It will be all smiles at the NATO summit today in London--but many of them will be forced. Behind the scenes, the alliance’s leaders are arguing about what its purpose should be. We also look at the disputed data behind the idea that inequality has been rising inexorably in recent years. And how a novel way to reduce cow and sheep burps could help in the fight against climate change. For full access to print, digital and audio editions of The Economist, subscribe here www.economist.com/radiooffer