Imagine for a moment what would happen if Albert Einstein met Marilyn Monroe. And then imagine their spirited discussion about the theory of relativity being interrupted by first Joe DiMaggio, who hasn’t seen his wife for two weeks and wants her to come home, and then Senator Joseph McCarthy, who’s trying to drag Einstein to an un-American Activities Committee hearing.

Having trouble? Well then get yourself along to the Arcola, where Terry Johnson’s Insignificance imagines it for you. Directed by David Mercatali, the result is an enjoyably (and perhaps predictably) bizarre encounter that begins as a comedy but ends up in significantly darker territory. Written in 1982, it’s a play that seems to be about a lot of things, much of which a 21st century audience can still relate to – among them the downsides of fame, the threat of nuclear war and the stereotyping of women.

Simon Rouse’s Professor and Alice Bailey Johnson’s Actress (none of the characters are referred to by their names, although the script, costumes and performances leave us in no doubt who we’re looking at) find a surprising connection when she bursts into his Manhattan hotel room eager to meet him and prove she understands the theory of relativity. As someone whose scientific knowledge is limited to say the least, I don’t mind admitting I got totally lost during her increasingly enthusiastic recital – not helped by the fact it’s delivered at the speed of light – but that doesn’t prevent it being the defining moment of the play. You can’t help but cheer a little bit to see Marilyn shrug off her dumb blonde persona and take on one of the brainiest men on the planet… and then again when she takes down the infinitely easier target that is her abrasive, gum-popping husband with a series of withering retorts.

At the root of this triumphant moment, though, is a deep sadness that only grows as the play goes on. The Actress desperately wants to be taken seriously, but is constantly thwarted by the image she’s created for herself. Similarly, the mild-mannered Professor just wants to sit and quietly work out the shape of space, but is pursued by the expectations of others, and the use to which his name and work could be put, should he allow them to be. Each has grown used to the world knowing them only by their public persona, which is why this odd pair make a strange kind of sense – certainly more so than the Actress and the Ball Player, who don’t seem to get each other at all. Joe DiMaggio, played with swagger and just a hint of appealing vulnerability by Oliver Hembrough, is fine with people seeing him exactly as he is, just as long as they still see him… which is probably why the suggestion that he’s merely a creation dreamed up by Tom Mannion’s malicious Senator riles him so badly.

Though rooted in troubling subject matter, Johnson’s script is full of witty one-liners, from inside jokes about Schrödinger’s cat and Arthur Miller to more universal gags, most at the expense of the less intellectually blessed characters. In between the four of them talk at length about various topics, from the scientific to the political to the domestic, in a production that tails off to a vaguely unsatisfactory conclusion – so much so that we end up wondering if the bizarre events of the night happened at all.

There’s a lot to enjoy in Insignificance, not least the strong performances from four actors seemingly unfazed by the pressure of playing real – and in at least two cases, iconic – historical figures. The Professor and the Actress might not succeed in teaching us much science, but their imagined encounter does pose some interesting questions about the self-defeating nature of celebrity. It’s a bit of a slow burner on the night, but this is the kind of play that stays in your mind, throwing up more ideas and discussions the longer you think about it. Well worth a visit, if only for the thrill of witnessing such an unlikely meeting of minds.