The last selfie of Arthur Cave

Ovingdean Gap is a hidden gem. Cars and buses leaving Brighton for Eastbourne whiz past a dent in the cliff top where steps with green iron railings spiral down to the sea; as you descend you can pause to admire the view from landings like the stages of a high diving board. At the bottom is a row of beach huts featuring a wavy modernist roofline. A hut with a hatch serves coffee and cake; people sit at tables in the shelter of the sea wall while their dogs fossick on the beach. There are walkers from Rottingdean and cyclists from Brighton but mostly the locals have had the place to themselves. Until last week, when Ovingdean Gap hit headlines all over the world.

Two days earlier, Brighton's paper, The Argus, printed a picture of some teenagers insouciantly perched on the cliff at Seven Sisters, a beauty spot further down the coast. Young legs dangling over a precipice. Every year, at the start of the long holidays, stories like this appear; children emerging from computer-game worlds need reminding that the real summer landscape has real edges – given to crumbling in the case of Sussex cliffs – and real falls onto real rocks. Within 48 hours, driving home the lesson with excessive brutality, the Argus announced that a 15 year old boy had been found dying on the undercliff path at Ovingdean.

Next day, we learned that the dead boy was Nick Cave's son. His parents were pictured visiting the place where he fell; black clothes, black glasses, dyed black hair among the white and purple moon daisies growing wild on the cliff top. Statements rapidly assured us that the death was not suspicious, though that is for the Coroner to decide.

All along this stretch of the coast, the cliff edge is fully fenced to the height of a teenager's head; here and there are signs saying TALK TO US and a number for the Samaritans. Near a broken and leaning concrete post, the strings of a shopping bag are tied to the fence wire. Inside the bag is a black hat, costume from a school Shakespeare. Amid the cards and stooks of long-stemmed flowers, an open letter in careful writing begins: Arthur, words cannot describe how much I will miss you...

Half a dozen teenagers in new teeshirts and shorts come along the path, examine the tributes , then stand looking out to sea. They might be the classmates who talked to the Argus about skating with Arthur and riding home with him on the bus. One of them received a last phone message, a selfie, smiling, with Rottingdean Windmill in the background. Sadness, cliché, bewilderment. Nothing that wouldn't be done and felt for a child whose father wasn't the poet laureate of violent death.

At the beach cafe the numbers are back to normal. There were flowers on the shingle but the tide has washed them away and Ovingdean has kept its secrets. Though its cliffs have the radiance of Sussex chalk they are featureless and relatively low. Ugly fences are not such a detraction here, but no one is suggesting putting obstructions in the famous views at Seven Sisters, or Beachy Head. We are left with safety warnings, Samaritans signs and, where people have fallen despite out best efforts, mysteries.

Arthur's father is at Ovingdean again. Wearing a sky blue shirt and not being photographed, he passes the cafe with a lopsided stride; youthful, Australian, impatient. A big shaggy man who looks more like a musician keeps pace with him. It was about this time, four days ago,that Arthur fell. The sky and the sea were like this.

A few minutes later, the child's mother comes, walking with a friend whose arm is around her waist. In a colourful summer skirt today, she is pacing out a slow march.