If you found the UK Government’s first Brexit “position paper” on avoiding a “cliff-edge” in trade borderline delusional, just try the second, on Northern Ireland. A lot of Irish magic will be needed if the proposals set out there are going to have any chance of success.

Three policies have commanded particular attention. On trade, most exchanges between Northern Ireland and the Republic would be regarded as local, and nothing to do with international rules at all. Except much hair-splitting about what constitutes small and medium-sized business. For the rest, tariff matters and payments would be handled by a whole new, hi-tech system – the UK’s track record of digital project management does not bode well.

As for the movement of people, well there would essentially be no need for change. Any risk that the Northern Irish-Republic of Ireland border could become a “back-door” into the UK (or vice versa) would be minimised because the Irish Republic is not – and would not be – a member of the Schengen, so the UK and Ireland could keep their own special passport-free regime, while keeping the outer borders secure.

Brexit Secretary: UK wants temporary EU customs deal

Except that there are no passport or ID checks between the UK and Ireland, whatever sort of papers you carry. Indeed, the only way, travelling by road, you know you have crossed from the Republic into Northern Ireland is a sign saying that the speed limit is now posted in miles per hour. Any indication that you are crossing into another country is vanishingly discreet. Like it or not, there is a “back door” (which predates both countries’ EU membership). Whether this longstanding “special arrangement” can continue after Brexit is another matter. How feasible is a “soft” border between a member and non-member of the EU?

Then there is food safety. Standards in Northern Ireland, the position paper boasts, are high, so there is really no need for any special checks on goods crossing what would become the EU border. But how well would that cheerful acceptance survive the first whiff of contaminated eggs, horsemeat masquerading as beef, or whatever comes next – in either direction?

Such problems were always lurking in the event of a UK vote for Brexit, and to an extent, with two different currencies, opportunities for gaming the system were always there. Strangely, though, the devolutionary focus during the referendum campaign was almost entirely on Scotland. What would happen if the Scots voted differently, and by a large margin, from the rest? (They did.) Would this spur demands for a new independence referendum? (Yes, and no.) What would come next? (Too soon to say.)

In pictures: European parliament Brexit discussions Show all 12 1 /12 In pictures: European parliament Brexit discussions In pictures: European parliament Brexit discussions European commission member in charge of Brexit negotiations with Britain, French Michel Barnier listens at the President of the European Commission Jean-Claude Juncker speaking at the European Parliament in Strasbourg Getty Images In pictures: European parliament Brexit discussions Frank-Walter Steinmeier, President of the Federal Republic of Germany, delivers his speech at the European Parliament in Strasbourg EPA In pictures: European parliament Brexit discussions European Union's chief Brexit negotiator Guy Verhofstadt, President of the Group of the Alliance of Liberals and Democrats for Europe (ALDE), addresses the European Parliament during a debate on Brexit priorities and the upcomming talks on the UK's withdrawal from the EU Reuters In pictures: European parliament Brexit discussions Michel Barnier, European Chief Negotiator for Brexit reacts during a meeting at the European Parliament in Strasbourg EPA In pictures: European parliament Brexit discussions Member of the European Parliament and former leader of the anti-EU UK Independence Party (UKIP) Nigel Farage wears socks with Union Jack flag at the European Parliament in Strasbourg Getty Images In pictures: European parliament Brexit discussions Nigel Farage, United Kingdom Independence Party (UKIP) member and MEP, addresses the European Parliament during a debate on Brexit priorities and the upcoming talks on the UK's withdrawal from the EU Reuters In pictures: European parliament Brexit discussions European commission member in charge of Brexit negotiations with Britain, French Michel Barnier gestures during speeches at the European Parliament in Strasbourg Getty In pictures: European parliament Brexit discussions The President of the European Commission Jean-Claude Juncker (L) speaks with European commission member in charge of Brexit negotiations with Britain, French Michel Barnier at the European Parliament in Strasbourg Getty In pictures: European parliament Brexit discussions European Union's chief Brexit negotiator Guy Verhofstadt, President of the Group of the Alliance of Liberals and Democrats for Europe (ALDE), addresses the European Parliament during a debate on Brexit priorities and the upcomming talks on the UK's withdrawal from the EU Reuters In pictures: European parliament Brexit discussions Member of the European Parliament and former leader of the anti-EU UK Independence Party (UKIP) Nigel Farage gestures during speeches at the European Parliament in Strasbourg, eastern France, on April 5, 2017. The European Parliament will on April 5 lay down its "red lines" for negotiations over a Brexit deal, on which the assembly will have the final say in two years' time. / AFP PHOTO / Sebastien BozonSEBASTIEN BOZON/AFP/Getty Images Getty In pictures: European parliament Brexit discussions German president Frank-Walter Steinmeier delivers a speech during a plenary session at the European Parliament in Strasbourg Getty In pictures: European parliament Brexit discussions The European Parliament in Strasbourg, eastern France Getty Images

But the effect of Scottish independence in the event of Brexit was comparatively clear-cut. Scotland would become an independent state. It would be recognised as such by the UK and internationally. It would re-join the EU (oh yes, it would); it could be required to join the euro and Schengen, and there might well be a “hard” border with England. But everyone would know the score.

The position with Northern Ireland is infinitely more difficult. And it was made more so because a majority of the Northern Irish voted to remain in the European Union. The margin (56 - 44 per cent) was not as sweeping as in Scotland (62 - 38 per cent), but it was solid. It was also bigger than the margin of victory for Leave in the UK as a whole (52-48), but also in England (53 - 47 per cent).

One reason why Northern Ireland, despite its unionist majority, voted more like Scotland than England or Wales may be that people on both sides of the sectarian divide saw EU membership as a kind of guarantee for the continuation of the Good Friday agreement that had (mostly) brought peace. Without the EU, the relatively relaxed relations with the Republic, the free movement of people and free trade across the border would all be called into question.

This is where we are now, with the UK trying desperately to hold on to the gains from EU membership as they relate to Northern Ireland, while preparing to break from the EU in almost every other respect. It is neither a logical nor comfortable position. No wonder Ireland’s Prime Minister, Leo Varadkar, recently expressed his frustration not just with the pace of negotiation, but with the whole UK approach.

Happily – and unhappily – there is a solution, which is as simple and obvious as it is elusive. The one sure way to enshrine free movement, free trade, and regulatory clarity in relations between the two parts of Ireland is to put them back together. The North would thus remain in the EU – which is what a majority of those who took part in the referendum voted for – while the rest of the UK, aka Great Britain, would leave. The only border needed would be the sea.

How feasible would this be? Alas, despite the pro-EU vote in Northern Ireland, not at all – at least in the short term. The Northern Ireland parties may be finding it hard to form a new power-sharing government, now that the politicians who made peace have left the scene, and the unionist share of the vote may be declining, but a forced march to unity risks the peace.

The differences are not to be underestimated. From a distance, it is easy to condemn the recent clashes in the American south as “only” about a monument. But monuments – and flags – cannot be dismissed lightly. Over the decades they have sealed Ireland’s division. One person’s patriot is another’s traitor. The two communities remain fenced off from each other in Belfast and (London)Derry; if they find it so hard to share a city, how can they share a country?

And yet... Is it really beyond the bounds of wise statespeople to devise a solution? Would a clearly federated state not be possible; a state, what is more, with world-class guarantees for the rights of what would become the Protestant minority? Is the fear that would precipitate a resort to arms really still there?

Since the Brexit vote, the unity question has been very quietly, very tentatively, reopened, after 10 years in which the Good Friday Agreement had pronounced it closed. But a twist of fate – the Conservatives’ need for the DUP’s parliamentary votes – at once enhanced the status of the DUP in Northern Ireland and regrettably put any new thinking on hold.

But such an obvious remedy to the Brexit-Northern Ireland conundrum cannot remain off limits for ever. Demographic change in the North is already affecting elections there. Socially and economically, the Republic is a very different country from the one it was before it joined the EU. Arguably, the country that has changed least, in its institutional attitudes, is the UK.