So far, this is a clever and (it turns out) useful way to formalise the mathematics of the quantum world. The next step is more controversial. All that really matters is that message, that list of bits. And what is a message? Information. Conclusion: the real stuff of the universe is raw information. Everything else is made from it according to quantum principles. Ponder would approve.
Information thereby takes its place in a small pantheon of similar concepts – velocity, energy, momentum – that have made the transition from convenient mathematical fiction to reality. Physicists like to convert their technically most useful mathematical concepts into real things: like Discworld, they reify the abstract. It does no physical harm to ‘project’ the mathematics back into the universe like this, but it may do philosophical harm if you take the result literally. Thanks to a similar process, for example, entirely sane physicists today insist that our universe is merely one of trillions that coexist in a quantum superposition. In one of them you left your house this morning and were hit by a meteorite; in the one in which you’re reading this book, that didn’t happen. ‘Oh, yes,’ they urge: ‘those other universes really do exist. We can do experiments to prove it.’
Not so.
Consistency with an experimental result is not a proof, not even a demonstration, that an explanation is valid. The ‘many-worlds’ concept, as it is called, is an interpretation of the experiments, within its own framework. But any experiment has many interpretations, not all of which can be ‘how the universe really does it’. For example, all experiments can be interpreted as ‘God made that happen’, but those selfsame physicists would reject their experiment as a proof of the existence of God. In that they are correct: it’s just one interpretation. But then, so are a trillion coexisting universes.
Quantum states do superpose. Quantum universes can also superpose. But separating them out into classical worlds in which real-life people do real-life things, and saying that those superpose, is nonsense. There isn’t a quantum physicist anywhere in the world that can write down the quantum-mechanical description of a person. How, then, can they claim that their experiment (usually done with a couple of electrons or photons) ‘proves’ that an alternate you was hit by a meteorite in another universe?
‘Information’ began its existence as a human construct, a concept that described certain processes in communication. This was ‘bit from it’, the abstraction of a metaphor from reality, rather than ‘it from bit’, the reconstruction of reality from the metaphor. The metaphor of information has since been extended far beyond its original bounds, often unwisely. Reifying information into the basic substance of the universe is probably even more unwise. Mathematically, it probably does no harm, but Reification Can Damage Your Philosophy.
NINETEEN
LETTER FROM LANCRE
GRANNY WEATHERWAX, KNOWN TO ALL and not least to herself as Discworld’s most competent witch, was gathering wood in the forests of Lancre, high in the mountains and far from any university at all.
Wood gathering was a task fraught with danger for an old lady so attractive to narrativium. It was quite hard these days, when gathering firewood, to avoid third sons of kings, young swineherds seeking their destiny and others whose unfolding adventure demanded that they be kind to an old lady who would with a certainty turn out to be a witch, thus proving that smug virtue is its own reward.
There is only a limited number of times even a kindly disposed person wishes to be carried across a stream that they had, in fact, not particularly desired to cross. These days, she kept a pocket full of small stones and pine cones to discourage that kind of thing.
She heard the soft sound of hooves behind her and turned with a pine cone raised.
‘I warn you, I’m fed up with you lads always on the ear’ole for three wishes—’ she began.
Shawn Ogg, astride his official donkey, waved his hands desperately.1
‘It’s me, Mistress Weatherwax! I wish you’d stop doing this!’
‘See?’ said Granny. ‘You ain’t havin’ another two!’
‘No, no, I’ve just come up to deliver this for you …’
Shawn waved quite a thick wad of paper.
‘What is it?’
‘’Tis a clacks for you, Mistress Weatherwax! It’s only the third one we’ve ever had!’ Shawn beamed at the thought of being so close to the cutting edge of technology.
‘What’s one of them things?’ Granny demanded.
‘It’s like a letter that’s taken to bits and sent through the air,’ said Sean.
‘By them towers I keep flyin’ into?’
‘That’s right, Mistress Weatherwax.’
‘They move ’em around at night, you know,’ said Granny. She took the paper.
‘Er … I don’t think they do …’ Shawn ventured.
‘Oh, so I don’t know how to fly a broomstick right, do I?’ said Granny, her eyes glinting.
‘Actually, yes, I’ve remembered,’ said Shawn quickly. ‘They move them around all the time. On carts. Big, big carts. They …’
‘Yes, yes,’ said Granny, sitting on a stump. ‘Be quiet now, I’m readin’…’
The forest went silent, except for the occasional shuffling of paper.
Finally, Granny Weatherwax finished. She sniffed. Birdsong came back into the forest.
‘Silly old fools think they can’t see the wood for the trees, and the trees are the wood,’ she muttered. ‘Cost a lot, does it, sendin’ messages like this?’
‘That message,’ said Shawn, in awe, ‘cost more than 600 dollars! I counted the words! Wizards must be made of money!’
‘Well, I ain’t,’ said the witch. ‘How much is one word?’
‘Five pence for the sending and five pence the first word,’ said Shawn, promptly.
‘Ah,’ said Granny. She frowned in concentration, and her lips moved silently. ‘I’ve never been one for numbers,’ she said, ‘but I reckon that comes to … sixpence and one half-penny?’
Sean knew his witches. It was best to give in right at the start.
‘That’s right,’ he said.
‘You have a pencil?’ said Granny. Shawn handed it over. With great care, the witch printed some block capitals on the back of one of the pages, and gave it to him.
‘That’s all?’ he said.
‘Long question, short answer,’ said Granny, as it if was some universal truth. ‘Was there anything else?’
Well, there might be the money, Sean thought. But in her own localised way, Granny Weatherwax had an academic position in these matters. Witches took the view that they helped society in all kinds of ways which couldn’t easily be explained but would become obvious if they stopped doing them, and that it was worth six pence and one half-penny not to find out what these were.
He didn’t get his pencil back.
The hole into L-space was quite obvious now. It fascinated Dr Dee, who was confidently expecting angels to come out of it, although all it had produced so far was an ape.
The wizards’ automatic response to any problem was to see if there was a book about it. L-space was providing plenty of books. The difficulty, however, was finding the ones that applied to the current history; when you potentially know everything, it’s hard to find anything you want to know.
‘So let’s see where we are now, shall we?’ said Ridcully, after a while. ‘The last known books in this leg of the trousers of time are due to be written in—?’
‘About a hundred years’ time,’ said the Lecturer in Recent Runes, looking at his notes. ‘Just before the collapse of civilisation, such as it is. Then there’s fire, famine, war … all the usual stuff.’
‘Hex says people here are back to living in villages when the asteroid hits,’ said Ponder. ‘Things are rather better on one or two other continents, but no one even sees it coming.’
‘There have been periods like it before,’ said the Dean. ‘But as far as we can tell, in the area where we are now there were always small isolated groups of
people who preserved what books there were.’
‘Ah. Our kind of people,’ said Ridcully.
‘Afraid not,’ said the Dean. ‘Religious.’
‘Oh dear,’ said Ridcully.
‘It’s hard to follow, but there appear to be about four main gods on this continent,’ said the Dean. ‘Loosely associated.’
‘Big beards in the sky?’ said Ridcully.
‘A couple, yes.’
‘Clearly a morphic memory of ourselves, then,’ said Ridcully.
‘It’s hard to tell, with religions,’ said the Dean. ‘But at least they preserved the idea that books were important and that reading and writing were more than just a skive for people too weedy to hack at one another with swords.’
‘Any of these religious places still around?’ said the Lecturer in Recent Runes. ‘Would it be useful to drop in, explain that we are, in fact, the creators of this universe, and put them right on a few points?’
There was silence. And then Ponder said, in his best talking-to-superiors voice: ‘I believe, sir, that this world is no different from our own in its attitude to apparent human beings who turn up and say that they’re a god.’
‘We wouldn’t get special treatment?’
‘Not of the sort you have in mind, sir, no,’ said Ponder. ‘Besides, the places in this country appear to have been closed down by a recent monarch. I’m not sure I understand it all, but it appears to have been some kind of cost-cutting exercise.’
‘Downsizing of redundant units, re-allocation of staff, that sort of thing?’ said Ridcully.
‘Yes, sir,’ said Ponder. ‘And a few murders, some torturing, that sort of thing.’
‘But probably nothing, I’m sure, that couldn’t be sorted out by getting everyone to go and run around in the woods shooting paint at one another,’ said the Lecturer in Recent Runes, innocently.
‘I shall ignore that, Runes,’ said Ridcully. ‘Now, gentlemen, we are supposed to be thinkers. We haven’t got magic. We can be moved in time and space, according to Hex. And we’ve got big sticks. What can we do?’
‘A message has arrived,’ said Hex.
‘From Lancre? That’s quick!’
‘Yes. The message is unsigned. It is: THEOSTRY.’
Hex spelled it out. Ponder wrote it down in his notebook.
‘What does that mean?’ Ridcully looked up at his wizards.
‘Looks a bit religious to me,’ said the Dean. ‘Rincewind? This sort of thing is right up your street, isn’t it?’
Rincewind looked at the word. Really, when you came to think of it, his whole life was a crossword puzzle …
‘The clacks people charge by the word, don’t they?’ he said.
‘Yes, it’s scandalous,’ said Ridcully. ‘Five pence a word, on the long-distance trunk!’
‘And this was sent back by an old woman in Lancre, where as far as I recall the chicken is the basic unit of currency?’ said Rincewind. ‘Not much money for fancy messages, then. It looks to me like a simple anagram of … THE STORY …’
‘I think it means “change the story”,’ said Ponder, without looking up. ‘At a saving of five pence.’
‘We tried changing it!’ said the Dean.
‘Change it in a different way, perhaps? At a different time?’ said Ponder. ‘We’ve got L-space. We ought to be able to get some guidance from books written in different futures—’
‘Ook!’
‘I’m sorry, sir, but the library rules don’t apply here!’ said Ponder.
‘Look at it this way, old chap,’ said Ridcully, to the angry Librarian. ‘The rules do of course apply here, everyone can see that, and we wouldn’t dream of asking you to interfere with the nature of causality in the normal way of things. It’s just that the nature of causality on this world is such that, if any libraries survive the next thousand years without being used for lighting fires or uncomfortable toilet paper, they’re due to be destroyed in a fireball and/or entombed in ice. Dr Dee’s wonderful books which you like so much, with their many delicate illustrations of completely useless magical circles and rather interesting mathematical cyphers, will go the way of the, the …’ He snapped his fingers. ‘Someone give me the name of something that’ll be going completely extinct,’ he demanded.
‘People,’ said Rincewind.
There was silence.
Then the Librarian said: ‘Ook ook.’
‘He says he’s just finding the books, okay?’ said Rincewind. ‘And he’ll leave them in a pile and go out of the room and no one is to look at them while he’s gone, because if they do he won’t know about it, and if he coughs loudly before he comes back in that will only be because he’s got a cough and not for any other reason, okay?’
1 Lancre was so backward that its population of 500 had only one civil servant, Shawn Ogg, who handled everything from national defence and tax gathering to mowing the castle lawns, although he was allowed help with the lawns. Lawns required care.
TWENTY
SMALL GODS
‘RELIGIOUS,’ SAID THE DEAN.
‘Oh dear,’ said Ridcully.
Discworld’s wizardry is not terribly keen on religion. Given the history of the Discworld, this is not surprising. One big problem is that on Discworld, gods are known to be real. We list a few later on, but we can set the scene with reference to the god of mayflies. In Reaper Man, an old mayfly is telling some youngsters about this god, as they hover just above the surface of a stream:
‘… you were telling us about the Great Trout.’
‘Ah. Yes. Right. The Trout. Well, you see, if you’ve been a good mayfly, zigzagging up and down properly—’
‘—taking heed of your elders and betters—’
‘—yes, and taking heed of your elders and betters, then eventually the Great Trout—’
Clop.
Clop.
‘Yes?’ said one of the younger mayflies.
There was no reply.
‘The Great Trout what?’ said another mayfly, nervously.
They looked down at a series of expanding concentric rings on the water.
‘The holy sign!’ said a mayfly. ‘I remember being told about that! A Great Circle in the water! Thus shall be the sign of the Great Trout!’
Roundworld religions avoid the difficulty of gods that you can actually see, or meet or be eaten by: most of the world’s current religions find it best to go the whole hog and locate their gods in a place that is not just outside Roundworld the planet, but outside Roundworld the universe. This demonstrates admirable foresight, for regions impenetrable today may be a forest of tourist hotels tomorrow. When the sky was an unexplored and unfathomable realm, it was fashionable to locate gods in the sky, or on top of unscalable Mount Olympus, or in the halls of Valhalla, which amounts to much the same thing. But now all significant mountains have been climbed, people routinely fly across the Atlantic, five miles up, and reports of encounters with gods are few.
However, it turns out that when gods don’t manifest themselves in physical form on an everyday basis, they acquire an impressive degree of ineffability. On Discworld, on the other hand, it is possible to run into gods in the street or even in the gutter. They also lounge around in Discworld’s equivalent of Valhalla, known as Dunmanifestin, which is situated on top of Cori Celesti, a ten mile high spire of green ice and grey stone at the Disc’s hub.
Because of the everyday presence of tangible gods, on Discworld there’s no problem about belief in gods; it’s more a matter of how much you disapprove of their lifestyle. On Roundworld, deities do not infest the highways and byways – or, if they do, they do so in such a subtle guise that the unbeliever does not notice them. It then becomes possible to have a serious debate about belief, because that’s what most people’s concept of God rests on.
We’ve already said that on Discworld everything is reified, and that’s pretty much the case there with belief. Now B-space, the space of beliefs, is huge, because people have vivid and varied imaginatio
ns and can believe almost anything. Therefore G-space, the space of gods, is also huge. And on Discworld, phase spaces are reified. So the Discworld not only has gods: it is infested with them. There are at least 3,000 major gods on the Disc, and scarcely a week passes without the research theologians discovering more. Some use props like false noses to appear in religious chronicles under hundreds of different names, which makes it difficult to keep count accurately. Among them are Cephut, the god of cutlery (Pyramids), Flatulus, god of the winds (Small Gods), Grune, the god of unseasonal fruit (Reaper Man), Hat, the vulture-headed god of unexpected guests (Pyramids), Offler, the crocodile god (Mort and Sourcery), Petulia, the goddess of negotiable affection (Small Gods), and Steikheigel, the god of isolated cow byres (Mort).
Then there are the minor gods. According to The Discworld Companion, ‘There are billions of them, tiny bundles containing nothing more than a pinch of pure ego and some hunger’. What they hunger for, at least to start with, is human belief, because on Discworld the size and power of a god is proportional to how many people believe in him, her, or it. Things are much the same on Roundworld, in fact, because the influence and power of a religion are proportional to the number of its adherents. So the parallel is much closer than you might expect – which is what you should always expect with Discworld, because it has an uncanny ability to reflect and illuminate the human condition in Roundworld. Actually, it’s not always human (or mayfly) belief that matters. According to Lords and Ladies:
There were a number of gods in the mountains and forests of Lancre. One of them was known as Herne the Hunted. He was a god of the chase and the hunt. More or less.
Most gods are created and sustained by belief and hope. Hunters danced in animal skins and created gods of the chase, who tended to be hearty and boisterous with the tact of a tidal wave. But they are not the only gods of hunting. The prey has an occult voice too, as the blood pounds and the hounds bay. Herne was the god of the chased and the hunted and all small animals whose ultimate destiny is to be an abrupt damp squeak.
The Science of Discworld II Page 22