The Science of Discworld III - Darwin's Watch

16. 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[44] 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 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.

The Worlds of If stories were divided on this issue. Some had each tiny change in the past getting amplified, resulting in vast changes now: we've mentioned Bradbury's story where you trod on a butterfly in the far past, on a dinosaur hunt, and came back to find a fascist regime. Or the changes you made were all wiped out, because there was a gigantic all-powerful inertia-of-events Kismet that you couldn't change. However you tried to avoid your fate, that only made it more certain to happen. And some stories took a middle way; some things converged and others didn't.

This, we think, is the rational way to think about time travel and altering the past.

After all, we don't change the rules by which the past works. Gravity still operates, sodium chloride crystals are still cubical, people fall in and out of love, misers hoard and spendthrifts squander. What we change is what physicists call the `initial conditions'. We change the positions of a few of the pieces on the Great Chessboard of Life, The Universe and Everything, but we still keep to the rules of chess. That's how the wizards operated in The Science of Discworld II. They went back in time to remove the Elves from the game board; then they went back again to stop themselves making that mistake.

We are now ready to think about our question above: would the names of newspapers have changed if Abraham Lincoln had lived to a ripe old age?

Perhaps some of them would, because some cultures would have become rather different. Perhaps Quebec wouldn't have been French; perhaps New York would have been Dutch. But names like Daily Mail, Daily News and New York Times are so obvious, so appropriate, that even if the Roman Empire were still running things, the Latin equivalents would seem fitting. Someone would have invented flush toilets, and there would have been a steam engine time, when several people invented steam power. Some things in Western culture seem so likely, from toilet paper on up to (as soon as paper is invented) daily newspapers to plastics to artificial wood ... Technology seems to have a set of rules for its advancement, so that it seems rational to expect gramophones of some kind if people make music with musical instruments, then tape players when people get used to electricity and its possibilities for amplifi cation. Then from analogue to digital, to computers ... some things seem inevitable.

Perhaps this feeling is misleading, but it's silly to insist that absolutely everything in a slightly divergent future has to end up different.

Organic evolution has lessons for us here, and these lessons can instruct us about how likely various advances in animal organisation were. Innovations like insect wings, vertebrate jaws, photosynthesis, life coming out from the seas on to the land ... if we ran evolution on Earth again, would the same things happen? If we went back to the beginning of life on this planet, and killed it, would another system evolve and give us a whole different range of creatures, or would Earth remain lifeless? Or would we be unable to decide whether we'd done anything, because everything would be just the same the second time around?

If history `healed up', we wouldn't be able to tell if it was the second, or the hundredth, or the millionth time around - each time sooner or later producing a version of us, whose time machine goes back to The Origin. There would be a consistent time loop, as happened with the Elves in The Science of Discworld II. If life is `easy' to originate (and the evidence does look that way) then this isn't an exercise in going back and killing your grandfather, or if it is, your grandfather is a vampire and doesn't remain killed. If life is easy to invent, then preventing it happening once, or a million times, will make no difference in the long run. The same process that generated it will happen again.

Looking at the panorama of life on this planet, in time as well as space, we can see that there are two kinds of evolutionary innovation. Photosynthesis, flight, fur, sex, and jointed limbs have all arisen independently in several different lineages. Surely, like toilet paper, we would expect to see them again each time we ran life on Earth.

And, presumably, we'll see them on other aqueous planets when we explore our local region of the galaxy. Such evolutionary attractors are called `universals', in contrast to 'parochials': unlikely innovations that have happened only once in Earth's history.

The classic parochial is the curious suite of characters possessed by land vertebrates, because a particular species of Devonian fish succeeded in invading the land in our, real, history. Those fishes' descendants were amphibians, reptiles, birds, and mammals - including us. Jointed limbs are a universal innovation. The limbs of spiders, hydraulically operated, differ in detail from the limbs of mammals, and were presumably acquired via a different ancestor, perhaps an earlier arthropod proto-spider. The mammalian internal skeleton, with one bone at the body end, then two, then a wrist or ankle, then five lines of bones for fingers or toes, was an independent evolution of the same universal trick.

This highly unlikely combination now occurs in all land vertebrates (except most of the legless ones), because they are all descended from those fishes that came out of the water to colonise the land. Other parochials are feathers and teeth (of the kind that evolved from scales, which are what we have). And, especially, each of the special body-plans that characterise Earth's animals and plants: mammal, insect, rotifer, trilobite, squid, conifer, orchid ... None of these would appear again after a rerun of Earth's evolutionary history, nor would we find exact replicas on other aqueous planets.

We would expect much the same processes to occur, though, in a repeat run of Earth or on another similar world: an atmosphere far from chemical equilibrium as life forms pump up their chemistry using light; planktonic layers of the seas colonised by the larvae of sedentary animals; flying creatures of many kinds. Such ecosystems would also probably have `layers', a hierarchical structure, fundamentally similar to the ecosystems that have emerged in so many different circumstances on Earth. So there would be 'plantlike' creatures, a productive majority of the biomass (like Earth's grass or marine algae). These would be browsed by tiny animals (mites, grasshoppers) and by larger animals (rabbits, antelopes), with a few very large creatures (elephants, whales). Comparable evolutionary histories would lead to the same dramatic scenarios, but performed by different actors.

The central lesson is that although natural selection has a very varied base to work with (recombinations of ancient mutations, differently assorted in all those `waste' progeny), clear large-scale themes emerge. Marine predators, such as sharks, dolphins, and ichthyosaurs all have much the same shape as barracuda, because hydrodynamic efficiency dictates that streamlining will catch you more prey, more cheaply. Very different lineages of planktonic larvae all have long spines or other extensions of the body to restrain the tendency to fall or rise because their density differs from that of seawater, and most of them pump ions in or out to adjust their densities too. As soon as creatures acquire blood systems, other creatures - leeches, fleas, mosquitoes - develop puncture tools to exploit them, and tiny parasites exploit both the blood as food and the bloodsuckers as postal systems. Examples are malaria, sleeping-sickness, and leishmaniasis in humans, and lots of other parasitic diseases in reptiles, fishes, and octopuses.

Large-scale themes may be the obvious lesson, but the last examples reveal a more important one: organisms mostly form their own environments, and nearly all of the important context for organisms is other organisms.

Human social history is like evolutionary history. We like to organise it into stories, but that's not how it really works. History, too, can be convergent or divergent. It seems quite sensible to believe that small changes mostly get smeared out, or lost in the noise, so that big changes are needed to divert the course of history. But anyone familiar with chaos theory will also expect some tiny differences to set off divergent histories, drifting progressively further away from what might have happened otherwise.

Changing history is a theme of time-travel stories, and the two issues come together in those stories called `worlds of if.

We have the strongest feeling that what we do, even what we decide, does change history. If I decide, now, not to go and meet Auntie Janie at the train station even though she's expecting me because I told her I would ... the universe will take a different path from the one it would have taken if I had done the expected. But we've just seen that even saving Abraham Lincoln from the assassin would have the tiniest, most local, of effects. Neighbours such as the gas-bag aliens on Jupiter wouldn't notice Lincoln's survival at all, or at least not for a very long time. After all, we haven't yet noticed them[45].

In fact, how will they, or we, notice? How will we be able to say, `Just a minute, this newspaper shouldn't be called the Daily Echo ... There must have been a time traveller interfering, so that we're now in the wrong leg of the Trousers of Time'?

Auntie Janie making her own way from the station won't topple empires - unless you believe, with Francis Thompson's The Mistress of Vision, that All things by immortal power Near or far Hiddenly To each other linked are That thou canst not stir a flower Without troubling of a star.

That is, all contingent chaos butterflies are responsible in some sense for all important events like hurricanes and typhoons - and newspaper titles. When a typhoon, or a newspaper tycoon, topples an empire, that event is caused by everything, all those butterflies, that preceded it. Because change in any one - or perhaps just in one of a very large number - can derail the important event.

So everything must be caused by everything before it, not just by a thin string of causality.

We think about causality as a thin string, a linear chain of events, link following link following link ... probably because that's the only way we can hold any kind of causal sequence in our minds. As we'll see, that's how we deal with our own memories and intentions, but none of this means that the universe can isolate such a causal string antecedent to any event at all, important or not. And surely 'important' or `trivial' is usually human judgement, unless the universe really does `smear out' most small changes (whatever that means), and major events are those whose singular influence can be distinguished at later times.

Because they are stories, committed to the way our minds work and not to the way the universe works its own causality, most timetravel stories assume that a big (localised) change is needed to have a big effect - kill Napoleon, invade China ... or save Lincoln. And time travel stories have another convention, another `conceit', because they are stories, nearer fee-fi-fo-fum than physics. This is the remembered timeline of the traveller. Usually the plot depends on it being unique to him. When he comes back to his present he remembers stepping on the butterfly, or killing his grandfather, or telling Leonardo about submarines. .. but no one else is conscious of anything other than their `altered' present.

Let's move from large events, large or small causes, to how we influence the apparent causality in our own lives. We have invented a very strange oxymoron to describe this: `free will'. These words appear prominently on the label of the can of worms called `determinism'. In Figments of Reality we titled the free will chapter: `We wanted to have a chapter on free will, but we decided not to, so here it is' in order to expose the paradoxical nature of the whole idea. Dennett's recent book Freedom Evolves is a very powerful treatment of the same topic. He shows that in regard to `free will' it doesn't matter whether the universe, including humans, is deterministic. Even if we can do only what we must, there are ways to make the inevitable evitable. Even if it is all butterflies, if tiny differences chaotically determine large historical trends, nevertheless creatures as evolved as us can have `the only free will worth having', according to Dennett. He writes of dodging a baseball coming for his face, and this being perhaps a culmination of a causal chain going right back to the Big Bang - yet if it will help his team, he might let it hit his face.

But then, what decides it is: will it help his team? That's not a free choice.

Inevitable, evitable.

Dennett's best example is more ancient: Odysseus's ship approaching the Sirens. Inevitably, if his men hear the Sirens' song, they will steer the ship on to the rocks. But the steersman must be able to hear the surf, so there seems no way to avoid their lure. Odysseus has himself lashed to the mast, while all his sailors plug their ears with wax so they cannot hear the Sirens. The vital issue for Dennett is that humans, and on this planet probably only humans, have evolved several stages beyond the observing-and-reacting that even quite advanced animals do. We observed ourselves and others observing, so got more context to embed our behaviour in - including our prospective behaviour. Then we developed a tactic of labelling good and bad imaginary outcomes, just as we labelled our memories with emotional tags. We, and some other apes - perhaps also dolphins, perhaps even some parrots - developed a `theory of mind', a way to imagine ourselves or others in invented scenarios and to anticipate the associated feelings and responses. Then we learned to run more than one scenario: `But on the other hand, if we did so-and-so, the lion couldn't get us anyway...', and that trick soon became a major part of our survival strategy. So with Odysseus ... and fiction ... and particularly that dissection of hypothetical alternatives that we call a time-travel story.

In our minds, we can hold many possible histories, just as Mead showed that every discovery about today implies a different past leading up to it. But whether there is any sense in which the universe has several possible pasts (or futures) is a much more difficult question. We've argued that popularisations of quantum indeterminacy, particularly the many-worlds model, have got confused about this. They tell us that the universe branches at every decision point, whereas we think that people have to invent a different mental causal path, a different explanatory history, for each possible present or future.

Antonio Damasio has written three books: Looking for Spinoza, Descartes' Error, and The Feeling of What Happens. These are popular accounts of what we know about the important attributes of our minds. He has documented our discoveries, now that we can use various experimental techniques to `watch the brain thinking' and see how the different parts of the brain are involved in what we feel about the things we think. We tend to forget that our brains are continually interacting with our bodies, which supply the brain with stance-determining hormones for longer-term behaviour, and moodchanging emotion-provoking chemicals for short-term modulation of our intentions and feelings, directing our thoughts.

According to these books, the result of having lived with a brain which we think we direct using a kind of tiller, but which actually is continually affected by cross-winds, occasional storms, rain and warm sun that provokes us into lazy days, is that we have evolved a series of memories with different flavours. Or, the result of having lived with a brain that we think we direct using a kind of automobile steering wheel and foot controls, but whose route is actually continually affected by long-term goals that change (`Let's go to a hotel, not to Auntie Janie's again'), short-term road signs and other traffic, is that we have evolved a series of memories with different flavours. Or, each of us has a personal history which we explain internally by feelings attached to emotional memories, so we have evolved a series of memories with different flavours.

Damasio has imported emotional biasing into how we think about our own intentions, choices, other people, memories, and prospective plans. He claims that this is what emotion is `for', and most psychologists now agree that emotionally labelled memories are the effect of having a brain whose interaction with its body paints emotions on to memories and intentions.

We habitually assume that real physical history, and particularly social history, works the same way as our own personal histories, with events labelled `good' or `bad' ... but it doesn't. It's misleading to think of the Big Bang, for example, as an explosion like a bomb or a firework, seen from outside. The whole point of the Big Bang metaphor is that at the moment the universe was bom, there was no outside. More subtly, perhaps, we tend to think of the birth of the universe in the same way that we think of our own birth, or even our conception.

Real history, post whatever the Big Bang `really' was, relies on the accumulation of countless tiny sequences of cause-and-effect. As soon as we begin to think about what any of these sequences looks like, taking it out of the context that drives it, we lose its causality. This seething sea of processes and appearances and disappearances, where no causality can be isolated, is sometimes called `Ant Country'. The name reflects three features: the seething, apparently purposeless activity of ants, which, in aggregate, makes ant colonies work; the metaphorical Aunt Hillary in Douglas Hofstadter's Godel, Fscber, Bach, who was a sentient anthill and recognised the approach of her friend the anteater because some of her constituent ants panicked; and Langton's Ant, a simple cellular automaton, which shows that even if we know all the rules that govern a system, its behaviour cannot be predicted except by running the rules and seeing what happens. Which in most people's book is not `prediction' at all.

For similar reasons, it is impossible to forecast the weather accurately, even a few weeks ahead. Yet, despite this apparent absence of causality at the micro-levels of weather, the impossibility of isolating causality in the swirling butterflies ... despite the chaotic nature of meteorology in both the large and the small, weather makes sense. So does a stone tumbling downhill. So does a lot of physics, engineering, and aeronautics: we can build a Boeing 747 that flies reliably. Nevertheless, all of our physical models are rooted in brains that get most of their perceptions wrong.

Shouting at the monkeys in the next tree. That's what brains evolved to do. Not mathematics and physics.

We get ecology and evolution mostly right, but often wrong, for the same reasons. The scenarios we build don't work, they're as false to fact as `weather'. But we can't help building them, and they're useful sufficiently often to be `good enough for government work'.

To underline this point, here's an important evolutionary example. Think of the first land vertebrate, that fish that came out of the water. We have the strongest feeling that if we took a time machine back to the Devonian, when that first important fish was emerging from the sea, there ought to be a moment that we could isolate: `Look, by wriggling out on to the mud that female has escaped that predator, so she's lived to lay her eggs, and some of them will become our ancestors ... If she hadn't got those leggy fins, she wouldn't quite have made it, and we wouldn't be here.'

Grandfather paradox again? Not quite, but we can illuminate the grandfather paradox neatly with this example. Ask yourself what would happen if you killed that fish. Would humanity never have happened? Not at all. By isolating a single event, we have tried mentally to make history follow a thin thread of causality. But we made the Adam-and-Eve mistake: ancestors don't get fewer as you go back, they multiply. You have two parents, four grandparents, maybe only seven great-grand parents, because cousin marriages were commoner then. By the time you've gone back a couple of dozen generations, a significant proportion of all the breeders of that period were your ancestors. That's why everyone finds some famous ancestors when they look - and the fact that famous people were rich and powerful and sexually successful helps too, so that they are reproductively better represented in that generation's descendants.

Note that we said `breeders' and `many'. Nearly all sexually produced creatures don't breed, including humans of most previous generations. Not only are most of the people alive at that previous generation young children who won't survive to breed; many of the apparently successful breeders contribute to lineages that die out before they get to the present day, because they are excluded from the limited ecosystem by more successful lineages as the generations pass.

So when we look at those Devonian fishes, there simply isn't just one that was our ancestor. All of the breeders, a very unsystematic small proportion of the fish population, contributed to the recombining and mutating mix of genes that passed down from those fishes that left the water, through generations of amphibians and mammallike reptiles, into the early mammals, were newly selected to characterise the early primates, and eventually ended up in us. There wasn't a single grandfather fish, or one grandfather primate, no thin line of descent, just as there isn't a thin line of causality leading from a butterfly's wing flap to a hurricane. Nearly any fish you went back and killed would make virtually no difference to history. We'd still be here, but history would have taken a slightly different route to get to us.

But that doesn't mean that history has no important accomplishments.

Some physicists, especially, have argued from this indeterminacy and chaotic influences at all the micro-levels that there is no pattern to history, that Heisenberg uncertainty rules. Wrong. Just because we cannot predict the weather more than about a week ahead, with the best and biggest computers, doesn't mean that there isn't such a thing as weather. Our thin-causal-thread evolutionary scenarios for the emergence of those fishes on to the land don't work, but that doesn't mean we must throw away all ideas of causality in evolution. Any event, when looked at in detail, seems not to have a clear cause, but that just means that our Damasio-minds are not suited to that way of analysing history.

We are much better at totally disregarding all the micro stuff, and making big guesses: I guess it'll be sunny again tomorrow; or I guess that among all those fishes eating each other on the Devonian mudflats, some will escape on to the land. We're confirmed in that guess by finding climbing perch, mudskippers and lots of other separate fish lineages doing exactly that on mudflats today.

The great evolutionary biologist Stephen Jay Gould got this point wrong in Wonderful Life: if evolution ran again, he stated, we would not get people, because of all the tiny chaotic butterflies that determined evolutionary outcomes, so there were no thin causal threads. We disagree: we might not, almost surely would not, get the same primate coming down from the trees, but equivalent major innovations would occur in the new and different lineages. People are good at finding high-level groupings, making analogies and metaphors, arguing from what Aunt Janie does today to what she'll do tomorrow, or did twenty years ago. But we oversimplify when we try to disentangle the maze of tiny causalities that lies behind any historical event, because we can't handle that kind of complexity.

So, even though all of the causality happens at the micro-level, and we can't analyse it except in terms of tens of particles interacting when it's really billions, this isn't what it's about. It's like the early twentieth-century physicists telling us that the dining-room table wasn't really there, it was nearly all empty space, and that concepts like `hard' and `brown' had no place in the physicist's view of the world. So much the worse for the physicist. Did he really not eat his dinner off just such a hard, brown table? And was not his brain designed to do really clever things with abstractions useful in his daily life, like hard and brown, rather than the very peculiarly unuseful concepts of atoms, nuclei, and so on?

On the contrary, our brains are excellent at all the higher-level judgements they're called on to make, especially in a world that is full of hard, brown tables, doors, houses, trees to make them out of, and other people to help us or compete with us. But nearly all human brains are poor when it comes to the physics of atoms and the micro-world.

Back to history. We `make sense' of large movements like the Enlightenment, democracy in ancient Athens, the Tudors; but we know that if we were to look at all the small-scale interactions, they would make little sense against the comprehensible backdrop. That is precisely why historical novels can be so fascinating, and why The Three Musketeers didn't really affect Cardinal Richelieu and all the important people in seventeenth-century France. Nevertheless, we greatly enjoy the fiction that makes sense of the great movements by tying them down to the motives and nobility of a few people like D'Artagnan, with whom we can identify. The sequels Ten Years After and Twenty Years Later intrigued some of us, as Dumas found that he was on to a good thing and turned out more of the same. Some of us, at least, then found that Athos's nobility rang increasingly false, and Porthos's good humour was boring, while Aramis's religiosity wore very thin as the years rushed by. The initial idea wedged into the history we knew, it was consistent and provided colourful incident. But the later money-spinners were increasingly at odds with how we knew history worked.

There is an excellent example of the converse of this, which makes that point even better than Dumas. Wells's The Time Machine, as we've said, was the absolute classic time travelogue, showing us the large picture from prehistory to the social consequences of the capitalism that the socialist Wells wanted to criticise. Then the cooling Sun, the great crabs on a post-diluvian beach ... lovely. But Stephen Baxter's modern sequel The Time Ships shows us how clever the Morlocks will be, how the Traveller is really a little bit prurient about the little girl from the future - a resonance with Lewis Carrol's Alice - who is innocent and a bit stupid.

It's like a historical novel that puts all the little sexy and despicable bits into the great tapestry of history. Such literary exercises add colour and flavour to history, just as Damasio has shown that we do with our own personal memories. The pleasure this exercise gives us shows how our human minds read history: in the large without flavour, in the small with the kind of colour that we paint on to our own small reminiscences. So historical romance is just that: romantic painting of the little, interesting items, whose causality might affect the big picture, but doesn't.

What does it mean, then, to ask whether time knits up any changes, or whether mischievous butterflies are ultimately responsible for the fall of empires?

Here fictional conventions cease to fit the real world. From the point of view of the wizards, Roundworld time is a one-dimensional sequence that they can access two-dimensionally like a book. For narrative reasons, we have to depict it like this because of all those thin-thread-of-causality historical stories that our minds find so congenial. In a fictional context, we have little choice. However, here we want to think about the nature of causality and free will in the `real' universe, which - as we've made clear throughout the Science of Discworld series - does not have any narrativium. In that context, we have to understand that this simple image of Roundworld history is a fraud. The Trousers of Time also work well as a story, but as genuine physics they are a fraud: you can't be pushed from one leg to the other by an event. Worse, you can't tell that there has been such an event. As far as you are concerned, this is the world. It doesn't have `ifs' in its past.

None of this stops us using `what ifs' (which by nature are fictions, not facts) to think about history. We can still ask, in our minds, what would have happened if, say, Lincoln had survived ... but in the real world he didn't, and we can't run a mock-up of `if he did' in the real world: only in our heads.

Science runs into precisely this difficulty. For instance, the main problem in testing medical treatments is that we can't both give Mrs Jones the treatment and not give Mrs Jones the treatment, simultaneously, and compare the results. We can do it sequentially, but then the second treatment (whether it is placebo or real treatment) is of a different Mrs Jones, one who's had the first treatment. So what the testers do is to have quite a large panel, do treatment first on some, placebo first on others - and they should perhaps do two placebos on a few, and two treatments on a few others.

What time-travel stories do, in our minds, is the same kind of test: `What would happen if Leonardo had really seen a submarine working?' or equivalently `Did Leonardo see a submarine working?' In The Science of Discworld, and more explicitly in The Science of Discworld II, we asked whether the interesting stories that we make up have some kind of coherent explanation, something like `evil' - which we personified in the second book as Elves. To what extent do such concepts relate to the real rules of the real world? Now we argue that we cannot know if any answer we get is useful; we can't even know whether we've got an answer at all. And that this is precisely why Dennett's kind of free will is the only one worth having. It's prospective, giving each of us the chance to make little items of an otherwise inevitable future evitable.

When we look back on something we've changed by that kind of an act of free will, it's just as causal as everything else - and if the universe is in any sense determinate, then it is determinate in that sense. Think of Odysseus looking back at what happened as his ship failed to be caught by the Sirens. His men didn't hear them, and he, who could hear them, couldn't act to steer the ship. So he and his crew came through in that most unlikely of passages. There is a sense, of course, in which every sea passage is equally unique, just as every deal of cards is unique; but Odysseus's journey, like a onesuit-per-player deal of cards, is totally remarkable too. Looking back into history, can we find journeys, events, and processes so remarkable that they seem to be the results of previous acts of free will?

What, then, is causality? For Damasio-like reasons, we tend to think that what gives history its dynamic is the big events, the `pivot points'. The fallacy is that we think big causes are needed to produce big effects. This is false (butterfly) but there is a problem: choosing the right tiny change (which butterfly?). And there are always billions of new butterflies, dragging new changes out from previously invisible differences `in the 13th decimal place', unobservable until their effects show up.

Real history is like this; causes are often distributed, with huge numbers of tiny events all coming together. It is just this problem that leads Ridcully to employ such a huge number of wizards, doing such a bizarre set of trivial things, merely to get The Origin written.

We only justify this sort of causality in retrospect: history didn't know `where it was going'. So changing the past creates a context for the future, not a causal chain, and this is how the wizards must operate, which is why we have thousands of them making endless trivial changes to Victorian history, instead of, say, assassinating Queen Victoria. Any Victorian, perhaps particularly the well-trained nursemaid, will tell you just that about your personal history: your heart must be pure (context) rather than your plans being subtle.