Initially they were painters, not sculptors. They made three-dimensional reconstructions only to have lifelike models to paint: They were that meticulous, that fixated on knowing how the musculature of a Neanderthal hung off its skeleton. Because they had to produce a three-dimensional individual, the brothers were forced to make decisions about what paleoanthropologists had the luxury of describing as spectra of variation. Geneticists can suggest a probable scope of skin and hair colors. But the brothers must imagine the wear on a particular Neanderthal’s skin after a hard life outside, or the abuse his toenails would take. And would Neanderthals wear ponytails? Would they shear their bangs away, to get their hair out of their faces? “Every culture does something with their hair!” Alfons insisted. “There’s no culture that does nothing with their hair.”

This uncorked a frantic seminar on known global hairstyles of the last several thousand years. They began pulling up photos on Adrie’s laptop, dozens of them, from anthropological archives or stills from old ethnographic films. These were some of the same photos they had shown Finlayson. The brothers had pored over them for years but still gasped or bellowed now as each new, improbable human form materialized. The pictures showed a panorama of divergent body types and grooming: spiky eyebrows; astonishingly asymmetrical breasts; a towering aboriginal man with the chiseled torso of an American underwear model, but two twigs for legs; a Hottentot woman with an extraordinarily convex rear end. “People would never let us make buttocks like this!” Alfons said regretfully. “All this variation! It’s beautiful!” shouted Adrie, refusing to look away from the screen. He had to look: These were reaches of reality that our minds didn’t travel to on their own. “If you live in the West, you’d never imagine,” he went on. The brothers’ delight seemed to come from feeling all these superficial differences quiver against a profound, self-evident sameness. Finally, Adrie turned to me and said very seriously, “These are all Homo sapiens.”

They showed me more photos. “It’s real, it’s real, it’s real!” Alfons kept shouting. Adrie said, “Unimaginable, unimaginable, unimaginable!” It only registered later: I had spent the day with identical twins who, since childhood, have been stupefied by how different human beings can be.

At the rear of Gorham’s Cave, past the hearth the team was excavating, there was a tall metal staircase. It led up to a long catwalk, which led to a locked steel gate. I waited there one morning while Finlayson fumbled around in his pocket. Then he turned his key.

The excavation had worked through this narrowed rear chamber of the cave years earlier and discovered, at the end of the 2012 season, an engraving on the floor: a crosshatched pattern of 13 grooves in the bedrock. A tide of specialists flowed into Gorham’s. They determined that the engraving was made at least 39,000 years ago and ruled out its having been created inadvertently — left over after skinning an animal, say. In controlled experiments, it took between 188 and 317 strokes with a flint tool to create the entire figure. “What we’ve always said,” Finlayson explained, “is it’s intentional and it’s not functional. You can call that art, if you like.”

The finding was published in The Proceedings of the National Academy of Sciences in 2014. The news media called the engraving “the hashtag.” One scientist described the elaborate crosshatch as watershed evidence of Neanderthals’ capacity for “complex symbolic thought” and “abstract expression.” But several archaeologists told me they believe that there are many clearer signs of Neanderthals’ capacity for complex cognition and symbolism, including a discovery in Southern France last year that seemed to dwarf the hashtag’s significance. (More than 1,000 feet into the Bruniquel Cave, Neanderthals assembled two rings of 400 deliberately broken stalagmites, with other material piled and propped around it — like a labyrinth, or a shrine.) But Finlayson was undaunted. He turned the hashtag into a logo for the Neanderthal-centric rebranding of his museum. There was a hashtag decal on the van he picked me up in every morning.

We stood and talked for a while until, finally, with Richard Attenborough-ish aplomb, Finlayson lifted a tarp and showed it to me. It did not make a tremendous impact at first — it was lines in rock. But Finlayson went on, pointing to a spot near the entrance to this isolated anteroom, a few feet across from the engraving, where the team had excavated another hearth. Neanderthals built fires in that exact spot, on and off, for 8,000 years, he said — until their disappearance from Gibraltar. But few animal bones were recovered here; it wasn’t a place they cooked. And the location of the fire was also puzzling: Neanderthals usually situated fires at the fronts of caves, to control smoke. And yet, Finlayson explained, “if you look up, this has a natural chimney.” We flung our heads back: A chute coursed through the high, craggy ceiling above us.