A sweep of historic data by Warwick University found compelling evidence that economies are more likely to stall as they age, what is known as "positive duration dependence". The business cycle becomes stretched. Inventories build up and companies defer spending, tipping over at a certain point into a self-feeding downturn.

Stephen King from HSBC warns that the global authorities have alarmingly few tools to combat the next crunch, given that interest rates are already zero across most of the developed world, debts levels are at or near record highs, and there is little scope for fiscal stimulus.

"The world economy is sailing across the ocean without any lifeboats to use in case of emergency," he said.

In a grim report - "The World Economy's Titanic Problem" - he says the US Federal Reserve has had to cut rates by over 500 basis points to right the ship in each of the recessions since the early 1970s. "That kind of traditional stimulus is now completely ruled out. Meanwhile, budget deficits are still uncomfortably large," he said.

The authorities are normally able to replenish their ammunition as recovery gathers steam. This time they are faced with a chronic low-growth malaise - partly due to a global 'savings glut', and increasingly to a slow ageing crisis across most of the Northern hemisphere. The Fed keeps having to defer its first rate rise as expectations fall short.

Each of the past four US recoveries has been weaker than the last one. The average growth rate has fallen from 4.5pc in the early 1980s to nearer 2pc this time. The US fiscal deficit has dropped to 2.8pc but is expected to climb again as pension and health care costs bite, even if the economy does well.

The US cannot easily launch a fresh New Deal. Public debt was just 38pc on GDP when Franklin Roosevelt took power in 1933, and there were few contingent liabilities hanging over future US finances.

"Fiscal stimulus – a novel idea at the time – may have been controversial, but the chances of it working to boost economic activity were quite high given the healthy starting position. Today, it is much more difficult to make the same argument," he said.

The great hope - and most likely outcome - is that the recent monetary expansion in the US and the eurozone starts to gain traction later this year. Broad 'M3' money data - a one-year advance indicator - has been growing briskly on both sides of the Atlantic. But nobody knows for sure whether the normal monetary mechanisms are working.

JP Morgan estimates that the US economy contracted at an rate of 1.1pc in the first quarter, far worse than originally supposed.

The instant tracking indicator of the Atlanta Fed – GDPnow – shows little sign that America is shaking off its mystery virus. Growth was just 0.7pc (annualised) in mid-May. It is becoming harder to argue the relapse is a winter blip or caused by temporary gridlock at California ports.

Over 100,000 lay-offs across the oil and gas belt seem to have taken their toll. The Fed thought the windfall gain of cheaper energy for everybody else would weigh more in the balance, but this time Americans have chosen to salt away the money.

Net saving jumped by $125bn to $728bn in the first quarter. There was no pick-up in April. Retail sales were flat.

It is now more likely than not that US economy has dropped through the Fed's stall-speed threshold of two consecutive quarters below 2pc growth. Exactly how far below is unclear. The Fed uses its own growth measure - gross domestic income (GDI) - and this data has not yet been published.

The stall speed concept is soft science but not to be ignored. "Output tends to transition to a slow-growth phase at the end of expansions," said a Fed research paper.

Much now depends on China, where the economy is starting to look "Japanese". Dario Perkins from Lombard Street Research says the Chinese economy is in a much deeper downturn than admitted so far by the authorities. It probably contracted outright in the first quarter.

Electricity use has turned negative. Rail freight has been falling at near double-digit rates. What began as a deliberate move by Beijing to choke off a credit bubble has taken on a life of its own, evolving into a primordial balance-sheet purge.

It was inevitable that China's investment bubble would lead to vast inventory of unsold property. The country produced more cement between 2011 and 2013 than the US in the 20th Century -

Mr Perkins said China is now in a “classic debt deflation spiral” as excess capacity holds down prices. Factory gate inflation is now minus 4.6pc. This in turn is tightening the noose further by pushing up real borrowing costs.

The Chinese authorities have so far resisted the temptation to flood the system with fresh stimulus, fearing that this would store up even greater trouble.

They have taken steps to offset a clampdown on local government spending and avert a “fiscal cliff” that might otherwise have occurred. They have loosened policy for banks just enough to offset the contractionary effects of capital flight. But they have not yet come to the rescue.

This matters enormously. Andrew Roberts from RBS says China accounted for 85pc of all global growth in 2012, 54pc in 2013, and 30pc in 2014. This is likely to fall to 24pc this year. “If there is only one statistic that you need to know in the world right now, this is it,” he said.

The effects are being felt across Asia. Japan keeps disappointing. Its exports to China have fallen 15pc over the last year. Korea is flirting with recession.

Russia, Brazil, Argentina, and Venezuela are all contracting sharply, casualties of the China-driven commodity bust. The UN says the growth rate for the emerging market nexus (ex-China) has dropped to 2.3pc from an average of 6.5pc in the glory years of 2004-2007.

Europe is doing better but it is hardly a boom. The eurozone is contributing little to global demand. The region has displaced China and to become the world's "saver of last resort" - or its biggest black hole in the view of critics - exploiting the weaker euro to rack up a current account surplus of $358bn.

It is far from clear whether Europe can act as an engine of world recovery. The composite purchasing managers index (PMI) for services and manufacturing slipped in May, and new orders fell. Oxford Economics thinks the “sugar rush” from quantitative easing may be wearing off.

HSBC's Mr King says the global authorities face awful choices if the world economy hits the reefs in its current condition. The last resort may have to be "helicopter money", a radically different form of QE that injects money directly into the veins of economy by funding government spending.

It is a Rubicon that no central bank wishes to cross, though the Bank of Japan is already in up to the knees.

The imperative is to avoid any premature tightening or policy error that could crystallize the danger. As Mr King puts it acidly. "Many – including the owner of the Titanic – thought it was unsinkable: its designer, however, was quick to point out that 'She is made of iron, sir, I assure you she can'."