Will the growing competition between China and the United States inevitably lead to military conflict? One leading American academic created huge attention when in 2017 he posed the idea of what he called a "Thucydides Trap". Drawing on the work of the ancient Greek historian, he warned that when a rising power (Sparta) threatens an existing power (Athens) they are destined to clash, unless both countries change their policies. He warned that the same pattern could play out with the US and China. Since then, President Trump has engaged in combative rhetoric over trade, while China has fast been modernising and upgrading its military. BBC Diplomatic Correspondent Jonathan Marcus considers whether Washington and Beijing can escape the trap - or whether the growing economic, strategic and technological rivalry between the two nations will inevitably end in conflict.
Producer: Stuart Hughes
Are we heading for a mass extinction?
Will human actions result in the demise of huge numbers of other species - in a mass die-off, comparable to the end of the era of the dinosaurs? Neal Razzell assesses the evidence that species are dying off at a rapid rate, and looks at some of the surprising things we might do to slow or reverse this process.
Producers: Beth Sagar-Fenton and Josephine Casserley
Will humans survive the century?
What is the chance of the human race surviving the 21st century? There are many dangers – climate change for example, or nuclear war, or a pandemic, or planet Earth being hit by a giant asteroid.
Around the world a number of research centres have sprung up to investigate and mitigate what’s called existential risk. How precarious is our civilisation and can we all play a part in preventing global catastrophe?
Anders Sandberg, Future of Humanity Institute.
Phil Torres, Future of Life Institute.
Karin Kuhlemann, University College London.
Simon Beard, Centre for Existential Risk.
Lalitha Sundaram, Centre for Existential Risk.
Seth Baum, Global Catastrophic Risk Institute.
Film clip: Armageddon, Touchstone Pictures (1998), Directed by Michael Bay.
Presented (cheerily) by David Edmonds.
Producer: Diane Richardson
Is there a better way to heal political divides - through panels of ordinary citizens? Sonia Sodha asks if the idea of citizens' assemblies, which have been used around the world to come up with solutions to polarising issues. Proponents argue that they avoid the risks of knee-jerk legislation, winner-takes-all outcomes or the pull of populism. Many in the Republic of Ireland believe that deliberative democracy was crucial in reforming the law on abortion without causing major political upheavals. Could this method still come up with a better way forward for Brexit?
Producer: Maire Devine
Voters and politicians in Britain claim to be perplexed that economic and political relations between the UK and the Republic of Ireland seem to be decisive in determining the course of Brexit. They shouldn't be, argues Edward Stourton. A glance at the history of the countries' relations since the Acts of Union in 1800 helps to explain the situation.
From at least the time of Catholic Emancipation in the 1820s, political, social, cultural and economic issues on the island of Ireland have influenced and shaped politics at Westminster. The point is that MPs and others at Westminster have seldom appreciated this and therefore underestimated the power of that history to affect the course of a contemporary issue like Brexit.
Looking at a range of issues from Emancipation, the 1840s Irish potato famine, Catholic clerical education, the campaign for Home Rule leading ultimately to the War of Irish Independence in the twentieth century and the bloody establishment of the Irish Free State, as well as the Troubles and the Good Friday Agreement in 1998, Edward Stourton explores the way in which issues in Ireland have determined British politics. He considers especially what lessons these episodes may hold for today's Westminster politicians and how to imagine the Anglo-Irish future.
Among those taking part: Lady Antonia Fraser, Professor The Lord Bew, Professor Sir David Cannadine, Professor Roy Foster, Professor Marianne Elliott, Fintan O'Toole and Declan Kiberd.
Producer: Simon Coates