The world has rarely seemed more hopeful, or more dangerous. Throughout the globe, great events are in play. In every case, all outcomes are possible, along the spectrum from triumph to disaster. Is this a friendly tide to sweep mankind onwards and upwards, or is it a tsunami?
Many of the answers lie in America. Here again, it is possible to make radically divergent assessments. America could be seen as the world's sole superpower, able to behave accordingly. Militarily, it is unchallengeable. Economically, given other countries' insatiable appetite for greenbacks, it can always buy its way out of the constraints which restrict lesser nations. Yet there is another perspective, in which America is the modern equivalent of Charles , the 16th-century holy Roman emperor. He may have had vast dominions, but he was rarely able to enjoy them. Throughout his reign, there was always trouble in some distant domain.
It would be easy to argue that America, too, is suffering from imperial overstretch. Before Iraq, some American strategists insisted that the US should, and would, be capable of fighting two wars simultaneously. No one now believes that, which restricts Mr Bush's options in both Iran and North Korea. Yet if the principal aim of the Bush foreign policy had been the de-fanging of hostile nations which should not be allowed to possess WMD, it is no longer clear that Iraq should have been the first priority.
North Korea is already a nuclear power, and it seems inevitable that Iran will become one, and remain one. Even US analysts who are basing their hopes on regime change in Iran do not believe that a more liberal, pro-Western government would abandon its nuclear programme. In such hands, nuclear weapons would not be such a threat, but they would encourage further proliferation. That is likely to happen anyway. Within the next 20 years, most middle-ranking powers will have acquired nuclear weaponry. Mandela's South Africa renounced its nuclear arsenal.Everyone applauds the idealism. No one will follow the example.
In a world full of nuclear weapons, no degree of superpower predominance can guarantee invulnerability. That thought has sunk more deeply into the American official psyche than many European policy-makers realise. It accounts for the tone of pessimism in the midst of plenitude which is often detectable below the rhetorical surface, as long as it is not Don Rumsfeld who is talking.
The Americans also have to worry about China, over Taiwan. Sino-American conflict would seem impossible. Without either nation planning it, the two are now locked in economic symbiosis. Rarely if ever before has there been such a vital economic relationship between nations with such different political systems.
That said, anyone who believes that economics prevents war should read Keynes on Central Europe just before the Great War. Capital markets, raw materials, trading patterns, domestic demand, railway systems: everything pointed to growing interdependence, and growing prosperity. Then the armies marched.
It is in no one's interests for the US and China to clash over Taiwan. Apart from a few Cold War nostalgics, most Americans would be content if the Chinese were to woo, seduce and marry the island. In those circumstances, the US would gladly pay for the festivities. But rape would be another matter.
If the Chinese government remained rational, rape would be out of the question. The economic, cultural and educational links between Taiwan and the mainland are constantly increasing, reinforced by a common ethnicity. It should be easy for China and Taiwan to grow together so that the ultimate negotiations merely ratified what had already occurred.
Yet no one can predict the development of Chinese politics over the next few decades. At present, it seems as if China might succeed in a peaceable evolution from authoritarian communism to authoritarian capitalism. The Chinese population has great incentives to remain peaceful. It is not so long ago that around one hundred million Chinese were eating grass in order to stave off starvation, while tens of millions did die. There is widespread gratitude for a political system which feeds everyone; widespread fear that change could lead to chaos.
This did not prevent Tiananmen Square. The Chinese are not a race of automata and there may be a time limit beyond which their government will not be able to defy the laws of Marxism. The old boy had a point. There is a relationship between economics and politics. Eventually, economic freedom will lead to demands for political rights. That might not seem a threat to the West, but what if another botched democratic process - Tiananmen II - led to repressive generals taking over in Peking? They might try to buttress their legitimacy by arousing nationalistic passions through a confrontation over Taiwan. Even if actual war were averted, that could be the worst peacetime shock to the world economy since 1929.
Iran, North Korea, China, not to mention Russia: there we are dealing with known unknowns, in Donald Rumsfeld's useful phrase. But there is also his equally useful "unknown unknowns". What would happen if Musharraf of Pakistan was assassinated tomorrow? Or Mubarak of Egypt? How long can the Saudi monarchy survive? On paper, American power is awesome. In vital regions, it could easily appear inadequate.
But not all is gloom. Elections have been held in Afghanistan. In a country which appears purpose-built to be inhospitable to electoral politics and the rule of law, there is a sort of democratic government. If Afghanistan, why not Iraq? If Iraq, why not Palestine?
I was in Israel recently and saw signs of movement. At the age of 76, Ariel Sharon has decided to crown his career by making peace with the Palestinians. This is a development of vital importance. Until recently, it seemed inconceivable that he could turn into a peacemaker or would ever agree to the territorial concessions - as he would see them - necessary to give the Palestinians a state that looked like one. Now, he seems to have changed, and he has never been known to falter in pursuit of his objectives.
In politics, there is no more exhilarating spectacle than an old man in a hurry. The consequences can be disruptive, or creative, or both. In General Sharon's case, he may have created a once in a generation chance for a settlement between the Israelis and the Palestinians. If that were to happen, while a democratic government was establishing itself in Baghdad, the Middle East would suddenly seem more manageable; the rest of the world, less dangerous.
Even though some people will always deny it, the credit for this would lie with George Bush. Though there is no mathematically provable relationship between the President's decision to go to war with Iraq and Mr Sharon's new openness to peace, the latter would not have happened without the former. George Bush has moved all the region's tectonic plates.
On 11 September 2001, al-Qa'ida set out to change the world. They succeeded, but not in the way that they wanted. Instead, George Bush took up the challenge of change. As long as his policy is poised between failure and success, the world will be poised between hazard and hope.