LONDON (Reuters) - Strip away all the complexities facing the world economy at the moment and you come down to three interlocking puzzles: America, Europe and China.

A man dressed as a destitute Uncle Sam begging for $12 trillion demonstrates in New York January 19, 2010.REUTERS/Brendan McDermid

Stumbling America, debt-strapped Europe and booming China, that is.

The three face different, sometimes contradictory, challenges. Yet they are so intertwined in this era of globalization that it is hard to imagine how events in one could possibly not spill over into the other.

Jim O’Neill and his economics team at Goldman Sachs recently sought to boil down the risks facing the world economy -- and, by extension, financial markets -- to three neat questions.

-- How deep will the U.S. economic slowdown be and what will the policy response be? (That’s two questions, actually, but let’s not nitpick).

-- How much decoupling is possible between the U.S. economy and others which are growing well, notably China?

-- Will sovereign and systemic risks intensify again or settle? (A clear reference to the euro zone, where the Greek debt crisis has gone to sleep but not disappeared.)

For the record, Goldman believes the answers will not necessarily signify trouble. “Our own forecasts envisage a period of some muddiness in the near term that ultimately resolves toward a more positive global view,” it says.

But it also notes there are fragilities in the economic system which require open-mindedness about the risks.

Burrow down a bit and you can come up with three subsections, part of which come courtesy of Mike Dicks, head of investment strategy at Barclays Wealth. They are:

-- America: Will the U.S. consumer stop spending?

-- Europe: Will attempts to control debt snuff out nascent signs of recovery?

-- China: Will it make a policy mistake and douse rather than cool its economic engine?

GORDIAN KNOT

For all their differences, these three risks and subsets are so closely woven together that a positive outcome for all is probably necessary for the world economy to move out of its current phase unscathed.

It is not so much the vaunted three-speed economy as a three-legged stool, ready to tip if one support gives way.

Consider, for example, a dive in U.S. consumer spending from its already moderate level. If spending actually starts to match sentiment -- and the recent jobs data does not bode well -- a booming China would find its key market drying up.

Attempts by U.S. authorities to reverse the slide into a double-dip recession and even deflation would almost certainly involve printing even more dollars than is currently the case, undermining, through devaluation, the competitiveness of European exporters, among others.

As for Europe’s big problem, the debt crisis triggered earlier this year by fears of a Greek default has eased, supported by a huge bailout plan and a generally positive stress test on the region’s banks.

But few analysts believe the problem has gone away for good. Governments, cognizant of this, have embarked on a variety of austerity plans that could threaten what nascent growth there is -- a worry for U.S. and Chinese exporters.

A renewed confidence crisis in Europe’s debt would not stay European for long. The U.S. deficit and debt pile is easily as worrying for those looking for fiscal balance as is Europe’s.

Turning to the third leg of the stool, Barclay’s Dicks argues that China poses the least problems. But that is a long way from saying that it can hold everything up on its own.

True, there are signs that China and other big emerging markets are beginning to create domestic demand. But it is early days and exporting is still the big game.

Controlling inflation in China is the biggest worry for economists, with fears mainly revolving around a policy mistake that will overdo the required slowdown.

As Dicks says: “We hope for a soft landing, but worry about a hard one.”

UNCERTAINTY

None of these fears may materialize, of course. U.S. consumers are renowned for their resilience. Chinese authorities can and do manage their economy tightly. Europe is currently showing signs of a rebound, not a rewind.

But the dangers are there and weighing both on authorities’ minds and on financial markets.

Where the world stands was graphically depicted in a recent report by the Ewing Marion Kauffman Foundation, which surveyed the opinions of influential economic bloggers.

As befits a study of the blogosphere, the foundation presented some of its findings in a “word cloud” made up of the most common words used by respondents to describe the U.S. economy.

One word stood out -- “Uncertain.” Not terribly useful, but then that is the nature of uncertainty.