Science of Discworld III

problem to one that has already been solved. (Of course the first step puts it back in the sink – that’s why it’s a joke.)
    3 Yes, traditionally ‘Indigo’ goes here, but that’s silly – Indigo is just another shade of blue. You could equally well insert ‘Turquoise’ between Green and Blue. Indigo was just included because seven is more mystical than six. Rewriting history, we find that we have left a place for Octarine, the Discworld’s eighth colour. Well, seventh, actually. Septarine, anyone?
    4 This is why, even today when the lustre of ‘the new mathematics’ has all but worn to dust, small children in mathematics classes spend hours drawing squiggly lines between circles containing pictures of cats to circles containing pictures of flowers, busily ‘matching’ the two sets. Neither the children nor their teachers have the foggiest idea why they are doing this. In fact they’re doing it because, decades ago, a bunch of demented educators couldn’t understand that just because something is logically prior to another, it may not be sensible to teach them in that order. Real mathematicians, who knew that you always put the roof on the house before you dug the foundation trench, looked on in bemused horror.
    5 Briefly: since the bit before the decimal point is a whole number, taking that into account multiplies the answer by aleph-zero. Now aleph-zero X aleph-zeroplex is less than or equal to aleph-zeroplex X aleph-zeroplex, which is (2 X aleph-zero)plex, which is aleph-zeroplex. OK?
    6 The proof isn’t hard, but it’s sophisticated. If you want to see it, consult a textbook on the foundations of mathematics.
    7 Curiously, it could expand to infinity in a finite time if it accelerated sufficiently rapidly. Expand by one light-year after one minute, by another light-year after half a minute, by another after a quarter of a minute … do a Zeno, and after two minutes, you have an infinite universe. But it’s not expanding that fast, and no one thinks it did so in the past, either.
    8 Actually a more sophisticated gadget called the Poincaré dodecahedral space, a slightly weird shape invented more than a century ago to show that topology is not as simple as we’d like it to be. But people understand ‘football’.
    9 Derived from a pun: m -brane for ‘membrane’. Opening up jokes about no-branes and p -branes. Oh well.

FIFTEEN
AUDITORS OF REALITY
    I T WAS ONE HOUR LATER . Wizards were ranged in rows across the width of the Great Hall in a variety of costumes, but mostly in what might be called Early Trouser; despite Rincewind’s view on nudity, a grubby shirt and pants would pass without comment in many ages and countries and lead to fewer arrests.
    ‘Right, then,’ said Ridcully, striding along the ranks ‘We’ve kept all this very simple so that even professors can understand! Ponder Stibbons has given all of you your tasks!’ He stopped in front of a middle-aged wizard. ‘You, sir, who are you?’
    ‘Don’t you know, sir?’ said the wizard, taken aback.
    ‘Slipped m’ mind, man!’ said Ridcully. ‘Big university, can’t be expected to recognise everyone !’
    ‘It’s Pennysmart, sir. Professor of Extreme Horticulture.’
    ‘Any good at it?’
    ‘Yes, sir!’
    ‘Any students?’
    ‘No, sir!’ said Pennysmart, looking offended.
    ‘That’s what I like to hear! And what will you be doin’ today?’
    ‘First, it appears, I shall be dropped waist-deep in a lagoon in the, the –’ he stopped, and fumbled a piece of paper out of his pocket ‘– Keeling Islands, where I shall attack the sand bottom round mewith this rake,’ he held up the implement, ‘and then return here as soon as I see any humans.’
    ‘And how will you do that?’
    ‘Say aloud, “Return Me, Hex”,’ said Pennysmart, smartly.
    ‘Well done, good man,’ said the Archchancellor. He raised his voice. ‘Remember that, everyone! Exactly those words! Write them down if you can’t remember them. Hex will bring you back on the lawn outside the building. There will be hundreds of you and many of you have several tasks, so we don’t want any collisions! Now, if—’
    ‘Excuse me,’ said Pennysmart, raising a hand.
    ‘Yes?’
    ‘ Why will I be standing in a lagoon flailing around with a rake, please?’
    ‘Because if you don’t do that, Darwin will tread on the dorsal spine of an extremely poisonous fish,’ said Ponder Stibbons. ‘Now—’
    ‘Excuse me again, please,’ Pennysmart