When the Cold War ended nearly three decades ago, “we believed that the danger of nuclear annihilation had gone away,” William J. Perry told Retro Report, a series of video documentaries examining how major news stories of the past shape present events. Mr. Perry, an emeritus professor at Stanford University, was defense secretary in the Clinton administration from 1994 to 1997. “We’ve never been able to re-grasp that it’s come back,” he said of the risk, adding ominously that, if anything, “the danger of some kind of a nuclear catastrophe today is actually greater than it was during the Cold War.”

At the moment, it may seem as if reason to fear cataclysm has receded, given that the United States and the two Koreas are engaged in diplomatic maneuvering that could — at least from the American and South Korean vantage — lead to dismantling North Korea’s nuclear stockpile. But this is not the first new dawn on the Korean Peninsula. And a collapse of the negotiations would not be the first failure. There is no guarantee that North Korea and the United States will not return to the bellicosity of just a few months ago, when the North’s leader, Kim Jong-un, said that “a nuclear button is always on my desk” and President Trump responded in a tweet that his own nuclear button was “much bigger & more powerful.”

In the meantime, the leaders of the two countries most capable of mutual annihilation, Mr. Trump and President Vladimir Putin of Russia, have promised to modernize their own arsenals and make them more menacing. Publicly, neither man has shown much interest in renewing soon-to-expire agreements that impose checks on their capabilities, like on-site inspections. That has experts like Mr. Perry worried.

The decades of nuclear standoff between the United States and the old Soviet Union were premised on an assumption that neither side would dare launch an attack because it would invite a devastating counterattack and amount to committing national suicide. But a calculated launching of missiles by one side or the other is not the big scare, Mr. Perry said. What troubles him more is the increased potential for error inherent to increased weaponry: a misread blip on a computer screen or a false alarm like the recent one in Hawaii.

When international tensions are high, as they were in the depths of the Cold War and as they have at times been of late, the risk grows, Mr. Perry said, that “we would blunder into a nuclear war.”

That kind of fear all but defined much of the 1950s and 1960s, vividly captured in popular culture. At about the time that American grade-school children were ducking under their desks, the English author Nevil Shute wrote “On the Beach,” a best-selling novel about nuclear apocalypse that became a 1959 movie. As deadly radiation spreads from the northern hemisphere to the southern, a scientist in Australia explains how humankind stumbled to its doom:

“Everybody had an atomic bomb, and counter-bombs, and counter-counter bombs. The devices outgrew us; we couldn’t control them. I know. I helped build them, God help me. Somewhere, some poor bloke probably looked at a radar screen and thought he saw something. He knew that if he hesitated one-thousandth of a second, his own country would be wiped off the map. So he pushed a button, and the world went crazy.”

The world has come closer to such moments than many people realize.

In September 1983, East-West tensions soared after Soviet missiles shot down a South Korean civilian airliner, killing all 269 people aboard. Having somehow deviated from its charted course and entered prohibited Russian airspace, the plane may have been mistaken for an American spy plane. Less than a month later, a Soviet early warning system appeared to detect the launching of five missiles from an American base. Fortunately, a lieutenant colonel in the Soviet air defenses, acting on intuition, decided after nerve-racking minutes that it was a false alarm.

In October 1960, American radar detected what seemed to be dozens of Soviet missiles headed to the United States. It turned out to be a moonrise over Norway, misinterpreted. In November 1979, someone touched off fears of a Soviet missile attack by mistakenly inserting a “war games” tape into a computer of the North American Air Defense Command. A similar foul-up occurred the following June; apparently a computer chip (cost: 46 cents) had malfunctioned.

“Machines do err, and will err again,” Mr. Perry said, “And humans will err again.”

For Alex Wellerstein, a specialist in the history of nuclear weapons at the Stevens Institute of Technology in Hoboken, N.J., the enemy may be complacency. With the Cold War in the rearview mirror and the Soviet Union long gone, “people don’t think nuclear war is on the table at all,” Mr. Wellerstein told Retro Report. “We stop preparing for it, we stop talking about it for the most part.”

But people must remember, he said, that nuclear missiles are “actual things that might be used in their lifetimes — they’re not fictional creations, they’re not cultural metaphors.”

The panic in Hawaii was a reminder of how easily things could go wrong. It perhaps also reinforced a lesson imparted in another cultural touchstone about nuclear dread. This was the 1983 film “WarGames,” in which a military supercomputer is put in control of the American arsenal. Thinking it is conducting a strategic exercise, the computer prepares to launch actual missiles — until it comes to understand the global devastation it would inflict.

“A strange game,” it concludes. “The only winning move is not to play.”

CLYDE HABERMAN, a regular contributor to Retro Report, has been a reporter, columnist and editorial writer for The New York Times, where he spent nearly 13 years based in Tokyo, Rome and Jerusalem. Subscribe to our newsletter here and follow us on Twitter @RetroReport.

This article first appeared in The New York Times.