“Then all of these things, if presented in the right attitude, will pass through a circular hole.”
“Correct. But if they fall through a big square hole, without registering their presence, touching the sides, if you like, then they won’t count.”
“What you are saying is they have to match the shape.”
“Precisely. You are getting quite good at this. The ones that fit the holes are the ones that survive.”
“And the ones that fit the most holes survive the best.”
“That’s pretty much it, Chris. Brilliant.”
“...and the trick is to catalogue all the holes you can find and then hunt around for what you think might fit through them.”
“You have been very well briefed,” he said. It was a throwaway comment, delivered as he vaulted the balcony rail so he could pause on the outside ledge before launching himself into the sea, where he swam for a full fifteen minutes.
Christine’s drink ran out and she made her own way along the balcony rail to the back to seek a refill. By the time she had negotiated the twenty metres or so of veranda with its two right angled turns each way, he was back, dripping, in his chair.
“You needed a pee,” she said as she placed her drink on the table by her still unoccupied chair. He laughed as he wrung out the end of his shorts that hung loose below the stump of his right leg.
“We have to talk about the third programme.”
“Classical music.”
Christine smiled. “Now that dates you.”
“And that will be the end of your assignment?”
“Pretty much.”
His silence was full of regret, unexpressed. “I was starting to enjoy the company.”
Christine turned to look at him. Had she been wearing glasses, her gaze would have been cast above the frames. “But what about your work? You said you come here to work, and since I came you have done hardly anything - certainly none at all in the last few days.”
He shrugged. “The work is at a stage where more of it happens here.” He tapped his forehead. “There is very little that has to be written down.”
“It had come to my notice that you don’t carry a notebook. You don’t seem to be actively involved with it. It’s not something that is with you all the time, and I find that surprising.”
“Quite the contrary, Chris.” His immediate reply was either sincere or practiced, or both. “The concepts are now so familiar they are firmly embedded in here.” There was another tap of the forehead. “I don’t write things out in full any more. I don’t need to. The ideas themselves were all worked out years ago. Since then they have combined and recombined as I have extended the dimensionality and now form a series of almost standard results, if you like, that are so thoroughly embedded in the way I think that I can recall complete pieces of work almost as single ideas.”
“Mathematics...”
“It’s nothing strange, Chris. If you think of calculus, it’s implicit in the use of dy by dx that what’s going on is the limit of the increment of one variable compared with the increment in the other variable.”
“If you say so.”
“But nowadays no-one would bother to write down the derivation of a differential function before they used it.”
“I’m sure I wouldn’t...”
“Well my work is just the same. Event theory, as I have come to call it, has matured to such an extent that now I can use it just by pushing around these big ideas that I have developed over the years.”
Christine was clearly trying to decide if this was worth pursuing. She knew, of course, that even if she did not follow what Cartwright said, then one of our specialists might. “So what do these things look like? How do you work with them?”
“It’s quite literally as I said. I take these big ideas and assemble them into different orders, the order being determined by the nature of the problem being considered. It’s a bit like baking a cake. To write it down chemically, you would need all the chemical formulae of sugar, flour, egg albumen and yolk, plus the fats. It would look hopelessly complicated to the average person, but that’s what the laboratory chemist would need to recreate or model a cake from chemical bits and pieces. Write down the recipe as this much flour, this much egg, this much sugar and fat, and it becomes easy to visualise the process.”
“Mathematics?”
“When you see mathematics written down, it is like a cake recipe written for an analytical chemist. It is detailed down to the chemical definitions of the ingredients. When I write down my work, that process has been done so many times in my previous work that I can put a load of it together and call it an egg, or call it sugar. To extend the work, I then just bake a cake by saying two eggs, a cup of flour, a piece of fat et cetera. And it’s this list of ingredients, plus notes on how to combine them that I write down when I work. Nothing else.”
“Show me.”
I don’t really know why I had ever doubted Christine’s professionalism. And now, I don’t know why I needed to write that last sentence, except to underline my own tendency to panic and fear the worst. Perhaps I was not born a pessimist: I merely had second thoughts about the timing. I know very well why I doubted Christine’s professionalism. Looking back, I had clear reasons to do so. It’s not every assignment that requires the operative to open her legs to admit the adversary. Is it possible to open a leg? No, sex with a protagonist is not usually on the agenda, but Christine was obviously still very much on task. Perhaps I ought to put her actions down to tactical decision on the ground, rather than personal decisions on the couch? The opportunity had arisen to have Cartwright explain his work while they were both in shot and she had leapt at it.
Cartwright got up with a giant sigh and hopped his way inside the house. It was only then that I realised that not only had they not locked any of the doors or windows before they left those days ago, but also that the doors and windows could not even be closed, let alone secured. Cartwright, it appeared, was not at all security conscious. He reappeared within the minute carrying one of the files from his office, a file into which I had already watched him entering his adjudged gibberish.
“Here,” he said, presenting the file to Christine before flopping back into his seat. He then leaned across and opened up the flap of the pocket folder which she now held. The sheets were loose, unbound. “Try this one.” He took hold of the top sheet and pulled it free of the folder.
Christine looked at the page. She held it for twenty seconds or so at the perfect angle for my camera, which was above them, slightly to their right. The page was thus angled away from Cartwright. I recognised it as one of the sheets I had already forwarded for analysis. There were only five or six sheets of paper left in the folder.
“Could you please tell me which way up I should hold it?”
Cartwright laughed. “It’s the right way up. Can’t you read it?”
It was a sheet of A4 paper, punched with two standard filing holes. It was squared, not lined, but nowhere did it contain any attempt at graphical work. In his small, obsessively neat hand, every other line was part-filled with symbols, the spaces between them apparently regular. Few of the lines extended to the width of the page. These were the very symbols our specialists had been unable to recognise or interpret.
“I have not the faintest idea what any of this means,” said Christine, handing back the sheet. She probably thought she had done her work, since she, of course, had no idea that I had already seen it. And Cartwright refused to accept it, pushing the arm that held it back towards her.
“I’ve already given you a clue. I referred to it quite consciously quite soon after you arrived,” he said. “And you will remember that before we left here the other day to go and visit my wife and kids, I advised you to take careful note of the street signs...”
“Presumably so I coul
d take note of where they lived?”
“You knew that already, Chris, unless I am completely mistaken. My advice was more subtle than that.”
Christine again fiddled with the paper. She turned the sheet this way and that as she mused on its illegibility. “Maybe some of these symbols are Arabic?”
“Certainly not,” he said. “But you are close. They are Jawi, the script that’s used over there alongside Roman letters on every street sign.” He gestured vaguely in the direction of the horizon.
“But it looks different...”
He laughed.
“And this...” Christine pointed to a group of symbols near the left margin.
“Ah,” he said in a tone that offered congratulation. “They are different.”
“Cut the crap, Tom. What is this?”
“As I said, these are various letters in Jawi script and these,” he said, pointing at the part of the sheet her finger still indicated, “are Cham, mostly numerals.” He let out a little groan as he strained in his chair to get a better look at the sheet to confirm.
“Why?”
“I ran out of symbols. And they’re all upside down.”
“Why, perchance?” It wasn’t impatience that quickened her delivery.
“Well, Leonardo da Vinci wrote everything backwards...”
“But he was left-handed and probably found it easier to pull the pen rather than push it.”
“Possibly, but maybe he was also interested in keeping his results to himself until they were complete, hence the need to make it hard to read for the casual observer. And it’s hard to copy. The Jawi is supposed to go from right to left, and I am left-handed. And I’ve only got one leg, so I wrote it upside down. Given Leonardo’s mirror writing, I thought it was a little joke.”
Christine let the hand holding the paper fall to her lap as she turned to look to her left. “Ho, bloody ho.”
“And so when I ran out of symbols, I started to use Cham as well, but followed the same regime and wrote them upside down as well:”
“Why?”
He did not speak.
“No reason, except to keep everything to yourself.”
He thought for a while before answering. His gaze was firmly set on an infinity beyond the forested horizon. “No. Even if it was all the right way round, no one else could understand what it means.”
“That’s precisely my point, Tom.”
The two of them sat in silence for several minutes. There was a gentle breeze across their veranda rattling the rope-ends that hung loose off the moorings. The sea was calm, however, with only a gentle swell rocking the boats that passed by in their distance. Christine took occasional sips of her drink, remaining overtly in control of her obvious desire to finish it and refill the glass.
“So what does it all mean?” It was Christine who broke their peace.
Cartwright seemed reluctant to begin. I have watched the sequence several times and I am convinced his silence represents merely a difficulty of not knowing where to start. He seemed to have no worries whatsoever that he might reveal something even useful, let alone fundamental. It was Christine who again tried to prompt.
“I expected to see at least some symbols I could recognise.” She took up the paper again and scanned its contents. She did the same with the other sheets in the folder before replacing them. “I can’t even see any plus signs, minus signs, multiplies or divides. Or even numbers...”
“Oh, there are loads of those, but they’re written in Cham.” He was quick to respond. “And as for arithmetical operators, Chris, I might point out that what you are looking at is mathematics, not accountancy.” He turned to his right and leaned towards her. She turned a little also, their faces virtually at near-point. “I modelled my notation on Algol.” He paused. “Now that dates me, doesn’t it?”
“I suppose it does...”
He laughed. “You have not the faintest idea of what I am talking about!”
“Of course I haven’t.”
I recalled his statements, delivered in the first interview, about Chris not having the skills to carry out this assignment. I remained unsure, however, as to just how much he knew about her motives and brief.
“Algol was an early computer programming language, but in fact it pre-dated computing. It stands for Algorithmic Language and it’s used to create a structure within which sequential and logical procedures can be notated. Basically, each paragraph of symbols on a sheet,” he said, tapping the folder that lay on the table between them, “is a set of instructions, do this, followed by that. Here and there are words such as ‘if’, ‘then’, ‘else’, ‘do’, ‘repeat’, ‘until’ and lots of others that effectively form the keywords of the language.”
“I didn’t recognise anything.”
“...because they are in Jawi and Cham, sometimes upside down and backwards. Rest assured, I can read them.” He seemed unsure as to whether he should continue. Christine did not prompt. “Each paragraph on the paper is like a sentence of text. And you will see,” he said, reaching across to extract the top sheet from the folder, “that some sections are quite long, while others are less than a line.” He passed the sheet to Christine and pointed to precisely six lines on the sheet that finished short of the margin. “These are the paragraph ends, and then,” he continued as he rummaged through the other sheets before selecting one in particular, “here you have something that looks quite different. This line is centred and I have written the characters larger.”
“Enlightening...”
“This is a conclusion. In other words, if all of the above procedures are followed, in sequence, and according to the rules they represent, then this indicates the conclusion we might expect.”
“And it’s all upside down...”
“And backwards as well, here and there. But it’s not all that way. There is method in my insanity.” He rummaged again through the sheets and selected another, which he passed to her. His hands were brushing very close to her breasts, but she did not flinch in any way. “If you were to look at some of my earlier material, it’s written the right way up. Here’s some material I quote directly from work I did a decade ago. I have included it here as a check on the current procedure, which is upside down.”
“How interesting...”
“Because this material is actually all conceived in the inverse of the original.”
“Inverse what?”
“Universe.”
Christine turned to look at him. Their faces were beyond the near-point. It would almost have been easier to kiss than speak. She delivered a long, determined stare, full of simultaneous affection and disbelief, while his eyes alternately examined her expression and the symbols on the paper she still held. “I have not the faintest idea of what is going on...”
He leaned back and laughed. “You did ask. Look here,” he said, leaning quickly across and placing his arm around Christine’s shoulders. I had to remind myself that these two individuals were both sixty years old. “Look here,” he said, as he pointed to a line on the sheet she held, and then to another on a sheet that lay on the table between them. “Can you see they are the same symbols? Except that the more recently written ones, on that sheet, are all upside down?”
“Why? Because it looks pretty cool and makes you feel like Leonardo da Vinci?”
“No, Chris, it’s because this one is the inverse of that one. It’s like shorthand. If I were to write this material out in full, it would be the length of a book.”
“Inverse..:”
“Opposite,” he said impatiently. He thumbed the older sheet. “If this one means with legs, then this one,” he continued, now pointing at the newer version, “means without legs. Legless, like you get after a few gins.”
She laughed and hit him. “I have one leg, stupid, so I am not in either
class.”
“And that condition,” he continued without pause, “is the part inverse of the original ‘with legs plural’, if Brouwer’s rejection of the excluded middle is allowed. Then I would write it on its side. It becomes a matter of intuition.”
“No doubt pointing left for you and right for me.”
“No, Chris, this really is quite serious. The attitude of the character would indicate merely a set of assumptions that must travel with the concept and relate to how it was formed.”
“I don’t get it.”
“And you’ll get it even less when I conclude by saying that the inverse procedures exist largely in an imaginary universe, whereas the right way up ones are in a real universe.”
“A real universe...”
“There can be more than one.”
“And on its side...”
“It bridges the real and imaginary.”
She was silent.
“...but only according to the conditions specified in the assumptions that travel with it.”
“I’m so glad you clarified that...” She was trying to get any handle she could on what his world might look like. “And each symbol ... what do they mean? You say they go together like sentences?”
“Basically, over the years I have done a mountain of work. Some of it was useless. Some of it, however, has proved fundamental to the things I do now.” He paused and thought. “Imagine I had written a paper years ago that examines a particular idea and contains a conclusion about a particular point. Each symbol I write represents one such finding from my previous work that has to be applied to the material under considerations. It’s like a list of ingredients, except, like the cake I described earlier, these list eggs, flour, et cetera and not the chemical constituents that make them up. Placed like this, the symbols represent sets of procedures that must be applied to data, with each symbol representing something from my previous work. And it’s all in here.” He tapped his forehead.
“And sometimes it’s an opposite of the finding...”
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