To communicate with the dolphins, Herman and his team invented a hand- and arm-signal language, complete with a simple grammar. For instance, a pumping motion of the closed fists meant "hoop," and both arms extended overhead (as in jumping jacks) meant "ball." A "come here" gesture with a single arm told them to "fetch." Responding to the request "hoop, ball, fetch," Akeakamai would push the ball to the hoop. But if the word order was changed to "ball, hoop, fetch," she would carry the hoop to the ball. Over time she could interpret more grammatically complex requests, such as "right, basket, left, Frisbee, in," asking that she put the Frisbee on her left in the basket on her right. Reversing "left" and "right" in the instruction would reverse Akeakamai's actions. Akeakamai could complete such requests the first time they were made, showing a deep understanding of the grammar of the language.

"They're a very vocal species," Herman adds. "Our studies showed that they could imitate arbitrary sounds that we broadcast into their tank, an ability that may be tied to their own need to communicate. I'm not saying they have a dolphin language. But they are capable of understanding the novel instructions that we convey to them in a tutored language; their brains have that ability.

"There are many things they could do that people have always doubted about animals. For example, they correctly interpreted, on the very first occasion, gestured instructions given by a person displayed on a TV screen behind an underwater window. They recognized that television images were representations of the real world that could be acted on in the same way as in the real world."

They readily imitated motor behaviors of their instructors too. If a trainer bent backward and lifted a leg, dolphin would turn on its back and lift its tail in the air. Although imitation was once regarded as a simpleminded skill, in recent years cognitive scientists have revealed that it's extremely difficult, requiring the imitator to form a mental image of the other person's body and pose, then adjust his own body parts into the same position—actions that imply an awareness of one's self.

"Here's Elele," Herman says, showing a film of her following a trainer's directions. "Surfboard, dorsal fin, touch." Instantly Elele swam to the board and, leaning to one side, gently laid her dorsal fin on it, an untrained behavior. The trainer stretched her arms straight up, signaling "Hooray!" and Elele leaped into the air, squeaking and clicking with delight.

"Elele just loved to be right," Herman said. "And she loved inventing things. We made up a sign for 'create,' which asked a dolphin to create its own behavior."

Dolphins often synchronize their movements in the wild, such as leaping and diving side by side, but scientists don't know what signal they use to stay so tightly coordinated. Herman thought he might be able to tease out the technique with his pupils. In the film, Akeakamai and Phoenix are asked to create a trick and do it together. The two dolphins swim away from the side of the pool, circle together underwater for about ten seconds, then leap out of the water, spinning clockwise on their long axis and squirting water from their mouths, every maneuver done at the same instant. "None of this was trained," Herman says, "and it looks to us absolutely mysterious. We don't know how they do it—or did it."

He never will. Akeakamai and Phoenix and the two others died accidentally four years ago. Through these dolphins, he made some of the most extraordinary breakthroughs ever in understanding another species' mind—a species that even Herman describes as "alien," given its aquatic life and the fact that dolphins and primates diverged millions of years ago. "That kind of cognitive convergence suggests there must be some similar pressures selecting for intellect," Herman said. "We don't share their biology or ecology. That leaves social similarities—the need to establish relationships and alliances superimposed on a lengthy period of maternal care and longevity—as the likely common driving force."

"I loved our dolphins," Herman says, "as I'm sure you love your pets. But it was more than that, more than the love you have for a pet. The dolphins were our colleagues. That's the only word that fits. They were our partners in this research, guiding us into all the capabilities of their minds. When they died, it was like losing our children."

Herman pulled a photograph from his file. In it, he is in the pool with Phoenix, who rests her head on his shoulder. He is smiling and reaching back to embrace her. She is sleek and silvery with appealingly large eyes, and she looks to be smiling too, as dolphins always do. It's an image of love between two beings. In that pool, at least for that moment, there was clearly a meeting of the minds.