When David Davis, Britain’s head negotiator, declared that Brexit negotiations are “as complicated as [the] moon landing,” others laughed. They should not, because he is right.

Focus so far has been on the dynamics at the table between Mr Davis and Mr Barnier, the EU’s head negotiator, but this is just the tip of the negotiations iceberg. Underneath, there are four dimensions of complexity.

First, this is not a simple two-way conversation between Britain and the European Union. This is a ‘multilateral’ negotiation involving twenty-seven other member states (each with their own domestic politics), the European Commission, the European Parliament, the Council of the European Union and the European Court of Justice. Brexit is less like a market-stall haggle and more like George R.R. Martin’s ‘Game of Thrones’: many characters with many motives will make many moves, none of which can be ignored.

Second, Brexit is one word for multiple negotiations. Starting with the divorce, the British government must then negotiate the terms of its future trade, defence and political arrangements with the European Union. Originally, the government declared that the two negotiations could take place at the same time but this argument was lost, despite recent efforts to bring it up again.

Even when both negotiations are concluded with the European Union, Liam Fox’s Department for International Trade must then commence negotiating separate trade deals with the USA, Australia, Canada and beyond. For reference, negotiations for the soon-to-be-enacted Comprehensive Economic and Trade Agreement (CETA) between Canada and the EU were launched in 2009 and only now is it almost ready to be applied.

Third, Mr Davis faces what experts call a ‘multi-level’ negotiation. Simply put, this means that he will be negotiating everywhere. He will negotiate with the EU’s delegation in Brussels in the morning, then he must return to the UK to negotiate with his British Cabinet colleagues at lunchtime, before preparing to negotiate with the Opposition Labour Party in the Commons in the afternoon, before heading to an evening event to negotiate with British business.

Fourth and finally, negotiation is a people business. At the table, Britain will need top talent. So far, recruitment has proved a challenge: negotiators are ironically good at negotiating their own roles as negotiators. In June, Canadian Jonathan Fried rejected the top job. Additionally, hundreds of civil servants will need to be trained and supported by new hires.

There is, however, cause for hope. Recent, complex conflict negotiations have been successful: the 1998 Good Friday Agreement in Northern Ireland or the FARC deal in Colombia, for example. When pessimists lament the ‘impossibility’ of negotiating Brexit, we should remember that such conflict agreements were much trickier.

Further, Britain has negotiated the terms of its relationship with the European community before: when, in 1972, the UK acceded to the European Economic Community in the first place. The current government should learn the lessons of that negotiation: look for win-win opportunities; be begrudgingly sensitive to European conventions and egos; and keep the public on side back home.

Negotiating Brexit is not for the faint of heart. Many scoffed when Mr Davis made the moon landings comparison, but I did not. At least in 1969, when Neil Armstrong made one giant leap for mankind, everyone agreed on the mission.

Benjamin Clayton is the Chair of Harvard’s Kennedy School Negotiations Project. He was formerly Chief of Staff at the British government’s National Infrastructure Commission.