The ferry from Bredstedt was meant to be the easy bit of the journey. I had checked the timetable three times, packed the car with unnecessary layers, and even remembered to put the beer in the cool bag. What I had not done, in my infinite wisdom, was check whether my booking confirmation actually matched the name on my passport. The chap at the terminal, a wiry Dane called Henning with eyebrows like two fat caterpillars having a disagreement, studied my paperwork for what felt like three verses of the Danish national anthem. "You are not Jorgensen," he said finally, in that flat Scandinavian way that makes statements sound like verdicts. I am not Jorgensen. I have never been Jorgensen. The cottage was booked in my brother-in-law's name, and he was currently sunning himself in Mallorca, the traitor. Henning let me through eventually, after I showed him seventeen emails, a bank statement, and a photograph of my cat. "Next time," he said, handing back my passport, "be Jorgensen."

The cottage at Kegnaes Strand sits down a lane that feels like it is trying to escape the rest of the island. I found it in the end, after reversing twice for tractors and once for a woman on a bicycle who simply stopped in the middle of the road to watch a heron. The place itself is one of those white wooden Danish numbers with a roof that seems to slope in several directions at once, as if it got tired during construction and decided to have a little lie down. The key was in a lockbox with a code that the owner, a fellow called Mogens, had described in his email as "the year Denmark won the European Championship." I stood there in the drizzle, trying 1992, then 1908, then 1948, before remembering that Mogens had a particular sense of humour and trying 0000. The door swung open. I still do not know if that was the actual code or if the lock had simply given up on me.

Mogens appeared the next morning while I was attempting to operate the coffee machine, a contraption that looked like it had been designed by someone who fundamentally distrusted simplicity. He is seventy-ish, built like a fire hydrant, and dresses exclusively in various shades of mustard yellow. "You are the not-Jorgensen," he announced, which I suppose counts as fame of a sort. He showed me how the coffee machine worked, which involved a lever, a ritual incantation in Danish, and what I can only describe as a threatening stance. Then he sat down at my kitchen table uninvited and told me about his divorce.

Bente from two doors down introduced herself by leaving a Tupperware of pickled herring on my doorstep with a note that read "You look like you need feeding." She is eighty-four, rides a moped with a basket on the front, and has opinions about everything from Brexit to herring migration patterns. We got talking over the fence, which is not really a fence but a row of wild roses that have gone feral and aggressive. Bente has lived in Kegnaes since 1958, when she arrived as a newlywed and promptly decided the place was too interesting to leave. Her husband disagreed and moved to Odense. She kept the cottage. "He was too tall," she explained, as if this clarified everything. She now runs what she calls "the intelligence service," which involves knowing everyone's business and occasionally correcting their recycling.

The fish man comes on Thursdays. I do not know his actual name because everyone calls him the fish man, including himself. He drives a van that smells powerfully of the North Sea and sells from the harbour car park for exactly ninety minutes. I arrived at minute eighty-seven, breathless and apologetic, to find him packing up with theatrical slowness. "Not-Jorgensen," he said, nodding. Word travels. I bought three plaice and what he described as "a mystery fish, very educational." It was, in fact, a herring. Everything here is herring if you do not ask specific questions.

There is a woman who walks the beach at dawn with a metal detector. I have seen her three times now and we have never spoken, only exchanged nods of the sort that suggest mutual recognition of life's absurdity. On the fourth morning she stopped, dug something from the sand, and held it up for my inspection across fifty metres of damp shingle. It was a spoon. She shrugged, as if to say this is what we have, and continued her patrol.

I am learning that Kegnaes Strand operates on its own frequency, one that requires patience and a willingness to be slightly wrong about everything. The cottage creaks at night in rhythms I cannot predict. The shower runs hot only if you threaten it. Mogens returns every few days with some new instruction or historical grievance, usually both. Yesterday he helped me fix a window that would not close, using a technique involving string, a clothes peg, and what he called "Danish engineering, very advanced." It works. I have stopped asking why.

The herring was excellent, by the way. I told Bente this and she looked at me with something approaching pity. "Of course," she said. "It is herring."