Ten Billion, Royal Court Theatre Upstairs

“I'm here because I'm concerned,” says scientist Stephen Emmott in direct, measured tones. “I'm concerned about the state of our planet. I think the situation that we're in right now can rightly be called a planetary emergency, an unprecedented planetary emergency.”

Emmott, 52, a professor of computing at the University of Oxford and head of Microsoft's Computational Science Laboratory in Cambridge, takes to the stage alone in director Katie Mitchell's latest project. Billed as “a new kind of scientific lecture”, Ten Billion examines the state of our planet when the population reaches 10 billion at the end of the century. Emmott talks us through the effects on land, food, energy, transport and climate change, packing in facts and figures. Mitchell, known for pushing at the boundaries of theatre in both content and form, ensures the pace is fast enough for the material to engage, yet slow enough for it to be digested. However, the outcome is still more lecture than show.

Emmott is not quite as charismatic as the scientist he describes as 'that bloody Brian Cox'

Giles Cadle's immaculately constructed set is, Emmott tells us, “a frighteningly accurate depiction” of his office in Cambridge. From a blue lever-arch file on top of the low-level bookshelves to a lone tangerine by the window, the detail is impressive. Emmott presents his lecture from a laptop on his desk. We share the intimate space of the scientist's office.

Emmott (pictured below), who slipped a disc during a recent fall, rests on crutches in one spot for most of the production. Yet in his material, he covers a vast distance. He whizzes through how the population has grown to seven billion, makes predictions and proposes solutions. Not that he thinks we will be brave enough to carry out what's needed. “We would have to consume a lot less: less food, less energy, less stuff,” he says. “And stop having children.”

As an hour-long lecture, Ten Billion is powerful and provocative. The material is well pitched at an intelligent lay audience, with Emmott giving persuasive everyday examples of the pressure on our resources. It takes 100 litres of water, for example, to produce a cup of coffee before the coffee sees a drop of water. A Google search uses almost as much energy as boiling a kettle.

Emmott's argument yields some fascinating if worrying visions. The UK is likely to become highly militarised to prevent the influx of millions of migrants fleeing climate change back home. Meanwhile, a rise in people living near animals because land is scarce, together with ever greater numbers of people travelling, will increase the risk of a global pandemic. With his West Yorkshire burr and his gentle humour, Emmott comes across as highly personable. And yet, he is not quite as charismatic as the scientist he describes as “that bloody Brian Cox”.

While as a lecture Ten Billion is interesting and engaging, as performance there are few dramatic moments

The animated visuals, designed by Tim Reid and Leo Warner for Fifty Nine Productions, are clever in their apparent simplicity. They are projected on to two screens. Each factor affected by population growth is illustrated by an icon, which moves when Emmott talks about it. A grain of corn, symbolising food, sways in an imaginary wind; a plane for transport moves back and forth. Paul Clark's (recorded) music starts effectively, with a quavering cello creating an air of menace. How much more chilling it would have been live. It is hard to see what was new about this “new kind of scientific lecture”, apart from the fact that theatre and multimedia designers orchestrated its production.

While as a lecture Ten Billion is interesting and engaging, as performance there are few dramatic moments. Mitchell and Emmott had the opportunity to do something unexpected for a lecture: to play with sounds and props, or to use the space in a radically new way. They make us wait until the very last line for the wow factor.

• Ten Billion is at the Royal Court from 31 July to 11 August