For those of us still clinging to the real world, where times are hard, the spectacle of five central banks conjuring "unlimited" billions of dollars for the sake of Europe's financial institutions is liable to be, let's say, disconcerting.

Didn’t someone say that there was no money left? Isn’t austerity the order of the day across the western hemisphere? What is this “liquidity” primed to flood the system – at below market rates – when British unemployment has just gone up again, and when 46.2 million Americans are living below the poverty line?

You can wonder about that while you ponder the miracle of the printing press and the ability of the US dollar to bend the laws of arithmetic. Allowing for certain nuances, the reasoning goes something like this.

International investors – Americans in particular, ironically enough – have grown wary of lending to European banks. With a high risk of Greek bond default and a contagious sovereign debt crisis, there is a real danger of another credit market seizure. The banks, French banks in particular, could buckle, crippling the entire system and tipping half the world back into recession, or worse. Self-evidently, that would be no picnic for anyone.

The less-than-elegant solution from the central banks on Thursday, third anniversary of the Lehman Brothers collapse, was a “show of force”. Between them, the Bank of England, US Federal Reserve, European Central Bank, Bank of Japan and the Swiss National Bank decided there was only one thing for it: print dollars and throw them at the problem. The tactic forbidden to domestic economies was overnight redefined as a sane response.

As no doubt, by its lights, it is. However, you are reminded that money means different things to different people. In times such as these, policy-makers seem to echo that apocryphal remark attributed to JM Keynes: “When the facts change, I change my mind. What do you do, sir?” The politicians might be better off remembering something he actually said: “Economics is a very dangerous science.”

Then we might be spared the likes of Christine Lagarde, former French finance minister and head of the International Monetary Fund, announcing that governments need to cut their debts, but not, certainly not, at the expense of growth. Like a host of others who have achieved the insight recently, she doesn’t quite say how this is to be done.

Greece, a country with a shrinking population of just over 11m, has debts of $485 billion. Taxes are up, $20bn of spending is gone or going, public sector wage cuts of between 15% and 30% have been imposed, benefits have been slashed and the Greek GDP – Ms Lagarde’s “growth” – is expected to fall by 4.5% this year. A bond default, orderly or “disorderly”, now seems almost inevitable. The intervention by the central banks may be nothing more than an attempt to cushion that blow.

Ms Lagarde blames Europe’s “political dysfunction”. In the circumstances, that sounds like a statement of the obvious. The eurozone has all the trappings of a single currency, up to and including a mighty central bank and a single interest rate, but nothing resembling political unity or political direction. Since Europe’s peoples have no appetite for more “integration”, and since the northern nations have grown exasperated with the habits of their southern neighbours, the answer seems plain. Let Greece drop out of the eurozone, and allow other profligates – Spain, Portugal, Ireland, Italy – follow the Greeks to the exit.

Very neat. For those who never warmed to the European project, a Greek default, and all it implies, can even seem like a welcome outcome, and a lesson in “moral hazard”. It leaves a few questions unanswered, though. For one, what becomes of the outcasts? By one estimate (that of the UBS economics unit) leaving the eurozone would cost Greece between 40% and 50% of its GDP. Should Germany decide to jump ship, its GDP would drop by at least 20%. What then would become of the wider European economy, such as remained?

Those who argue, like Ms Lagarde, that cuts and growth must (somehow) be combined seem to think that every nation on the planet can reach salvation by exporting furiously while cutting consumption, and doing so simultaneously. Mr Keynes was familiar with that voodoo. But for a country such as Germany, less export-led than export-dominated, the collapse of the eurozone is no sort of palliative. Europe meanwhile accounts for 60% of Britain’s exports. Sceptics might despise the euro, but what if the alternative is chaos and depression?

For now, the tactic seems to be to nurse Greece along until its brutal “reforms” pay off. The European Union taskforce despatched to Athens reports that the government there is showing “enormous political will” amid the misery. Meanwhile, in Poland yesterday, European finance ministers began the task of agreeing a second Greek bail-out and the larger job of somehow ending the debt crisis.

Is such a thing possible, or is the European project inherently flawed? Fine talk of greater political integration is one thing, but how do you yoke together Silvio Berlusconi’s disreputable Italy and austere Finland? How do you arrange a semi-permanent system of fiscal transfers between rich regions and poor, in the American style, without a United States of Europe? And how do you dare to seek that goal in the teeth of opposition from Europe’s citizens?

This isn’t an either/or problem, bail-out or break-up. Even our own Chancellor, the eurosceptic George Osborne, admitted in Manchester yesterday that “a successful euro is massively in our interest”. He failed to add the peculiar corollary: so important is the project, we want nothing to do with it. That would sound like common sense, given the depth of the current debt crisis, but Mr Osborne and his kind – meaning most British politicians – also fail to admit another truth. De facto European integration is already a reality, and it goes deeper than their bluster allows.

Seen from the 20th century, in any case, all of this could seem like one of the world’s lesser crises. That era endured a banking collapse, a prolonged depression, and two world wars. Those facts were not incidental to the European Union’s creation, and they remain relevant now. The prize – peace and stability – remains. But it is, patently, a hard sell this autumn.

The solution to a crisis is not a worse crisis. You might not want to take Barack Obama’s advice on the matter just at the moment, given those 42.6m Americans in poverty and the absurd political squabbles over the US debt ceiling, but the president makes a fair point. Europe needs to fix this for everyone’s sake. In Washington’s view, the euro’s collapse is not an option. Mr Obama’s Treasury Secretary, Tim Geithner, arrived in Poland yesterday urging the Europeans to stop talking about the possibility.

The pity is that he didn’t also call for ways to be found to end speculative attacks on entire countries. Greece is in a deep hole, there is no doubt about that. But the answer to a struggling nation’s debt problem is surely not ever-increasing interest rates. The profits from a Greek default might gladden a few market-making hearts, but it is no way to run a world.