HE'S CLOSE. VERY CLOSE. RUMORS place him here just yesterday, playing with a sea kayaker along this beach. He hung around for 15 minutes or so, swimming in circles, splashing and making his usual sing­song squeals and clicks. No, he didn't put on his trademark Big Show. But then, in recent years that spectacle has come less and less often.

Still, he's nearby. A forty-ish Atlantic bottle­nose dolphin, with a number freeze-branded on both sides of his dorsal fin, giving him his now familiar moniker: Dolphin 56.

As usual, he's spending late summer and fall hugging this stretch of southern New Jersey shore, a rugged line of dunes and sand known as Island Beach State Park, roughly a thousand miles from his Florida birthplace. I'm here, and hoping for a glimpse, aboard the 26-foot fishing boat Phyllis Ann, owned by captain Rod Houck. Two weeks ago to the day, Dolphin 56 swam up to the Phyllis Ann's gunwale, lifted his head and upper body from the water, and let Houck and some fishing buddies rub his shoulders, snout, and forehead in amiable human-to-dolphin congress.

"It was one of the unforgettable moments of my life," Houck says. He's steering the Phyllis Ann out the narrow passage of Bar­negat Inlet, past the last navigational pilings and into the broad Atlantic horizon just south of the park. It's a warm late-summer Sunday. The ocean shimmers, flat and calm. Conditions are exactly like yesterday; exactly like two weeks ago, when the 44-year-old Houck first made contact with the dolphin who has become my obsession.

"It was the strangest thing," Houck says. "We were motoring about a quarter-mile offshore, and I saw a single dolphin off our port side. So I shouted 'Dolphin!' to the guys and pointed at him, then backed off the engine. Soon as we slowed, he came toward the boat. Not porpoise-ing like normal dolphins, but with the top of his body a full third out of the water. He came toward us like a surfaced submarine. I thought, Now, that's unusual. I didn't know yet that he was so famous."