What determines our character? Nature or nurture? Genetic inheritance or social environment? It is an age-old debate, and Alice Birch now adds to it with this startling theatrical triptych about three generations of mothers and daughters. Whatever my doubts about Birchs conclusion, the play is odd, arresting and, in Katie Mitchells immaculate production, highly original in its form.

Birchs progress as a writer has been fascinating to watch. She delivered a short, sharp shock in 2014 with Revolt, She Said, Revolt Again which was a subversive, playful piece calling for revolution in everything from sexual relationships to the workplace. In 2015, the Orange Tree brought us an earlier Birch play, Little Light, about sibling rivalries, that suffered from too much withheld information. Since then Birch has written a polemical piece about porn, We Want You to Watch; the admired Ophelias Zimmer, which I missed; and the recent film Lady Macbeth, which transposed a Russian novel to Victorian England and got a five-star review from Peter Bradshaw.

On the evidence so far, I would say Birch has a gift for radical experiment in the style of Caryl Churchill and Sarah Kane. In her new play we are confronted by three women, Carol, Anna and Bonnie, who we learn are mother, daughter and granddaughter. They exist in three different time zones but the story of their lives is told simultaneously. As Birch herself says, the text has been scored and can be read, or viewed, horizontally. In practical terms that means that, as dialogue and action often overlap, we decide where to focus our attention.

It is simpler than it sounds. We first meet Carol when she is emerging from hospital having tried to kill herself by slitting her wrists; subsequently giving birth does little to quell her visible unease. While following Carols story, we also see her grownup daughter Anna suffering from drug addiction, joining a commune and marrying a documentary film-maker by whom she has a daughter. That daughter, Bonnie, has grown up to be a skilled physician who is gay, guarded in her relationships and determined to avoid the possibility of procreation.

If I say that panels above the stage reveal early scenes to be taking place in 1973, 1998 and 2033 and that by the end the story has moved on by roughly a decade, you will get the general idea.

So what is Birch suggesting? Evidently that inherited suicide is a possibility and that the trauma of Carols life is transmitted to the next generation and beyond. I am not qualified to say whether that is psychologically true, but behind the play lies a genetic determinism that I resist. We all know what Larkin said about what parents do to their children (They fuck you up) but Birchs play leaves little scope either for self-invention or the impact of social and economic forces. Even Bonnies choice of profession seems shaped by her grandmothers actions, and you are led to wonder whether Carols momentary surrender to a womans kiss has some connection with Bonnies sexual preference.

Even if I question many of Birchs assumptions, she has found the ideal form in which to explore her subject. I can, in fact, think of few exact parallels to this play. Charlotte Keatley in My Mother Said I Never Should interwove four generations of mothers and daughters and Edward Albee in Three Tall Women cross-cut between the different stages of his adoptive mothers life. But Birch not only presents three lives concurrently but deftly establishes overt and subliminal links between them: Carols anguish over childbirth is echoed in Annas experience and even a word such as radiant takes on varied associations when applied to all three characters.

Mitchells production is characteristically precise and detailed, and Alex Ealess design of a strip-lit institutional room with five doors proves highly adaptable.

Casting also ensures that the three women, although linked by blood, are idiosyncratically different. Hattie Morahan plausibly lends Carol the air of a once-golden girl infinitely baffled by her inability to find happiness in marriage or parenthood. Kate OFlynn exactly captures Annas congenital instability and resentment at being treated by her future husband as a case history. Adelle Leonce meanwhile is all wariness and isolation as Bonnie, and there is good support from Jodie McNee as her ardent suitor and Paul Hilton as Carols perplexed husband.

Its a play that raises many more questions than it answers but for two uninterrupted hours it kept me hooked. It also confirms that Birch is a questingly experimental writer who, even if she insufficiently acknowledges our capacity to escape our parental legacy, has a remarkable gift for reinventing dramatic form.

At the Royal Court theatre, London, until 8 July. Box office: 020-7565 5000.

In the UK, the Samaritans can be contacted on 116 123. In the US, the National Suicide Prevention Hotline is 1-800-273-8255. In Australia, the crisis support service Lifeline is on 13 11 14. Hotlines in other countries can be found here.

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Anatomy of a Suicide review a startling study of mothers and daughters - The Guardian