There! Eleven o’clock,” our guide shouts.

Our eyes dart left, just in time to see a bat ray throw itself out of the water. This manta-like creature cartwheels several feet skyward, and then tumbles back into the sea. Though rays are quite common in eastern Pacific waters from Oregon to Baja California, as well as around the Galapagos Islands, this display is a rare treat for me, a Midwestern kayaker on her first trip to the Sea of Cortez, which separates the Baja California peninsula from mainland Mexico.

“Why do they do that?” I ask.

“No one knows for sure,” Francisco replies, shaking his head. “Maybe to get barnacles off, maybe just for fun.”

The ray performs a few more stunts before vanishing.

Our kayaking group, 15 of us, paddle on into the sheltered bay at Playa Ballena, a beach on the scalloped west coast of Isla Espíritu Santo, the Holy Spirit Island, an uninhabited, 15-mile-long island in the southern Sea of Cortez.

Rounding the point, my first impression of the bay is that of a natural cathedral. A palette of burnt amber, sienna, terra cotta and russet explodes along steep slopes of ancient volcanic lava and ash, which cradle a gleaming, empty stretch of white sand: It’s an otherworldly juxtaposition of vibrant tropical sea and Sonoran desert. Frigate birds glide in lazy circles above us, and as we paddle, the shallow water becomes translucent, revealing pufferfish, Gumbylike starfish and a school of striped sergeant majors.

While the majority of tourists become acquainted with Isla Espíritu Santo by taking day trips from the nearby city of La Paz, I sought a more intimate experience: I opted for a four-day sea-kayaking trip to this island wilderness, which has the most intact ecosystem remaining in the Mexican state of Baja California Sur and is a United Nations Biosphere Reserve. Chosen for the significance of its ecosystem and designed to be a model for how humans should live and interact with nature, the island is one of approximately 350 biosphere reserves worldwide.

Isla Espíritu Santo’s beaches and tide pools and its arroyos, caves and mountains preserve a slice of Baja that has existed since the San Andreas Fault tore the peninsula away from the mainland, a process that started approximately 20 million years ago. Several animals on the island are found nowhere else, including the black jackrabbit, and since we would be camping on the island’s beaches, there would be a chance of spotting a rare, nocturnal ring-tailed cat.

I wade to shore, shuffling my feet in the sand to make sure I don’t step on any stingrays as I pull my kayak’s nose onto the untouched beach, and join Francisco and the other kayakers in setting up our shade tarp and unloading supplies from the kayaks’ forward hatches. We have already spent our first night on the beach at Coralito, and we are getting faster and more efficient at our tasks with every landfall.

While Baja Outdoor Activities does offer fully catered trips, with motor skiffs called pangas providing support crew and supplies on a daily basis, I opted for a less expensive, cooperatively catered one. Francisco is unquestionably in charge, particularly in his “camping kitchen,” but everyone assists with meal preparation, washing dishes, setting up our beach camps and loading and unloading the kayaks.

For lunch today, we are looking forward to crunchy tostadas, fresh salad with tomatoes and avocados, crumbly Mexican queso and jalapeños mixed with tender cactus strips called nopalitos. Francisco is happy to let others handle this simple meal for him, as tonight, once again, he will be deftly juggling multiple pans over the propane stove and shooing away campers who seek his secret recipes. We have christened him the Alpha Chef, and with twinkling eyes he hints at such savory delights as Argentinian steak, poblano peppers in rich cream, warm tortillas and bottles of red wine – all this, plus our happy-hour cocktails with fresh-squeezed key-lime juice.

Before we embark on lunch preparations, however, Francisco wants to show us another face of Isla Espíritu Santo, one we cannot see from our kayaks. He leads us along the beach to a steep-looking cliff that marks Playa Ballena’s north end. Here, he says we will follow a trail to the cliff top for unparalleled views of land as well as sea.

“This is an easy hike,” he cajoles.

I stare up at the cliff rim and can’t help but wonder where the trail is. The baking noontime slope, scattered haphazardly with boulders, scree and the odd cactus, looks impenetrable.

“No hay problema,” assures Francisco, a longtime Baja resident who has guided expeditions in many of the world’s best sea-kayaking spots, from Canada and Greenland to Patagonia in his native Chile.

With only Crocs for footwear, he seems to glide effortlessly upward. I’m not quite so nimble, scanning the rough terrain for rattlesnake holes and gingerly choosing handholds amid prickly desert flora. Behind me, skittering noises and startled gasps reveal someone else’s less successful foot placement.

Sweat trickles into my eyes. Upward, upward… then our group is standing on the rim. I draw in my breath.

Spreading out before me is a fingerlike plateau, orange and yellow in the desert sun, extending seaward from Isla Espíritu Santo’s more mountainous eastern terrain, where armies of cardón cacti march into the distance. Chollas, whiplike ocotillos and a variety of succulents seem to grow right out of the rock, and the smooth surface bears little piles of broken seashells Francisco explains may be archaeological evidence of the long-gone Guaicura and Pericú peoples. This is a place the La Paz day-trippers do not see as they hurry in their fiberglass pangas to the most popular island beaches for their tightly scheduled picnic lunches.

To the west, the banded, multihued Sierra de Giganta mountains hover over the cobalt Bahía de La Paz like a mirage. Below, on Playa Ballena, our miniature beach camp and brightly colored kayaks seem like an absent-minded scattering of Lilliputian toys. When we repack our kayaks this afternoon and paddle on to Candelero, our next overnight destination, it will be as if we had never existed here.

As we carefully descend to the golden beach for our eagerly anticipated lunch and perhaps a snorkel in the bay, I realize that while Isla Espíritu Santo has little to do with the human world, it has much to teach. From its ancient, fractured rock to the bouncing shadow in Coralito’s darkness that I think might have been a jackrabbit, it reminds us that we are all part of something much bigger.