Two Chinas inhabit the American imagination: One is a technology and manufacturing superpower poised to lead the world. The other is an economy that’s on the verge of collapse.

Each reflect a real aspect of China.

One China — let’s call it hopeful China — is defined by companies like the A.I. start-up DeepSeek, the electric vehicle giant BYD and the tech powerhouse Huawei. All are innovation leaders.

Jensen Huang, the chief executive of the Silicon Valley chip giant Nvidia, said China was “not behind” the United States in artificial intelligence development. Quite a few pundits have declared that China would dominate the 21st century.

The other China — gloomy China — tells a different story: sluggish consumer spending, rising unemployment, a chronic housing crisis and a business community bracing for the impact of the trade war.

President Trump, as he tries to negotiate a resolution of a trade war, must reckon with both versions of its arch geopolitical rival.

The stakes have never been higher to understand China. It’s not enough to fear its successes, or take solace in its economic hardships. To know America’s biggest rival requires seeing how the two Chinas are able to coexist.