AS the art of diplomacy goes, this meeting called for the skills of a Dali or a Miro, one of those surrealist cats.

Here was Condoleezza Rice, US Secretary of State, in the lair of the mad dog that was Gaddafi. One thought was prominent in her mind: how quickly can I get out of here?

The answer to that was, not before the Libyan leader had shown her a special video he had made for her. Had they been on a date, this is the point at which the police and the impassioned suitor’s psychiatrist would have burst in.

Over to Condi, who tells the story in an interview with ABC News’s George Stephanopoulos, to be shown next week. “I thought, ‘Oh my goodness, what is this going to be?’ But it was actually just a bunch of pictures of me with Vladimir Putin, me with Hu Jintao. And then he said, ‘I have Libya’s best composer, most famous composer, write this song for you,’ and it was called ‘Black Flower in the White House’.”

Quite the story, and Ms Rice is telling it now because she has, you will not be surprised to learn, a book coming out next Tuesday. Ever the high achiever, No Higher Honor is Ms Rice’s second doorstopper since she left office three years ago. The first was Extraordinary, Ordinary People: A Memoir of Family Life, which took her story from childhood in Birmingham, Alabama, to the door of the White House. No Higher Honor is what happened next as she served first as national security adviser, then Secretary of State under President George W Bush.

It is telling that Ms Rice should separate her life into the personal and the political as if a Berlin Wall could be built between them. One wonders, even after this second book, how much more of a picture will emerge, whether the “real” Condi Rice will finally step through the curtains. Despite being one of the most prominent African-American women of her generation, she remains an enigma. She is the pastor’s daughter who became “the warrior princess”; the Carter voter who turned to Reagan; the academic who served a defiantly non-academic (that’s putting it politely) president. Who is Condi Rice and wouldn’t we all like to know?

Extraordinary, Ordinary People didn’t have the lyricism of Obama’s Dreams from My Father, but as an introduction to a political figure and a summation of the American dream, it was just the ticket. Few could read of Ms Rice’s achievements without realising that this was an extraordinarily driven, intelligent, even gifted individual. Her childhood days began at 4.30am with skating practice and ended with bed at 9.30pm after cramming in studies, more sports and piano lessons. College at 15, graduation at 19 in political science, a masters, a doctorate, a fellow at Stanford University, then on to the National Security Council under Bush Snr. The perfect background with which to run for political office.

As it was, Condoleezza Rice was content to stay in the wings, to be the prompt, not the lead actor. The spotlight found her anyway. How could it not? As a woman, as an African-American, her presence in one of the most conservative administrations since Reagan’s was remarkable. Strong as she was, as close to the president as she was – the two were genuine pals – Rice, like many others in the administration, was unable to counter the influence of the real boss, vice-president Dick Cheney. Still, she must have got under his skin judging by the way he took several swipes at her in his memoir, In My Time, for, among other things, naiveté. To be slated by Dick Cheney, the Darth Vader of the Bush administration – in most people’s books that would be another accolade for the cv.

In 2008, as the race for the White House got under way, the question of Ms Rice running for office, a question that had followed her for years, could no longer be ignored. Yet she declined then, saying it was not something she had ever seen herself doing.

Her refusal sits with one part of the Rice persona – the academic, deeply private, reserved side. Yet it is at odds with the Condoleezza Rice who from a young age was taught that if she worked hard enough, tried hard enough, there was nothing she could not do. As she once told Newsweek: “My parents had me absolutely convinced that, well, you may not be able to have a hamburger at Woolworth’s but you can be President of the United States.”

Curious, then, that this fiercely determined woman, one who never saw a goal she didn’t want to reach, should not go for the most glittering prize of all. It’s not impossible that she might change her mind. Although she has now gone back to academia, the fact that she has written a second book shows she’s not quite done with political life.

Yet there’s good cause to believe that the reason this ferociously smart woman won’t run for office is just that – she’s too smart. She’s been around long enough to know that she might embody the American dream, but when Americans dream of their first woman president – if they dream of such a thing at all – they don’t see her.

Single, no children, cool to the point of chilly, she would tick few boxes with women or male voters. In an age of touchy-feely politics, the reserved Ms Rice is about as emotionally open as George W Bush was intellectually adventurous. Whoever tries to become the first female president of the US will need the heart of a lion, the back story of a nun, and the hide of a sun-baked rhino.

If that still makes her sound like a runner, there is the not-inconsiderable matter of her time in office to consider. For all her achievements, there is no escaping the fact that she served in a US administration that had more international goodwill on its side than any other since the Second World War, yet it failed, spectacularly, disastrously, to leave the world a better, safer, more civilised place.

Ms Rice can rationalise the case for war against Iraq as much as she likes, she can write no end of books on the subject, yet she will never convince the world that she was right. In the end, the perfect Ms Rice simply chose the wrong team, the wrong cause to serve. However much mystery surrounds her personally, her political choices have been exposed and found wanting. An extraordinary person, certainly, but as a political visionary, she will forever be marked down as a failure.