‘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.’

‘So what you are saying is that really, really weird coincidences are caused by a drop in entropy?’

‘Exactly so. But it’s only a theory. Why entropy might spontaneously decrease and how one might conduct experiments into localised entropic field decreasement. I have only a few untried notions that I won’t trouble you with here, but look, take this—it could save your life.’

He passed me a sealed jam jar, the contents of which were half rice and half lentils.

‘I’m not hungry, thanks,’ I told him.

‘No, no I call this device an entroposcope. Shake it for me.’

I shook the jamjar and the rice and lentils settled together in that sort of random clumping way that chance usually dictates.

‘So?’ I asked.

‘Entirely usual,’ replied Mycroft. ‘Standard clumping, entropy levels normal. Shake it every now and then. You’ll know when a decrease in entropy occurs as the rice and lentils will separate into more ordered patterns—and that’s the time to watch out for ludicrously unlikely coincidences.’

Polly entered the workshop and gave her husband a hug.

‘Hello, you two,’ she said. ‘Having fun?’

‘I’m showing Thursday what I’ve been up to, my dear,’ replied Mycroft graciously.

‘Did you show her your memory erasure device, Crofty?’

‘No, he didn’t,’ I said.

‘Yes I did,’ replied Mycroft with a smile, adding: ‘You’re going to have to leave me, pet—I’ve work to do. I retire in fifty-six minutes precisely.’

My father didn’t turn up that evening, much to my mother’s disappointment. At five minutes to ten Mycroft, true to his word, and with Polly behind him, emerged from his laboratory to join us for dinner. Next family dinners are always noisy affairs and tonight was no different. Landen sat next to Orville and did a very good impression of someone who was trying not to be bored. Joffy, who was next to Wilbur, thought his new job was utter crap and Wilbur, who had been needled by Joffy for at least three decades, replied that he thought the Global Standard Deity faith was the biggest load of phoney codswallop he had ever come across.

‘Ah,’ replied Joffy loftily, ‘wait until you meet the Brotherhood of Unconstrained Verbosity.’

Gloria and Charlotte always sat next to one another, Gloria to talk about something trivial and Charlotte to agree with her. Mum and Polly talked about the Women’s Federation and I sat next to Mycroft.