We've been close to a nuclear World War III more often than you would like to think.
1. On the evening of October 25, 1962, at the height of the Cuban Missile Crisis, an air force sentry at a military base near Duluth, Minnesota "spotted someone climbing the base fence, shot at the figure, and sounded the sabotage alarm." As alarms at airfields all over the region were sounded, at Volk Field, Wisconsin, the wrong alarm, the one signaling nuclear war (the "P.S., we mean it, this is not a drill" alarm) went off, and pilots scrambled and headed down the runway, being stopped only at the last second by the post commander. The "intruder" was a bear.
2. Also in the midst of the Cuban Missile Crisis, only two days later, October 27, 1962, on the same day that an American U-2 spy plane was shot down over Cuba: At this point, Soviet submarines were being subjected to depth charges to make them rise to the surface (we were unaware they had nuclear weapons aboard). Despite strict orders not to use their nuclear torpedoes absent authorization from Moscow, the three Soviet officers aboard Foxtrot submarine B-59 had decided to use theirs if under attack and unable to reach Moscow but only if all three officers agreed. They were, in fact, unable to reach Moscow, and in the end, one officer, Vasili Alexandrovich Arkipov, finally made the fateful decision not to start WWIII.
3. In 1983, U.S.-NATO military maneuvers in Europe, called "Able Archer 83," were interpreted for a time by the Soviets as the prelude to a -- not so good -- full-scale nuclear attack.
4. On January 25, 1995, technicians at the Olengrosk early warning radar facility detected an unidentified ballistic missile over Norway which appeared to be heading for Russia. Because the missile was manufactured in the United States, its "signature trail" was therefor identified by Russian computers as hostile and apparently fired from a U.S. submarine in the Arctic Sea, even though it was actually only a Norwegian research rocket researching the Northern Lights. President Yeltsin's "nuclear briefcase" was activated and Russian missile submarines ordered to battle stations. Finally, with three minutes to spare, the missile was correctly identified. Happily, for the human race, this incident took place at a time when Yeltsin was President and not earlier (or subsequent) presidents.
But this is the mere tip of the iceberg of close calls known to experts. There have been literally hundreds of false alerts of a nuclear attack in this country alone, triggered by such things as a flock of geese, the rising of the moon, the sun's reflection on a cloud, a strong solar storm, and space debris re-entering the atmosphere. And of course, there have been who knows how many similar or worse incidents in other countries. (From World Peace Through Law, by James Taylor Ranney)
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Truth is...if history teaches us anything, we should know by now that mankind is capable of horrific, and horrifically short-sighted, acts of aggression. Our hope for peaceful coexistence can't reside in the strength of our armaments to deter, or the openness of our hearts to live and let live.
Some trust in chariots and some in horses, but we trust in the name of the Lord our God. (Psalm 20:7 NIV)