PopCo
5449 5471 5477 5479 5483 5501 5503 5507 5519 5521
5527 5531 5557 5563 5569 5573 5581 5591 5623 5639
5641 5647 5651 5653 5657 5659 5669 5683 5689 5693
5701 5711 5717 5737 5741 5743 5749 5779 5783 5791
5801 5807 5813 5821 5827 5839 5843 5849 5851 5857
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5953 5981 5987 6007 6011 6029 6037 6043 6047 6053
6067 6073 6079 6089 6091 6101 6113 6121 6131 6133
6143 6151 6163 6173 6197 6199 6203 6211 6217 6221
6229 6247 6257 6263 6269 6271 6277 6287 6299 6301
6311 6317 6323 6329 6337 6343 6353 6359 6361 6367
6373 6379 6389 6397 6421 6427 6449 6451 6469 6473
6481 6491 6521 6529 6547 6551 6553 6563 6569 6571
6577 6581 6599 6607 6619 6637 6653 6659 6661 6673
6679 6689 6691 6701 6703 6709 6719 6733 6737 6761
6763 6779 6781 6791 6793 6803 6823 6827 6829 6833
6841 6857 6863 6869 6871 6883 6899 6907 6911 6917
6947 6949 6959 6961 6967 6971 6977 6983 6991 6997
7001 7013 7019 7027 7039 7043 7057 7069 7079 7103
7109 7121 7127 7129 7151 7159 7177 7187 7193 7207
7211 7213 7219 7229 7237 7243 7247 7253 7283 7297
7307 7309 7321 7331 7333 7349 7351 7369 7393 7411
7417 7433 7451 7457 7459 7477 7481 7487 7489 7499
7507 7517 7523 7529 7537 7541 7547 7549 7559 7561
7573 7577 7583 7589 7591 7603 7607 7621 7639 7643
7649 7669 7673 7681 7687 7691 7699 7703 7717 7723
7727 7741 7753 7757 7759 7789 7793 7817 7823 7829
7841 7853 7867 7873 7877 7879 7883 7901 7907 7919
Solution
It was a beautiful scarabaeus, and, at that time, unknown to naturalists – of course a great prize in a scientific point of view. There were two round black spots near one extremity of the back, and a long one near the other. The scales were exceedingly hard and glossy, with all the appearance of burnished gold.
‘The Gold Bug’ by Edgar Allan Poe
It’s late September, and I am washing up in the small kitchen in my house in Gypsy Hill, looking out of the small window at the moon. It’s like someone has taken a sheet of blotting paper and covered the whole sky with it, smudging everything, taking the edges away. And this is all I am thinking about: the blotting-paper moon. I’m not thinking about switching on the radio, or playing videogames, or even doing any work. For a while now I have been planning to start writing a book about PopCo, and about my childhood and the Stevenson/Heath manuscript, but I keep putting it off: the NoCo code project has been taking up all my time. But tonight I am thinking of nothing apart from the moon. For the past few years or so I have been frightened of this, of letting my mind roam unsupervised in this house, because it always goes back to the same thing: my grandfather and how much I miss him. It’s OK when I am at Ben’s house (and I have been there a lot recently) but I am worried about my book. It’s going to be made of memories, after all. But tonight, for some reason, it’s OK. Tonight I seem able to just look at the moon without anything bad happening.
I finish washing up, dry my hands on a thin cotton tea-towel and fetch a tin of cat food from the larder. Atari weaves through my legs as I open the tin on the small table next to the sink (we never did get a fitted kitchen), still looking out of the window. I think about a note I wrote in my ‘ideas’ book yesterday, about the moon looking like it had been punched in the sky like a hole. But today’s moon has been ripped, not cut, from the sky, and the fabric is frayed around it. So now I have two ideas. I have a blotting-paper moon, and a moon ripped out of a fabric sky. I put Atari’s dinner down on the kitchen floor and walk through the hallway and up the stairs. I’ll put both ideas down in my tattered red book (already stained with green tea) but I probably won’t use either of them. What’s the point? And how can I possibly think of writing a book when I don’t have a proper ending? I have the PopCo story to tell (I’m pleased with that name for the company: PopCo. I think it’s better than the actual name – maybe I’ll win another case of champagne if I suggest it to the board) but what’s the point of telling the Stevenson/Heath story when it has no end? Nothing about that half of my story seems to have an end. No proof for the Riemann Hypothesis. No solution to the Voynich Manuscript. And the one thing that there is an answer for, well, I know there is an answer, but I don’t know it.
The study has always been the warmest room in this house. When we moved here, my grandfather and I took the most care over the decoration of this room: in fact, it’s the only one we really changed. The downstairs sitting room was left wearing its house-sale yellow paint, and the hallway still has the woodchip we’d vowed to remove. But we took a lot of care over the study. After all, it was the most used room in the house. My grandfather would sit in there all day, burning coal in the small Victorian fireplace, setting crosswords or working on the Voynich Manuscript. In the evenings I would join him, and we’d work in silence together before I would make our supper: soup and homemade bread (if he made the bread during the day), or scrambled eggs on toast (if the bread was yesterday’s).
After supper we would go back into the study and play chess or Go for an hour or so before getting back to work. I’d lost interest in the Voynich Manuscript by then. Or, not exactly lost interest … To be honest, it was making me angry. I felt that my grandfather was wasting his life on it; that there probably was no solution. But still he’d sit there with his books and his new copy of the manuscript that he’d obtained from the Beinecke Rare Book and Manuscript Library at Yale University. I had hoped he would go back to the idea that he’d worked on for a time in the mid-nineties, that the book had been forged by Voynich himself. At least that hypothesis was fun. Voynich had claimed to have discovered the manuscript in a Jesuit monastery in 1912, but there was never any record of this. And Voynich was not only a rare-books dealer but also a trained chemist with access to vellum – and experience forging documents for the Polish Proletariat movement. But hardly anyone who works on the Voynich Manuscript wants it to be a forgery, and my grandfather moved on from this hypothesis after a year or two. After that, he worked on another theory that has become very popular: that the book had been created by John Dee and Edward Kelley to further their chances of patronage in Europe.
But in those last couple of years before he died, my grandfather had gone back to the task I’d helped with when I was ten: counting words and letters and putting the results into mathematical functions to see what happened. Nothing ever did.
One night, after he had beaten me at Go for the fourth night running, my grandfather sat down in his big brown armchair and, after poking the fire, took out his magnifying glass and set about recounting the letters on one particular page. It happened to be one of the most famous pages in the whole manuscript. I remembered my grandfather telling me about William Newbold, who worked on the text from about 1919 and came up with a crazy mixture of cabalistic Gematria, anagramisation and hocus pocus to eventually decipher a section beginning ‘Scripsi Rogerus Bacon …’, although, with the method he used, the text could have said anything he wanted (and it has been recorded that both Newbold and Voynich believed the manuscript to be the work of Roger Bacon). James Martin Feely attempted a decipherment based on only one plate from Newbold’s book, one showing the same page that my grandfather was now working on. Feely thought he had found a simple substitution cipher, from Latin to ‘Voynichese’, and part of his translation reads: ‘Well humidified, it ramifies; afterward it is broken down smaller; afterwards, at a distance, into the fore bladder it comes.’ Not totally convincing, but the page does appear to show ‘plumbing’, and naked women in strange tanks of green liquid. So now my grandfather was obsessed with this page too. If he could make the total come out as an odd, rather than an even, number of letters, then something interesting might happen. He didn’t tell me what this would be. I could see that he had his original calculation
on his side-table, along with a small blue exercise book I hadn’t seen for years.
‘Is that my book?’ I said to him, intrigued.
‘Mmm hmm,’ he said back, still looking through his magnifying glass.
‘Can I see?’ I asked.
He passed me the book and I opened it. It was just as I remembered it: columns of numbers neatly labelled in my funny ten-yearold’s handwriting. I laughed.
‘God, I took all this so seriously,’ I said, flicking through the book. Towards the end were the results of the most difficult and boring task: the prime factorisation. ‘Bloody hell,’ I said to my grandfather. ‘I’d forgotten I’d done all this as well. It took ages, didn’t it?’
He looked up at me and frowned for a second.
‘Do you know what the funny thing is?’ he said.
‘What?’
‘You got all of them right. All the calculations you did were correct.’
I smiled. ‘Wow.’
He smiled back. ‘Hmm.’ He returned to his magnifying glass again.
‘I always wondered …’ I said.
‘What?’
‘Did you give me that task to, you know, take my mind off those two men and my fear of the dark and everything? Because it did, you know, and …’
He looked up at me and frowned again. ‘No,’ he said. ‘No. I wanted you to learn about prime factorisation. I wanted to be sure you would always know how to do it.’
I’m standing outside the study now, remembering this, and I’m thinking, Why this conversation? Why now? Why, when I thought I could fill my head with nothing more complicated than thoughts about the moon, is this suddenly not enough?
I haven’t been in the study much since my grandfather died: it’s as if all those conversations we had, and everything we ever did together, are locked up in there. But now I am opening the door and going in. And I am not going to cry. It’s hard: there’s a sad little pile of coal in the fireplace with two firelighters and some kindling. I remember building that fire the night after my grand father died. Of course, I couldn’t light it. I remember sitting in his armchair, looking at his notes and his magnifying glass and everything and wondering why these items hadn’t realised that something in their world had changed, that they didn’t belong to anyone any more. I wished that they could have just tidied themselves away so I didn’t have to do it; so I didn’t have to be the one to admit that it was all over and I didn’t know what came next.
I must have sat there for almost ten minutes before I just got up, went downstairs and plugged in my videogame.
Today I do light the fire. I hold the flame close to one of the white, greasy firelighters until it catches, and then I calmly pick up the magnifying glass and the pencil and the stack of papers from my grandfather’s small table and put them away. Then I take all the books from the pile on the floor by his chair and put them on the shelves, slotting each one neatly into place. It’s funny how he always left an odd kind of code explaining exactly what he was working on at the time. A magnifying glass, a page of the Voynich Manuscript, my blue book, lists and lists of numbers and mathematical functions … Perhaps you have to know him well to be able to read the code, but it’s there. The things around his chair tell a story, quite a simple one: that he was working on the Voynich Manuscript, and nothing else, on the day he died. And this is what I am thinking about now. I’m not thinking He’s dead, he’s dead, oh God, he’s dead, any more, like I used to. I’m thinking about how much I loved him, which is different, and for a moment I see him in Heaven, reading some transfinite book. As the fire catches and the red walls glow with reflected flames, I consider moving my desk back up here after all (it’s been downstairs ever since he died). I bet he knows the answers now. I bet he knows whether or not the Voynich Manuscript was a forgery. And I bet my grandmother knows everything she would ever want to know about the Riemann Hypothesis.
There’s only one thing still bothering me: the living world doesn’t know about the Stevenson/Heath manuscript and my grandfather’s solution. It’s supposed to be part of my book but I never did work out the code on my necklace. And what would be the point of writing a book with no solution? All I ever did work out was that 2.14488156Ex48 is shorthand for a longer number. It was when I was learning about Gödel’s Incompleteness Theorem and trying out his number code. Every calculation I did came out with a number so big that it wouldn’t fit on my calculator. And when this happened the calculator displayed something similar to my necklace number. 2.14488156Ex48 really means 2144881560000000000000000000000000000000000000000. Ex48 just means you raise the number by 1048. It means the number you want is too big to fit on your calculator, so the calculator rounds it up and gives it to you in this form. I remember the afternoon when I worked this out – it was rainy and grey and a snail kept crawling up and down my bedroom window – and I thought it was a major breakthrough. I even remember what I was doing: I was trying to write ‘I love you’ to my grandfather, using Gödel’s code. I’d written the letters out first as numbers according to their place in the alphabet: I=9, L=12, O=15, V=22, E=5, Y=25, O=15, U=21, and then I had tried making the code-number. What I needed to calculate was 29 × 312 × 515 × 722 × 115 × 1325 × 1715 × 1921. This was a list of the first eight primes, with each raised to the power of the corresponding number in my sequence.
I worked out that 29 was 512, and 312 was 531,441. But then it started to go wrong. 515 came out as 3.051757812Ex10. I checked my calculator instructions and found out that this actually meant 30517578120. I wrote this down in my notebook and moved on. But 722 was even bigger. It equalled 3.909821049Ex18. But that was when I got suspicious. I realised that this number would end in a zero (in fact, in nine zeroes), implying it was divisible by 2 and 5. But I knew that a number with one prime factor – 7 – could not be divisible by 5 and 2. It was very confusing, so I looked back at my instructions again. And there it was: This calculator is accurate to 10 digits only. All those zeroes weren’t really zeroes: they were other numbers – but the calculator couldn’t display them. And this made me feel uncertain and confused about my necklace code. Why give me an inaccurate number? Maybe it wasn’t inaccurate, but I couldn’t work it out. Of course I tried to prime factorise it, but it was too big. I could tell just by looking at it that it would be made up of lots of 2s and 5s. Was my grandfather trying to tell me something about 2s and 5s? I couldn’t see why he would want to do this. Even if you lop off all the zeroes (240 × 540) and concentrate on the rest of the number, you end up with another 22, 3, 23 and then nothing that I could find. The prime factors obviously became pretty big. It felt wrong. If 2 and 5 related to things – letters or words from another document, perhaps – why would you need so many of them?
There’s a large metal trunk on the other side of the study, a larger version of the two small ones I have in my bedroom. I haven’t looked in any of the trunks since my grandfather died. The silver one in my bedroom contains everything to do with the Voynich Manuscript, and the other one, a sort of brassy colour, contains all my childhood diaries and bits and pieces. But the one in here contains older papers – all the stuff my grandmother told me I would inherit when my grandfather died. And then a snatch of another conversation comes into my mind. My grandmother: … if you want to, you can work out the code and then make your own choice about what to do about it. How did they think I would do this? Did I miss the clues? Have I forgotten them?
I open the chest, using the combination my grandfather taught me.
Inside are manuscripts from his Mind Mangle collections, and flat proofs corrected in his large, almost unreadable handwriting. There are bundles of letters and old photos, some going back to the thirties in Cambridge. Then there are the papers that I always vowed I would put aside a weekend to sort out: reams and reams of handwritten notes, mostly unreadable due either to my grandfather’s handwriting or, more often, to the fact that they were written in code. I know that part of the answer is here, and part of it is on my necklace. But I
don’t know how any of it fits together.
I sit back on the floor, cross-legged, with a bundle of papers. I start going through them, but an hour later I haven’t found anything that looks like it will help. There are a couple of essays, handwritten in English, on the subjects ‘Exploitation in the Workplace’ and ‘SOE: Remembering’. But most of the papers are lists of numbers, a Beale-type code: a Stevenson-type code. It’s unclear how I would go about sorting and arranging them. Shall I take them downstairs and make a cup of tea? Shall I leave this until another time? No. The fire is now going and it’s starting to get warm in here. Maybe I will make a cup of tea and bring it up. I will bring my tea upstairs and actually go through these documents properly – however long it takes. That decided, I grab a handful of photographs – something to look at while I wait for the kettle to boil – and go downstairs.
Atari is asleep on top of the Aga, and I don’t blame him: it’s a cold evening. I put the kettle on and lean against the Aga myself, warming my back, and start flicking through the photographs. There are quite a lot that I haven’t seen before. Photos of my father, with his beard and jeans, and, every so often, my mother: sitting in the sun in my grandparents’ old city garden, or reading. There’s one of my grandfather in his old study, sitting posed at his desk, with a little twinkle in his eyes suggesting that somewhere behind the photo is a serious occasion that he is not taking entirely seriously. I remember the layout of that little study only vaguely, although I do remember that it always smelled of earth and pencil shavings. In the photo my grandfather sits slightly back from his desk with his legs crossed, right loosely dangling over left. The picture is well composed and has been taken side-on, with my grandfather in the right-hand side of the frame and the desk in the left. It’s a mess, as his desk always was.
I wonder who was behind the camera. It can’t have been my grandmother, as she is in the next photo, sitting on his lap, laughing and – bizarrely, because I never saw my grandmother in anything other than full dress – wearing a yellow bathing costume. Was it my mother? Did she take these? The next photo is of my grandfather reaching to pin or unpin something on the notice board that hung above his desk. I look at the series again. They seem like a text that has fallen out of order: a non linear narrative. But the actual story is clear. My grandfather was busy working in his study, getting a document off his notice board, when someone, perhaps my mother, disturbed him with a camera. ‘Come on, Dad, we’re all having fun outside,’ she’d probably have said. And then she would have made him pose at his desk for his own inside-while-everyone-else-is-out-in-the-sun photo. Then my grandmother would have come in and teased him and joined in, sitting on his lap for another photo.