Long ago, in the early 1960s, President John Kennedy worked with Prime Minister Harold Macmillan to try to shepherd the United Kingdom into what was then the European Economic Community (EEC). They failed, on that occasion, to force the French and President de Gaulle to allow the British 'into Europe', only to succeed more than a decade, and two more great diplomatic heaves, later.
Why did the Americans do that? Why had they tried to push the Labour government of Clement Attlee into the EEC's forerunner, the Coal and Steel Community? In part all this was a natural desire to build up the economy of Western Europe so that the Americans had a viable trading partner. But much, much more important was the idea that Europe might serve as a diplomatic pillar, and a means of projecting the force of ideas and ideals, to set against the military North Atlantic Treaty Organisation: that an idea of Europe might fire citizens' imaginations, to come together against Soviet Communism and the so-called socialist regimes then consolidating their own power in Eastern Europe.
In many ways, not much has changed since then. There was a similar motivation in the background when President Obama made his now-famous intervention into our present UK debate about whether to stay in what has now become the European Union (EU). Mr Obama worries (rightly) that there will be a recession on any disorderly British retreat from the EU; but he worries much more about what will fill the void if and when that does happen. The answer is right-wing populism and craven no-principles bread and circuses - on offer in slightly ridiculous and clown-like form from the former Mayor of London Boris Johnson here in Britain of course, but also in far nastier hues by the French National Front, Greece's Golden Dawn, the Austrian Far Right and Eastern Europe's new breed of pseudo-'democratic' autocrats.
All of whom - all of whom - Russian President Vladimir Putin (above) thinks he will be able to manipulate and impress more than the present holders of those offices. In which suspicion he is almost certainly right.
Mr Putin is an opportunist. He watches and he waits. He sees Europe's weakness. He detects the splits between the Germans and the southern Mediterranean nations. He knows that the UK Labour Party (or at least its leader's office) has now been taken over by people who sympathise with him far more than they would ever side with Washington. He sees the damage that he can do to the European project by pushing hundreds of thousands of Syrian refugees into Turkey. He is happy to offer money to Greece and Cyprus, if they want to reject Germany's draconian economic terms. He understands the way in which his media blitz, expertly marshalled by his propaganda station Russia Today and programmes such as the English-language Sputnik, are dissolving Western Europe's morale and backbone. He knows that large swathes of the European Left are in thrall to ideas that he can easily distort and sell back to them: that 'America' must always be bad; that the USA and NATO, and not Russia, caused the crisis in Ukraine; that Europe's elites are economically corrupt and politically hollow; that Israel is behind everything that passes in the Middle East; that US-backed regimes in Iraq and Afghanistan cannot and will not succeed.
So he floods the Twitterverse and Facebook with utter nonsense, much of which - it just so happens - helps to undermine the EU's legitimacy and popular support. What a coincidence. You see the influences of this non-news and non-comment all the time on social media, as the same people fire off posts about the dangers of water fluoridation, nuclear power, the 'Zionists' and the bankers: the idea that there is something irretrievably rotten about the modern democratic state, which could all be solved if only the Americans and their allies had a bit more order, a little more statism, and a dose of puritanical moral structure... If only, in short, they looked a lot more like Russia.
For Brexit offers Mr Putin more than just a great diplomatic success that shows up his critics as a rag-bag of small powers in disarray. It will show that his philosophy and his outlook - involving state controls, censorship, autarky, aid-as-power, the lightning use of small-scale military force as a key element of diplomacy - are winning. Liberal international co-operation on the basis of a democratic Parliament and votes in an open Council of Ministers? The free movement of peoples? Free trade and the attack on monopolies? Pan-Europeanism, in contradistinction to narrow racial and religious identities? All anathema to the Kremlin. All upheld by the EU, which is why Sputnik and RT lay into it all the time. They long to see Brexit, because that will roll the dice.
In some ways shuffling the cards like this might be a bit more benign than it looks. Some Russian politicians apparently think that, upon Brexit, they would be able to link up more with London, as in 1908-17 and 1941-45, negotiating with another 'peripheral' European power and upping their clout in that manner. Certainly the influence of Russian money and investors would be even more notable in this scenario than it is already. But it won't be all 'great game' chess pieces on a board. There are real-world consequences to this type of messing about. Maybe some Russian analysts hope that an exit from the EU will lead to the break-up of the UK - Moscow having used its state-run news agencies to cast doubt on the fairness of the last vote on Scottish independence, held in 2014. They'd love to see Britain's Trident nuclear forces kicked out of Scotland, making them even more expensive and of dubious operational utility than they already are. Perhaps they dream of Brexit because that might mean that the whole EU unravels, forcing German Chancellor Angela Merkel to resign, pushing the Baltic States back into Russia's orbit and leaving the Ukraine and Georgia in their shadow. And so on.
It's important to be clear about what we mean here. There's no need to engage in some sort of Dr Strangelove-style ranting, or summon up some new Cold War that we needn't and musn't have, to see clearly where the pressure points are in the international system. We are dealing with an opponent, not an enemy. Common cause can and must be made to - for instance - bring stability and then peace to Syria. Full-scale Western military intervention there now, with the Russians in the mix as well, would probably only add to the chaos. And there's no point posturing over the Crimea when it's so deeply in Moscow's orbit now. Russia is a great standing fact and power in Europe. That's as it should be. The Russian state has interests. It tries to give effect to them. That's how the world works.
But no-one should be in any doubt: Mr Putin is willing you to get into that polling booth on June 23 and put a great big 'X' next to the 'Leave' box. He wants us to start the dominoes falling, so that he can further expand his influence and his power. He wants us to negotiate, chaotically and raggedly, for the next four or five years - all the better for him to tell everyone on his borders, and ours, what to do.
Vladimir Putin wants you to vote 'Leave'. So vote 'Remain' instead.
