Life, they believe, is an unwanted by-product. The multiverse would be more reliable if there wasn't any. Unfortunately, there are rules. Gravity is not allowed to increase a millionfold and laminate all local life forms to the bedrock, highly desirable though that would appear to be. Simply mugging life forms merely walking, flying, swimming or oozing past would attract attention from higher authority, which Auditors dread.

They are weak, not very clever and always afraid. But they can be subtle. And the wonderful thing about intelligent life, they have discovered, is that with some care it can be persuaded to destroy itself.

MANIFEST DESTINY

THE WIZARDS ARE DISCOVERING THAT changing history is not so easy, even when you've got a time machine. The Auditors aren't helping, but history has its own metaphorical Auditor, often called `historical inertia'.

Inertia is the innate tendency of moving objects to continue moving along much the same track, even if you try to divert them; it is a consequence of Newton's laws of motion. Historical inertia has a similar effect but a different cause: changing a single historical event, however important it may appear, may have no significant effect on the social context that directs the path of history.

Imagine we've got a time machine, and go back to the past. Not too far, just to the assassination of Abraham Lincoln. In our history, the President lived till the following morning, so a tiny deflection of the assassin's bullet could make all the difference. So we arrange a small deflection, and he is hit but recovers, with no noticeable brain damage. He cuts a couple of appointments while he recuperates, and then he goes on to do ... what?

We don't know anything about that new version of history.

Or do we? Of course we do. He doesn't turn into a hippopotamus, for a start, or a Ford Model T Or disappear. He goes on being President Abraham Lincoln, hedged in by all the political expediencies and impossibilities that existed in our version of history and still exist in his.

The counterfactual [1] scenario of a live Lincoln raises many questions. How much do you think being the American President is like driving a car, going where you want to? Or sitting in a train, observing the terrain that others drive you through?

Somewhere in between, no doubt.

Ordinarily, we don't have to think much about counterfactuals, precisely because they are contrary to fact. But mathematicians think about them all the time -'if what I think happens is wrong, what can I deduce that might prove it wrong?' Any consideration of phase spaces automatically gets tangled up in worlds of if. You don't really understand history unless you can take a stab at what might have happened if some major historical event had not occurred. That's a good way to appreciate the significance of that event, for a start.

In that spirit, let's think about that altered `now': the beginning of the West's third millennium of history, but without Lincoln having been assassinated in its past. What would your morning newspaper be called? Would it be different? Would you still be having much the same breakfast ritual, bacon and eggs and a sausage perhaps? What about the World Wars? Hiroshima?

A very large number of stories have been written with this kind of theme: Wilson Tucker's The Lincoln Hunters is set in such an 'alternat(iv)e universe' and tackles the Lincoln question.

Curious things happen in our minds when they are presented with any fictional world. Consider for a moment the London of the late nineteenth century. It did have Jack the Ripper, and we can wonder about the real-world puzzle of who he was. It had Darwin, Huxley and Wallace, too. But it did not have Sherlock Holmes, Dracula, Nicholas Nickleby, or Mr Polly. Nevertheless, some of the best

[1] Counterfactual: a more acceptable word for what has for a long time been a very common feature of science fiction, the 'alternate world' or 'worlds of if story (there was a pulp SF magazine in the 1950s called Worlds of If, in fact). 'Counterfactual' is now used when said stories are written by real writers and historians, to save them the indignity of sharing a genre with all those strange sci-fi people.

portrayals of the Victorian world are centred around those characters. Sometimes the fictional portrayals are intended to paint a humorous gloss on the society of the period. The Flintstones put just such a gloss on human prehistory, so much so that in order to think rationally about our evolution we must excise all those images, which is probably an impossible task.

Sherlock Holmes and Mr Polly were Victorians in just the same sense that the tyrannosaur and triceratops in Jurassic Park were dinosaurs. When we envisage Triceratops, we cannot avoid the memory of that warty purple-spotted Jurassic Park skin, as the beast lies on its side, breathing stertorously. And Tyrannosaur, in our mind's eye, is running after the jeep, bobbing its head like a bird. When we envisage late nineteenth-century Baker Street it's very difficult not to see Holmes and Watson (probably in one of their filmic versions) hailing a four-wheeler, off to solve another crime. Our pictures of the past are a mixture of real historical figures and scenarios peopled by fictional entities, and it's difficult to keep them apart, especially as films and TV series acquire better technologies to latch into those spurious pictures in our heads.

The 1930s philosopher George Herbert Mead made much of the rather obvious point that the present, in a causal world, does not only determine (`constrain' if you prefer) the future, it also affects the past, in just this sense: if I discover a new fact about the present, then the (conceptual) past that led up to the new present must also have been different. Mead thereby enabled a rather cute way of seeing how good the portrayals of Sherlock Holmes, or of the Jurassic Park tyrannosaur, are. If my picture of the present isn't altered at all by the presence or absence of Sherlock Holmes in the 1880s, or if my construction of the present by evolutionary processes isn't altered at all by seeing Jurassic Park, then these are consistent inventions.

Dracula and the Flintstones are inconsistent inventions: if they really existed in our past; then the present isn't what we think it is. Much of the fun of `worlds of if' stories, and of many consistent fictions like The Three Musketeers, is that they show closed-loop causalities in our apparent past. Whether or not D'Artagnan had aggregated the Musketeers and thereby brought into being much of the causal history of seventeenth-century France, children of later centuries would learn the same history in the textbooks. Ultimately, consistent historical fictions make no difference.

In The Science of Discworld II we played with this idea in several ways: the, presence of the Elves was, surprisingly, consistent with our history; stopping them led to stagnation of humans and had to be reversed. In this book the meddling of the Unseen University wizards, in Victorian history this time, is trying to create an apparently internally caused history in which Darwin wrote The Origin of Species and not Theology of Species. We are going to use this trick to illuminate the causalities of human history.

In order to do this convincingly, we must make the Discworld intrusions consistent, but even then we must address the convergence/ divergence problem, which is this. Would such a meddled-with world converge on to ours, demonstrating that history is stable, or would any tiny difference start a divergence that became wider and wider, proving history to be unstable?

Most people think the latter. Indeed, even the wildly imaginative physicists who believe that a new world history is created by each and every decision in this universe, spawning new universes in which the other choices were implemented, don't imagine that the histories converge. No, each universe goes its own way, spitting out new and divergent universes as it goes. The Trousers of Time are a tree: their legs can branch but never merge.