Something Rotten (Thursday Next 4)

'The Prose Portal. A device for entering fiction.'

'They were asking me about something like that, now you mention it. It would be very intriguing to try and redevelop it but Polly says I shouldn't. My lab is full of devices, the purpose of which I haven't the foggiest notion about. An ovinator, for example – it's clearly something to do with eggs, but what?'

'I don't know.'

'Well, perhaps it's all for the best. These days I only work for peaceful means. Intellect is worthless if it isn't for the betterment of us all.'

'I'll agree with you on that one. What work were you presenting to MadCon '88?'

'Theoretical Nextian mathematics, mostly,' replied Mycroft, warming to the subject dearest to his heart – his work. 'I told you all about Nextian geometry, didn't I?'

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.'