Everyone got excited when the 20-foot-shark, inches below the surface of the water, started circling slowly under our little fiberglass boat and wouldn't leave.
What to do? Get in the water, of course.
"This is special," said our guide, Christina Colpitts, as three passengers from our boat eased into the tepid Sea of Cortez and swam carefully toward the creature to get a snorkel-eye view.
Anyone who saw a "Sharks of the World" poster as a youngster surely felt the mystique of the whale shark, largest shark in the world and biggest fish in the sea. Lurking behind the other shark species - bigger, even, than the mighty great white - the enormous size and peculiar spots of the whale shark stood out.
Very definitely the whale shark was coolest of all sharks.
The Sea of Cortez, a three-hour flight south of San Diego, is one of the few places in the world where whale sharks congregate predictably. They start showing up in summer, with peak season for whale shark-watching from the start of September through the end of October. My trip was run by a small San Diego-based company called Baja Airventures.
"We've had a lot of people who've gone on our trips and they've been down to Australia, they've been off of Belize and they've been all over the place and had yet to be able to snorkel with whale sharks," said Baja Airventures owner Kevin Warren. "Our last five years in a row, every one of our trips we saw them throughout the trip."
Baja Airventures flies its guests in single-engine planes to the remote Mexican fishing village of Bahia de los Angeles, population 500. From there, basic but powerful and seaworthy 26-foot boats shuttle guests another hour south to the rustic Las Animas Wilderness Lodge on a turquoise cove.
The Baja Airventures pilots also serve as knowledgeable guides, leading guests in small groups to kayak, fish, hike and snorkel with whale sharks and the other abundant sea life in the area.
Just be ready to rough it. You must enjoy sleeping in little more than a tent and doing without electricity and running water - not to mention no television, Internet or cell phone service.
"I want to be completely self-sustaining out there," said Warren, adding that he would like to install a desalination unit to supply water and intends to replace the resort's only generator with solar panels.
Whale sharks grow up to 40 feet but have very small teeth and aren't predatory. That means they won't try to eat you. Gentle giants, they gather each fall at Bahia de Los Angeles - almost halfway down the Baja Peninsula on the Sea of Cortez - to filter-feed on microscopic organisms called plankton.
The sharks swim slowly near the surface, keeping their large mouths open to gorge on the clouds of plankton that color the water jade that time of year.
"Absolutely mysterious and absolutely still very rare," said Jason Holmberg with the Ecocean Whale Shark Photo ID Laboratory. "The more we discover about them, the more our preconceptions about them, even from a few years ago, are shattered."
The Portland, Ore.-based nonprofit is deciphering the migration patterns of whale sharks. To do that, the group collects and catalogs underwater photographs of whale sharks taken by divers and snorkelers.
Holmberg employs sophisticated software to examine the light-colored spots unique to each shark. He then looks for matches among the more than 10,000 photos in his database. When he finds a match, he notes where that shark has been photographed before.
"Tourism definitely helps with the conservation, because it's only through large-scale data collection that we can get a picture of the species," Holmberg said.
The Mexican government also seems concerned about whale sharks, marking off with buoys the part of Bahia de los Angeles where whale sharks congregate and enforcing rules for interacting with the animals. Chasing or herding sharks isn't allowed. No more than three people per boat may be in the water at any time. Touching sharks is prohibited.
Whale sharks have recently been in the news because of the Deepwater Horizon oil spill, with some seen swimming near and through the oil in the Gulf of Mexico. But the Sea of Cortez population is off the west coast of Mexico, while the Gulf waters are on the other side, well east of Mexico.
Those who make the trip with Baja Airventures must be willing to rough it a bit. Accommodations are in spacious yurts - a type of large, round tent with a conical top, traditional housing of Mongolian nomads. Baja Airventures has eight beachside yurts for lodging plus a larger, central yurt for dining and entertainment at its Las Animas Wilderness Lodge.
The yurts have no electricity. And there's no running water - guests carry water for their showers in 5-gallon bags and set them in the sun to warm up. There are composting toilets.
The single-engine Piper Cherokee planes Baja Airventures operates are comfortable and smooth-flying but small, able to carry no more than six passengers plus the pilot. For an entire week, guests are limited to no more than 15 pounds of tightly packed clothes, toiletries, camera gear and anything else they think they might need.
In other words, don't expect to dress to impress.
"We strive to make it more like a trip you would make with friends and family," said Warren, who began flying to Baja to explore surfing opportunities on the peninsula's west coast and has been in business 20 years.
While the accommodations are primitive, the food at the lodge is not. Two outstanding cooks prepare authentic Mexican meals, often using fresh fish caught right offshore. And the camp's remoteness doesn't impede its ample supply of Mexican beer - which always tastes better in Mexico - and Colpitts makes a mean margarita.
Best of all, though, is the scenery and wildlife. The desert landscape roughened by volcanic rock and 30-foot cardon cactus tumbles unimpeded into the ocean from nearby mountaintops. Cliffs that seem about to crumble into the water at any moment host crowds of pelicans and boobys while osprey and frigate birds circle above.
And there is nothing like the experience of floating still next to a creature many times your size, hearing the soft swish of water and wondering what this mellow fish might be thinking with its beady eye watching you.
If you go...
Baja Airventures: http://www.bajaairventures.com/ or 800-221-9283. Packages start at $1,595 for four days, including all lodging, meals, drinks and frequent excursions to see whale sharks and other adventures. Whale sharks can be seen throughout the summer but peak season is beginning of September through end of October. Baja Airventures offers whale-dolphin and sea-lion watching tours in February and March.
Getting there: Baja Airventures trips depart from Brown Field, a small airport in San Diego right across from the Tijuana border. The planes refuel at San Felipe, Mexico, about halfway to Bahia de Los Angeles. Pack lightly: The company requires guests to sign an agreement to honor its 25-pound luggage limit.
Bahia de Los Angeles: http://www.bahiadelosangeles.info/
WHALE SHARK TRACKING: http://www.whaleshark.org/