A second term gives a US president a chance to make up for some of the mistakes he made the first time around. This is especially true in foreign policy, where few presidents have much prior experience. Most discover that the world is more unpredictable and refractory than they had imagined.
It is, of course, almost unheard-of for presidents and their senior officials to admit that the world took them by surprise, but their actions betray the painful process of education.
President Bill Clinton thought that someone else - the UN, Europe - would take care of crises in Africa and the Balkans. He learned that everyone was waiting for the US. In his second term, Clinton installed a much more hard-nosed national security team that engineered the removal of the UN secretary general and took the lead in Kosovo.
Even President George W Bush, he of the righteous certainties, ultimately figured out that he could not make others see the world as he did simply by repeating himself more and more passionately. In his second term, he got rid of his high-handed secretary of defence, deferred less to his belligerent vice-president and paid attention to diplomatic advice from his secretary of state. He even cooperated with France.
Barack Obama is no more likely than was George Bush to say, "I was wrong." But Mr Obama is Bush's temperamental opposite: he understands that the world looks very different to people standing in different places, that truth is by its nature provisional and unstable, that we always act with imperfect knowledge. Mr Obama often cites the work of Reinhold Niebuhr, the 20th century Protestant philosopher who wrote of the virtues of prudence and humility. Mr Obama is, quintessentially, a man who learns from experience.
So what has he learnt about the world over the last four years? Among other things, he has learnt that his own considerable gifts for summoning rivals to common ground do not overcome the kind of rivalries that govern nations or tribes (or Democrats and Republicans, for that matter).
In the famous speech that he delivered in Cairo in June 2009, Mr Obama offered a finely tuned mutual acknowledgement of the grievances, and of the rights, of Israelis and Palestinians. He hoped that doing so would help each side to acknowledge the other - and induce Arab states to play a more active role in the peace process.
He believed that if he could persuade Israel to make the good-faith gesture of freezing settlement construction, the Palestinians would respond with concessions on final-status issues such as territorial boundaries. But he was wrong.
Israel, which holds the high cards, did not trust the Palestinians, did not trust Mr Obama, and did not really care about mutual acknowledgement.
As a candidate, Mr Obama had deployed his oratorical gift to great effect. The American people came to believe in his voice, his face, his story. In the Cairo speech, Mr Obama, in effect, offered himself to the Arab world. It was a beautiful speech, and it raised hopes across the Middle East.
But not for long, for it became clear soon enough that Mr Obama had no new policies to offer either on peace or on traditional American support for Arab autocrats. Mr Obama promised to restore America's standing in the world, and to some extent he did so by ending torture and speaking modestly. But he found, like George Bush before him, that the magic of his person and of his words was weaker than he thought.
Mr Obama's intuitive faith in his own convening capacity led him to embrace the paradigm of "engagement" - the doctrine that America would talk even to its enemies, adopting a posture of respect in the hope of finding mutual interests. Mr Obama conscientiously referred to America's most inveterate rival as "The Islamic Republic of Iran". He sent Tehran a Nowruz message. But Iran cared no more for fine words than Israel did. The mullahs who control the country's fate dream of dominating the region through the threat of nuclear attack and the use of militant proxies like Hizbollah and Hamas. Their interests, as they understand them, are hostile to the interests of the West.
The "reset" with Russia was more effective, in part because Russia's 2008 war with Georgia had plunged relations with Moscow into the nether regions. But President Vladimir Putin appears to have concluded that antagonistic relations with the US serve his domestic political purposes, and has put the quietus to this branch of engagement policy.
Mr Obama has more sober expectations than Mr Bush had, but the world has defied even those modest hopes. The president understood that he could not bring democracy to Afghanistan. It would be enough, he concluded, to bolster the state's effectiveness and legitimacy in order to ensure that the Afghan people preferred their own government to the Taliban.
But even after tens of billions of dollars - maybe because of them - the Afghan state remains hapless and corrupt.
The counterinsurgency plan Mr Obama authorised was a mistake and now the US has to cross its fingers and hope that Afghanistan can survive intact without Nato troops.
The world is intransigent. Niebuhr understood that, and so did Mr Obama. But Mr Obama also has a streak that makes him dream big dreams. That was why the American people elected him in 2008 - and why the world thrilled to his election.
Now he must find a way forward that adapts to reality without surrendering his sense of the possible. Mr Obama is pivoting to Asia because the US has vast interests there, but also because Asia doesn't need nation-building, counterinsurgency or high-wire peacemaking. Mr Obama would like to close out the bloodshed and melodrama of his first term by moving to a calmer neighbourhood.
He would like to spend his second term focusing on the forward-looking transnational issues to which he would have devoted more of his first term if Afghanistan hadn't turned into a bottomless pit. These include climate change, nuclear nonproliferation and energy policy (although almost all such issues require Congressional action, and thus may continue to be a source of frustration).
Mr Obama would almost certainly like to spend more time working with emerging powers such as India and Brazil and speeding their progress into the driver's seat, or at least out of the cabin, of global institutions. And he and his secretary of state will try to navigate the narrow ground between confronting China and accommodating its increasingly strident ambitions.
Mr Obama is already a pragmatist, so it's hard to say if a second term will feel more pragmatic than the first, as was the case with George Bush. He is not likely to push too many chips on the Israel-Palestine table. He may well give fewer stirring speeches. He will expect less of Iran and Russia, and perhaps also China, and so will feel more free to criticise them. He may actually wind up sounding less like a Niebuhrian realist simply because he can afford to be less equivocal.
Mr Obama spent much of his first term trying to extricate himself from inherited calamities, both domestic and foreign. The second term, by comparison, might feel like a bed of roses.
James Traub is a contributing writer for The New York Times Magazine and a visiting professor at New York University, Abu Dhabi.
Ÿ He will be in conversation with Jules Coleman tomorrow evening at an NYUAD Institute event at Manarat Al Saadiyat, Abu Dhabi, on the topic "Is 'engagement' dead? The US after 2012"