A leading indicator of octopus intelligence is that they get bored.

A leading indicator of human intelligence is that the humans at Washington's National Aquarium have figured out this, despite long-standing prejudice against octopuses: That they are invertebrates, all squish and shape-change, and one of their greatest tricks is squeezing through something that's the dimension of their eye -- which makes them sound like worms.

Out of hunger for amusement -- not necessarily food or freedom -- they can maneuver out of tanks whose covers have been held down by 40 pounds of concrete blocks, and climb into the tanks of other sea creatures and eat them. They can die of boredom -- by climbing out, but not finding a tank to climb back in. Perhaps recalling the suicide note of British actor George Sanders: "Goodbye. I am leaving because I am bored."

Hence, while better-behaved angelfish and clams entertain themselves, it is the job of the aquarium staff to entertain octopuses as if they were bright, spoiled and manipulative children demanding attention.

Just now, one of those humans has dropped a green plastic alien action figure into the tank.

"Oooooo," croons the crowd as a 6-month-old, five-pound great Pacific octopus stretches out a long, red arm. She lassos the alien's head and swings it toward her mouth.

"What's he doing with the alien?" worries Patrick Orwin, 9.

Then a pair of big blue feet splashes into the tank. The octopus drops the alien and reaches for the feet, which sink fast. The objects are followed by a brown body, a Tom Selleck mustache, a red Bozo nose and a green plastic ball cap.

"Mr. Potato Head!" a few children squeal, and immediately Shania (who came from Canada and was dubbed Shania Twain by the aquarium's director) hugs herself around him. Minutes pass. The octopus-keeper has hidden smelt inside the plastic potato, but so far, Shania ignores the food. She's more into snuggling.

"You guys!" shouts a boy in the crowd. "Look at that! Look at that!"

Ah, the creepy-crawly creature, the swarming arms, that deep-sea demeanor. This is the bearer of intelligence?

"That was my attitude, too," confesses science writer Eugene Linden, who has written about animal intelligence since the 1970s and had focused, mostly, on the "big-brained" creatures such as apes, dolphins, elephants and whales. "I shared all the prejudices everybody else has."

Then he started hearing octopus stories. Like how they can open screw-top jars and hamster balls and child-proof caps. They can do mazes and learn shapes and distinguish colors and use tools.

"They play," says Jennifer Mather, a psychologist and octopus expert at Canada's University of Lethbridge.

There are even hints that octopuses have a sense of humor, Linden says.

He talks about the finicky octopus who, in a lab in Pennsylvania, was served slightly spoiled shrimp. The octopus refused to finish its dinner, and when the feeding researcher returned to its tank, the octopus made eye contact with her, then meaningfully pushed all the shrimp down the drain.

And Linden talks about the octopus that glided along the seafloor while holding a shell like a helmet over its head, as seen by the former director of the New York Aquarium, who was scuba diving in New England. As Linden writes in his 2002 book "The Octopus and the Orangutan: More True Tales of Animal Intrigue, Intelligence, and Ingenuity," it was as if the octopus were saying: I want to be a mollusk protected by its shell -- and not a mollusk protected by its wits.

"If you don't have a shell to hide in," says octopus-expert Mather, "you better be smart."

"They're really quite beguiling and fun to spend time with," says Linden. "They seem to have a personality."

Their personalities can be so strong that, at the Seattle Aquarium, octopus names describe their characteristics, like "Emily Dickinson," the shy mollusk who always hid; and "Lucretia McEvil," the troublemaker who tore up her tank; and "Leisure Suit Larry," who, notes Seattle Aquarium biologist Roland C. Anderson, "would have been arrested for sexual assault because his arms were all over you."

"Look!" chirps a mother, Stephanie Sanders. "She's got Potato Head glued to the wall!"

The crowd in front of Shania's tank keeps growing: About a dozen people jostle for a better view, and small children squeeze between the adults and push their hands and faces to the glass.

Shania lets go of Mr. Potato Head. Rick Quintero, an aquarist, herpetologist and Shania's keeper and personal enrichment tutor, dips a hand into her tank. He's holding an inch-long slice of smelt. Ignoring the fish, she grabs hold of Quintero's hand and doesn't let go, even when he starts to pull away. He nearly lifts the five-pound animal out of the water.

"Wow -- look at the suction on those limbs!" Patrick Orwin says.

An 8-year-old named Mary Mills Lochala starts giggling. "The octopus is tickling him!"

Eventually the day's class ends. Shania has played with a chartreuse hamster ball, has plucked the mustache from Mr. Potato Head's face and is still holding on to his Bozo nose. She hasn't eaten much, so Quintero leaves behind the toys in which her food is hidden.

Shania's tank is kept much dimmer than others at the aquarium, lest too much light make her nervous. Octopuses have been around since the dinosaurs and can seem more primitive than ancient or wise. They're capable of lifting four times their body weight -- a feat that screams muscle beach, not ivory tower. They change color.

Ask Quintero exactly what shade of red she is, and he answers: "She'll make a liar out of you: As soon as you call her one color, she'll change." And she does. Just before she starts playing with the alien and Mr. Potato Head, and before the thick crowd has gathered around her tank, Shania is a solid, vivid coral-red. But by the time she's cuddling with the Potato, she's turned an elaborately patterned white-and-crimson polka dot.

Replacing the Velcro-sealed top to Shania's tank, Quintero weights it with concrete blocks. The children remain pressed against the window. A 7-year-old from Michigan named Jill Neumann says, almost to herself: "That's a sweet octopus. I would like it for a pet."

Her mother, Jeanne Neumann, reacts quickly: "Uh, nooo thank you," she says. "No."

Quintero reappears in front of Shania's tank, in his blue National Aquarium staff polo shirt. He is talking about how Shania's predecessor, a shy male, spent about 80 percent of his time hiding within the tank's rocks, while Shania spends 80 percent of her time in plain view. It's a question of personality. She will soon move to a new and bigger tank, here in the basement of the Commerce Building, and they expect her to grow to about 30 or 40 pounds.

Another mother, Julia Helveston, turns away from the tank and says to Quintero, "They're smart, aren't they?"

He beams. Shania is his girl -- the smartest in the aquarium. Other animals get attention and enrichment, too, but it's nothing like what she gets.

Once a week, the two alligators are thrown some big leaves of lettuce and hundreds of crickets -- stuff that glints and moves and gives the animals an excuse to attack something that isn't the other alligator. But there it's aggression, not intelligence or boredom, that demands attention.

As Quintero says, "Not every tank gets Mr. Potato Head."

The National Aquariumis in the Commerce Department Building, on 14th Street NW between Pennsylvania and Constitution avenues. Open daily 9 a.m.-5 p.m.; admission $2-$5. See http://www.nationalaquarium.comor call 202-482-2825.