The Eyjafjallajokull volcano in Iceland has so many variables, unknowns and hard-to-measure risks that make modelling its behaviour almost impossible, say experts.
In fact, no one can accurately predict what the volcano - or its larger neighbour, which might also erupt - will do.
Short-term weather forecasts might be good, but long-term weather forecasting is a notoriously inexact science.
Worst of all, no one can categorically say how much ash is dangerous to aircraft.
Predicting accurately the economic and market impact is not much easier. Businesses and consumers are in unknown territory and no one knows quite how they will react or what methods they may find to get around the flight restrictions.
"I really don't think you can model it," says Howard Archer, chief European and UK economist at IHS Global Insight. "There are so many uncertainties, unquantifiable knock-on effects, winners as well as losers."
Scenarios can be sketched out for different levels of shutdown over different periods, but any calculations made on economic growth or impact on firms are rough at best.
All told, travel and tourism account for around 5% of global gross domestic product - some US$3 trillion (A$3.22 trillion) - with Europe accounting for a third of that. But working out how much of that will be lost is much harder.
Increased spending on holidays at home might partly mitigate the reduced spending on flights - but quantifying that is another matter. So is working out knock-on effects on other industries.
Nevertheless, if a prolonged slowdown were to knock 1% to 2% off growth, mainly through travel and tourism, that could be enough to push the continent back into recession.
The impact on the airline industry is relatively easily quantifiable, and put at some US$250 million (A$268 million) a day. But the final impact on the airlines will also come down to what level of support they might receive from their governments.
Limits of science
Some firms are already learning to work around the shutdown. Supermarkets are flying perishable horticultural produce to Spain and then trucking it to northern Europe, but that brings additional costs.
Such adaptation makes forward-looking predictions of loss difficult. Kenya's horticultural industry says it had already lost US$12 million (A$12.9 million) to the European airspace closure.
The recent resumption of flights may be seen as more a political decision than a scientific one.
Britain's Royal Institution's Science Media Centre - which provides quotes from scientists to the media on a range of stories - is pumping out a series of comments that essentially highlight the limits of knowledge in this case.
"The concentrations of ash which are dangerous to jet engines are simply unknown," says Grant Allen, an expert at the University of Manchester's Centre of Atmospheric Science. "No one knows for sure what density of ash plume can bring a plane down."
Airlines have been desperate to resume flying, but no policymaker wants to take the blame for a crash and so they are predictably erring on the side of caution.
The vast number of flights in European airspace - some 20-22,000 a day - means that even a tiny risk could produce catastrophic consequences. If 99.99% of flights suffered no serious harm, that would still leave roughly 20 aircraft a day suffering damage or outright engine failure, possibly over a populated area.
Airlines say some 40 test flights over the weekend showed little risk and some flights have resumed, but experts say the dispersal of the ash appears to be far from uniform. That means patches of relatively dense ash may be scattered all over Europe, with potentially disastrous consequences.
"Since forward-looking weather radar and other sensor systems aboard modern aircraft cannot see this stuff, the very real possibility exists that a passenger jet could fly into one of these high concentration pockets and suffer serious damage," says aviation consultant Chris Yates.
Determining that risk is zero is probably impossible.
"Once the existence (of the) cloud was known, just one incident of major engine failure, let alone an accident caused by the ash, would have left the airlines and aviation regulators with a heavy responsibility as well as a legacy of distrust amongst the public, possibly for years to come," says Nick Pidgeon, professor of psychology at Cardiff University.
"Under such circumstances, it is hardly surprising that the cautionary approach to risk has been adopted."