When the US Secretary of State Hillary Clinton left India this week, clutching contracts for defence and nuclear energy worth up to $40 billion for US companies, she was understandably grateful to her hosts. "I consider India not just a regional power, but a global power," she said.

America has good reason to want India to think and act like a world power. It sees a lot of itself in the country: the US may be the world's greatest democracy, but India is its largest. Its people have entrepreneurship in their DNA; its business leaders have embraced globalisation and are busy taking over iconic brands and businesses throughout the world.

Like the US President Barack Obama, its leaders are pro-market social democrats; and a level of religious tolerance is maintained in the face of regular terrorist atrocities. Referring to posters she had seen during an earlier visit, bearing the slogan "India poised", Clinton insisted the country "was poised for economic growth, for global peace. It was poised to become a more powerful nation."

Yet India's great fortune, and possibly its real power, is that it is the beneficiary of so much wishful thinking. Its great democracy yields governments disabled by institutional corruption. Its literacy rate of 65 per cent is lower than tiny, war-ravaged Sri Lanka's (92 per cent). It might be the second fastest-growing economy in the world, but just under half of its billion people live on 76p per day or less, and it has the highest rate of child malnutrition in the world.

The problems don't end there. Development is constricted by shabby infrastructure, with daily power cuts, water shortages, and potholed roads blocked with bullock carts. The agricultural system is so archaic that an estimated 40 per cent of farm produce rots behind those carts before it gets to market.

In military terms, the pride and self-esteem of India's armed forces was dented by just 10 well-trained terrorists last November, when they held India's elite commandos at bay for three days in Mumbai and murdered the chief of the city's anti-terrorist squad and two of his top officers when they left their desks to confront them.

Beyond India's borders, Beijing is steadily winning over countries which New Delhi has traditionally regarded as its junior partners, as well as humiliating India at every opportunity. China has not only armed and sustained Myanmar and Pakistan, but has won friends in Nepal and Sri Lanka by funding key infrastructure projects.

Its development of nuclear submarines highlights its ambition to become a more visible presence in the Indian Ocean, and its officials have renewed its claim on Indian border states such as Arunachal Pradesh, where China recently vetoed an Asian Development Bank grant for aid projects to put pressure on India.

One retired senior navy commander last night described India's "global power" as a "joke" - no more than "borrowed feathers" from genuine powers such as the United States.

"We are huge importers of weapons systems. China, which has a blossoming navy, has tried to sabotage our nuclear deal with the United States, and while it has not yet reached its full potential to patrol the Indian Ocean, it is on its way. The fact is, we are not on the global scene."

So where is India's great power? The answer is in its growing economy, the stability of its democracy, and its unrivalled reserves of international goodwill: almost everyone, with the exception of China, Pakistan and jihadist groups, loves the idea of India.

Pavan K. Varma, the respected Indian diplomat and cultural commentator, says he believes his country will eventually overtake its regional rivals because its democratic system has created a stable political climate, while its people's entrepreneurial instincts and technological talent will continue to exploit the opportunities that arise. His is a "hare and tortoise" argument for India's rising power: an unshakeable conviction that India will slowly but surely overcome the considerable obstacles in its way to claim ever more prizes, like its successful unmanned lunar mission last autumn, the creation of the world's cheapest car, the Tata Nano, or the acquisition of Jaguar Land Rover last year by the same company.

But a telling explanation for India's power came, again, from the US secretary of state, during her visit to Mumbai and New Delhi this week. "People from other Asian countries watching Indian films think all Indians look good [and] have dramatic lives with happy endings," she said.

The extraordinary appeal of the Bollywood film industry transmits the country's liberal, secular values from Myanmar through Bangladesh, into clandestine showings in Pakistani homes, throughout Islamic Afghanistan, and across West Asia into North Africa, where stars such as Amitabh Bachchan and Shah Rukh Khan are household names.

Across that broad sweep of mostly conservative societies, Bollywood tales of Muslim boys eloping with Hindu girls, of rags to riches businessmen and slumdog millionaires, India is seen as a mostly harmless home of action heroes, saucy dancers and true romance: the world's first soft superpower.