Science of Discworld III

moving, even though instantaneously it stays in the same place’. Momentum encodes the next change of position, and it encodes it now . Its value now is not observable now, but it is (will be) observable. You just have to wait to find out what it was. Momentum is a ‘hidden variable’ that encodes transitions from one position to another.
    Can we find an analogue of momentum in quantum snakes and ladders? Yes, we can. It is the overall probability of going from any given square to any other. These ‘transition probabilities’ depend only on the squares concerned, not on the time at which the moveis made, so in Barbour’s sense they are ‘timeless’. But when you are on some given square, the transition probabilities tell you where your next move can lead, so you can reconstruct the possible sequences of moves, thereby putting time back into the physics.
    For exactly the same reason, a single fixed probability mist is not the only statistical structure with which Platonia can be endowed. Platonia can also be equipped with transition probabilities between pairs of states. The result is to convert Platonia into what statisticians call a ‘Markov chain’, which is just like the list of transition probabilities for snakes and ladders, but more general. If Platonia is made into a Markov chain, each sequence of configurations gets its own probability. The most probable sequences are those that contain large numbers of highly probable states – these look oddly like Barbour’s time capsules. So instead of single-state Platonia we get sequential-state Markovia, where the universe makes transitions through whole sequences of configurations, and the most likely transitions are the ones that provide a coherent history – narrativium.
    This Markovian approach offers the prospect of bringing time back into existence in a Platonian universe. In fact, it’s very similar to how Susan Sto Helit and Ronnie Soak managed to operate in the cracks between the instants, in Thief of Time .
    Tick .
    1 Actually, foot.
    2 Well, let’s not exaggerate. You can publish papers on it without risking losing your job. It’s certainly better than publishing nothing, which definitely will lose you your job.
    3 Indeed, in the Back to the Future movie sequence, it was a car. A Delorean. Though it did need the assistance of a railway locomotive at one point.
    4 Provided it is fired by someone who has been in the pub since lunchtime.
    5 Actually this is the ambiguous puzuma, which travels at near-lightspeed (which on the Disc is about the speed of sound). If you see a puzuma, it’s not there. If you hear it, it’s not there either.
    6 As one does. Palaeontologists have just announced that they have found remarkably well-preserved fossils in an East Anglian quarry, showing that giant hippos weighing six or seven tons – roughly twice the weight of modern hippos – wallowed in the rivers of Norfolk 600,000 years ago. It was a warm period sandwiched between two ice ages, probably a few degrees warmer than the present day (you can tell that from insect fossils) and hyenas prowled the banks in search of carrion.
    7 See The Annotated Flatland by Edwin A. Abbott and Ian Stewart (Basic Books, 2002).

SEVEN
THE FISH IS OFF
    T WO HOURS LATER A SINGLE sheet of paper slid off Hex’s writing table. Ponder picked it up.
    ‘There are about ten points where we must intervene to ensure that The Origin is written,’ he said. ‘Well, that doesn’t seem too bad,’ said Ridcully. ‘We got Shakespeare born, didn’t we? 1 We just have to tinker.’
    ‘These look a little more complicated,’ said Ponder, doubtfully.
    ‘But Hex can move us around,’ said Ridcully. ‘It could be fun, especially if something or someone is playing les buggeurs risibles . It could be educational, Mr Stibbons.’
    ‘And they do really good beer,’ said the Dean. ‘And the food was excellent. Remember that goose we had last time? I’ve seldom eaten better.’
    ‘We will be setting out to save the world,’ said Ridcully, severely. ‘We will have other things on our minds!’
    ‘But there will be mealtimes, yes?’ said the Dean
    Second Lunch and Mid-afternoon Snack went past almost unnoticed. Perhaps the wizards were already leaving space for goose …
*
    It was turning out to be a long day. Easels had been set up around Hex. Paper was strewn across every table. The Librarian had practically built up a branch library in one corner, and was still fetching books from