Something rotten

I nodded.

'Well, Nextian number theory is very closely related to that, and in its simplest form allows me to work backwards to discover the original sum from which the product is derived.'

'Eh?'

'Well, say you have the numbers twelve and sixteen. You multiply them together and get 192, yes? Now, in conventional maths if you were given the number 192 you would not know how that number was derived. It might just as easily have been three times sixty-four or six times thirty-two or even 194 minus two. But you couldn't tell just from looking at the number alone, now, could you?'

'I suppose not.'

'You suppose wrong,' said Mycroft with a smile. 'Nextian number theory works in an inverse fashion from ordinary maths — it allows you to discover the precise question from a stated answer.'

'And the practical applications of this?'

'Hundreds.' He pulled a scrap of paper from his pocket and passed it over. I unfolded it and found a simple number written upon it: 2216091 -1, or two raised to the power of two hundred and sixteen thousand and ninety- one, minus one.

'It looks like a big number.'

'It's a medium—sized number,' he corrected.

'And?'

'Well, if I was to give you a short story of ten thousand words, instructed you to give a value for each letter and punctuation mark and then wrote them down, you'd get a number with sixty-five thousand or so digits. All you need to do then is to find a simpler way of expressing it. Using a branch of Nextian maths that I call FactorZip we can reduce any sized number to a short, notated style.'

I looked at the number in my hand again.

'So this is?'

'A FactorZipped Sleepy Hollow. I'm working on reducing all the books ever written to a number less than fifty digits long. Makes you think, eh? Instead of buying a newspaper every day you'd simply jot down today's number and pop it in your Nexpanding calculator to read it.'

'Ingenious!' I breathed.

'It's still early days but I hope one day to be able to predict a cause simply by looking at the event. And after that, trying to construct unknown questions from known answers.'

'Such as?'

'Well, the answer: 'Good lord, no, quite the reverse!' I've always wanted to know the question to that.'

'Right,' I replied, still trying to figure out how you'd know by looking at the number nine that it had got there by being three squared or the square root of eighty-one.

'Isn't it just?' he said with a smile, thanking my mother for the bacon and eggs she had just put down in front of him.

Lady Hamilton's departure at 8.30 was really only sad for Hamlet. He went into a glowering mood and made up a long soliloquy about his heart that was aching fit to break and how cruel was the hand that fate had dealt him. He said that Emma was his one true love and her departure made his life bereft; a life that had little meaning and would be better ended — and so on and so forth until eventually Emma had to interrupt him and thank him but she really must go or else she'd be late for something she couldn't specify. So he then screamed abuse at her for five minutes, told her she was a whore and marched out, muttering something about being a chameleon. With him gone we could all get on with our goodbyes.

'Goodbye, Thursday,' said Emma, holding my hand, 'you've always been very kind to me. I hope you get your husband back. Would you permit me to afford you a small observation that I think might be of help?'

'Of course.'

'Don't let Smudger dominate the forward hoop positions. He works best in defence, especially if backed up by Biffo — and play offensively if you want to win.'

'Thank you,' I said slowly, 'you're very kind.'

I gave her a hug and my mother did too — a tad awkwardly as she had never fully divested herself of the suspicion that Emma had been carrying on with Dad. Then, a moment later, Emma vanished — which must be what it's like when Father arrives and stops the clock for other people.

'Well,' said my mother, wiping her hands on her pinafore, 'that's her gone. I'm glad she got her husband back.'

'Yes,' I agreed somewhat diffidently, and walked off to find Hamlet. He was outside, sitting on the bench in the rose garden, deep in thought.

'You okay?' I asked, sitting down next to him.

'Tell me truthfully, Miss Next. Do I dither?'

'Well — not really.'

'Truthfully now!'

'Perhaps ... a bit.'

Hamlet gave out a groan and buried his face in his hands.

'Oh what a rogue and peasant slave am I! A slave to this play with contradictions so legion that scholars write volumes attempting to explain me. One moment I love Ophelia, the next I treat her cruelly. I am by turns a petulant adolescent and a mature man, a melancholy loner and a wit telling actors their trade. I cannot decide whether I'm a philosopher or a moping teenager, a poet or a murderer, a procrastinator or a man of action. I might be truly mad or sane pretending to be mad or even mad pretending to be sane. By all accounts my father was a war-hungry monster — was Claudius's act of assassination so bad after all? Did I really see a ghost of my father or was it Fortinbrass in disguise, trying to sow discord within Denmark? How long did I spend in England? How old am I? I've watched sixteen different film adaptations of Hamlet, two plays, read three comic books and listened to a wireless adaptation. Everything from Olivier to Gibson to Barrymore to William Shatner in Conscience of the King.'

'And?'

'Every single one of them is different.'

He looked around in quiet desperation for his skull, found it and then stared at it meditatively for a few moments before continuing:

'Do you have any idea the pressure I'm under being the world's leading dramatic enigma?'

'It must be intolerable.'

'It is. I'd feel worse if anyone else had figured me out — but they haven't. Do you know how many books there are about me?'

'Hundreds?'

'Thousands. And the slanders they write! The Oedipal thing is by far the most insulting. The goodnight kiss with Mum has got longer and longer. That Freud fellow will have a bloody nose if ever I meet him. My play is a complete and utter mess — four acts of talking and one of action. Why does anyone trouble to watch it?'

His shoulders sagged and he appeared to sob quietly to himself. I rested a hand on his shoulder.

'It is your complexity and philosophical soul-searching that we pay money to see — you are the quintessential tragic figure, questioning everything, dissecting all life's shames and betrayals. If all we wanted was action, we'd watch nothing but Chuck Norris movies. It is your journey to resolving your demons that makes the play the prevaricating tour de force that it is.'

'All four and a half hours of it?'

'Yes,' I said, wary of his feelings, 'all four and a half hours of it.'

He shook his head sadly.

'I wish I could agree with you but I need more answers, Horatio.'

'Thursday.'