With its manned space programme Beijing is boldly going where pretty much everyone else has gone before - but some analysts caution that it is always dangerous to underestimate Chinese ambition, expertise and ability to play the long game.
Last week Chinese explorers achieved a curious high-low national double-first which, according to the many nostalgic supporters of Mao Zedong, the still revered founder of the modern China who died in 1976, was predicted in a poem by the Great Helmsman almost 50 years ago.
"We can clasp the moon in the Ninth Heaven/And seize turtles deep down in the Five Seas," Mao wrote in May 1965, in a poem entitled Reascending Jinggang Mountain.
On Monday three Chinese astronauts, including the country's first woman in space, carried out the first docking with China's orbiting space laboratory Tiangong-1 - Heavenly Palace - making China only the third country with a manned space programme.
Barely a day later, the Jiaolong, a manned submersible, set a new national record for a deep-sea dive of 6,965 metres, in the Mariana Trench in the western Pacific.
The lines, written from the historical perspective of the man who, by force of will and force of arms, had dragged the vast but backward nation into the modern world, were doubtless meant as a celebration of all that China had achieved.
Certainly, reported Xinhua, the state news agency, last week, Chinese "netizens" were busy celebrating the twin feats as exemplars of how much farther China had come since then.
"It is unimaginable that Chairman Mao's wild aspirations have become reality in China today," wrote one user on Sina Weibo, the Chinese equivalent of Twitter. "It's a very proud time to be Chinese."
Another wrote simply: "Did you see that, Grandpa Mao?"
But were China's latest "great leaps" - into the sea and into space - really anything to be proud of?
Take the deep-sea dive. It might have been a national record, but China was merely going where others have been before - and not even as deep.
In the car park of the US Naval National Undersea Museum in Washington can be found the manned submersible Trieste, which made underwater history by touching down on the seabed in the Mariana Trench on January 23, 1960 - at a depth of more than 10,900 metres.
And when it comes to space, the Chinese are light years behind.
For all her increasing financial clout and growing influence in the world, China, which did not make its first manned launch until 2003, appears to be a late entrant in the space race.
Since 2003 there have been only three other major space events. There was a second manned launch with a two-man crew in 2005 and a third, with three on board this time, in 2008, a mission that culminated in the country's first space walk.
Last year the Chinese sent aloft their first space station, the Heavenly Palace 1, but, at about a sixth the size of the International Space Station, it might be described as less a palace and more a garden shed.
And, of course, it's all been done - and then some - before: from Russian Yuri Gagarin's first orbit of Earth on April 12, 1961, and the earliest US Gemini missions during that same year to the landing of the first man on the Moon on July 21, 1969 - eight short years later and almost 43 years to the day before China's latest, more modest space achievement.
"China," sniffed a commentary last week in Time magazine, "is standing on the shoulders of those long-ago giants. You have every reason to be proud if you're able to summit Mt Everest, but don't kid yourself: you ain't Sir Edmund Hillary."
So why are the Chinese bothering?
According to one American strategist and space expert, it would be unwise for the US or anyone else to dismiss Project 921 - the Chinese space programme, a 30-year plan devised in 1992 - as merely an exercise in national ego boosting.
"China is not overtaking the United States in space," Joan Johnson-Freese, professor of national security affairs at the US Naval War College, told CNN last week. "It is, however, advancing."
The execution of China's space programme had "led to 'tortoise and hare' comparisons with the United States", said the author of Heavenly Ambitions: America's Quest to Dominate Space.
"During the Apollo phase, the United States advanced very quickly. In contrast, China launches a mission about every two years, but takes large steps with each one and has a much longer timeline for achieving its goals.
"What China has that the United States lacks - and what may give the Chinese an advantage over the long run - is patience."
Quite whether China's sole aims are peacefully scientific or commercial remains uncertain - this is, after all, a country that still plays its cards close to its chest, and allows the world to know only what it wants it to know. The Chinese media, for instance, has made great play of one touchy-feely "experiment" being conducted by the three astronauts currently orbiting the Earth - the hatching of butterfly pupae in zero gravity.
"Should Americans be worried that China will overtake us in both space exploration and military capability in space?" CNN asked Johnson-Freese, and her answer ("No - not yet") was far from conclusive, or reassuring.
"The United States," she added, "largely knows what space technology China possesses, but it doesn't know what China's intentions are."
There are, says Klaus Becher, managing partner of London-based Knowledge & Analysis, an international policy consultancy specialising in defence and space policy, "plenty of people in America who are genuinely concerned that space build-up in China is of major significance in a strategic sense and a challenge directly to the US".
There is "something to it, but it is also clear that people who say that have an agenda driven by the need to drum up defence dollars".
It is, he believes, irrelevant that China's achievements in space apparently lag behind those of America. "I'm not convinced that space is so high on the agenda of Chinese politics as some people make it sound, but what they are doing is clearly impressive," he says.
But as to exactly why they are doing it, well, that's anyone's guess: "It depends on what you assume their objectives are and who's really behind it. It's a bit difficult to read and I guess everyone who looks at China comes with that observation."
On the one hand, "you have the military, controlling all the assets of the Chinese space sector, from industry to launch and so on. But they don't set the policies - at least, not officially."
Quite possibly China is pursuing a manned space programme "because they get money for it, to keep their space infrastructure going, because it is hugely popular in China, because it enhances the standing of the country and all of that.
"It's something they can do, they are proud of it, so they do it."
But while manned flight grabs the headlines, he says, the true evidence of China's elevation to the status of superpower can be found in a cloud of debris circling 800 kilometres above the Earth.
On January 11, 2007, China launched a rocket that knocked out one of its redundant weather satellites and that, says Becher, "was the most significant Chinese space achievement in the past decade".
The demonstration of military might and precision caused a major international incident because "it contaminated a very useful orbit for many centuries to come, creating danger for people on the Space Station and other satellites".
But a point had been made.
"The people who did that in China didn't understand what they were doing; they just looked at the military advantage of signalling to potential opponents, 'We can shoot down your satellites'.
"It's a capability considered part of what a superpower can do and of course is strategically important because the US is so dependent on its own space infrastructure for its military capability."
In a way, America has only itself to blame for China's burgeoning space programme - for years it refused to let Beijing play with the US-led International Space Station.
For now, at least, China is unlikely to be raining down destruction on America from space. On the other hand, it could soon be raining on everyone's parade when it comes to the profitable business of launching satellites and other commercial payloads.
Last year Yin Liming, president of China Great Wall Industry, told the People's Daily newspaper that his company planned to invest "hundreds of millions of yuan in the next few years for a batch of communications satellites and launch vehicles", with the intention of seizing 10 per cent of the world's market for commercial satellites and 15 per cent of the launch sector by 2015.
It may have taken China a long time to get into space, but then it has always played the long game. As the fifth-century BC Chinese philospher Confucius put it: "It does not matter how slowly you go, so long as you do not stop."
And Mao himself, who rose to power during the Long March, the retreat of the embattled but ultimately victorious Red Army in 1934, would have approved of the naming of the rocket family that first began carrying Chinese ambitions skywards in 1969 and sent aloft the three Chinese astronauts last week: Chang Zheng - or Long March.