Image caption Nassim Taleb has had several meetings with Prime Minister David Cameron to discuss political ideas

The work of a Lebanese-American philosopher has captivated Downing Street, including the Prime Minister David Cameron.

"I like going to 10 Downing," says Nassim Nicholas Taleb, the Lebanese-American thinker and former Wall Street trader, "seeing the offices and the most powerful person in his T-shirt and jeans".

The powerful person he is referring to is British Prime Minister David Cameron, whom he has been invited to meet several times - including at the official residence he refers to affectionately as "10 Downing".

The admiration is reciprocated. Taleb has described the prime minister as "extraordinary" and "the best thing we have left on this planet".

The striking closeness between this once obscure writer and the British leader encapsulates how Nassim Taleb's thinking has captivated senior British Conservatives.

There's a very close link between black swan thinking and what we're doing [on] health or education, David Willetts MP, Universities Minister

His work focuses on understanding unpredictable, high-impact events, which he calls "black swans" - after the fact that Europeans once assumed all swans were white, until a black one was spotted in the southern hemisphere.

For example, Taleb has labelled the 2008 financial crash as a "black swan" event.

Anticipating the 2008 crash is part of what is given The Black Swan [Taleb's book] so much traction says David Willetts, Minister for Universities and Science.

"The big events that now shape the world today are ones that barely anyone was forecasting five years ago," Mr Willetts says.

This partly explains why many top British Conservatives remain closer to him than to perhaps any other contemporary intellectual.

Black Swans

So what does this closeness tell us about David Cameron and his party's particular brand of Conservatism?

"Nassim Taleb is probably the closest thing which Cameron has to a guru," says Fraser Nelson, editor of the Spectator magazine.

Image caption Nassim Taleb labelled the 2008 financial crash as a "black swan" event - a rare event

The fact thatDavid Cameron shared a public stage with Talebbefore he was elected, sends out a powerful signal, says Nelson, even though Cameron is usually "not the type of guy" to follow particular thinkers.

So how exactly are Nassim Nicholas Taleb's ideas and influence changing our lives? Taleb's central insight concerns randomness, which he says is responsible for more than we usually think.

He argues that we do not know very much, especially about the future, and what is worse we think we do - influenced as we are by the grand theories and models produced by economists, scientists and other experts.

"My focus is simply risk," says Taleb. "You want to build a society that is robust and with the smallest amount of these large exposures to unnatural black swans."

The term "black swan" encapsulates the fragility of human knowledge.

Classic Tory impulse

Centuries ago, we postulated that all swans were white because we had only ever seen white swans. When we discovered a black one, that theory instantly died. But it was a relatively costless event.

Yet in some domains, such as economic and social life, unforeseen events can wipe us out.

As a Wall Street trader, Taleb himself profited by being more vigilant to such events than the market herd, such as the financial crashes of 1987 and 2008.

He worries that in economic life, instead of proceeding with caution, we are dangerously bold.

We borrow money during the good times, expecting them to continue forever. Then one random event, like a financial crash, ruins us.

Taleb's appeal to Conservatives should be starting to become apparent now. Risk aversion is a classic Tory impulse.

Conservative philosophers such as Edmund Burke and Michael Oakeshott - a hero of Taleb - agreed.

In modern policy, one of the key expressions of this is the coalition government's emphasis on austerity and aversion to national debt.

"These big uncertainties do remind us of how limited the foresight of governments and commentators can be," says David Willetts. "Therefore it's an argument for prudence - certainly prudence in the public finances."

But there is much more to Taleb's influence than that. Nassim Taleb's work also argues against scale and size, which has helped inspire initiatives such as welfare reform and The Big Society.

What is Black Swan theory? "The problem of induction" - that any theory based on observations could be wrong - has long preoccupied philosophy.

20th Century British philosopher Sir Karl Popper also considered how new observations affected knowledge - such as spotting a black swan when it was thought all swans were white.

Nassim Nicholas Taleb's 2007 book The Black Swan looks at the problem anew and describes the disproportionate role played by hard-to-predict events.

Such 'black swan events' are considered extremely rare but have huge historical consequences.

Examples include World War I, the September 11 attacks and the emergence of the internet.

While these events are a surprise, they are then rationalised in hindsight - they could have been predicted as the evidence was there, but went ignored.

The black swan reference derives from a Latin expression " rara avis in terris nigroque simillima cygno"

This translates as"a rare bird in the lands, and very like a black swan" -when first written it was thought that black swans did not even exist.

Taleb argues that politicians must give up trying to predict the unpredictable, and instead make sure that society can withstand shocking events when they happen.

This means not only a presumption against debt, but also a bias against over-sized organisations.

In the private sector, banks and companies should not be "too big to fail". In the government, power must be dispersed so that bad decisions in one place do not doom everyone.

The ideal form of government, says Taleb, is the city state. Seen in this light, the parallels between Taleb's work and the government's policies start to multiply.

As well as fiscal conservatism, the coalition espouses city mayors, elected police commissioners, independently run state schools, more charitable and commercial providers of welfare-to-work and other services.

"There's a very close link between black swan thinking and what we're doing [on] health or education," says David Willetts.

"Because it's wrong to think of the health service or the education system as a great, big monolith - thousands of GPs, thousands of schools in some kind of pyramid which ends up at Whitehall.

"Instead we think of them as an eco-system, as a network," he says. "And that is black swan thinking because what Taleb does is reminds us of the perils of being big."

'Intellectual crime'

Of course, there is a negative side to all this scepticism and prudence.

The Tories have historically been accused of being the "do-nothing" party, excessively sceptical about our ability to achieve progress through reason and planning.

If it's this blanket scepticism that we're always at the mercy of the black swans, then I would be very frightened of it Prof John Worrall, London School of Economics

So is the Conservative Party's fascination with Taleb a good thing?

"It depends of course which parts they're taking," says John Worrall, professor of the philosophy of science at the London School of Economics.

"If it's this blanket scepticism that we're always at the mercy of the black swans, then I would be very frightened of it."

Prof Worrall studied under the famous philosopher of science Sir Karl Popper, whose work Taleb admires.

But Worrall says Taleb goes further than Popper, especially when he argues that events such the September 11 attacks could have been prevented if we were more risk averse.

"The intellectual crime the whole time I think is to generalise too quickly, which, part of the time, is what Taleb himself is saying," he argues.

"It sounds like his impact on the Conservative Party is exactly an instance of that - that you don't really need to think about individual cases because you know that there'll be black swans around."

These criticisms capture the quandary facing conservatives, especially those who are part of the coalition government.

They have a philosophy that leads them to relinquish power, but face an electorate that expects them to show grip and leadership.

Image caption David Cameron has met with Nassim Nicholas Taleb on several occasions to discuss political ideas

It is, perhaps, the eternal conservative dilemma and today's Tory leaders seem well aware of it.

"There is a danger of a kind of crippling doubt that you can't do anything," admits David Willetts.

"Someone said of American Republicans that Republicans believe government doesn't work and get elected to prove it. You can't fall into that trap."

But senior Tories do use Nassim Taleb's "black swan" thinking work as a guiding philosophy. That should tell us that their view of the world is, in fact, a traditional conservative one.

It stands for scepticism towards grand plans and favours the small and the local over the big and the central. For all his youth and modernising spirit, that is the kind of conservative that Prime Minister David Cameron is.

Analysisis onBBC Radio 4on Monday 12th March at 20:30 GMT and Sunday 18th March at 21:30 GMT. You can listen again via theRadio 4 websiteor by downloading thepodcast.