We walk up the scrub slope, passing juniper-like queñua trees—the highest-altitude trees in the world. The false summit is dead ahead, bathed in early sunlight; glacier-covered Sajama is directly at our backs.

"I think this is going to be easy—a piece of cake," says Paolo.

"I think it's going to be harder than we think," says Greg.

"Tomorrow we should go on a jeep tour," says Paolo.

"Let's think about tomorrow tomorrow," says Greg. "Right now let's think about the confluence."

After an hour and a half, we gain the ridge, which greets us with a blast of cold wind that nearly knocks Greg and Paolo down. The confluence is before us, somewhere on an escarpment in the middle of a vast bowl of scree—our first good view. Greg waves his arms and yells through the wind: "I've got to take a bearing!" When he's done, we back away from the edge until we're out of the wind. He fiddles with his altimeter watch and peers up the hill. "You know," he says, "people thought it was stupid when Edmund Hillary tried to climb Everest, too."

The altitude sinks in. My head starts to pound. Greg starts taking break after break, hunching over with his right hand on his knee, almost hyperventilating. Only Paolo seems unaffected: He's bounding ahead, waiting for us at every rise and flat spot. We reach the final pitch just after 2 p.m., and Greg stuffs his mouth with the rest of the coca leaves. He surges forward—the first to reach the false summit, the first to take in its vertiginous views of Sajama, the twin volcanoes to our west, and the twin lakes at their base. Paolo and I follow, and in that instant, confluence hunting makes perfect sense: It's an excuse to see places like this. For 20 minutes, we take photos in every direction. Greg gets antsy. "All right, all right, let's go get it," he says. "Let's go." We snap a few last shots. When we look up again, he's gone, running with newfound energy downhill toward the confluence.

Paolo and I follow Greg's footsteps down a scree slope, skirting the couloirs and the first band of cliffs, then sliding on our tails down a ten-foot patch of steep, icy snow. Greg waits just long enough at the saddle for me to catch up. "We're 134 meters away," he says, breathless. We run up a small knoll, weave through vertical fins of reddish rock, and start dropping again. "One hundred meters!" he yells. Up ahead, the escarpment appears to fall off into nothing. "What the hell is on the other side of this?" he asks—this isn't how Google Earth said it would be.

We proceed slowly. The rock underfoot is loose. The wind picks up. At 40 meters out, we begin downclimbing a steep slope that rolls over into a true cliff; at 17 meters, Greg ditches his pack and descends alone into a scree-filled chute. Below him, one slip away, is a yawning drop tens or hundreds of feet high—we can't see the bottom. The wind sends pebbles avalanching over the edge. "I'm going to try to get all zeroes," Greg yells. He inches downward, his left hand on the rock wall, his right hand holding the GPS. He swings the receiver right, then left—17°59.994'S, 69°00.008'W … 17°59.993'S, 69°00.006'W. He's still a dozen meters away. Shaking, with gloved hands, he documents the imperfect visit—photos of the north, east, south, and west—and then gets a slightly better reading, 17°59.994'S, 69°00.000'W, that appears as he and I scramble out. And he's not done.

Back on the rim we find a shivering, suddenly delirious Paolo, who's being blasted by the wind as he shoots photos of Greg's conquest. His Camelbak has frozen; his head hurts; he's dehydrated. Greg jogs past him. "Wait, wait, where are you going?" Paolo asks. Greg tells him we're going the long way around—a route back that could take us closer to the base of the cliff, closer to the confluence. "It's getting really windy," Paolo growls. "It's getting late. If anything happens now, it's a big deal. If anyone gets hurt, it's a big deal."

Greg is unmoved, and I, admittedly, back him up—I want to see him bag it. We climb to the saddle and race down a scree field, surfing on sliding rocks and kicking up clouds of sulfurous yellow dust. Our shadows grow long. Once parallel to the base of the cliff, Greg begins to traverse a steep slope of loose rock—an inch or two of gravel over frozen earth, too slippery to stand on. He pulls out his ice ax for extra purchase. He crawls eastward like a crab, confluence-bound, and for a moment I believe nothing will stop him. But then he slips and falls, and he slips and falls again, and he sits down and stares wistfully at his prize, 200 yards away. Reality sets in. He starts to descend.

The slope funnels us to the bottom of a broad valley, and we're alone in the Andes, our footprints the only ones as we tromp through the sand. Sajama is a beacon, the last thing illuminated by the fleeting daylight, and the wind is gone, the air calm. We walk toward the volcano and slow our pace. Greg gives Paolo some of his water. He looks up at the cliff. "Well, we got the confluence," he says. "We didn't get to check out that bottom part, but we got it. We got the highest confluence in the Americas." He pauses. "I might have to come here someday with ropes," he says. He pauses again. "We can still go back tomorrow and get the bottom," he says. "I mean, if you guys want to."