Viewed on 7th August, 2011.

Only in the Edinburgh festival, with its enormous profusion of theatre, would you be unsurprised to come across not one but two plays involving the separation of conjoined twins. One was Mokwha Repertory Company's production of The Tempest in the Edinburgh International Festival. Drawing on Korean folklore, it presented Caliban as a squabbling two-headed monster called Ssangdua who was eventually split in two by a benevolent Prospero.

The other one was Futureproof by Lynda Radley, one of the founder members of Cork's Playgroup and now resident in Glasgow. The final production in the reign Dominic Hill as artistic director of the Traverse Theatre, it tells the story of Riley's Odditorium, a travelling freak show trying to make ends meet in the face of an increasingly indifferent public.

As well as the fat man, the bearded lady and the real-life mermaid, there are Lillie and Millie, Siamese twins joined at the pelvis. Played with beautiful synchronicity by Ashley Smith and Nicola Roy, they have the most distressing story in Radley's thoughtful play.

For as long as the circus remains successful, their medical condition is something they accept with good grace. The inconveniences of sexual desire and their individual wills are offset by the cheery companionship they give each other. They come across as the least narcissistic of an oddball group of entertainers.

But the economic tide is turning and, with it, the social acceptability of being different. In the case of Robert Paterson's Tiny, this is a bit of a joke. He reached his inordinate size through sheer gluttonous will-power after realising he could make money claiming to be the fattest man in the world. When John Buik's ring-master Riley warns of the end of the freak show if they don't change with the times, Tiny accepts with similar gusto the challenge to shed his weight. He is willing to shift his shape in any direction the market demands.

According to Riley, that demand is for something more conventional. "Embrace amendment towards the norm," he writes in a speech he is too cowardly to deliver himself. He believes a modern audience will be more impressed by people who have escaped their peculiarities than by the peculiarities in themselves. For Lillie and Millie, the consequences of being made normal – ie. to be separated from each other – are potentially fatal.

What Radley builds, with her bold characterisations and striking imagery, is a metaphor for the pressure on all of us to conform. Hill's colourful, end-of-the-pier production celebrates the troupe's life and exuberance to such an extent that we are alarmed to think of them being made more ordinary. Futureproof may be set in some Victorian past, but it speaks eloquently – and touchingly – about the homogeneity our own mass market thrives upon.

Designer Colin Richmond makes the most of the carnival theme, with a string of fairy lights across the stage, red-and-white striped awning, a lonely pianola playing to itself at the back and a side-show caravan onto which old-school black-and-white film is projected. His costumes, all earthy russets and browns, show off the extraordinary nature of the performers – Paterson's fat suit is particularly impressive – while maintaining a sense of fading Victoriana.

As a play, it feels like a big step forward for Radley who is better known in Scotland for performing her own one-person shows. There was a quirky charm to The Art of Swimming (about the first woman to swim the English Channel) and Birds and Other Things I Am Afraid Of (performed to an audience of 12 in a garden shed built on the altar of a Glasgow church) and Futureproof demonstrates she can also flex some dramatic muscle. Powerful though her idea is, however, it isn't quite strong enough to justify the 90-minute running time of the play. It seems like a visually striking but low-key end to Hill's tenure as well as a promising start to a new stage in Radley's career. 

Mark Fisher is a freelance writer based in Edinburgh, contributing to publications including the Guardian, the Scotsman and Scotland on Sunday.