My hat, it has three corners

One hat on the hat pegs and one in his hands. Both tricorns, but one of new, stiff, black felt and the other of worn, brown hide. He turned the latter over and over—was there some secret to it? Some hidden significance?

Three corners has my hat

He had gone down to the brig to relay the pirate's sentence upon disembarking—death by hanging, as he rightly deserved. The miscreant had only nodded lazily and lounged in the corner of his cell, waving off the sentence with an elegant flop of his hand. He'd asked for his hat back with an air of command better-suited to a king than a to filthy brigand under lock and key.

Norrington had refused. He had also refused to hand over the pirate's effects—what man was dim-witted enough to press weaponry into the hands of a prisoner?

At last, Jack Sparrow had asked to be held on the Black Pearl. If the commodore had been unable to see the desperation in that man's eyes, he was no human at all, but an unfeeling wretch.

He was, however, a sensible unfeeling wretch, and he'd bidden the pirate good day and asked the guards to find leg-manacles for their guest.

All the while, Jack had glared at him from the corner of the brig as though his heart were breaking and he intended to use the jagged bits like daggers.

"I will be having my hat back."

And had it not three corners

It was, of course, the pirate's natural affection for material things. Their kind cared only about money, or ships, or weaponry.

Where, though, did the hat fit?

Money bought food, supplies, and lodgings. Ships were essential for carrying out the pirate's trade. Weaponry provided irresistible persuasion in the event that sheer terror or force of numbers did not bring a merchant ship to acknowledge the inevitable. All useful things, and it was sensible (if immoral) to hold them sovereign.

Why did the pirate insist on having his hat?

Norrington turned it over and over, searching for hidden lock picks or pins, but he could find nothing special or significant beyond its essential hatness. It was heavy and probably hotter than felt; it had obviously been through the mill, in that it was creased, battered, scuffed, and dirty. Why did Jack Sparrow want his hat back so much?

And as the commodore hung the hat on the pegs beside his own, he understood.

It wasn't the hat itself. It was the fact that someone else had it.

It would not be my hat.

No one knew how Jack Sparrow had managed to escape in the night, manacle his guards' legs together, steal a lifeboat and steal out to his ship, overpower the men occupying the Black Pearl, and free his crew.

And Norrington didn't know how, but he knew why both his hat and the pirate's had disappeared from the pegs in his cabin. He cursed.