Science of Discworld III

about. We saw them, remember? Not the big ones, the little ones who painted their bodies and herded animals? And the octopuses building cities under the sea? Not to mention the crabs! Oh, yes, the crabs. They were really doing well, the crabs. They were building rafts with sails and enslaving other crab nations. That’s practically civilisation! But they all got wiped out. Was that part of a divine plan?’
    Ponder hesitated.
    ‘They did worship a crab-shaped god,’ he said, as a holding statement until actual thought happened.
    ‘Well, they would, wouldn’t they?’ said Ridcully. ‘They were crabs .’
    ‘Um. Perhaps they just weren’t … satisfactory?’ said Ponder. ‘In some way?’
    ‘They were pretty clever,’ said Ridcully.
    Ponder squirmed. ‘Darwin didn’t know about them,’ he said. ‘They didn’t build anything that lasted. I suppose the Darwin who wrote The Ology would have taken the view that they simply failed, or were wicked in some way. One of the major religious texts does mention a divine flood that drowned everything in the world except one family and a boatload of animals.’
    ‘Why?’
    ‘Because they were all wicked, I believe.’
    ‘How can animals be wicked? How can a crab be wicked, for that matter?’
    ‘I don’t know, Archchancellor!’ Ponder burst out. ‘Maybe if they eat forbidden seaweed? Dig a burrow on the wrong day? I’m not a theologian!’
    They sat in despondent silence.
    ‘It’s a bit of mess, isn’t it?,’ said Ridcully.
    ‘Yes, sir.’
    ‘We’ve really got to see to it that The Origin gets written.’
    ‘We have indeed, sir.’
    ‘But you’d like to think there’s someone in charge, yes?’ saidRidcully, gently. ‘Of everything, I mean.’
    ‘Yes! Yes, I would, sir! Not a big beard in the sky, but … something! Some kind of frame, some sense that good and bad have real meanings! I can see why The Ology was so popular. It wrapped everything up! But how does evolution get passed on? Where does order come from? If you start with a lot of exploding firmament, how do you end up with butterflies? Were butterflies built in from the start? How? What bit of burning hydrogen carried the plans for people? Even the Darwin who wrote The Origin called on a god to start life. It’s be nice to know that underneath it all is some kind of … sense.’
    ‘You didn’t used to talk like this, Mr Stibbons.’
    Ponder sagged. ‘Sorry, sir. It’s all getting me down, I think.’
    ‘Well, I can see why,’ said Ridcully. ‘Surely there must be some Deitium here. Some things can’t just happen. Now, the eyeball –’
    Ponder gave a little yelp.
    ‘– is easy,’ said Ridcully. ‘Are you all right, Stibbons?’
    ‘Er, fine, fine, sir. I’m fine. Easy, is it?’
    ‘Seeing keeps you alive,’ said Ridcully. ‘Any kind of seeing is better than nothing. I can see, ha, what the Origin Darwin is getting at there. You don’t have to have a god. But there’s a kind of wasp that’s parasitical on a spider … unless I’m thinking about a kind of spider that is parasitical on a wasp … anyway, what it does is, it waits until—’
    ‘Ah,’ said Ponder brightly, ‘wasn’t that the gong for Early Breakfast?’
    ‘ I didn’t hear anything,’ said Ridcully.
    ‘I’m positive,’ said Ponder, edging towards the door. ‘I’ll tell you what, sir, I’ll just go and check.’

FOURTEEN
ALEPH-UMPTYPLEX
    T HE WIZARDS ARE NOT ONLY grappling with the apparent absurdities of ‘quantum’, their catch-all phrase for advanced physics and cosmology, but with the explosive philosophical/mathematical concept of infinity. In their own way, they have rediscovered one of the great insights of nineteenth-century mathematics: that there can be many infinities, some of them bigger than others.
    If this sounds ridiculous, it is. Nonetheless, there is an entirely natural sense in which it turns out to be true.
    There are two important things to understand about infinity. Although the infinite is often compared with numbers like 1, 2, 3, infinity is not itself a number in any conventional sense. As Ponder Stibbons says, you can’t get there from 1. The other is that, even within mathematics, there are many distinct notions that all bear the same label ‘infinity’. If you mix up their meanings, all you’ll get is nonsense.
    And then – sorry, three important things – you have to appreciate that infinity is often a process, not a thing.
    But – oh, four important