To Who or not to Who? That is the question. Doctor Who was playing Hamlet in the Royal Shakespeare Company’s new production at Stratford-upon-Avon last night.

All preview accounts describe David Tennant’s performance as an extrovert Prince. His two eyes like stars start from their spheres; his tombstone teeth are sharper than a serpent’s; and his voice on occasion tears a passion to tatters. In today’s Times our theatre critic Benedict Nightingale awards the production four stars. But Hamlet is refusing to sign Doctor Who memorabilia for members of the audience: “It is just turning this into a sci-fi convention.”

There are more connections between Doctor Who and Hamlet than meet Gertrude’s wanton eye. Both are obsessed with this brave o’erhang-ing firmament, this majestical roof fretted with golden fire, or filled with flying saucers in pursuit. Both deal with miching malecho: it means mischief. Both have winsome female assistants, with whom the protagonist’s relationship is problematic. But Hamlet 2008 is wrong to consider his play as caviare to the general. It is also burger and chips. For Hamlet is the great lake, in which elephants and highbrows can swim, and lambs and lowbrows can paddle.

It is as sensational as Doctor Who, and as frightening in parts. Why do you suppose that its first words, “Who’s there?”, are spoken not by the soldier on watch but by his nocturnal visitor? “Nay, answer me. Stand and unfold yourself.” Celebrities from Sarah Bernhardt to the Lion King have reinterpreted the Prince. He really is the man (and woman too) for all seasons. Doctor Whofans are in for the treat of their young lives.