Where will the cloud go? Nobody seems to have a handle on it. And so the agony of hundreds of thousands of stranded air travelers will continue at least throughout this weekend.

British Airways isn’t flying into or out of any London airports Saturday. Ryanair, the Irish budget airline, isn’t expecting to fly anywhere in northern Europe until Monday. And today President Obama and German Chancellor Angela Merkel canceled flights to Poland to attend the funeral of the country's president.

From Singapore to Johannesburg, Los Angeles to Buenos Aires, hundreds of airplanes are stuck in the wrong place.

The behavior of the cloud poses a problem that most Americans will find it hard to understand. Weather forecasting in the U.S. is so refined that you can usually get at least three days’ warning of when it will rain, snow, or cook. Our weather more or less always tracks west to east. Forecasters can see it through every minute of its development. So why can’t the Met Office, Britain’s meteorological headquarters, tell us with more confidence when that cloud is going to move, and where?

They have powerful computers and some of finest weather-system modeling in the world, but no country has a harder time predicting its day-to-day weather than the United Kingdom. The island is a complex arrangement of hundreds of micro-climates famous for their whimsy. As Sinatra said about London, “If you don’t like the climate, wait five minutes.”

Which is why the enormous trans-Atlantic cloud's path over London creates the perfect storm, so to speak. The 21st century has just met the 19th century, and the 19th century is winning—so far. The last time the Icelandic volcano erupted was in 1821, and it continued spouting until 1823. This historical detail seemed too distant to consider as we built the modern airways over the Atlantic and Europe. Now we realize how vulnerable we are to what was, literally, a sleeper. Today, anyone trying to guess when normal jet service will return to Europe’s skies has about as much chance of being right as the forecasters.

The cloud has not only affected flights to and from Europe, but the world over. U.S. travel agents, trying to help clients stranded in, say, South America, are unable to provide back-up itineraries because airline schedules have suddenly been rendered meaningless. From Singapore to Johannesburg, Los Angeles to Buenos Aires, hundreds of airplanes are stuck in the wrong place.

As soon as the cloud allows, airlines will begin improvising schedules, making it up as they go along to clear the accumulated passenger lists. It will take as long as a week to see anything approaching normal. People who have invested a lot of money in their dream vacation have missed their dates. And since no travel insurance covers acts of nature like this—whom do you sue?—it will be left to the mercy of the companies to resolve the issues.

Meanwhile, some of the numbers are staggering: 46,500 people using the Eurostar trains between London and Paris in a day; 600,000 people per day unable to fly out of London’s airports; and $5,100 for a taxi ride from Oslo, Norway to Brussels, Belgium. The passenger? John Cleese, surrealist comedian and one of the creators of the absurdist Monty Python—the perfect posterboy for the present situation.

Clive Irving is senior consulting editor at Conde Nast Traveler, specializing in aviation—find his blog, Clive Alive, at CliveAlive.Truth.Travel.