It is an annual ritual for tens of thousands of residents of Delhi: the sumptuous sight of floats, soldiers, tanks, dancers and dromedaries. Overhead roar jets. In the stands lining the path of the Republic Day parade , thousands cheer and wave. The visiting dignitaries – France’s François Hollande this year, Barack Obama last year – nod, smile and try not to let their envy at the latest set of topline figures about their host’s economic growth show too obviously

For that growth is as impressive as any of the displays of traditional arts or freshly painted armoured vehicles. It is certainly more important to India than either. New figures released by Indian authorities last week put economic growth in the emerging power at 7.5% in 2015, the highest in the world, and up from 6.9% the year before. Growth in China is heading in the opposite direction – predicted to be only 6.3% in 2016 – while the US will expand by a mere 2.6%. To spare Hollande’s blushes, let’s not even mention the predictions for France.

So, after several disappointing years, the elephant has once again begun to dance. And, in a world shaken by a series of rolling crises, anything remotely cheerful gets noticed. India’s economy is the 10th or 11th biggest in the world and is forecast to reach third, after the US and China, in less than 15 years.

This leads to two important questions: is India’s rise, which looked to be slowing, really back on track? And if so, what will India’s eventual emergence as a major economic power actually mean? The answers to both challenge many of the easy assumptions often made in the west.

The first is that India’s rise is certainly unlikely to be linear and uniform; after all, very little else in the chaotic, immensely varied nation of 1.3bn is. The Indian growth calculations were made according to a new – and generous – formula. A year ago, Rushir Sharma, an expert on emerging economies, banker and best-selling author, dismissed them as “a bad joke”. More recently, other commentators have been less scathing.

No one claims the blunt GDP growth statistics describe ground reality, however. Anyone who has spent any time in India knows that the country still suffers enormous problems: grossly inadequate infrastructure and a deep skills deficit that could easily turn the “demographic dividend” of a youthful population into soaring inequality, massive corporate debt, political gridlock ,patchy rule of law, poor governance and horrendous environmental degradation.

François Hollande and his Indian counterpart Pranab Mukherjee drink tea. Photograph: Adnan Abidi/Reuters

Still, to dismiss the rise of India would be wrong. Whatever the doubts, it is difficult to deny the huge wealth generated over the past 30 years, and the powerful motors of urbanisation and aspiration. It is likely that the coming years will see more of the same.

So what does this mean for the rest of the world? So far India has not converted its new-found wealth into commensurate global clout. This vast nation has always punched below its weight on the international stage, other than perhaps during the 1950s, when Jawaharlal Nehru, the independence leader and prime minister, converted moral prestige into influence.

One reason has been the absence of a UN Security Council seat, and the often urgent distractions of a tough neighbourhood. Another is, as former prime minister Manmohan Singh said as recently as 2013, that, despite the boom years, India remains a “poor country”. But others include an under-resourced diplomatic service, an unwillingness to take strong positions on international issues, a weak military and a sense of exceptionalism which means that little that is done overseas – such as driving in lanes, or global norms of insurance of nuclear reactors – is seen as having much relevance to India itself. This latter belief may be partially justified – south Asian problems usually require south Asian solutions – but it doesn’t help India engage globally and win arguments.

This lack of power projection also means India is badly misunderstood. The image of the US overseas incorporates hard elements (a willingness to use military force or to impose trade agreements favouring US businesses) with softer elements (film and TV, music, hamburgers).

It will mean a lot of arguing, and some serious rethinking, in the chancelleries of Paris, Washington and London

One of the consequences of India’s profound lack of hard power is that its image is defined almost entirely by soft elements: Bollywood, Mahatma Gandhi, curry, films such as the Last Best Marigold Hotel or Slumdog Millionaire, and the country’s reputation as a global information technology hub. This distorts the reality.

This distortion is reinforced by the focus on India’s democratic institutions, the widespread use of English and even the enthusiasm for cricket. One result is a sense among many western commentators and politicians that India is a “natural ally”.

Yet there is no immediately obvious reason why a colony that was exploited for 200 years before winning its independence, and that has since maintained an ambivalent relationship with Washington, has been close to Moscow and, at one point, made considerable efforts to befriend Beijing, should align itself with western powers.

Obama and Narendra Modi, the Indian prime minister who won a landslide victory in 2014, have made apparently successful efforts to establish some kind of rapport. And Modi’s visit to London last year was largely viewed as a success. But Modi himself represents, literally and figuratively, a strong conservative, nationalist, Hindu majoritarian strand in India that has existed for at least 150 years, yet barely affects the image of the country overseas.

Some have claimed Modi was elected primarily through the support of industrialists and sections of the media. This is not the case. He won because his nationalist rhetoric and his promise of development was attractive to a large number of his compatriots. This link will not weaken as India’s economy grows and with it, however haphazardly, its influence. The nation is likely to behave on the international stage much like any other power: with a strong sense of its own interests and that its foreign policy goals are legitimate and attainable, with or without western approval.

This does not mean violent clashes, or active animosity, but it will mean an awful lot of arguing, and some serious rethinking, in the chancelleries of Paris, Washington, London and elsewhere.

Jason Burke, until recently the Observer’s south Asia correspondent, will move to Johannesburg as our Africa correspondent this spring