There are two main tasks. First, some formula must be found to persuade the Danish opposition that they have won a new kind of Maastricht treaty, and the voters that they can back it in a new referendum. Associated with this are the search for a definition of subsidiarity, which the Government has called 'minimum interference' by the EC, and the opening of decision-making to greater public scrutiny.
Secondly, the EC's budget must be decided, setting a ceiling for spending and the pace by which it is to be increased. These two link in to enlargement, another topic for Edinburgh. At the Lisbon summit, it was decided that until both were completed, new applicants for the EC could not begin formal negotiations. This makes it sound simple, but it is not. The summit must deal with a jumble of issues.
In search of a metaphor to describe this intermeshing, the Government settled on Rubik's Cube, a toy with coloured faces that requires the operator to fiddle with it until each side is the same shade. It is a convenient shorthand for an intricate diplomatic task.
Last year the metaphor of choice was 12-dimensional chess. The new image may be intended to suggest that Britain does not see this as a competitive game. Instead, it is an intellectual wrangle, a race against time rather than against the other players. But this clinical description does not convey the reality: an aura of betrayal, mistrust and anger hangs over this parlour game.
Some of Britain's EC partners do not believe that John Major has simply acted as the guardian of the Community while this country has held the EC presidency. They believe that London has kept its interests to the fore, protecting and advancing them over issues such as the budget and the Danish problem.
There is bad blood in some capitals, especially Madrid, which believes Britain has ignored virtually every Spanish proposal. The four poorest member states - Spain, Ireland, Greece and Portugal - were promised extra cash at Maastricht, and now they think their eight richer partners want to renege.
The more federalist nations, such as Belgium and the Netherlands, see treason in attempts to water down treaty commitments while propitiating the angry Dane. Britain's tergiversation over the Danish problem has aroused suspicion. The government sometimes gives the impression that it cannot ratify until Denmark has done so; at other times, that it is waiting for Danish intentions to be clear. The message that other members take is that Britain is hiding behind Denmark's skirts when it should be giving a discreet push.
These issues were always entangled: that is why they were gathered together in the accords struck in Maastricht. It is the nature of the EC that it deals with the problems of what academics call complex interdependence. When states' economies have become so interlinked, when conflict is ruled out as a means of resolving disputes, what remains is this often unseemly trading and compromise.
It is primarily the diplomatic tensions between states' interests that make the process so complicated. Adding to this is the uncertainty in many capitals about where these interests lie. The French government has become virtually hostage to the right-wing opposition, the left-wing anti-Maastricht fragments and rural interests that oppose the Gatt deal. In Denmark, the government is acting as a front while the anti-European opposition calls the shots. In Britain, opposition and government are riddled with conflict.
The summit can start to create a more user-friendly EC, but this is only part of the problem. The storms of public opinion blowing for the last year have threatened virtually every government in Europe. Economic distress is only part of the answer; and refugees are just the blameless victims.
Each of the Twelve is anxiously peeping beyond the fringes of the EC. The shock waves from the eastern European earthquake have created a new political landscape, then threatened to crumble it again. There has been an economic jolt, piling up debt in Germany, sweeping away jobs and sucking in cash. The refugees have spread out across both east and west, finding a cold reception if they are lucky, petrol bombs and baseball bats if they are not. The military waves are only now breaking on the western shores of the continent, as the implications of Yugoslavia's breakdown become clear in the southern Balkans.
For those outside the charmed circles - and some inside - it is these which seem the real problems. Mr Major is frequently pressed: why is he wasting time at these orgies of superfluity when he could be wrestling with the British economy? Douglas Hurd, the Foreign Secretary, has often professed himself eager to press on and tackle the challenges to the east. These are the real problems, the British mutter: what is all this nonsense about cohesion?
Some agenda items show that the EC is finally grappling with the challenge. There will be a growth initiative, welding together a British proposal with one from the Commission. Inspired by Norman Lamont's Autumn Statement, it will seek to kickstart the European economy, without adding to the already crushing burden of debt.
There will be discussion of the Yugoslav problem. Pressure is mounting for greater involvement. The obdurate Greek resistance to recognising Macedonia will be confronted, and a compromise may just be found. Proposals for extending the EC to the east will be unveiled.
But the amount of time and energy dedicated to these items will be dwarfed by the time spent manipulating 'that damned cube', as one official calls it. As skilled cubesters know, the last stage in getting it right involves putting everything out of line before a complex twist of the wrist brings every face together. For the EC, that almost certainly means a stupendous storm before the calm.
(Graphic omitted)Reuse content