We’ve got a lot of big heads in Chicago, but this must be the biggest.

(Wait, is Donald Trump in town?)

It’s Awilda, Spanish sculptor Jaume Plensa’s 39-foot noggin, officially installed last week in Millennium Park as part of the park’s tenth anniversary celebration. (Full title for the piece is Look Into My Dreams, Awilda; the larger exhibit is “Jaume Plensa: 1004 Portraits.”)

White as an iceberg and nearly as blank, she presides over the park entrance at Michigan and Madison with a commanding view to the west. Except she’s not looking.

While crowds of people swarm around her, she sleeps, eyes shut, tranquil as a Buddha—if Buddha could be a giant, plastic, nine-year-old girl.

She’s in another place.

“Dreaming,” says Plensa—who was at the park for the opening—like her equally serene sisters, Laura, Paula, and Ines, the trio of twenty-footers recently installed on the terrace overlooking Plensa’s riotous, well-loved Crown Fountain.

Plensa says his statues are made to be caressed. The sisters are warm where the sun hits them, and (last week, at least) sticky. Their deep-brown, cast-iron skin is pocked like real flesh, and the backs of their heads are flattened. They’re stationary, but when you move, they seem to move too—subtly shifting their orientation. (Check them out from the north, the south, the sidewalk on Michigan Avenue. Which way, exactly, are they facing?)

Unlike Crown Fountain, with its thousand real local faces, these pieces are not unique to Chicago. They’re visiting, on loan from the artist for the next 18 months. In fact, for the past five years or so (ever since Dream, a 66-foot, 500-ton monument he made for an English mining town), Plensa has been cranking out similar heads in various sizes and materials, and planting them all over the world. Two years ago, for example, you could have spotted this Awilda a few feet offshore in Rio de Janeiro’s Guanabara Bay. A smaller version, in marble, was installed at the University of Salzburg in 2010. Richard Gray Gallery is currently exhibiting five limited edition “midsize” heads, about six feet tall, in bronze or volcanic basalt, and a few shelf-size smaller pieces in luminous Murano glass.

Like Awilda, the heads are all elongated and abstracted enough to be generic. The models for them, however, are real girls between the ages of “seven or eight and fourteen,” Plensa says. Their images are captured in 3D photographs, then manipulated and recreated through computer modeling. Plensa says girls (not boys) are the future, and at that age, “no longer children, but not yet women,” they have a certain nascent quality that makes them the appropriate symbol for the world to come, a “special kind of beauty.”

This could be creepy, or a move to gender balance in a body of humanistic public work that has repeatedly depicted the common “anonymous” person as a figure that looks male. But placidity isn’t characteristic of nine-year-olds of either sex: Plensa’s big girls can strike one as more tranquilized than tranquil. His sleeping (or inward-gazing) sisters don’t see the real, active girls at play in the fountain below them. But in their dreams, that might be where they go. Because if you’re nine, that’s nirvana.