“A circle.”
He stood the bottle upright on the balustrade next to the lemon.
“Be careful with that,” she said, self-interest getting the better of her continued participation.
Cartwright then took up a soft-drink can from his tray. Again he presented this end-on towards Christine.
“Circle,” she said, without prompt.
“You’re getting the hang of it.”
Next was a coconut.
“Circle.”
And then there was a rambutan.
“I suppose it’s a circle ... but a hairy one.”
Impatiently, he peeled the fruit, throwing the hairy red skin into the sea. He then held up the soft white pulp before Christine’s now rapt gaze.
“Now it’s a circle,” she said with a primary school teacher’s patronising nod.
He placed the fruit on the balcony rail, alongside the other items.
“Now tell me where you see a circle.”
Christine pointed towards the soft white ball of rambutan flesh. “It’s not exact, but it is the answer you want me to give.”
“Brilliant!” he said. “You see, even you can do it. You can read my mind!”
“If only... if only... You were just the same on the bowling green when you were eighteen. You couldn’t just bowl the ball and accept where it finished. You would dash after it, bring it back, try again, get worked up, repeat the process, get angry, do it all over again... And then the groundsman would come and play hell with you for trampling his grass.”
Cartwright stood next to his admixture of objects, almost proud. Christine was clearly mystified.
“Can I eat the rambutan?” she asked.
“Of course,” he said and passed it to her. It went whole into her mouth. The stone appeared in her palm a few seconds later.
“Now that’s perfumed,” she said, “and not a hint of sewage.”
“And now there are no circles,” he said, gesturing toward the assemblage.
“Now I’ll eat the coconut.”
“Christine, listen. This is serious. A moment ago these were all circles, weren’t they? How is it that there are now no circles in view?”
“Because I am not looking at the parts that are circles?”
“Correct!”
Christine offered the sort of look that a mother reserves for her three-year-old’s artwork. Cartwright laughed and began to replace the items onto his tray which, when loaded, he placed on the floor next to his chair.
“So?”
“The two dimensions I presented to you prompted you to admit you saw a circle each time. In the real world, as real as we may perceive it unaided, a third dimension complicated each object so that their commonality of circularity became obscured. Thus you no longer recognised their similarity, but it was still there and your memory confirmed it, despite the fact that you could no longer see it.” His short pause performed the function of starting a new paragraph. “I deal with something called event theory. Much modern work in the area uses significantly more than three dimensions. I am talking dimensions,” he said, half-turning towards her, finger raised in emphasis, “and not variables.”
“The confusion never crossed my mind...” she said.
“In modelling the appearance or not of that flower, there are literally thousands of possible variables that could be taken into account. About fifty are crucial, in my estimation, and some of them are dependent...”
“I’m losing you...”
“They vary together, not independently, so they can be combined. But the effects of all these variables can only be understood - properly understood - if they are modelled in multiple dimensions, in the same way that cosmologists model the universe as a whole. Then, when we reduce our view, in other words restrict the dimensions we consider, then patterns emerge. And the patterns, though complex, repeat. Of course, they are far more complex than the circles to which these objects reduced, but they are clear and recognisable, if you know what you are looking for and where to find them. Knowing that they repeat and working back to the conditions upon which they do repeat, future behaviour becomes statistically predictable.”
Christine was trying to absorb his words. “Dimensions...”
Cartwright motioned towards his tray of objects. “These were interpreted in three dimensions, four if we include time, because it has played its part in how you saw them. I currently work in seventeen dimensions, a few more than cosmologists currently use to model the universe.”
“And the circles? The patterns?”
“Our circles were revealed in two dimensions, which was a reduction from the original three, or four if we include time, since when you see the bottle determines what you see, just as much as its attitude or position. You saw circles when we reduced the objects to a two-dimensional view. So you see a circle on the end only, a bottle shape from the side and very little by the time it’s empty.”
Christine turned to hit him, again. They were behaving like a pair of children. Christine’s laptop was now fully loaded.
“You never asked me for a password to connect to the internet.”
“I don’t need one. I have a roving facility.”
“It must be a damned good facility to rove out to this place.”
“You were saying... the patterns..:”
“You saw circles in two dimensions, reduced from the four. My patterns happen in every reduction below seventeen, apart from one, of course, because you cannot reduce that.”
Christine tapped away at her keyboard and then stopped abruptly. She turned to look at him as her screen loaded her email client. “You mean to tell me that when your systems operate, they deal with hundreds of variables...”
“...some of them are dependent, but yes...okay, hundreds...”
“They deal with hundreds of variables in seventeen dimensions and then you analyse the lot to search for patterns in two, three, four ... up to sixteen dimensions?”
Cartwright nodded. “I underestimated you,” he said.
“That’s ridiculous.”
He paused. “What? My underestimation of you or my system?”
“Both. But your systems sound quite incredible, meaning not credible.”
“I know. That’s why they have to be distributed across tens of thousands of computers, each of which carries out a few basic calculations. One dedicated machine could never manage it, especially since the system also requires, on occasions, that results are obtained as near as damn it simultaneously, meaning that they have to be generated faster than any possible computer could generate them, no matter how fast it is.”
“And then your patterns appear and that tells you what to trade.”
“You are very bright, Christine.” He looked down at her laptop. “Or you may have been well briefed... There is a message from your husband, if Tony Green is his name. It’s on top of the list.”
“Noting wrong with your eyesight, then,” said Christine, doing a professional job of hiding her surprise.
Fortunately, Christine then angled the laptop away from Cartwright’s gaze. He raised his hands in mock innocence and turned away.
“I wouldn’t want to intrude on domestic affairs.”
“Why did you not tell us you were going, you stupid idiot? You’ll be the death of both of us if we blow this one. I have put you onto emergency notification. Wherever you are, please contact me. Now. Tony,” is what she read from the screen when she opened my message
“Bastard,” is what she said.
***
I had not slept for four days. I had anticipated their return at the passing of every minute of every one of those days. When it came, it took me by surprise. I had dozed off and awoken only as they were in the process of unloading themselves and their go
odies from the boat. But I missed nothing, since there was always an opportunity to replay what had gone before.
Regretfully, I had sent that email in a fit of panic a full two days before. Just like the last one, I had rued what I did from the moment I hit the ‘Send’ button. I was confused, clearly confused. If Christine had logged on to her email account, from anywhere, then my emergency tracking, which was already in place, would have picked it up. She couldn’t read the message without logging in, so what I did was entirely redundant. But it made me feel better, and I still needed to send it. I had to send it. I could feel her drifting away from our task.
She replied immediately, naturally. With Cartwright standing there in front of her, probably able to see the movement of her fingers on the keyboard, his vision no doubt of the same superhuman quality as his physique, it would have been suspicious if she had not immediately responded. Her reply, needless to say, was succinct, running to just two entirely predictable words. And, I’m afraid, I became depressed. I knew I had ballsed up. The mess was of my own making and once again the word ‘incompetence’ attached itself, limpet-like, to me. I had to sleep. I knew they would carry on talking, but I had to sleep. But I didn’t sleep, of course. It all went round and round and it all made such perfect sense it had to be wrong. And by the time I was back on station they were asleep. I reviewed what they had exchanged in the meantime before they disappeared, together, behind the high and obscuring back of the couch.
“Problem?” Cartwright had asked immediately.
“No, nothing,” said Christine without pause as she typed her brief reply and mouse-clicked on ‘Send’. She then logged off and began to stow the laptop in its sealed bag.
“If you want more time, then I’ll go round the back and cook, or have a swim,” he said, without hesitation.
“No.” Her reply was ambiguous. Her mind was adrift while several silent seconds passed. She turned to him. “I want to know more about your current work. First, though, a question... Does this current focus on other things mean that your interest in predicting markets is over?”
He shrugged. “There is little more to do. You know how the theory has performed. It works. And it will continue to work, until everyone else discovers the technique. At that point, our world will be different, but the competitive advantage will be gone. I have moved on to bigger things.”
“So when we see you at work, you are concentrating only on your current interests which lie in the natural world.”
“Indeed. Who is ‘we’?”
She ignored the question. Her mistake was inexcusable. “So how did you know there would be a flower up there?”
He cleared his throat in the manner he habitually used, no doubt, before beginning one of his lectures. “In very simple terms, we have three groups of functions. One is environmental and includes everything climatic, such as temperature profiles of the area, rainfall, humidity, et cetera. And then there’s a topographical group, including measures of altitude, gradient, drainage, attitude...”
“And there’s far too much of that around, if you ask me...”
“All this means is the way the land is facing... especially relative to the sun’s travel.”
“Then why don’t you just say that?”
“I did.” He turned to face her. She was staring straight ahead, cradling her gin and tonic to her midriff, as if for comfort. “Another group of factors relate to similar concepts concerning what we currently know of the plant’s biology. When, where, how long, what frequency... What we know on the appearance of the flowers and what we know of the plant’s parasitic life in its host. Are you following me?”
“Of course. It all seems so obvious up to now.”
“Because it is obvious. It’s just that no-one has ever bothered to do it. Perhaps no-one has ever had the resources or time, or more likely the commercial motive... The life cycle of this particular plant is reasonably well documented, because it has been quite seriously studied. Most species have not and we know very little about them. We know lots of qualities, but my systems will only work with quantified data, and the more accurate the better.”
Christine was surprised. “I would have thought that scientists would have an enormous amount of research data about almost everything.”
Cartwright stiffened theatrically in his chair. “I am not a scientist, Chris. I’m a mathematician. And as far as things natural and biological, we know hardly anything. That something happens is not knowledge until we can also answer such things as how much, how often and the like. We have an enormous amount of research and thus data about most things that can be used in warfare, or for killing people. We have very little on most other things, because no-one has ever wanted to fund the work. You can’t shoot flowers at other people, so they don’t get the study grants.” He paused for a drink of water.
“So what’s special about this plant?”
“Every plant ... and every animal for that matter ... is special.” A hand reached across the table between them to brush a forearm.
“Why does that sound like sentimental claptrap? You ought to be in a film.”
“I probably am,” he said, and withdrew the arm.
She did not respond to the offer of diversion. “The flower ... its life cycle?”
“Well, the first thing of note is that it’s a parasite. Most of the time you don’t even know it’s there, because its only existence is as a set of spores and filaments inside the stems of its unwilling host. It starts as a miniscule nodule, we think, and then it invades the whole plant.”
“And you can’t see it?”
“Exactly. Sometimes it doesn’t even seem to cause its host plant any problem, Sometimes it does.”
“It just lives inside and grows...”
“Precisely. Then at an instant that I now seem to be able to predict with a modicum of confidence, it throws out an external nodule that grows to look like an old football. It then bursts open to form the flower.”
“That smells like shit.”
“As you put it. And it’s a metre across. Its job is to attract insects, those that might be attracted to detritus...”
“I know a few people like that.”
“...and they visit the flower...”
“And then?”
“Well, the flowers are sexed.”
“I knew there’d be a complication.”
“Hardly unique, though, is it?”
Christine laughed. “If only...”
“The flowers are male or female in the species we saw. In a couple of varieties..:”
“There are varieties of that thing?” Christine sounded genuinely surprised. She was actually listening. “Do your results apply in general, then, or only to the one type?”
“Only to the one we saw. Each new species, or even variant within a species, presents a new problem. The whole analysis would have to be repeated for the technique to be applied to a different type.”
“But that’s insane...”
Cartwright paused. “That’s life, Chris. And that’s science. Everything is different until it is proven to be the same. Someone, somewhere, does the work, and if it is done properly it adds to the sum of what we all know. It only helps if the work and its products are shared. Then its findings can become assumptions upon which we build other work, other knowledge. In the process, we continually test what we already think we know and modify it if it doesn’t quite fit what we find. Welcome to knowledge. It’s pragmatic, valueless and democratic.”
“We stand on the shoulders of giants.”
“And thus ourselves become taller.”
Christine turned again to look at him. “So you are a progress man? You believe in the concept of progress?”
Cartwright looked genuinely perturbed, taken aback. He thought before answering. “It’s self-evident
. If you think it isn’t, I suggest you go and interview smallpox.”
Christine’s response was measured. “But you also said it was valueless. So where does your espousal of Islam fit in?”
“I also said it was pragmatic.”
There was a long silence. He was not going to offer any more. Christine therefore back-tracked. “Male and female?”
He paused to replay memory. “As I said, there can be male and female elements on some flowers, but in our species they are distinctly either one or the other. Whatever the case, the insects have to pollinate, to transfer male bits to female bits.”
“And it’s easier if they are together on a single flower.”
“Considerably. A male flower may not bloom at the same time as the female. They may not be in the same location ... at least that’s what we thought.”
“But now your event theory, as you call it, can predict when it happens.”
“Not as such. That would be taking things off the scale. What it can do is identify a whole series of conditions, other events, circumstances, call them whatever you want, but factors is the precise term, that can come together in many different combinations. And when these happen, male and female flowers are more likely to bloom at nearly the same time and procreation follows.”
“But it’s still random.”
“Yes and no. It appears to be a random process, but that’s only because it’s being observed from a limited viewpoint. It’s not random when the mechanisms that underpin the process, though do not themselves explain it, are considered.” He stood and made his little hop towards the balcony, whose rail he grasped with his left hand. He took up his objects, still balanced there, and again presented them one by one to Christine. “Circle... Circle... Circle... Circles. Now imagine there’s a little test that these objects have to pass. Let’s imagine they have to go through a hole in the floor. Let’s imagine circular holes, square ones, irregularly shaped ones. But there’s a condition for the object to pass the test. It must just fit the hole, scrape through, if you like. It’s very hard to explain... Now imagine that each hole can get bigger or smaller as required, but it still retains its shape.”
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