Last night I watched a group of Chinese doing dance exercises in front of a giant portrait of Deng Xiaoping, the leader who introduced capitalism to communist China in 1978. Here in Shenzhen, across the border from Hong Kong, Deng is a hero because his “reform and opening up” policy has brought huge wealth. Thirty-four years on I think he would have approved of what’s happened in China – it was Deng after all who said, “To get rich is glorious.”

ChinaUp1 China rising, the low profile superpower

But Deng understood that the Americans, who on the face of it welcomed China joining the capitalist club, would nonetheless view the country’s success with suspicion. China’s, he said, would be a “peaceful rise”. That hasn’t stopped American politicians from talking about the “China threat”. Deng advised the Chinese people to “Keep a cool head and maintain a low profile. Never take the lead – but aim to do something big.” Many American politicians believe that now, after three decades of rapid economic growth, China is about to do something very big indeed – replace the US as the world’s superpower. They watch China’s growing diplomatic and military confidence fearing that as China rises so America must decline. Chinese and American leaders deny this, saying the two countries must work together to increase prosperity and maintain peace around the world, but the power balance is shifting and everyone knows it.

That’s the reason both candidates in the US election have been talking tough.

06 lindseychina1 x China rising, the low profile superpower

Mitt Romney has been especially keen to be seen to be “standing up to China”. One constant theme is that China keeps its currency artificially low, so Chinese goods remain cheap, thus undercutting American products and stealing American jobs.

Romney has said he’ll name China a “currency manipulator” on day one in office, triggering all sorts of sanctions. But Americans want to buy cheaply, and China’s policies help contain inflation and make life affordable for millions of Americans. Few in China think policy would really change under Romney. Deng certainly wouldn’t have worried.

“The United States brags about its political system, but the president says one thing during the election, something else when he takes office, something else at midterm and something else when he leaves,” he observed.

Americans who see China as a threat might be surprised to know how the two powers are perceived here in the Middle Kingdom.

Read Matt Frei on America:  US in decline, the new normal?

“Chinese analysts see their country as heir to an agrarian, eastern strategic tradition that is pacifistic, defence-minded, non-expansionist, and ethical,” wrote Andrew Nathan and Andrew Scobell in their essay “How China Sees America,” in this month’s Foreign Affairs. “In contrast they see western strategic culture – especially that of the United States – as militaristic, offense-minded, expansionist and selfish.”

06 lindseychina4 x China rising, the low profile superpower

The wars in Iraq and Afghanistan are frequently cited as evidence of US belligerence, and when Hillary Clinton negotiates the release of a persecuted blind human rights lawyer who’s taken refuge in the US embassy that’s not regarded as a humanitarian gesture. “Chinese officials contend that the United States uses the ideas of democracy and human rights to delegitimise and destabilise regimes that espouse alternative values, such as socialism and Asian-style developmental authoritarianism,” write Nathan and Scobell.

A Chinese businessman I met put it more simply. “We’re becoming more powerful and they don’t like it,” he said.

Follow @lindseyhilsum on Twitter.