The immediate priority must, of course, be restoring stability. The markets, having been unduly bullish about the prospects of a Remain vote, have reacted with a panicked rush to correct their miscalculation. There will be a degree of turmoil, political and economic, not only in European countries but internationally. Indeed, markets will likely remain nervous for some time to come, though extreme volatility will not be a permanent fixture. Negotiations will take time, and a calmer mood should prevail.
When negotiations begin, European states should not try to punish the British. Bitterness is always bad council, and calm heads are essential for the period ahead. Europe and the UK have no choice but to maintain a working relationship with one another; both sides will have to make compromises. Nevertheless, the UK will evidently end up in a less positive situation than the one it enjoyed before leaving; if an EU Member State has a better life outside Europe than inside, why should anybody stay inside?
Yet it would greatly benefit both parties to find a solution by which the losses are as small as possible. Life will be less positive outside, but not excessively so. The agreements with Switzerland or Norway can serve as a likely blueprint, where there are a number of obligations that are part of the relationship and which do not simply limit themselves to a purely technical trade agreement. This may be difficult to swallow for the more Eurosceptic elements within British politics, but it is the arrangement that guarantees the least discomfort and disruption.
Parallel to negotiations with the UK, however, European leaders must begin a dialogue with their own citizens. They no longer have the luxury of putting off difficult decisions. They are now confronted with a direct challenge to their record of decision-making since the 2007-2008 financial crisis. The can they had been kicking has come to the end of the road.
Is the European project at risk of unravelling? That will very much depend on how European leaders now react. The British leaving Europe still means that there are 27 countries in the European Union, with shared structures, with commitments, and with obligations. This has not changed. What has changed it that it is now no longer possible to ignore the popular dissatisfaction over political decision-making-at-large.
So, confronted with this challenge, what do European leaders tell their citizens? How do we respond to the dissatisfaction of so many citizens, particularly as the reasons for this dissatisfaction are so disparate and varied? There are citizens on the extreme Left who dislike the European Union because they want another system like the Communists in the old days; there are people on the extreme Right who want a radical purging of society and a return to an imagined historical Europe; and there is another (greater) part that is dissatisfied with how Europe works today, but is not dissatisfied with Europe as an idea. The challenge for Europe's leadership is to address the legitimate grievances of people dissatisfied with Europe, without kowtowing to the ideologies of the extreme Left or Right.
At the same time, we must not use the current crisis as an excuse to push endlessly for "More Europe". All of the issues which are now dealt with inside the Union are of a political nature. Economic convergence, banking union, energy union, these are all political issues related to specific problems. So, it's not a question of handing over more sovereignty in bulk to the Union, it's about identifying specific problems where we already agree that sharing our sovereignty is a common-sense answer to something we can't settle alone. This means political commitments are necessary for each of the issues we have to deal with. Simply saying we're going to jump to a federal political Europe is not the answer. The answer is responding quickly to specific questions from citizens who want a better and more secure life.
Ultimately, we must remember that we still have a Union of 27 countries, with all that it has brought. The fact that the UK is leaving does not mean the others do not have obligations, commitments, or an active involvement in the European Union. There have been previous crises in Europe, and there will be others in future. But the remaining 27 EU countries are still together, and we must still agree on our shared future together.
It took several months to find a compromise 'renegotiation' with the UK ahead of the referendum, and that compromise played no role whatsoever during the actual campaign. So, the British public were not impressed by the agreement reached by Cameron. It was irrelevant to voters. That teaches us a lesson also: If you try to fudge the issues, you will get nowhere. Brexit means that politicians can no longer ignore their citizens' frustrations. Before the Brexit vote, they could sidestep difficult questions, but no longer.