Two of the most intriguing walk-on characters in Elif Shafak’s How to Stay Sane are the little Egyptian girl named “Facebook” by her parents in that brief, optimistic phase of the Arab spring – and another baby given the name “Like” in Israel just a few months later. They are poignant reminders of another age in which social media looked set to deliver a new and better world. It is hard not to wonder, as Shafak does, what has become of this pair. “Do they view the buoyancy that presided when they were born as a relic of the past … ?” Or to put it more simply, “what on earth have they done with their names?” Discarded them at the earliest opportunity would be my guess – whether because of the misplaced optimism with which their parents had branded them, or simple embarrassment in the playground.

How to Stay Sane in an Age of Division is a sharp and elegant pamphlet of just 90 pages. Though better known as a novelist (10 Minutes 38 Seconds in This Strange World was shortlisted for the Booker last year), Shafak is a political theorist by academic training. Here she combines her two skills, drawing on some of her favourite fictional themes (the complexities of storytelling, multiple identities, women’s voices) to dissect the anger and anxieties of contemporary society, and the disappointments so neatly symbolised by the names of little Facebook and Like.

Much of her focus is on the divisions of modern political and cultural debate, and the apparent refusal of all sides to listen to opposing points of view. She broaches some of the themes raised in the open letter, recently published by Harper’s magazine, which deplored the current climate of intolerance, censoriousness and blind moral certainty (“cancel culture”, as the writers were careful not to call it). This was an intervention understandably, but perhaps unfairly, dismissed by some as an unseemly whinge on the part of a traditional intellectual elite, bemoaning their own loss of privilege, an elegy for a lost sense of entitlement. These lofty signatories were not concerned, so critics insisted, with free expression in itself; they were more bothered by the fact that fewer people were listening to them. This letter, and the controversy it raised, presumably came too late for Shafak to have seen when she was writing How to Stay Sane, but – forewarned or not – she does not fall into that trap.

She is very clear about the harm that comes with the polarisation of debate in social media, and she has no time at all for the communal narcissism – the whispering galleries, the echo chambers and groupthink – that underpins cancel culture (a term that she does not use either). She also sees an important continuum between the harangues on Twitter and the “clashing certainties” you find on television, radio or YouTube discussions. The participants, she claims (rightly in many cases), “are not there to listen and they are not there to learn. They are there … to fulminate.” But her analysis of the cause of this malaise is a more generous one than what was laid out in the open letter, going back to her leitmotiv of storytelling.

If you cannot tell your own story, she argues, you will not be willing to listen to the stories of others. Those who are “systematically unheard” will systematically not engage with ideas that conflict with their own. (Why on earth should they?) When “a growing number of citizens feel left out, not so much forgotten as never noticed in the first place”, it is no wonder that public debate has become increasingly crude. In an argument that is closer to the critics of the Harper’s letter than to the letter itself, she implies that many of those who now complain at the decline of free expression only have themselves to blame.

It is not, of course, quite so simple. If (to reverse the logic of her argument) having the privilege of being able to tell your own story were a sufficient qualification for being a good listener and nuanced debater, then many of those on the current Tory frontbench should be some of the best listeners we have. They are not. And historians may bridle at her sweeping claims about “power and wealth” now being “increasingly concentrated in the hands of a few”, or about the “growing number of citizens” who feel excluded. Try telling that to a 17th-century slave or peasant: for all its faults, the culture of the last hundred years has spread power more widely than almost ever before.

But Shafak hasn’t set out to offer an overview of world history. As the example of young Facebook and Like reminds us, she is really pointing to the revolutionary expectations that were raised but never fulfilled by the advent of social media – and to the disappointments as well as to the achievements of the last century of western liberal democracy, which have obviously left much of the traditional power structure (and traditional exclusions) more or less intact.

Social media were hailed as providing a platform on which everyone could communicate with the elite on more or less equal terms, and on which status and real-life power differentials would be eroded. It is true there have been a few examples of exactly that: of popular hashtag campaigns, or the rise of “influencers”. But, for the most part, social media confirmed the political and cultural capital of those who had it already (as the combined total of the Twitter followers of the signatories of the Harper’s letter would nicely illustrate). It can be no surprise, Shafak implies, that the internet has become a world of self-reinforcing bubbles – for group narcissism seems like some “compensation for personal frustrations”. And it is no surprise either that it is increasingly a forum of shouting and anger. How else do you get anyone to listen?

Shafak understands these angry responses, and more generally she recognises the dignity of rage “in the face of injustice and oppression” (she was still writing the book at the time of the killing of George Floyd, and the horrified reactions to that are clearly very much in her mind). But she cautions against seeing anger by itself as a “guiding force and a good friend”, not only because it so easily turns “blindly destructive”, but because the sheer emotional intensity of anger can become a substitute for actually doing anything more positive. She quotes Toni Morrison with warm approval: “I get angry about things, then go on and work.”

If you are looking for the advice promised by the title, How to Stay Sane in an Age of Division, then “channelling anger” into a calmer and more productive force is one part of it. So too is the embrace of complexity over simplicity (“Be afraid of people who promise an easy shortcut to simplicity”) and the cherishing of multiple identities and multiple “belongings”. For Shafak, identity is not so much a badge of who you are or stamps in your passport, but a fluid set of relationships, or of stories you tell about yourself, that bring you closer to – rather than divide you from – your fellow occupants of the planet. And with one eye on the aftermath of pandemic and the other (I couldn’t help thinking) on some of the worst modern cliches of “well-being”, she invites us to accept that we shall feel despondent in the face of real disasters in the outside world. Or, as she observes: “It is totally fine not to feel fine.”

If I have made some of this seem rather elusive, or lapidary, that is because some of it is. And I was not entirely sure how Shafak’s clever reflections and sometimes moving stories out of her own past – from learning to write, as a “left-hander”, to the invisible genies in her grandmother’s house in Ankara – added up to a recipe for “staying sane”, whatever “sanity” might mean. But I did find myself hoping that Facebook and Like (or whatever they are now called) might one day come across this little book – and thinking that its calm and generous view of the world might give them back some part of the optimism that had greeted their arrival.

• How to Stay Sane in an Age of Division is published by Wellcome (£4.99). To order a copy go to guardianbookshop.com. Delivery charges may apply.