Obama on the tourist trail in China

US President takes in the sights and pays a visit to his half-brother
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It had the look of an unscripted moment in what has been a minutely micromanaged visit. The President of the United States of America took time out from his hectic, difficult maiden voyage to the world's rising superpower, China, to contemplate destiny and the games that history can play.

The weather has turned sharply cold in Beijing. His hands deep in the pockets of his windcheater, Barack Obama nimbly covered three sections of the world's greatest historical fortification on the last day of his visit to China.

Just for a second, Mr Obama was able to shake off the weight of the world and gaze out at the stunning view from the ramparts, getting a sense of the ancient culture that made this wall.

"It's magical. It reminds you of the sweep of history and that our time here on Earth is not that long. We better make the best of it," he said, after shrugging off his guides for a few moments of solitude.

That this solitude ended up on YouTube within minutes did not take away from the image of a man clearing his head on what has been a difficult trip. Trade issues, China's cheap currency making American goods uncompetitive, human rights problems that refuse to go away, Tibet, and the changing nature of the relationship between the United States and the nation to which it is most indebted – all these have weighed on him.

It was a distinctly human moment in a visit that has mostly passed in a blur of black-suited groups and motorcades, culminating at one point in that bastion of the power of the masses, the Great Hall of the People.

Another human dimension to Mr Obama's visit was the meeting with his younger half-brother, Mark Okoth Obama Ndesandjo, who lives in Shenzhen, and with whom he shares a father. The younger man recently published a novel that he says is closely based on his own experience, in which he describes their father's problems. The two brothers met in Beijing.

"I don't know him well. I met him for the first time a couple of years ago," Mr Obama told CNN. "He stopped by with his wife for about five minutes during the trip." He said he was unconcerned about his brother's book. "It's no secret that my father was a troubled person," he said. "It's not something that I spend a lot of time brooding over."

Mr Ndesandjo described the meeting as "overwhelming". "He came directly off the plane, changed some clothes and then came down and saw us," he told the Associated Press. "He just gave me a big hug. And it was so intense. I'm still over the moon on it. And my wife... I think she is still recovering."

Mr Obama also took time to make peace with Fox News, granting its presenter Major Garrett an interview which signalled the end of a freeze in relations brought on by what were seen as Fox's persistent, needling criticisms.

Obama left China en route for Seoul, the South Korean capital, where he will meet President Lee Myung-bak and try to make progress in a agreeing on a strategy for keeping North Korea's nuclear ambitions in check.