The United States faces a new nuclear power ruled by a communist dictator. Washington is worried that the leadership of that country is crazy enough to use its new weapons — even against the United States. Meanwhile, other countries fear that the “madman” in the Oval Office might just launch a pre-emptive nuclear attack.

This description captures the situation today, with U.S. President Donald Trump facing off against North Korean leader Kim Jong-un.

But it also describes a similar conflict in the late 1960s, between the United States and China. That confrontation ended not in war but in detente and a close economic relationship between the two countries. It’s an important reminder that diplomacy can work even in seemingly intractable situations.

In the early 1960s, the United States was terrified that Communist China would acquire a nuclear weapon. By 1964, China tested its first nuclear bomb. Two years later, the Cultural Revolution began, and China descended into political chaos.

Even though the Cultural Revolution would last for the next 10 years and Chinese leader Mao Zedong became increasingly senile during this period, the United States made a strategic decision at the beginning of the 1970s to engage the leadership in Beijing.

This detente started out with highly secret negotiations conducted by national security adviser Henry Kissinger. The United States was still deeply involved in the Vietnam War, and President Richard Nixon didn’t want to give the impression that he was weak on communism.

Indeed, the president was projecting the image of a “madman” on the theory that North Vietnam would accede to U.S. demands for fear of being hit by a nuclear strike. Since he had credibility as a hardliner, Nixon ultimately could sell a deal with China to Congress and the American public.

Today, the United States faces a leadership in Pyongyang that is rhetorically aggressive — and a terrible abuser of human rights at home — but a good deal less ideological than Beijing was in the late 1960s. North Korea wants a nuclear weapon for quite rational reasons: to deter any possible attacks from outside and to balance the overwhelming conventional military edge maintained by the United States and South Korea.

North Korea has also demonstrated that it’s quite pragmatic. It will work with anyone — churches, multinational corporations — if it’s a win-win deal.

North Korea has even negotiated successfully with the United States on nuclear issues: with the Clinton administration in 1994 and the Bush administration in 2005. Although it might be very difficult to negotiate away the current nuclear program, the United States could still work toward a freeze on Pyongyang’s nuclear capability and a moratorium on missile launches.

But that means, as with China in the 1970s, giving North Korea some of what it wants: a place at the international table, a recognition of its sovereignty, and some stake in the global economy.

North Korea, of course, is different from China. It’s a much smaller country, with a consumer market that doesn’t much interest U.S. businesses. Nor does it represent a major geopolitical counterforce, as China once did against the Soviet Union.

Still, despite his “fire and fury” rhetoric, Donald Trump might be persuaded to engage Pyongyang.

First, Trump wants to prove that he’s a winning dealmaker. What better way to prove that than to negotiate an agreement with Pyongyang that eluded President Obama.

Second, Trump loves to break new ground with his real estate deals. A deal that opened North Korea to U.S. foreign investment, and that included an option for a Trump Hotel Pyongyang, would be geopolitical and corporate twofer.

Third, the Trump administration has been casting around for ways to reduce Chinese influence in the world. Driving a wedge between Beijing and Pyongyang could satisfy Trump’s desire to wrangle some leverage over China.

Of course, the most important reason to support negotiations with North Korea is to avoid a catastrophic war that would leave hundreds of thousands dead. In the 1970s, when it was still knee-deep in the Vietnam War, the United States wisely decided not to denuclearize China by force and possibly spark World War III.

In the 2010s, still knee-deep in the Afghanistan War (among others), the Trump administration would be wise to learn from that example.