Mum stopped trying to chastise DH-82, who, soporific through gluttony, had settled down for a long nap.
‘No,’ she admitted. ‘The man in the shop said there would be a shortage so I bought his entire stock.’
I walked down to Mycroft’s laboratory, knocked and, when there was no reply, entered. All his machines had been dismantled and now lay about the room, tagged and carefully stacked. Mycroft himself, having obviously finished testing the ejection system, was now tweaking a small bronze object. He seemed somewhat startled when I spoke his name but relaxed as soon as he saw it was me.
‘Hello, love!’ he said kindly. ‘I’m off on retirement in one hour and nine minutes. You looked good on the telly last night.’
‘Thank you. What are you up to, Uncle?’
He handed me a large book.
‘Enhanced indexing. In a Nextian dictionary, godliness can be next to cleanliness—or anything else for that matter.’
I opened the book to look up ‘trout’ and found it on the first page I came to.
‘Saves time, eh?’
‘Yes; but—’
Mycroft had moved on.
‘Over here is a Lego filter for vacuum cleaners. Did you know that over a million pounds’ worth of Lego is hoovered up every year, and a total often thousand man-hours are wasted sorting through the dust bags?’
‘I didn’t know that, no.’
‘This device will sort any sucked-up bits of Lego into colours or shapes, according to how you set this knob here.’
‘Very impressive.’
‘This is just hobby stuff. Come and look at some real innovation.’
He beckoned me across to a blackboard, its surface covered with a jumbled mass of complicated algebraic functions.
‘This is Polly’s hobby, really. It’s a new form of mathematical theory that makes Euclid’s work seem like little more than long division. We have called it Nextian geometry. I won’t bother you with the details but watch this.’
Mycroft rolled up his shirtsleeves and placed a large ball of dough on the workbench and rolled it out into a flat ovoid.
‘Scone dough,’ he explained. ‘I’ve left out the raisins for purposes of clarity. Using conventional geometry a round scone cutter always leaves waste behind, agreed?’
‘Agreed.’
‘Not with Nextian geometry! You see this pastry cutter? Circular, wouldn’t you say?’
‘Perfectly circular, yes.’
‘Well,’ carried on Mycroft in an excited voice, ‘it isn’t. It appears circular but actually it’s a square. A Nextian square. Watch.’
And so saying he deftly cut the dough into twelve perfectly circular shapes with no waste. I frowned and stared at the small pile of discs, not quite believing what I had just seen.
‘How—?’
‘Clever, isn’t it?’ He chuckled. ‘But quite, quite simple, really. A baked-bean tin is circular, wouldn’t you say?’
I nodded.
‘But viewed from the side it looks like an oblong. What Nextian geometry does—in very simple terms—is bring the plane of a solid from the horizontal to the vertical but without altering the vertices of the solid in space Admittedly it only works with Nextian dough, which doesn’t rise so well and tastes like denture paste, but we’re working on that.’
‘It seems impossible, Uncle.’
‘We didn’t know the nature of lightning or rainbows for three and a half million years, pet. Don’t reject it just because it seems impossible. If we closed our minds there would never be the Gravitube, antimatter, Prose Portals, Thermos flasks—’
‘Wait!’ I interrupted ‘How does a Thermos fit in with that little lot?’
‘Because, my dear girl, no one has the least idea why they work.’ He stared at me for a moment and continued: ‘You will agree that a vacuum flask keeps hot things hot in the winter and cold things cold in the summer?’
‘Yes.’
‘Well, how does it know? I’ve studied vacuum flasks for many years and not one of them gave any clues as to their inherent seasonal cognitive ability. It’s a mystery to me, I can tell you.’
‘Okay, okay, Uncle—how about applications for Nextian geometry?’
‘Hundreds. Packaging and space management will be revolutionised overnight. I can pack Ping-Pong balls in a cardboard box without any gaps, punch steel bottle tops with no waste, drill a square hole, tunnel to the moon, divide cake more efficiently, and also—and this is the most exciting part—collapse matter.’
‘Isn’t that dangerous?’
‘Not at all,’ replied Mycroft airily. ‘You accept that all matter is mainly empty space? The void between the nucleus and the electrons? Well, by applying Nextian geometry to the subatomic level. I can collapse matter to a fraction of its former size. I will be able to reduce almost anything to the microscopic!’
‘Are you going to market this idea?’
It was a good question. Most of Mycroft’s ideas were far too dangerous to even think about, much less let loose on a world unprepared for hyper-radical thought.
‘Miniaturisation is a technology that needs to be utilised,’ explained Mycroft. ‘Can you imagine tiny nanomachines barely bigger than a cell building, say, food protein out of nothing more than garbage? Banoffee pie from landfills, ships from scrap iron—! It’s a fantastic notion. Consolidated Useful Stuff are financing some R&D with me as we speak.’
‘It’s very impressive, Uncle, but what do you know about coincidences?’
‘Well,’ said Mycroft thoughtfully, ‘it is my considered opinion that most coincidences are simply quirks of chance—if you extrapolate the bell curve of probability you will find statistical abnormalities that seem unusual but are, in actual fact, quite likely given the number of people on the planet and the number of different things we do in our lives.’
‘I see,’ I replied slowly. ‘That explains things on a minor coincidental level, but what about the bigger coincidences? How high would you rate seven people in a Skyrail shuttle all called Irma Cohen and the answers to crossword clues reading out “meddlesome Thursday goodbye” just before someone tried to kill me?’
Mycroft gave a low whistle.
‘That’s quite a coincidence. More than a coincidence, I think.’ He took a deep breath. ‘Thursday, think for a moment about the fact that the universe always moves from an ordered state to a disordered one; that a glass may fall to the ground and shatter yet you never see a broken glass reassemble itself and then jump back on to the table.’
‘I accept that.’
‘But why doesn’t it?’
‘Search me.’
‘Every atom of that glass that shattered would contravene no laws of physics if they were to rejoin—on a subatomic level all particle interactions are reversible. Down there we can’t tell which event precedes which. It’s only out here that we can see things age and define a strict direction in which time travels.’
‘So what are you saying, Uncle?’
‘That these things don’t happen is because of the second law of thermodynamics, which states that disorder in the universe always increases; the amount of this disorder is a quantity known as entropy.’
‘So how does this relate to coincidences?’
‘I’m getting to that; imagine a box with a partition—the left side is filled with gas, the right a vacuum. Remove the partition and the gas will expand into the other side of the box—yes?’
I nodded.
‘And you wouldn’t expect the gas to cramp itself up in the left-hand side again, would you?’
‘No’
‘Ah!’ replied Mycroft with a smile ‘Not quite right. You see, since every interaction of gas atoms is reversible, some time, sooner or later, the gas must cramp itself back into the left-hand side!’
‘It must?’
‘Yes, the key here is how much later. Since even a small box of gas might contain 1020 atoms, the time taken for them to try all possible combinations would be far greater than the age of the universe, a decrease in entropy strong enough to allow gas to separate, a shattered glass to re-form or the statue of St Zvlkx outside to get down and walk to the pub is not, I think, against any physical laws but just fantastically unlikely.’