Crouching at the side of the pool, I reached in and did a little flutter kick with two fingers. The water was like a bathtub, thick as syrup, too warm for me but the theory is that kids learn to swim easier if they’re not thinking about how cold they are. Sure enough, my daughter, Eliza, just four that summer, splashed across the width of the pool, face down, kicking out of rhythm but with total abandon, hands gripping the edge of a faded blue Styrofoam board.

My father sat behind me in a small triangle of shade, tipping back in a plastic chair at a table under a broken white umbrella, chewing, as always, the cuticle on the side of his thumb. Waiting.

I caught the teacher’s eye, gestured back to the umbrella table with my chin, “Eddie,” I said, “my father would like to buy your hat.”

My father, silent as a foreign ambassador, nodded at Eddie, who was just a kid, bronzed, hairless, wearing long red trunks, a white T-shirt, dark glasses and a monster sombrero with a leather string that went around the brim and dangled just below his collar bone. There was a frayed hole in the straw on the side and the hat was graying like a cottage on the Cape from all that water and sun.

Eddie laughed at the joke and to my daughter, who had reached the other side of the pool and was blowing bubbles, he said, “One more time across, Eliza. Let me see your strokes, now, and you can dive for rings afterwards, okay?”

“Name your price,” my father barked, fluent in English after all, tilting forward in his undersized seat.

Eddie said he needed his hat and couldn’t possibly sell it.

“How much do you want?” My father spoke slowly, with as much patience as he could muster. His assistant, his staff, as it were (that was me), had failed him. He’d have to make the deal himself.

Eliza shouted at me to watch and she bounced up and down not far from the steps, where the water reached only to her shoulders.

“I see you, sweetie,” I said, squinting into the sun, then crossing away from the glare to stand in the little wedge of shade beside my father’s umbrella table.

“C’mon, Eliza, show me one more lap,” said Eddie, and when she pushed off from the side, arms flailing like a broken propeller, he told my father, “I’m sorry, sir, this hat is not for sale.”

“That’s right,” I said. “You stick to your guns—don’t give in—he thinks he can boss everybody around.”

My father leaned back again, legs crossed. He was starting to have fun, I could tell.

“Name your price.”

A woman sitting cross-legged on the cement on the other side of the pool looked up from the newspaper spread across her knees and stared at him. Suddenly embarrassed, I reminded him, my voice a little too loud, that Eddie needed his hat teaching lessons back to back under the mid-day sun.

There were two pools side by side on the flat expanse of lawn, two shimmering pools reflecting a cloudless sky. Beyond them the grass was brown, although the oleander grew thick and high along the fence between this yard and those of the neighbors on either side. Two teachers worked in each pool and all four of them wore the informal uniform; some kind of T-shirt over some sort of bathing suit, dark shades and wide-brimmed head gear.

“You don’t want this old hat,” Eddie said. “It’s got a hole in it, see? It’s falling apart.”

“It’s priceless,” my father replied. “It’s a relic, for Christ’s sake, they don’t make them like that anymore.”

Now he was confiding in the kid, talking up his golf game. Loved the sport, he said, suddenly expansive, but all that sun exposure was a problem. Just a few days ago a dermatologist had charged him an arm and a leg to burn some growths off his face. He stroked his cheek, feeling for the scab with his fingertips.

“That’s just the hat I need,” he said.

The woman, who had a child in the other pool, shook her head almost imperceptibly, and looked back down at her paper.

“Dad, leave him alone,” I said.

I needed the woman to know that in this case, the apple had nothing to do with the tree—I was as confounded by this vulgarity as she.

Eddie threw three rings, fluorescent pink, orange and green, and Eliza half-jumped, half-dove from the steps, wriggling to the bottom to retrieve them.

“How much do you make an hour?” asked my father.

I winced, watching Eddie shrug, smile, pat the surface of the water with his palms.

“Tell you what. I’ll give you fifty bucks for the hat.”

Eddie’s eyes widened. “Shoot,” he gasped.

My father slowly extracted a new fifty dollar bill from the thick wad in his money clip and put the rest back in his pocket.

“Here it is.” He put the bill on the table without getting up. “Take it or leave it.”

I was ready for the bill to blow off the table and into the pool and I stuck my hands in my pockets.

“I’ll take it,” said Eddie, removing the hat.

My father looked at me and nodded in Eddie’s direction. I started to laugh, bit my lip, took the money off the table and walked it over to the kid, who handed me the hat in return.

“More rings?” Eliza squealed, “More rings, more rings, more rings!”

“Time’s up,” Eddie said, glancing at the clock on the wall of an old shed behind the far pool. He was folding the bill into a square the size of a postage stamp, promising her more rings next week. He held the green square in one fist just out of the water and I wondered when he would get out of the pool and put it away. His hair was flat on his head, a color somewhere between brown and green, shiny like tinsel from all the chlorine.

I held up an oversized beach towel and Eliza shimmied out of the pool and into my arms, smelling of bleach and baby shampoo and Coppertone and leaving a big wet print where she had pressed her head against my cotton sweater. My father examined his new hat, stood up and put it on.

“Whaddayathink?” he asked my daughter.

“It has a hole,” she observed, and she led the way up the driveway to the street, pausing to search for roly-poly bugs in the flower bed at the back of the house, trailing her yellow terrycloth train across the gravel behind her.

The woman with the newspaper was staring again and when my father met her eye, acknowledging her role in the conspiracy, she gave him a terse, little smile. On his way past her, he pulled a cherry tomato from the vine that straggled along the fence between the pools and the driveway and popped it into his mouth.

“Ummm,” he said to her over his shoulder, as he grabbed another for the car.

“That’s sweet.”