While widely derided as science fiction, it was a fundamental shift away from the doctrine of Mutually Assured Destruction which for four decades had dissuaded the American and Soviet empires from settling their differences once and for all.
For the Soviet leaders, already deeply suspicious of Reagan because of his history of bellicose anti-communism, the SDI was a clear sign America was now thinking the unthinkable: that there was such a thing as a winnable nuclear war.
In September 1983, a Soviet fighter plane shot down a Korean Airlines 747 with 269 passengers and crew on a flight from New York to Seoul.
The Soviets claimed KAL007 was on a spying mission — because of navigation and instrument error the plane had strayed into Soviet airspace.
Take the outcry over the downing of MH17 and multiply it by 10 and you'd be somewhere close to the level of acrimony this incident generated.
Two months later, the American-led Nato alliance started Able Archer 83, a huge military exercise that simulated conflict up to Defcon 1 — nuclear war imminent.
The combination of high tension and the realistic nature of the exercise persuaded some in the Kremlin and the Soviet High Command that Able Archer was an elaborate ruse concealing preparations for a pre-emptive strike.
The USSR put its entire arsenal into actual — as opposed to simulated — launch mode, one command away from all-out nuclear war.
It was against this backdrop that the new Labour Government headed by David Lange announced in mid-1984 that nuclear-armed and powered ships would not be admitted to New Zealand ports, thereby setting in motion the train of events culminating in the US suspending its obligations under the Anzus treaty and recategorising us as a friend, not an ally.
A combination of isolation and introspection sometimes causes us to ignore or fail to appreciate the interconnectedness of events. We saw the anti-nuclear stance as being essentially about us, a declaration of independence and principled stand for a self-evidently good cause.
In most Western capitals it was viewed as part of a big picture, an act of anti-solidarity at a critical period in world affairs that had its origins in the pernicious notion of moral equivalence — that the only real difference between the USA and USSR was a few letters of the alphabet.
Three decades on, Russia — or its proxies — seems to have struck again, bringing down another airliner and compounding the offence with obfuscation and disrespect for the victims.
Watching from a Western European perspective — this column was written in a swelteringly hot Paris — the interconnectedness of events is apparent, but the situation seems less ominous.
Tit-for-tat sanctions could lead to Russia halting its oil and gas exports in the depths of winter. Moscow's neo-imperialists may decide they have little to lose and therefore this is as good a time as any to extend their borders.
It's hard to believe, however, that either side has any desire to plunge Europe back into the state of dread that prevailed in 1983/84.
Hopefully some good will come of this tragedy. It's probably too much to expect contrition or compassion from Mother Russia — that has never been her style — but in his private moments, Vladimir Putin must be questioning his decision to unleash forces he cannot ultimately control and weighing the domestic rewards of adventurism against the prospect of isolation in an interconnected world.
