'It's silly," says Jacob, the family's Lego aficionado. "That doesn't work." He's got a point. My three-year-old son is looking at a picture of the Lego hat worn to the American Music Awards at the weekend by Will.i.am and he's already spotted a design flaw. Quite a major flaw, in fact: it is impossible to make such a hat with normal Lego bricks.

Father and son, united in frustration at how a Black Eyed Pea could display such a poor understanding of the square-edged symmetry that underpins Lego's genius, empty a box of Lego on to the kitchen table and set forth on making our own hat.

"What sort of hat should we make?" I inquire. "A bowler? A baseball cap?"

"No, just a hat, Daddy."

So I gesture him to show me. A hollow pyramid begins to rise from the table. "You find the long, red bricks," he instructs me. I quickly get the message that I am very much the milliner's apprentice in this game.

Jacob tops out the pyramid with some flat green strips and presses on some flourishes – two Lego trees, a dog, a helicopter blade and two Lego men. He then fixes a cap to the "front".

"Is that a Philip Treacy?"

He ignores my gentle mocking of his design and tentatively pulls the hat on to his head. It's far from what you'd call a perfect fit. The square base of the pyramid is not that forgiving on the human head, after all.

There's just time for me to photograph his creation before he drops it on the kitchen floor and it smashes into 100 pieces.

"Can we build a robot now?"