“SO THAT’S WHAT A SONATA LOOKS LIKE,” SUE ELLEN SAID. We were standing at the edge of a shimmery chasm in the floor of the Mexican jungle. Shaped like a teardrop, the chasm measured perhaps three hundred feet from one end to the other, and it was filled to its limestone rim with the water of an underground river. The Spanish word for such a sinkhole is “cenote,” not “sonata,” but I kept myself from correcting Sue Ellen, remembering that in twenty years of marriage she had never been grateful for this particular service. And as malapropisms go, it was inspired. The water in the cenote seemed as pure as music.

We stood there listening for a moment more, Sue Ellen, our three girls, and I, and then we dug our masks and fins out of the gear bag and leapt in. The water, even with the tropical sun to warm it, carried a charge, and the kids surfaced from that first plunge yelling with mock distress that they were freezing to death. I swam down to the center of the pool and looked upward, through twelve feet of water transparent almost beyond comprehension. It gave me a peculiar feeling of satisfaction to see my family snorkeling above me in a V formation, as if they were not in the water at all but sharing the sky with the birds that soared and swooped above them.

This had been my idea: a family snorkeling vacation in Yucatán, the five of us traveling light with our trusty masks and fins, roving from one supernal body of water to the next. It was a backwater tour that I had in mind: no cattle-boat diving on Cozumel, where the Mexican government had just given the go-ahead to dynamite a section of the island’s exquisite reefs to accommodate more cruise ships; no parasailing or jet-skiing or rides on giant inflatable bananas pulled by speedboats off the beaches of Cancún. Instead, we would follow the one highway leading out of that unholy resort city, pulling over at some sagging jacal with a hand-lettered cardboard sign out front that read “Visite el cenote” or veering onto an unmarked dirt track in the hope that it would lead us to the edge of a sparkling lagoon.

Now on this bright spring morning in 1995 we stood at the banks of Car Wash, which was the prosaic gringo name that had been bestowed upon the teardrop-shaped cenote. No doubt it bore an ancient Mayan name as well, because in this part of the country, which is without surface streams or rivers, cenotes have always been vital features of the landscape. For the ancient Maya, they were the only access to fresh water, but they served as spiritual portals too, leading from the Middleworld of surface life to the highly complex Otherworld, an unseen realm of dark waters and shifting heavens.

We spent several hours exploring the cenote, basking on the sunny surface or diving to the bottom, which was not a bottom at all but a broad pinnacle, the summit of all that rock that had long ago collapsed into a hollow cavern beneath the earth. The sinkhole sloped downward on all sides from this cone of fallen limestone, leading into dark underwater rooms that extended into the vast porous tableland of the Yucatán Peninsula. When I took a deep breath and swam cautiously to the brink of one of these caverns, I encountered a sign, ghostly white against the blackness, that warned “Stop—Go No Further—Prevent Your Death.” Not far beyond this sign, I had been told, was some sort of ancient temple or fire pit, a reminder of the time when a lower water table had made this a system of dry caves. And 3,500 feet upstream from this altar was a large submerged cavern called the Room of Tears, so named because one of the divers who had found it supposedly wept at its beauty.

That afternoon, standing on the summit of Nohoch Mul, the towering pyramid at Cobá, I could not get that watery Otherworld out of my mind. Cobá, an extensive Mayan ruin a few miles up the road from Car Wash, had once been an imperial rival to the great city of Chichén Itzá. But Chichén Itzá conquered Cobá and its allied cities in the Puuc hills and endures to this day as one of the most visited Mayan sites. Cobá, not nearly so well known, is still mostly hidden—seventy square miles of shattered, jungle-covered temples, with two mighty pyramids rearing up out of the canopy.

All five of us had started up the broken stairway of Nohoch Mul, but Sue Ellen and the two older girls—eighteen-year-old Marjorie and thirteen-year-old Dorothy—decided to turn around midway up the pyramid, when the climb began to grow frighteningly steep and precarious. Only Charlotte, our surefooted eleven-year-old, made it to the summit with me. We sat up there on a terrace in front of a temple decorated with friezes of the Diving God and looked out over an endless ragged forest punctuated by several shallow lakes. (In Maya the word “Cobá” means “Water Stirred By Wind.”) The only other thing that broke the flat sweep of the forest was the pyramid known as La Iglesia, which emerged from the canopy a mile away, a pile of rubble half-sheathed in vegetation. An iguana sunned itself on the stones below us. It had molted away the scabrous skin of its tail, which now looked as tender as the shoot of a plant. A constant chatter rose up from the dense forest beneath us, made up of who knows what—jays, tanagers, toucans, motmots, spider monkeys.

The world we saw from the top of this pyramid was a nearly seamless forest stretching out to touch the horizon in all directions, a landscape that appeared as timeless and unconquerable as the open ocean. But buried beneath these trees, I had read, were some five thousand unexcavated structures and an extensive network of roads leading out to other vanished cities, roads that Mayan workers had constructed of masonry and white marl that they crushed with giant rolling pins.

And surely there were dozens, if not hundreds, of cenotes down there as well, hidden beneath the forest canopy. The immense limestone shelf that makes up the Yucatán Peninsula is veined with underground rivers, which flow beneath the earth in total darkness and silence, constantly eating away at the rock, carving out an infinity of channels and caverns. When the ceiling of one of these caverns happens to collapse, a cenote is formed and a window is opened onto one of the most secret regions of the planet.

A great deal of that subterranean water flows into the ocean, discharging into the wildly picturesque lagoons that are found all along this part of the coast. We visited several of these lagoons the next day, stopping first at Chac al lal, which was only a short walk from our hotel in Puerto Aventuras. We came by boat, however, coasting in on the ocean swells through a narrow pass into a shallow basin ringed by coral rock. The lagoon spread out before us, an expanse of perhaps five or six acres, its water as searingly blue as the flame of a furnace.

And there, perched at the very edge of the ragged coral shoreline, standing guard over this dazzling waterscape, stood a single Mayan temple not much bigger than a toolshed. There was no plaque or sign to identify this building, to tell us whether it had been a shrine to an ancient Mayan god or a lighthouse or a customs station connected with the coastal trade that once flourished along these shores. In any case, the structure had been a relic for at least four hundred years, and by now it was as weathered as the ironshore shelf on which it had been built.

The lagoon was vacant except for a dozen German tourists who came trooping down the path with their snorkeling gear as we anchored the boat in front of the temple. Like many tourists, they had planned their trip for the most congenial time of the year—the dry season, which lasts from November to April. During these months, the water appears exquisitely clear from above, but when we slipped overboard and looked beneath the surface, it not only was opaque but had a strange visual texture, like wrinkled wax paper. Various fish—sergeant majors and parrot fish—swam in front of my mask lens, but I perceived them only in a nearsighted haze.

“What’s wrong with the water?” the kids wanted to know. But there was nothing wrong with it. The peculiar haziness was merely proof that fresh water from those underground streams was pouring out of the rock, mixing unevenly with the salt water surging into the lagoon from the sea. When fresh and salt water meet, they have a tendency to stack themselves, the heavier salt water settling to the bottom, the fresh water riding on top. The plane that separates them is known as the halocline.

Sometimes a halocline is hard to miss, a sharp divide that sorts the water into strata as clearly defined as the rock in a road cut. In this lagoon the distinction was far more subtle, a strange wavy blending that reminded me of an old episode of The Twilight Zone I had seen as a kid in which a family discovers that their house contains a secret door to the fifth dimension. When they work up the nerve to go through the door, they find themselves in a world of undulating, distorted images, with imperceptible and barely audible figures beckoning them farther.

My own family, I knew, felt a little as if they had been dragged into a strange dimension as well. I had originally told the kids we were going to Cancún for spring break, and while this had been true in a technical sense (we would be arriving and departing at the Cancún airport), I had not adequately prepared them for the fact that they would not be spending their days sipping virgin daiquiris at the swim-up bars of luxury hotels or hanging out at Planet Hollywood and the Hard Rock Cafe. They had been cruelly disappointed in these fantasies once before, years earlier, when I accidentally left them with the impression that we would be spending a weekend in fabulous Cancún, when in fact we were going to a sleepy little hideaway on the Frio River called Concan. Once again, we were not going through the main door, but through a secret door, into a world of mute Mayan temples and wrinkly water and endless submerged grottoes.

We wore ourselves out that day, visiting another solitary tem-ple/lighthouse a few miles down the coast and then stopping to snorkel another lagoon or two and to browse along their shorelines for beautiful cobbles of fossilized coral. By the end of the afternoon only Marjorie had the energy to accompany me to Xel-Ha, a national park at a broad lagoon between Puerto Aventuras and Tulum.

The admission fee for Xel-Ha was $10 apiece, and “National Park” struck me as a highly suspect designation for what turned out to be an assemblage of swimwear boutiques, cafes, towel rental facilities, and juice bars. The lagoon  that spread out in front of all this, however, was the real thing. It was a vast and tranquil sheet of water with a few craggy islets rising from it. The low afternoon sun cast a flat, soothing light across the surface.

When Marjorie and I entered the lagoon, we encountered once again that tricky mixture of fresh and salt water. Here, however, the halocline was more apparent. The fresh water on top was chilly and blurry, but when we dove to six feet or so, we hit a band of warm, clear water, in which schools of big parrot fish were suddenly, magically visible, grazing along the sand bottom of the lagoon. I noticed that the passage of my body through the halocline stirred up the layers, causing them to commingle in eerie ways. When I came across a large barracuda on the bottom, half the fish was clearly visible, but the other half melted away into a gauzy abstraction.

ADMIT IT, DAD, it’s a purse,” Dorothy chided me the next morning as we made our way along a rocky path deep into the forest.

“It’s not a purse,” I said, referring to the canvas shoulder bag that contained several bottles of water and a notebook that I could not handle without soaking the pages with sweat. “I believe Eddie Bauer refers to it as a guide pouch.”

“As if you were a guide,” she said. “It’s a purse.”

We had embarked on the first phase of the Indiana Jones Jungle Adventure, a mile-and-a-half walk through a humid tropical forest that led to a cenote known as Nohoch Nah Chich, a Mayan phrase meaning “the Giant Bird House.” Nohoch Nah Chich is the main hub in a remarkable attempt to map the underground river systems of this part of the Yucatán. The leader of the enterprise, Mike Madden, the American owner of a dive center based in Puerto Aventuras, had shown me a map that morning of the Nohoch system. When Madden set the rolled-up map down on the floor of his office and opened it, it took up nine feet, and it depicted a fibrous network of caverns, tunnels, and cenotes spreading aimlessly in all directions. Madden and his teams of cave divers have been exploring this system since 1987, using underwater scooters to roam through enormous water-filled rooms that can be 1,400 feet long by 400 feet wide, and then can pinch off to narrow passageways through which a diver has to wiggle like an eel. Except for the occasional distant light of a surface crack or a cenote opening, the caves are perfectly dark, and the divers must swim through them bearing their own light as well as their own air, sometimes carrying 250 pounds of survival equipment. By using the scooters, and by caching extra scuba tanks and lights at critical intervals, they have traveled more than 30,000 feet in a single dive. There is no telling where the thing begins or ends. It is already the longest underwater cave system in the world. At the time we visited, Madden and his divers had mapped 129,000 feet, painstakingly connecting one cenote to the next, and were on the verge of following the passageways all the way to the sea.

To the degree that this sprawling subterranean complex has a front door, Nohoch Nah Chich is it. Madden started the Indiana Jones tour as a way of allowing casual tourists such as us a relatively safe peek into a lethal and unnervingly beautiful counterworld.

The Indiana Jones Jungle Adventure is a hokey name for an authentically strange experience, though I must admit I did swagger a bit along that forest path, with my Eddie Bauer guide pouch slung over my shoulder and sweat pouring into my eyes from my sodden hatband. The path was an irregular ribbon of coral rock, and the kids seemed to enjoy the challenge of keeping their footing as they hurried along. More than a dozen people were on the tour this morning, along with several horses carrying ice chests and snorkeling gear.

At the end of the path we came to a Mayan farm, where a man named Don Pedro lived with his wife, Doña Rafaela, in a breezy compound of palapas, fruit trees, and Brahman cattle. The cenote was on their land, and as we passed the main house—where Doña Rafaela had set up a display of embroidered dresses to sell to the Indiana Jones adventurers—we could see the land disappearing into a deep crater fifty or sixty yards away. The Nohoch cenote was eight hundred feet in diameter and appeared to be completely dry except for a crescent of dark water far below. To reach the bottom of the sinkhole, we climbed down a wooden stairway and then walked across the broad summit of the rubble cone to a wooden platform built at the edge of the water. Above us rose the raw chasm of the sinkhole, the rock festooned with the long stringy roots of the trees that grew along the lip of the precipice. Perpetually shaded by the steep overhang that rose above it, the narrow strip of water here was dark, but achingly clear. Schools of minnows patrolled the area beneath us, and when Charlotte—eating a grotesque Mexican cookie crowned by a bright pink marshmallow—dropped a crumb into the water, the minnows converged on it with the fury of an atomic fusion reaction.

“Where are we going exactly?” Dorothy asked as we pulled on our fins.

“In there,” I said, pointing to a dark maw at the base of the cliff face. It looked like the entrance to some theme park thrill ride—the mouth of a cavern with a few stalactites hanging down like fangs, ready to swallow anyone who ventured too close.

The guide, a young woman with a Brooklyn accent, divided the expedition into two groups of ten and passed out an underwater flashlight to every two snorkelers. She explained that we would be swimming into the cavern to a distance of eight hundred feet, beyond the reach of sunlight, traveling a circular course that would bring us out the way we came in. She reminded us that we would not be going into the regions accessible only to cave divers; there would always be air above us.

“Youse guys stay together now,” she admonished.

Silently, our little flotilla of snorkelers entered the cavern. We kept our eyes underwater, transfixed by the velvety blue light from the receding sun. I dove to the bottom, looking up at my children paddling above, glowing in that brilliant pane of blue light like figures in a stained-glass window.

But by and by, that light disappeared, and we had only our flashlights to guide us as we floated deeper into the cavern. The rooms we passed through were the size of houses, filled with cantilevered boulders and cave formations that glowed in the flashlight beams with a milky radiance. There were cascading flowstones and stalactites that hung from the ceiling and pierced the surface of the water like daggers. The water’s clarity suggested a kind of nothingness, the void of deep space. I swam around and below the children, watchful and a little worried, because the water was so deep, the rooms so vast, and unspeakable dangers so easy to imagine. The kids were all good swimmers, and there were shelves of flowstone to rest on if they got tired, but just the same, I would periodically take hold of their hands, to reassure myself that this strange universe was not somehow tugging them away.

DURING THE NEXT FEW DAYS WE DROVE up and down the road between Playa del Carmen and Tulum, visiting one cenote after another. Some of them were large, nearly dry craters like Nohoch, with a rim of water at the bottom leading back infinitely into the rock. Others were filled almost to the edge, with the surface so still and translucent, it looked as if it had been sealed with a giant sheet of Saran Wrap. When we snorkeled through the waters of these cenotes, the sunlight fell across the boulders below us in waving curtains of light. We saw turtles and golden fish with accordion-pleated sailfins they raised above their backs to catch the sun’s rays, and peculiar little diving birds—grebes, I think—that pedaled along underwater for great distances with their enormous feet.

At the entrance to one cenote, we found a dilapidated old school bus. Through its open windows the children had the opportunity to see an ancient hippie, completely unclothed, sashaying down the aisle as he sang a mournful a cappella version of “Paint It Black.”

“Okay, we’ve seen a naked hippie,” Dorothy said. “Now can we go to that Xcaret place?”

We had passed the entrance to Xcaret many times in our meanderings up and down the road, had seen the tour buses streaming into it and the colorful billboards advertising the theme park as “Nature’s Sacred Paradise.” Robbed of Cancún, the kids had focused their hopes on this place, which seemed to offer exactly the sort of exotic synthetic experience their gringo souls most deeply craved.

So Sue Ellen and I relented and we drove into Xcaret, passed through a fake Mayan temple, and paid $20 apiece for a wristband that was our token of admittance. What we found inside was an incredibly well-groomed, well-run, and utterly dispiriting tourist trap. There were uniformed attendants everywhere, and restaurants and gift boutiques, one-hour photo shops, horse-riding demonstrations, botanical gardens, and snack bars squeezed around authentic Mayan ruins. There was a manicured beach and a man-made breakwater to protect it and an enclosure where, for an extra fee, visitors could swim with captive dolphins.

The centerpiece of Xcaret, however, was a snorkeling tour of an underground river that flowed through the park. A few years before, this river—a winding channel that worked its way above and below the surface before discharging into a sparkling lagoon—had been one of the loveliest features of the entire coast, or so I’d been told. But now that it had become part of “Nature’s Sacred Paradise,” it had been blasted and diverted, its opening to the sea closed off and its aura of beauty and mystery debased.

To enter the underground river, it was necessary to put all our valuables into plastic bags to be ferried to the exit point. We were then required to don orange safety vests, and when we entered the water, we became part of a crush of bobbing snorkelers, moving passively along on a gentle current, flailing about with our orange safety vests and wristbands.

“This is stupid!” Charlotte said, and I allowed myself a little thrill of triumph, proud that this trip had helped further what I considered one of the most crucial elements of the children’s education: the ability to tell the difference between what is real and what is fake.

My attitude toward Xcaret was partly the environmental hauteur of a privileged American. In this desperate country, where the peso fell every day and showed every sign of falling through eternity, places such as this meant jobs. Still, my mood was low when we left—I was thinking of all the beautiful places we had visited in the past few days that would no doubt someday suffer the same fate as Xcaret.

But when we turned off the road for lunch, heading to a beach and campground known as Xcacel, things began to improve. For one thing, there was a two-headed sea turtle, maintained alive in a shaded tank just above the beach. An old American woman, a fierce advocate of the turtles that crawl ashore on these beaches to nest, put her hands into the tank and lifted out a turtle with eight waving flippers and two heads that strained in opposite directions.

“This is Boo-Boo,” she said, indicating each of the heads in turn. “And this is Bo-Bo. They’ve got two of everything—two sets of lungs, two hearts—but only one rectum. So when one of them wants to go to the baño, the other one has to go too.”

We admired the two-headed turtle for a moment more, made a contribution to a fund to protect the turtles’ nests from human egg poachers, and then strolled over to an open-air restaurant that overlooked one of the prettiest beaches in the Yucatán. The turquoise water was blinding, an assault of color, and the breeze moved gently beneath the palm fronds, where we sat eating our pescado tikin xik. 

This beach, the local rumor went, had been sold to the Japanese, so who knew how long before it too went the way of Xcaret and Cancún? How long would that Mayan temple on the edge of the lagoon stand there in its pure solitude, and how long would the cenotes we had snorkeled in remain untapped and unpolluted?

I thought of that trip into the perfect darkness of the Nohoch cenote, with the light beams sweeping across the lustrous flowstone and bats flapping in the airspaces above our heads. Ancient Mayan kings had once performed bloodletting rituals, piercing their penises with stingray spines and running knotted cords through their tongues as a way of reaching a level of spiritual intensity sufficient to allow them entrance into the Otherworld. The places we had visited did not require such a cruel price of admission, and though they were off the normal tourist path, they could hardly be considered a part of the secret Mayan cosmos. But sitting and recollecting in the bright glare of the sun, I felt we had at least touched the margins of that ancient dreamscape, and that when we looked back on this trip, it would be in dreams that we remembered it best.