The New York Times Op-Docs and Annapurna Pictures are presenting a virtual-reality film, "The Click Effect," about the free-diving researchers in this Opinion essay. To view it, download the NYT VR app on your mobile device, if you don’t already have it. (Go here for Android, and here for iPhone.)

I HELD my breath and swam deeper, 10, 20, 30 feet. I heard a thunderous crack, then another, so loud they vibrated my chest. Below my kicking feet, two sperm whales emerged from the shadows, each as long as a school bus.

The cracking was coming from the whales; it’s a form of sonar called echolocation that species of dolphins, whales and other cetaceans use to “see” underwater. With these vocalizations, called clicks, the whales were snapping three-dimensional images of my body, and those of my diving companions, from the inside out — scanning us to see if we were a threat, or if we were food.

As we kicked down deeper, within just a few feet of the mother whale’s gaping mouth, the click patterns changed, becoming slower, softer. They sounded to me like “coda clicks,” the sounds sperm whales use to identify themselves to others in the pod. The whales were probably introducing themselves. They were saying hello.

Fabrice Schnöller, a French engineer with a degree in biology, was leading the dive. For the past six years, he has traveled the world’s oceans seeking out these face-to-face encounters. His goal is to record close-up audio and video data of sperm whales passing one another coda clicks, which he believes contain coded information, possibly a language.

Sperm whales use coda clicks most often during socializing. They sound unremarkable, like a popgun firing in quick succession. But when the clicks are viewed on a spectrogram, a visual representation of an audio signal, each reveals a remarkably complex pattern. Inside these clicks are a series of shorter clicks, each lasting a few thousandths of a second, and so on. The more we focus in on a click, the more detailed it becomes. And sperm whales can repeat these millisecond-long clicks, which suggests, Mr. Schnöller says, that this is “some form of communication.”

We know little about sperm whale clicks and behavior because sperm whales are too large to put in a laboratory and, until recently, few researchers have been willing to study the animals up close in the wild. Who could blame them?

Sperm whales are the world’s largest predators. They have eight-inch-long teeth and can grow as long as 60 feet and weigh up to 110,000 pounds. Their vocalizations, along with blue whales’, are the loudest animal sounds on the planet; the pressure waves can blow out human eardrums and conceivably rupture lungs. Diving with them was considered suicide.

As a result, most research on sperm whales’ communication has been conducted from a boat. This has nonetheless revealed some fascinating facts: Sperm whales live in close-knit societies; they are raised by matriarchal units that can include three generations; they appear to share regional dialects and family nicknames. But studying the animals from the deck of a boat can also be limiting. Researchers can analyze their clicks but can’t see how the whales’ interactions change in response to those clicks, which is crucial for understanding how they communicate.

Those willing to get in the water with the whales face another problem: The disruptive gurgle of scuba gear scares the animals away. They avoid submarines and robots. Rebreathers, which recycle the divers’ exhaled breath into breathable air, are relatively quiet but also expensive, finicky and too difficult to deploy on a moment’s notice when pods approach.

The best option for studying the behavior and communication of whales is free diving. This is what it sounds like: diving dozens, sometimes hundreds of feet, on a single breath of air.

After a chance, bone-rattling encounter with a pod of sperm whales off the coast of Mauritius in 2007, Mr. Schnöller became fascinated by clicks. Two years later he started working with Fred Buyle, a Belgian former world-champion free diver and underwater photographer, and the pair formed a volunteer-run cetacean communication research project called DareWin. (I am now a member of their group.)

They wanted to record up-close sperm whale social behavior and clicks, so they began approaching the animals while free diving. When they entered the water wearing only a wet suit, mask and fins, the notoriously shy whales didn’t scatter or attack. They were curious, and welcomed the divers into the pods for hours, circling them and peppering them with communication clicks.

Free diving has another big advantage. It is totally silent, allowing Mr. Schnöller and Mr. Buyle to record a clear audio signal of whale vocalizations. The team began shooting video, including from 360 degrees, of their encounters.

DareWin has collected and made publicly available more of this footage than any scientific institution or university. The group has built audio and video rigs and software systems that will allow researchers to record their encounters and see all the whales in a pod at all times, which should help them determine who is clicking to whom, and how each whale responds.

Along with Mr. Schnöller and Mr. Buyle, the group includes the speech pattern expert Hervé Glotin, from the University of Toulon, in France. It also collaborates with Olivier Adam, a professor of bioacoustics at the University of Paris. All of the data the researchers find will be given away to whoever wants it.

Not everyone is a fan of this approach. Every few months Mr. Schnöller gets an angry note from institutional researchers claiming his data is “unscientific,” or that he’s harassing the animals, or that he’s a hack. He and Mr. Buyle insist they are not trying to subvert the scientific system; they want to work within it. But the current pace of research is far too slow and its approach is too timid.

In the past 150 years, humans have killed off about 70 percent of the sperm whale population. Around 360,000 remain. That number is expected to decline, perhaps precipitously, as the ocean warms and acidifies.

Sperm whales’ brains are the largest ever known, around six times the size of humans’. They have an oversize neocortex and a profusion of highly developed neurons called spindle cells that, in humans, govern things like emotional suffering, compassion and speech.

“We finally have the technology and methods to significantly increase our understanding of one of the planet’s most intelligent animals,” said Mr. Schnöller. “We can’t just sit here and do nothing. You’ve got to get in the water!”

Outsiders, he pointed out, were often behind the biggest advancements in science. “You think of Einstein or Newton,” he said. “They were math guys working regular jobs who set out to prove a crazy idea.”

Here’s the “crazy” part of his idea: DareWin is working with a team of engineers on a small submersible machine capable of recording more information about the coda clicks. Mr. Schnöller and Mr. Buyle believe that sonar artifacts (like images) might be embedded in these vocalizations — that because these animals are already viewing their world through echoes, they may also be able to send these echoed images to one another. They’ll test the theory by capturing these clicks, sending them back to the animals, and seeing if they repeat them. Next, the researchers will create artificial clicks containing three-dimensional sonographic images of things in our world — a tree, a human — and send these as well, prompting, perhaps, a kind of dialogue.

While all almost all cetacean experts agree that the whales’ clicks are a form of communication, most are skeptical, at best, that we will be able to understand, and even join, these conversations.

Yes, I realize that the idea of talking to sperm whales sounds nuts. It certainly sounded ludicrous to me when I first met Mr. Schnöller and Mr. Buyle in 2012 on an unrelated magazine assignment. And the team’s free-diving approach seemed like a death wish. The only free diving I’d ever witnessed or read about was competitive free diving — a reckless and often deadly sport. Then there were the terrifying whales themselves. I’d read “Moby-Dick.”

But after a few months of witnessing Mr. Schnöller and Mr. Buyle’s close encounters from the deck of a boat, I changed my mind. The free diving they employed seemed safe and natural, a kind of underwater meditation that connected them with the ocean and its inhabitants more closely than any researchers before them.

Soon I was practicing this form of free diving myself. I learned that anyone in reasonably good health is capable of holding his breath for three, four, even five minutes underwater and diving to depths below 100 feet. The hard part is convincing your mind that you’re not going to die down there. I spent about four months practicing, and then I dove in — and had my body shaken by the vocalizations of the world’s largest predator.

The whales could have easily eaten us or pulped us with their 15-foot-wide flukes. But they didn’t. As I stared into the tennis-ball-size eyes of a sperm whale mother and her calf, I immediately recognized that these were extraordinarily intelligent, fully conscious beings. I believe the whales saw the same in us.

This wasn’t a scientific epiphany but an emotional one. That still means something. You can’t share that connection on the deck of a boat. You’ve got to get in the water.