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.