Given the times, these were bold words indeed. In the years it took the message to travel from his cell to his supporters, Margaret Thatcher was elected and Ronald Reagan was on his way to the White House. While two of apartheid's most powerful supporters came to office, the ANC's principal backer, the Soviet Union, was in inexorable decline. When the uprising took place, Mandela had already served 13 years in prison; it would be another 14 before he would emerge a free man. In short, victory was anything but certain.
There is a necessary psychological optimism that goes with progressive politics. Its culture hinges on the notion that a better world is possible and that a critical mass of people could rise to the challenge of creating it. It is rooted in the belief that there is an essential decency in humanity that, given sufficient political space, economic resources and cultural capital, can override naked, narrow and short-term self-interest and be translated into power.
There are times, such as during the euphoria of Mandela's release, when such optimism appears justified. There are others, such as after the Soweto uprising, when it seems deluded. Now, the week after a dismal Labour party conference and the day before Arnold Schwarzenegger is set to become governor of California, it feels like the latter.
In Britain we have a war-mongering, privatising, race-baiting administration that governs in the name of a party set up to represent the interests of working people. In America, the most rightwing Republican party since Nixon's time controls the presidency and both houses of Congress. Israel is intent on building its own version of the Berlin wall through Palestinian land. Fundamentalism, be it Christian, Islamic or Hindu, is on the rise, with all the intolerance and violence that goes with it.
At home, the largest demonstration, produced by one of the most broad-based political movements in British history, failed in its central objective. We did not stop the war. In short, there seems little to feel optimistic about.
And yet it is in these bleakest of moments that optimism on the left is most crucial. Extinguish the flame and there is no torch to pass on in more hopeful times. Wishful thinking will not help us. But a hard-headed assessment of what has been achieved can provide the basis for working out what still can be done.
First, we must recognise that the anti-war movement had a decisive impact on exposing the bankrupt rationale of attacking Iraq. This was no mean feat. Neither Bush nor Blair would have bothered trying to persuade the UN to give its blessing were it not for the pressure they were under. The fact that they failed showed the war for what it was - a criminal act of military violence expressly executed against the global will.
The implications of this exposure are anything but abstract. It explains the reluctance of other nations to relieve America of the burden of clearing up its mistakes, and has left Blair and Bush isolated on the world stage. It contributed significantly to the critical climate that produced the Hutton inquiry and the row over Bush's misleading comments in his state of the union speech.
The anti-war movement got the German chancellor, Gerhard Schröder, re-elected, and has pushed the centre of gravity in the Democratic primaries in a more progressive direction. Political leaders need not only geographical but also ideological constituencies. Over the past two years the left has built a strong enough base to support those who chose to challenge American hegemony.
True, none of this has saved Iraqi lives. But with ratings for Bush and Blair plummeting, it may keep Iranians, North Koreans or whoever else they are considering bombing out of harm's way.
We should also be buoyed by the fact that the sweep of the left's analysis since the beginning of the war on terror has been proved correct. We said the bombing would not stamp out terrorism - the atrocities in Bali, Jakarta and Mombasa show it hasn't - but fuel resentment that would create more terrorists; and Iraq is a far greater threat to global security than six months ago.
With each passing day these criticisms prove more prescient. We argued that the war was a bad idea, even if Saddam did have weapons of mass destruction - given enough time the inspectors would have found them. News that he didn't have them blows away the final fig leaf and leaves the emperors naked. Given the thousands who have been killed so far, this is not a victory. But the fact that we have understood the problem means that, unlike Blair and Bush, we are at least theoretically equipped to resolve it.
The issue, as ever on the left, is how to convert theory into practice. The war exposed the global crisis in democratic legitimacy. Not one national poll, including in the US, supported a US-led war without UN support. That it happened begs the question of how we get rid of these people who have been so bare-faced in their lies, so brutal in their destruction and so bold in defence of both.
By far the greatest weakness of the left is translating the energy of the popular movements into a potent electoral force. This is the source of our pessimism - the despondency brought on by the lack of any obvious alternative, which in Britain has led to the rise of the far right and the decline in voter turnout.
With a few exceptions (notably in Scotland), the left's electoral challenges to the status quo have proved either reckless or ineffectual. The Green candidate Ralph Nader made a crucial difference in the last US election, but since then he has failed to do anything that would make that difference count. In the French presidential elections last year, 21% of the vote went to six hard-left and green candidates. Meanwhile, the socialists were pipped into second place by the National Front by 0.7%. The left was forced to vote for Jacques Chirac in the second round just to keep the fascists out.
This cannot go on. The notion that a better world is possible should always drive us. But the awareness that a worse world is possible should, at times, encourage us to change direction. Whether we should forgo trying to create political parties from scratch and build movements that can keep those that already exist in check is a moot point.
We have not been able to halt the political degradation that has led to war and the erosion of civil liberties. But we have slowed its pace and shaped a clearer understanding of what is at stake. In the words of Mandela, who had 27 years to ponder on how and when hope can curdle into cynicism or flourish into resistance: "Much has been achieved and much remains to be done."