On the left: Europe. Timid, flaccid, pulled hither and thither by internal differences, unaccountably blind to threats to its future well being.
On the right: The United States. Muscle-bound, insensitive, unyielding, unthinking, always acting first and thinking later, except when not thinking at all.
Those are the two protagonists views of each other. There's nothing new in this; Europe and the USA have been bickering happily for decades.
They can do it because at heart the two superpower blocs know perfectly well that they are on the same side.
The arguments are ever present, but so is the deep awareness - perhaps deeper since 11 September - that a transatlantic alliance is an essential part of the world diplomatic furniture.
Criticism for unilateralism
So this summit, like other before it, will begin with some coded and some uncoded messages about differences.In the last few days on the European side there have been calls for the United States to rein in its unilateralist tendencies and resist growing domestic demands for "an unapologetic pursuit of national interest".
European leaders argue that transatlantic co-operation has to be rekindled to bring peace to the Middle East and defuse damaging trade disputes.
"I see the US unilateralist temptation as one of the central problems, perils, challenges and opportunities confronting the English-speaking peoples of today," Chris Patten, the EU's External Affairs Commissioner, told an English-Speaking Union audience in London this week.
If America wished to maintain moral authority for its leadership, it had to carry the world with it and not ignore its international obligations in "an unapologetic pursuit of national interest".
Terror and trade
So will the US listen and will the two sides agree?
On counter terrorism measures - the two sides fully recognise that they need each other.
They will agree to intensify cooperation in the fields of asylum migration policy, and frontiers.
The Europeans have agreed as well to begin the long and difficult process of working out a joint extradition policy with the United States so progress in this area is certainly likely.
On trade the row about the US decision to slap tariffs of between 8% and 30% on steel imports to allow its steel industry to restructure is likely to be less easy to solve.
The Europeans are deeply upset at what they see as American hypocrisy.
The American side feel that they have plenty of other trade issues they could point to, where the Europeans are in the wrong. The likely outcome is an agreement to disagree.
The Middle East
On the Middle East the Europeans - particularly the European Commission President Romano Prodi - will be pressing for a much tougher line to be taken against Israel.
The Bush administration will probably listen politely but the President can afford to take little notice of the European complaints, given the fact that all sides in the Middle East look to America to help them solve their crisis.
There is also a subject not on the official agenda but nonetheless vitally important and hugely controversial: what to do about Saddam Hussein.
There's a massive difference between the two sides on this. Most continental Europeans are opposed to an attack on Iraq but the US hosts of this summit are known to be considering the military options day by day.
There will be no big row because the US is still some way off a final decision to fight, but the approach to Iraq is symptomatic of the difference in worldview between the Europeans and the US.
Nothing said at this summit is likely to mask that fact or change it.
At the end of the day though everyone will go home reasonably happy.
Europe and the US will have had the chance to let off a little steam, marvel at the differences there are in perception of the world but also celebrate the ties that bind the continents together across the Atlantic.