Sitting on my own in the bar of the Royal Court theatre on Wednesday with my orange juice and lightly sea-salted packet of crisps, I remembered that I was first here more than 50 years ago, as a teenager down on holiday from Scotland and determined to witness England's cultural revolution. In 1961 that still meant John Osborne, whose new play, Luther, had just opened at the Court with Albert Finney. I queued at the box office and got two tickets to stand at the back of the stalls, where my brother and I were so thrilled (so this is what the Reformation was like!) that when the play came to the Edinburgh festival later that year, I bought another ticket and stood through it all over again.

The contrast between Luther and the performance I was about to see couldn't have been starker. Luther was intensely theatrical – as gorgeous as a pantomime – the stage filled sometimes with pious monks and at other times with flag-waving knights. Finney's Luther grappled loudly with his faith and his constipation, while a cynical huckster sold the weirdest of Papal indulgences. Comedy, seriousness, noise, colour and, above all, those biting monologues that were Osborne's trademark: they made for that thing called "a wonderful night at the theatre", but the play's message, whatever it was, would never have fitted under the rubric "news you can use". When you left the theatre, you stepped out of the Reformation and into the relevance of the present day.

Ten Billion, on the other hand, is a piece of theatre only because it occurs in a theatre. The curtain rises on a reconstruction of a modern office; we hear the melancholy sound of a cello; a middle-aged man walks on stage, opens his laptop and begins to talk. He says he's a scientist and not an actor – that will become obvious – but that the set is a "depressingly accurate" reproduction of his office in Cambridge. His name is Stephen Emmott. He's head of computational science at Microsoft Research in Cambridge and professor of computational science at Oxford, and what he wants to tell us about is the future of life, particularly human life, on Earth. And for the next 75 minutes that's what he does, moving just a little around the set with the help of a stick (because a disc in his lower spine has popped out) as visuals appear on screens to illustrate what soon becomes a tide of frightening facts and predictions.

Taken singly, few of these facts would be new to even the most casual Monbiot reader or the least faithful friend of the Earth, but their accumulation and the connections between them are terrifying. Rarely can a lay audience have heard their implications spelled out so clearly and informally: a global population that was 1 billion in 1800 and 4 billion in 1980 will probably have grown to 10 billion by the end of this century; the demand for food will have doubled by 2050; food production already accounts for 30% of greenhouse gases – more than manufacturing or transport; more food needs more land, especially when the food is meat; more fields mean fewer forests, which means even more carbon dioxide in the atmosphere, which means an even less stable climate, which means less reliable agriculture – witness the present grain crisis in the US.

On and on he goes, remorselessly. It takes 3,000 litres of water to make a burger and the UK eats 10bn burgers a year. A world population of 10 billion will need 960 new dams, each of them the size of the world's largest in China's Three Gorges, plus 15,000 nuclear power stations and/or (my note-taking in the dark isn't up to his speed) 11m wind farms. The great objective of intergovernmental action, such as it is, has been to restrict the rise in average global temperature to no more than 2C, but a growing body of research suggests a warming by 6C is becoming more and more likely. In which case, Emmott says, the world will become "a complete hellhole" riven by conflict, famine, flood and drought. Go to a climate change conference these days, he says, and as well as all the traditional attendees there will usually be a small detachment of the forward-looking military.

What's to be done? Emmott takes us through the ideas offered by "the rational optimists" who believe that, faced with the species' near extinction, human inventiveness will engineer a solution. Desalination plants, a new green revolution, seeding the oceans with iron filings to absorb more CO2: all of these threaten to produce as many problems as they solve. He believes the only answer is behavioural change. We need to have far fewer children and consume less. How much less? A lot less; two sheets of toilet paper rather than three, a Prius instead of a Range Rover – that kind of sacrifice won't really do it. And does he believe we're capable of making this necessarily far bigger curb on our desires? Not really. He describes himself as a rational pessimist. "We're fucked," he says. If a large asteroid were on course to the Earth and we knew when and where it would hit – say France in 2022 – then every government would marshal its scientific resources to find ways of altering the asteroid's path or mitigating its damage. But there is no asteroid. The problem is us.

Recently he asked one of his younger academic colleagues what he thought could be done. "Teach my son how to use a gun," said the colleague.

And there the performance ends. Emmott steps forward to take the applause and then the audience files down the stairs to Sloane Square, busy with taxis and young people standing on the pavement with plastic beakers of white wine, as though there would be infinite tomorrows. It isn't quite clear what we've seen – a lecture or a theatrical event – but what its ominous content most resembled, or so it seemed to me, was the kind of Protestant sermon brought about by the Reformation, in which humankind was told to repair its ways if it wanted to avoid damnation. In retrospect, this looks a relatively easy matter of regular churchgoing, refraining from obvious adultery and not doing the washing on Sundays. Light qualifications for entry to heaven compared to the levels of material renunciation needed to save the species.

The speed at which our likely future has arrived is the frightening thing. How little we realised, leaving Luther in 1961, that the atmosphere's carbon content had been increasing since the industrial revolution, which you might argue was a Lutheran/Calvinist byproduct. We had our worries, of course, but the cold war and nuclear weapons didn't seem intractable threats. They produced protest rather than the fearful depression that touches some of us from time to time, when every distraction has failed. Emmott sees his performance as a wake-up call and it has apparently had that effect on its young audiences (its entire run is sold out). But it would be just as easy to see it as a well-articulated piece of despair, a scientist's soliloquy in front of the final curtain.