“Tom, I haven’t come here to waste my time.”
“...or mine, I hope.”
“You seem to have quite a lot of time.”
He became mildly aggressive. “I work every minute of every day, and have done for decades. I am working now, because there are ideas of how to proceed with my analysis in my head all the time, even as I speak. If I appear to be unoccupied, it’s because I am required to attend to a visitor, who asked for the invitation.” Christine did not respond when he remained silent for several seconds.
Clearly she was considering whether there was advantage to be gained in pushing him. She decided there was. “So why did you accept this time? Why did you agree to do a One-On-One when thus far you have refused all other contact with the media?”
He answered immediately, surprisingly without pause for thought. “Because the request came from you.” He looked at her, stared for several silent seconds before continuing. “And then there was the joke, of course.”
“Joke?”
“Well it made me laugh... One-On-One - it’s a good title for a confrontation between two monopedal adversaries.”
Christine laughed. “It never occurred to me.”
“It should have. We shared the experience, after all...”
“But that was a long time ago... and our lives have turned out so differently. I have to admit that I have concentrated so much on the differences that the obvious similarities have just passed me by.”
They both drank their tea and were silent for a while, allowing the self-adjusting microphones to amplify the distant hum of marine engines. They exchanged small talk about the view, with Cartwright helping Christine identify exactly what could be seen from the balcony. On that cool morning, he was able to point out the faint outline of Mount Kinabalu to the north, but it faded behind clouds even as she tried to discern it.
“But why this time, Tom? Was it just because it was me?”
“There was the joke, as well...”
“Of course. But why change the habit of a lifetime?”
He smiled. “Hardly a lifetime, Chris...In the first fifty-eight years of my life, the media could have unlimited access to me, if they had ever asked for it.” He paused, but the comment was obviously rhetorical. “But there comes a time...”
They were still standing at the balcony rail and neither seemed inclined to sit.
“I never thought my project would prove quite so successful. I never expected to achieve the growth rate my theory had predicted. I knew it was possible, and my theory had identified that it was likely. But I was still convinced I had overlooked something, a flaw that would dilute or undermine the eventual outcome.”
“And there were no flaws...”
“Apparently not. The system performed as theory had predicted.”
“But the results have been spectacular, to say the least. You must have expected...”
“No,” he interrupted, raising a finger to make his point. “...not spectacular. They have been in line with what theory predicted, so they add evidence to suggest that the theory might even be correct.”
“So what did your theory suggest?”
Cartwright turned to face her before answering. He looked long and hard before saying, “Is this an official question?”
“Meaning?”
“Who is asking? Is it you, out of interest, or is it your pay-masters, the interests that want to get their hands on my material, to undermine that ‘commercial advantage’ I mentioned earlier?”
“Now you are being silly...”
Cartwright said nothing for some time. He finished his tea - or almost finished it, deciding to throw the dregs into the sea below. He then followed his tea into the water, this time pausing to stand on the balcony rail, fully balanced on his one leg, before diving, still holding his mug, into the sea. “It saves washing up,” he said just a couple of minutes later as he clambered up his pole ladder. He could raise himself just using his arms, his remarkable upper body strength again in evidence.
“You were about to tell me...”
“Five per cent a day ... on a good day.”
“And a bad one?”
“Flat, at worst.”
Christine paused. There was an effort of calculation about her expression. “Five per cent... That doesn’t sound very much...”
Cartwright laughed. “You ancient historians just don’t get exponentiation. Come here. Follow me, I’ll show you.”
He led her to his office, where he powered up his desktop computer. In rapt silence, apparently with concentration, they both watched the screen deliver its start-up messages. Cartwright then loaded his spreadsheet, typed a few characters and swept his mouse down the column. “Look. Let’s say I started with ten thousand and grew at five per cent a day. After a hundred days - just three months into the project - I have one and a quarter million. I hit a hundred million before six months are up and by the end of the year I am over twenty billion.”
“I had no idea... and this is what you have done?”
“Not quite... there has been an occasional hitch, but I have achieved more than sixty per cent of what was predicted by the theory.”
“Why should there be a shortfall?”
“Noise.”
“Noise?”
“Noise.” The word had already become a surreal absurdity. “Unforeseen factors - miniscule effects that were too small to quantify in the model... they add up... When we mathematicians have to return to the real world, we have to become engineers. The models had to ignore some factors in order to identify the important principles. Back in the real world, you can’t ignore them any more. Their effects are small, hardly measurable in themselves, but the deviations arising from them can be cumulative, in which case the end result predicted by theory can be different from what is actually achieved.”
“So everything could have gone wrong anyway...”
Cartwright sighed. “Media people...” he muttered under his breath. “I said nothing about everything. I said, and repeated that these variations were small, even minuscule. The theory works, but does not deliver every cent of its predictions. I offer you five dollars as a present and it turns out to be four ninety-seven. Are you going to complain? But the shortfall was not predicted.”
“...but they do reduce your returns...”
“They can also increase them, but if they do that on a regular basis, then there was something wrong with the model. What they do is prevent the theoretical target from being achieved exactly.”
“And they don’t go away?”
“Well yes, in fact they do, but not of their own accord. The model is programmed to learn. It continually monitors its actual performance against its theoretical predictions. Discrepancies are analysed and any adjustment that produces a better fit with reality is automatically incorporated into future calculations.”
“So in theory, your system should get even better over time.”
“Correct. Unless, of course, there is a major shift in the system we are modelling. And that does happen, such as when markets fall or rise steeply. The system then takes a while to recalibrate.”
“But your system would adapt to that, from what you have just said.”
“I wish I could say ‘yes, in theory’, but I can’t. I am still working on the idea.”
“But...” Christine was confused, not just acting.
“Imagine a car that steers itself automatically by following the white line down the middle of the road. If it goes slightly off course, the sensors can hunt a little to each side to relocate the line. But imagine it comes to a stretch where the line disappears and the car runs into the ditch. It can hunt all day, but it will not be able to find a line to set it back on course.”
“But that has not happened to your system thus fa
r, because it has performed well until now.”
“Correct.”
“But...” Christine had a question to ask, but clearly lacked a framework in which to construct it. “Wait... Can we step back a moment? Okay, five per cent a day is the target...” He nodded. “But that was an initial estimate that you did not achieve?”
“Correct... but now often I do better than that because the system is already more refined as a result of its self-optimisation.”
“So you are now guaranteed that return?”
“No. There are no guarantees. But I actually do achieve it now, if I aim for it.”
“And after a year you finish with twenty billion?”
“If you achieve that result every day.”
“So where did that figure on my screen last night come from?”
Cartwright shook his head. It seemed that Christine was a seven year old who could not add up. He made another stroke of the mouse down his spreadsheet. “After two years at five per cent, would finish with about five times ten to the sixteen.”
“Meaning?”
He sighed impatiently, but paused to visualise the number. Fifty thousand trillion in your language. And that’s American trillions, of course.”
“But you have nothing like that.”
“You were just complaining I had too much, not too little! So I’m a failure now. What on earth are you doing here then?”
Christine laughed. “You know what I mean. Why is there a discrepancy?”
“These figures are for trading in one market only. I trade several markets - not quite all of them, because some of them will obviously not adhere to the model, but, as I have said, I never achieve the theoretical results. From what I have described, given that I trade several markets, I should be worth many times the figure you showed me last night.”
“So why aren’t you worth that much?”
“Because like all investors I have been very conservative. I was afraid to be too aggressive, at the start because I was afraid of grinding to halt before the ideas had been tested, and now I am careful because I have a lot to lose.”
“So after eighteen months we finish with the figure on my screen last night.”
“We? In fact, I finish with substantially more than that, as I said last night, but a lot less than I could have been worth, had I followed the theory to the letter.”
“That brings me on to another question. You are not merely trading now, are you? These days you are very much a holder as well, aren’t you?”
“I never did ‘merely’ trade.” Cartwright gave her a sidelong glance. He was still wet, of course, and now stood in a small puddle of drips, since the office floor was tightly slatted. His foot made comical squeaks on the laths as he adjusted his position. “You are clearly well informed about my affairs.”
Christine said nothing, but looked straight at him, inviting him to continue.
“About six months into the project, six months of pursuing growth as my primary goal, I realised that, broadly speaking, the theory worked and could even be relied upon. So I changed the emphasis. Instead of looking for short term gains, I consolidated the gains I had already made and begun buying long term stakes in blue chip companies. I continued to trade more aggressively with a proportion of the funds.”
“You were consolidating your profits, like any good capitalist would.”
“Correct.”
“So the shortfall between the times ten to the whatever and where you actually are is down to the fact that you began to trade only a fraction of your total assets.”
“Broadly.”
“And now you own some significant stakes in many of the world’s biggest companies.”
“And that’s why you’ve been sent here, isn’t it?”
Christine did not reply.
We had discussed at length how we would handle the situation, should Cartwright opt for the strategy of denial, which we had expected. I remember how surprised I was, the first time I went through this material, at how much he appeared to offer. On review, however, I realise that he had told us nothing we did not already know, and thus he knew precisely what he was doing. Not only did he understand implicitly how much we knew about his work, he had correctly anticipated the level of Christine’s briefing, and had thus carefully told her nothing significant. What he had sought via these apparent revelations, of course, was this opportunity to put her on the spot. And Christine was thrown momentarily. There was no point in her denying the involvement of others in her declared project, because he clearly had some inside knowledge of her intentions. What he perhaps still did not know was from where this interest in him originated. Fortunately, neither did Christine. Her silence, therefore, was in fact born of ignorance. Her eventual reply was anodyne, but at least it was truthful, thus offering him no avenue of duplicity that he might later exploit.
“Your achievements have been noted by several governments. The problem is the secrecy...”
“All my interests are declared. You know that. I am just like a big pension fund.”
“But you have no shareholders of your own. Potentially, you’re an unguided missile.”
“I’m no missile and I am much more guided than most, certainly more than anyone else who trades for profit. I am wholly underpinned by theory. And you would not be here unless I had succeeded. Essentially, you are telling me that I can do as I like, as long as I fail and put money into other people’s pockets.”
“But you keep your theories secret.”
“Like any other commercial advantage...”
Christine did not offer comment.
He continued. “It took thirty years to develop my ideas. I had no idea where they would lead. They started because there were things I could not explain, such as why that bowling ball in the park was so hard to control across the crown of a green. It has taken me thirty years of intense, concentrated and unrelenting effort to get to where I am today. I have devoted my life to my work, my life’s work. And my work is my life.”
“And you have shared it with no-one.”
Cartwright said no more. He simply disappeared from Christine’s view and headed for the back balcony where he began to prepare a meal. Chris neither followed him nor pursued the matter, despite the fact that she still had not confirmed a time to start her interview. Her comment had hit a nerve and this clearly was a defensive reaction on his part. This inability to communicate, this tendency always to play the loner we knew was something that would bug him. We had already identified the idea as the lever to help us lift the interviews. Back in the days when he worked briefly as a teacher, professional assessments had identified his tendency to seek isolation. They had been only passing references, of course, since considerations of his complete inability to control his students in class were always uppermost. He could never cope with their comments about his disability, and his tendency to draw attention to it as his own coping mechanism simply made things worse. As we know, he did manage to survive the year, but only on short-term, supply-teacher arrangements. Thus his decision to leave the country at the age of just twenty-five can only be interpreted as a desire to seek a complete break from Britain.
He did have his Master’s degree at that stage, but no doctorate, of course, since he completed that as an extra-mural student with the Australian university mentioned in the briefing papers, by which time he was already established in Asia. He was in his mid-thirties by the time he submitted his thesis whose title, “n-dimensional probability spaces - a digital analysis of distribution characteristics” shows that he had already begun work on the two main areas of his current work, probability and numerical analysis algorithms. It was the PhD award, of course, that facilitated his subsequent transfer on completion of his then current contract.
He had already worked in secondary schools quietly and apparently succ
essfully, without once drawing attention to himself. His application to join the university was supported by his future head of department, whom he had befriended socially and who was also at the time a close neighbour. Both men shared a north of England, working class background and thus clearly felt they had much in common. There are no surviving reports of Cartwright’s service as a secondary school teacher and those colleagues from the period we have been able to trace and contact remember him only for his being utterly non-memorable, barring his disability, which always registered. He went to work every morning, never had a day off, taught the classes he was assigned, stuck to the tasks he was given, asked no questions and went home every afternoon. Even his Ministry of Education file, which still exists and has been copied, contains nothing other than administrative documents, such as official forms, leave requests and contract renewal formalities. Reports on his work included in these renewal applications merely state how boringly dependable a teacher he was.
This was a pattern he repeated when he took up his new post in the university. He was assigned teaching in the areas of applied mathematics and statistics, but gave only four hours of classes per week. The rest of his time, we now know, he devoted to his research. It was clearly a successful project eventually, but there are no records of his progress, or indeed of his areas of interest, since he published nothing during his years in his academic post, apart from a handful of papers on pedagogy, most of which were no more than regurgitations from other published work. He thus did just enough to satisfy his professional evaluation requirements and more than enough, given the country in which he worked, to divert any official criticism. So, head down, he worked another ten years, through three more contracts and then, to everyone’s complete astonishment, in his mid-forties, he suddenly announced he was getting married and thus converted to Islam.
***
I paid only scant attention to the next couple of hours. After my rest I took time to review the material a couple of times on high speed, but this only confirmed that there was nothing of substance to record. Cartwright swam again, and Christine sat, essentially watching him, while she wrote a few notes. When he clambered back up his pole, after more than half an hour in the water, Cartwright prepared fried rice for their meal, using the leftovers from the previous evening, none of which, incidentally, had been refrigerated. He ate his own serving quickly with a spoon, but Christine only nibbled at hers, despite Cartwright’s repeated advice to her that she should keep her energy levels up to cope with the climate. He eventually finished her rice as well. Then he disappeared into his office and there he stayed until late morning.
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