the Incas, complete with their downfall.

The villain in that story is Francisco Pizarro, who landed in Peru in 1532 with 110 soldiers, some horses, and a cannon. He captured the Inca ruler, Atahualpa, held him for ransom, and then, after the loot was delivered, killed him and burned his body. Pizarro seized all the gold and silver he could find, melted it down, and sent it back to Spain. He dismantled the Inca temples and used the stones to build churches.

The natives, who gradually mixed with the Spanish, found ways to keep Inca symbols alive, even in the most Christian of places. The condor, the puma and the snake — symbols of the Inca empire — show up on church doors and statues. Inside the cathedral are magnificent paintings by local artists with their own version of the crucifixion. Instead of showing Jesus on the cross looking toward heaven and wearing a loin cloth, as European painters did, the Cusqueños showed him looking down, toward the Incas’ Mother Earth, and wearing an Inca skirt. In one particularly famous painting, Jesus and his disciples are eating guinea pig and other traditional Inca foods at the Last Supper, and Judas, the betrayer, has the face of Pizarro. (In a more flippant version of this theme, a contemporary T-shirt shows a llama and Pizarro facing off under the title of “Two Worlds Meet.” The llama is spitting into the Spaniard’s face.)

Inca walls, instantly recognizable for their precision, are visible throughout the old part of the city, especially in alleyways and the foundations of churches. And even more Inca reminders are outside the city limits.

A local man drove us to the nearby mountain fortress of Sachsayhuaman, another collection of ruins covering an area bigger than Machu Picchu. We walked between giant boulders to an unmarked place that would have been among the Incas’ most sacred sites. Inside a cave-like opening, benches and an altar had been carved into the stone. High above the altar was an opening in the rock, positioned so that a full moon’s light would fall exactly on the altar. When that happened a priest would make a human sacrifice, ceremonially killing a girl raised from birth for that purpose.

Alone in that small space, we stood hushed, thinking about the distant past and humbled by where we were.

We had experienced similar thoughts at the beginning of our trip. It was a cold, clear night in Ollantaytambo. The constellation Orion was out, upside down to us, with the Southern Cross nearby. We were walking down a narrow Inca street, one so old it could have been from Europe’s Middle Ages. A grooved channel built by the Incas sent rushing water past us, chilling the air. Gradually we became aware of voices and music. We approached a small window and looked inside.

In dim light, some local people were having a party. Quechua, the ancient language of the Incas, was flowing. So was chicha, the corn beer used by the Incas in ceremonies. The women were dressed in their fanciest headgear and rainbow-colored clothes. Everyone was dancing and smiling. It was a celebration that could have been happening hundreds of years earlier, one we would have missed if we had focused only on Machu Picchu. By showing us another culture and another world, the Sacred Valley made us feel blessed.