In fact, Obama’s approach has already produced remarkable results. Russia and China, after long opposition, agreed last week to a toughening of the nuclear Non-Proliferation Treaty. In a striking shift, Russia signaled that it may support tougher sanctions against Iran. The Obama administration’s decision to cultivate a relationship with both countries, to listen to their concerns, is paying off.

Obama’s outreach to the world is an experiment, and not merely to see if the world will respond. He wants to demonstrate at home that engagement does not make America weak. For decades, it’s been thought deadly for an American politician to be seen as seeking international cooperation. Denouncing, demeaning and insulting other countries was a cheap and easy way to seem strong. In the battle of images, tough and stupid always seemed to win.

Obama is gambling that America is mature enough to understand that machismo is not foreign policy and that grandstanding on the global stage won’t succeed.