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Self-driving vehicles are an example of the crosscurrents.

Ad sales agents and pilots are two jobs that the Bureau of Labor Statistics projects will decline in number over the next decade. Flying a plane is largely automated today and will become more so.

Telemarketers are among those most at risk

More than 16 percent of men between the ages of 25 and 54 are not working, up from 5 percent in the late 1960s; 30 percent of women in this age group are not working, up from 25 percent in the late 1990s.

“The answer is surely not to try to stop technical change,” Mr. Summers said, “but the answer is not to just suppose that everything’s going to be O.K. because the magic of the market will assure that’s true.”

Michael A. Cusumano, a professor in the Sloan School of Management at M.I.T., said he thought Apple no longer had the juice to create the world-beating product it needs.

Between 1991 and 2012 the average annual increase in real wages in Britain was 1.5% and in America 1%, according to the Organisation for Economic Co-operation and Development, a club of mostly rich countries.

Real wage growth in Germany from 1992 to 2012 was just 0.6%; Italy and Japan saw hardly any increase at all.

And the dramatic dip in productivity growth after 2000 seems to have coincided with an apparent acceleration in technological advances as the web and smartphones spread everywhere and machine intelligence and robotics made rapid progress.

A second explanation for the Solow paradox, put forward by Erik Brynjolfsson and Andrew McAfee (as well as plenty of techno-optimists in Silicon Valley), is that technological advances increase productivity only after a long lag.

John Fernald, an economist at the Federal Reserve Bank of San Francisco and perhaps the foremost authority on American productivity figures, earlier this year published a study of productivity growth over the past decade. He found that its slowness had nothing to do with the housing boom and bust, the financial crisis or the recession. Instead, it was concentrated in ICT industries and those that use ICT intensively.

Once an online course has been developed, it can be offered to unlimited numbers of extra students at little extra cost.

For example, new techniques and technologies in medical care appear to be slowing the rise in health-care costs in America. Machine intelligence could aid diagnosis, allowing a given doctor or nurse to diagnose more patients more effectively at lower cost. The use of mobile technology to monitor chronically ill patients at home could also produce huge savings.

Health care and education are expensive, in large part, because expansion involves putting up new buildings and filling them with costly employees. Rising productivity in those sectors would probably cut employment.

The integration of large emerging markets into the global economy added a large pool of relatively low-skilled labour which many workers in rich countries had to compete with. That meant firms were able to keep workers’ pay low.

Productivity growth has always meant cutting down on labour. In 1900 some 40% of Americans worked in agriculture, and just over 40% of the typical household budget was spent on food. Over the next century automation reduced agricultural employment in most rich countries to below 5%,

A new paper by Peter Cappelli, of the University of Pennsylvania, concludes that in recent years over-education has been a consistent problem in most developed economies, which do not produce enough suitable jobs to absorb the growing number of college-educated workers.

about 1.3 percent of GDP is devoted to the military.

Germany is reducing the size of its army, which is expected to slightly trim military spending in coming years.

1.2 percent of its GDP on the military

1.3 percent of its GDP on the military.

Poland's President Bronislaw Komorowski announced Tuesday that Poland would raise that figure to 2 percent as "a very tangible, very clear engagement" in the alliance

inancially challenged Spain's defense budget has shrunk from 1.2 percent of GDP in 2009 to 0.9 percent, NATO statistics show.

When teachers demand rigorous work, students often rise to the occasion, whereas tracking students at different cognitive levels tends to “diminish learning and boost inequality”. Low expectations are often duly rewarded.

America’s classrooms do not fare well in this book. Against these examples of academic achievement, the country’s expensive mistakes look all the more foolish. For example, unlike the schools in Finland, which channel more resources to the neediest kids, America funds its schools through property taxes, ensuring the most disadvantaged students are warehoused together in the worst schools.

Another potential sticking point is Turkey itself. For one thing, the country obtains about 60 percent of its gas from Russia, a dependence the government is not necessarily eager to increase.

Industry analysts estimate that the cost of Turkish Stream would be about $10 billion for Gazprom, which so far has spent an estimated $4.7 billion on the Black Sea project.

Mr. Putin already publicly offered a 6 percent reduction to Turkey. But Ankara, which pays substantially more for Russian gas than Germany does, is pressing for a better deal.

The country accounts for over a quarter of global greenhouse gas emissions.

Even assuming that China’s population does not grow at all over the next 30 years, that the energy efficiency of its economy increases at a faster pace than most developed and developing countries and that it manages to decarbonize its energy sources faster than pretty much anybody else, China would still be emitting a lot more carbon in 2040 than it does today, according to E.I.A. calculations.

Can the United States or anybody else do anything to speed China down a low-carbon path?

The latest report from the United Nations Intergovernmental Panel on Climate Change, issued in April, suggested several ways to allot responsibilities. If one starts counting in the 18th century and counts only emissions from industry and energy generation, the United States is responsible for more than a quarter of all greenhouse gases that humanity has put into the air. China, by contrast, is responsible for 10 percent.But if one starts counting in 1990, when the world first became aware that CO2 was a problem, and includes greenhouse gases emitted from changes in land use, the United States is responsible for only 18 percent, and China’s share rises to 15 percent. Rich and poor countries, unsurprisingly, disagree on the proper measure. Photo

Not everybody will meet their Copenhagen pledges. Japan, which unplugged its nuclear energy after the disaster at the Fukushima nuclear power plant, will fall behind. So will Canada and Australia, whose new conservative governments have lost interest in the pledges of their predecessors.