The Edinburgh fringe is like a game of Scottish whispers, I think, as I sit on the train north. You have to listen out – as well as making your own choices. With 3,269 shows in 294 venues this year, some quadruple checking seems in order. And the whispers are sure to be in every language (although I’ve just read Richard Demarco, co-founder of the Traverse, in Scotland on Sunday, lamenting Brexit’s likely effect on the international diversity of the festival’s future).

My first stop – international festival, not fringe – is The Glass Menagerie (King’s theatre). A hit on Broadway, this Tony-nominated production, attentively directed by John Tiffany, makes me see this broken ornament of a play afresh – as a tragedy of parental interference. The actors never lose sight of its emotional core: Tennessee Williams understood pity, that most uncomfortable of human emotions, better than any playwright. Cherry Jones is splendid as Amanda, a faded bloom in the bouquet of family. Kate O’Flynn is excellently troubling as Laura, her handicapped daughter, with a high, helpless voice as lame as her gait. Michael Esper’s Tom has an exuberance born of despair, and gentlemen callers don’t come nicer or more devastatingly tactless than Seth Numrich. Designer Bob Crowley’s set is dominated by a black fire escape to one side of a hexagonal room, surrounded by a hem of water. This turns the sitting room into an island, reinforcing the sense that, at least for the two women on stage, escape is impossible.

The play’s most cheerful line is about a moon rising over a delicatessen. Leaving the theatre, in lieu of a moon, a high wind – this is an Edinburgh summer – blows through the city and threatens to upend the tents in which the Ladyboys of Bangkok are lip-synching their way through the afternoons.

Two shows I see early on have this in common: the living voice is not used without mediation on stage. This is anti-theatre – and surprisingly powerful. The subject of refugees is in the air, and in Last Dream (on Earth) (Assembly Hall, part of the Made in Scotland showcase), the audience listens through headphones. The effect is of distance from performers, displacement, a sense that the story is happening inside one’s head. It is a bold, unusual, moving piece about two journeys; the epic ascent of astronaut Yuri Gagarin contrasted with the frantic anonymous traversing of refugees between Morocco and Spain in a dinghy. The atmosphere is intent, peaceful – the cast is united. Suspense builds and music is used inventively – skittish riffs on a guitar stand in as the panicky reactions of a mother to her refugee daughter’s plight. The contrast between the astronaut coached to stay positive, although possibly under-explored, is suggestively set against the untaught fortitude of the refugees.

The Destroyed Room (Lyceum, also international festival) could almost have been devised as a commentary on Last Dream. It is a discomfiting conversation piece from Scotland’s artist-led independent theatre company, Vanishing Point, in which three middle-class people discuss their reactions not so much to terrorism and refugees as to the way that news comes to – and at – us. It looks into the complicated reasons that people might look at images of, say, the Paris killings. Cameras on stage film the conversation (which we can also see on screen) and mediate it. Does watching other people’s disasters make us feel more alive? I admired the way the piece swerves between the lives of the speakers and the subjects scrutinised. It was a subdued audience that left the theatre – a compliment to the material’s thought-provoking, conscience-stirring power.

Writer-performer Bea Roberts goes one further in Infinity Pool: a Modern Retelling of Madame Bovary (Bedlam). This is hugely enjoyable, offbeat installation theatre, made with two screens, a projector, a TV monitor and a sound deck… and no live speech at all. Roberts is the technician, a silent operator working away busily at the front of the stage, at one point rifling through and unspooling images of beautiful women and letting them pour over her body in streamers of light.

The show begins with a projected quote from the novel; “Poor little woman! She is gaping after love like a carp on a kitchen table.” The modern Emma is a lustful, overweight anti-heroine who works for a plumber in Plymouth. The show has a panicky comedy and pain about it. It begins unforgettably with what seems to be a fight to the death with a duvet – you cannot see “Emma” at all as she gyrates frantically beneath it, enacting a fantasy to one of her pop idols. Flaubert would turn in his grave, but surely – if he had any sense – with pleasure.

Satie hated critics. At one point McGowan surprised me by swiping the notebook out of my lap and holding it on high
I’ve always loved one-man shows that succeed in summing up a life. Erik Satie’s Faction (Pleasance), performed by Alistair McGowan and directed by his wife, Charlotte Page, is one of my top fringe experiences: a beautifully polished portrait of the French composer (whose music haunted the film Last Tango in Paris). Satie was an eccentric, a misanthrope and a hypochondriac – prone to despair about his compositions and his life. He would only eat white food, liked what he perceived as a whiteness in his own music, and wore a black bowler hat. McGowan has skilfully filleted Satie’s essays and poems and performs him with a gimlet-eyed facetiousness and relish. And he plays piano splendidly. Each time he plays Satie’s music – icy, melancholy, eerie – the lighting becomes glacial to mark the change in mood. Listening to it, you feel you are meeting the truest version of the man.

Satie hated his critics – with reason. At one point McGowan took me by surprise by swiping the notebook out of my lap and holding it up on high – Exhibit A – to the mirth of the crowd.

Waves (Summerhall), which I see on the same day, is another life-in-an-hour, gracefully enacted. Alice Mary Cooper remembers Elizabeth Moncello, Australian inventor of the butterfly stroke, who ended her days in an Edinburgh hospice where Cooper worked. It is a (butterfly) stroke of luck happening upon this show (it has early morning timing on its side). A miniaturist gem, a must for swimmers and a reminder that simple story-telling still works.

Familie Flöz is a Berlin-based company that uses masks to formidable effect, and its Teatro Delusio (Pleasance) attracts a deservedly packed house. The masks have a family likeness: beige, with vast noses and expressions varying between uncomprehending and outraged. And yet, as with all the best mask work, you could swear their expressions keep changing.

‘A family likeness’: Familie Flöz’s Teatro Delusio.
The show is based on life backstage at an Italian opera house where the stagehands are, often disastrously, ad hoc performers in their own right. It is about runaway bodies, uncertain intentions, hilarious results. Again, it is a wordless show but relatively lo-tech (just as well, given that the stagehands play poor electricians, their wires in a permanent tangle). The single most beautiful moment is at the start as a puppet catches sight of a puppeteer and shies away. She then slowly turns her anguished papier mache face to stare cautiously into his eyes.

The following day I saw two rough-at-the-edges pieces that had the courage to explore ideas that one looks for on the fringe. The first was Tank (Pleasance). This intelligent, zany, disturbing piece is based on the strange story of an American researcher and college dropout in the 60s who undertook an ill-judged experiment, living with and trying to teach English to a dolphin. A powerful extended metaphor about imperialism, the story was told with pluck, a plastic dolphin mask and yards of masking tape. Faslane (Summerhall), written and performed by Jenna Watt, was a courageous, humane, penetrating piece about Trident. Watt has relatives who work at Faslane, where Trident is based. She interviewed them, and the anti-nuclear protesters camping there. What emerged – unnervingly – was evasion (“This is my job – I don’t have an opinion.”) This included a protester who told Watt he was there for “private reasons”. It makes a piece like this – thinking about the unthinkable – all the more precious and necessary.

The sheer miscellany of the fringe has an almost addictive pleasure… and yet, if you see more than four shows a day, your mind starts to whirl. I was grateful for a calm interlude with Ockham’s Razor: Tipping Point (Venue 166), five mesmerising acrobats performing within a chalk circle with long white poles that support and, at times, obstruct them – like an elegantly graphic metaphor for life. They play with the idea of betrayal: there is a not-always-to-be-trusted affection between them – a hand caressing another’s head, a smile, an I’ll-be-there-to-catch-you-when-you-fall glance. It is magical, at one point, to see the gigantic climbing shadow of one of the acrobats (looking disconcertingly like Ralph Fiennes) projected against the wall. Sitting on the rim of their circle, I succumb to the fancy that these performers are immortal.

The following day, asylum-seekers rule once more. David Greig and Cora Bissett’s buoyant musical Glasgow Girls (Assembly Hall) lets us into a secret: Glasgow girls can come from anywhere. Callum Cuthbertson is great as Mr Girvan, an unconventional teacher who delights us by setting Burns’s poem about a mouse to music (there is a touch of Alan Bennett’s Hector in The History Boys about him). He teaches English/Scottish to his asylum-seeker pupils, makes them feel at home. The musical’s achievement is to wear its generous Glaswegian heart on its sleeve without losing the seriousness of its plot to sentimentality.

I loved Terry Neason’s Noreen, a working-class matron who claims to have been dragooned into the show by mistake. Her singing, when it eventually comes, brings tears to the eyes. A lovely, spirited anti-bigotry romp to make Scots proud and the rest of us wonder whether to move up north.

‘Fidgety brightness’: Shvorne Marks as the ‘prodigal daughter’ in House. Photograph: Jane Hobson
Clean Break, the company founded in 1979 by two women prisoners, offers us an impressive, absorbing and intimate (Box is a small venue)double bill. House, by Somalia Seaton, is about a prodigal daughter. Shvorne Marks plays Patricia with a fidgety brightness that reveals her nerves about coming home. Michelle Greenidge is her rejecting mother and Rebecca Omogbehin is Jemima, her peace-seeking sister. The performances are perfectly focused and every word compels. Amongst the Reeds, by Chino Odimba, is a snapshot of a story about what happens to a pregnant Vietnamese asylum-seeker (Jan Le’s affecting Gillian), holed up with her 17-year-old friend, Oni (the charismatic Omogbehin again). Gillian thinks only of her unborn child. Oni worries persistently about deportation. This is moving work of unmistakable integrity and not to be missed.

Her version of Bob Dylan’s Simple Twist of Fate tells you more than the riddling original
On my final evening, I see Camille O’Sullivan in her extraordinary new show, The Carny Dream (Circus Hub). Her charm as a singer is irresistible, although she insists on describing herself as an “Irish chancer”. It is not her voice, grand though it is, that makes her. It is her interpretation of lyrics – she seems to live the songs she sings. Her version of Bob Dylan’s Simple Twist of Fate tells you more than the riddling original. Her homage to Bowie is thrilling. And when she sings Peggy Lee’s Is That All There Is? while flying overhead on a circus swing, she makes you want to answer that “all there is”, in her company, is quite enough.