Zia Rahman - In the Light of What We Know

My lasting regret is that I made my excuses and did not go with them to Headington for breakfast. At the time, and immediately afterward, I told myself that I had sensed that in his heart my friend did not want me to. But the truth is that I myself, to my own shame, felt embarrassed for my friend. Sharper still was the disconcerting feeling I had in those few minutes that a distance had opened up between him and me for reasons I did not grasp in their full subtleties. After that day, Zafar did not mention his parents again. If friendship has a cost, then perhaps it is that at its heart there is always a burden of guilt. I don’t deny that I’ve failed to do certain things, failed, for instance, to provide support in the hour of need, or step in when that’s what a friend should do, failed as a friend. But my regrets for the things I did not do pale against the guilt I bear for an act of commission and its consequences.

All the same, it is not guilt alone that brings me to my desk to put pen to paper and reckon with Zafar’s story, my role, and our friendship. Rather, it is something that no single word can begin to describe but which, I hope, will take form as I carry on. All this is quite fitting, really — how it ought to be — when I call to mind the subject of my friend’s long-standing obsession. Described as the greatest mathematical discovery of the last century, it is a theorem with the simple message that the farthest reaches of what we can ever know fall short of the limits of what is true, even in mathematics. In a sense, then, I have sat down to venture somewhere undiscovered, without the certainty that it is discoverable.

* * *

When he stood before me on the doorstep of our home, my disheveled friend uttered the name of Gödel clearly and correctly, and I recalled instantly the bright afternoon of a Sunday in New York when I suggested to Zafar that I had caught up with him mathematically. I had assumed that Zafar’s grasp of mathematics must have slipped, for after taking a first-class degree at Oxford, he left the study of mathematics entirely, quite to everyone’s surprise, to study law at Harvard, while I, on the other hand, after completing my third year and then taking a year off, continued with graduate studies in economics and applied mathematics.

My suggestion to him, as we walked along a tree-lined street in Greenwich Village on that Sunday all those years ago, invited from him what seemed then the cryptic response that mathematics was full of beauty. I felt compelled to ask what he considered the most beautiful mathematics he had come across, and perhaps that is what he had intended, that I ask this question — I cannot tell. Gödel’s Incompleteness Theorem was his unhesitating answer, and though I remembered the statement of the theorem well enough, I nevertheless failed to perceive why he regarded it as particularly beautiful. Within any given system, there are claims which are true but which cannot be proven to be true. So states the theorem. So simple. In its implications, it is a shocking theorem, granted, and some time later, that is to say in the weeks following his sudden reappearance on our doorstep, years after that July day in New York, Zafar would explain to me in simple terms why Gödel’s Incompleteness Theorem mattered so much to him and why, if I may be allowed to interpose my own view, the world was foolish to ignore it in an age of dogma.

Walking with him down that New York street, I thought to myself that perhaps such beauty, as he perceived, might lie in the theorem’s proof rather than in the statement itself. Yet I could not recall the proof of Gödel’s disturbing result — I am not sure I ever knew — and I assumed that after his departure from mathematics some years before, Zafar would also have lost all memory of it. I was wrong, of course, for when I prompted him, he began in the manner of an excited child to describe an argument, setting down apparently irrelevant pieces of the puzzle in all its corners. Barely a few such pieces had been laid, before the fragmentary image of a proof reared up toward me. I caught something then of beauty, unfortunately a beauty so nascent that I cannot tell if I had truly seen it or if I had merely been carried away on my friend’s euphoria. Presently his animated exposition was interrupted when we ran into a colleague and, so to speak, lost our way.

We had many walks on the streets of New York, a city to which I returned on business nearly every month, and in the streets of London later. Many of those walks abide in the memory, but if any of them stand out from the rest, then a good claim may be made by two others.

The first was near Wall Street, and, while arguably of little consequence insofar as Zafar’s story goes, it remains a fond memory for me, despite present circumstances. For the better part of the walk, my friend coached me, helping me to commit to memory a poem by e. e. cummings, somewhere i have never travelled , as he discussed its rhythms and cadences and parsed its images into a sequence. His memory held a prodigious store of poetry, and this poem was his answer to my request for something with which I could woo the woman who was to become my wife.

The second was of an altogether different kind, disconcerting, for it revealed a side of Zafar that I had not the slightest knowledge of until then, when I had known him already for close to a decade. It was 1996, and my wife and I were settled into our new home in South Kensington, while Zafar had returned from New York and was living in London. At the end of the working day, our ties slack around our necks, the two of us met for a quick drink at a pub in Notting Hill, though our meeting up was by then less and less frequent. I had a few beers, and Zafar, as always, ordered one glass of champagne. His choice might have seemed rather pretentious but for the fact that Zafar could not hold his drink, did not much like alcohol, and, moreover, as he once explained to me, found champagne agreeable because it had all the fun of fizzy lemonade without the latter’s unsettling effects on the stomach. At college, as was to be expected, his predilection attracted some mocking, but I like to think that over time his habit was seen as an endearing quirk.

After an hour, we set off on Portobello Road toward the crossroads where we were to part, I to catch a cab home and he to join Emily. I later learned that the troubles with Emily were already in full throe by this time, and I marvel now to think that as we sat in the pub and talked, he had disclosed nothing of those difficulties.

We were walking along the road when a voice boomed: Oi, mate. Zafar and I turned to see two men leaning against a railing, looking at us. Both had closely shaved heads and wore jeans, and both had a certain barbell muscularity. The first man, the one who had apparently spoken, was several inches taller than the other and wore only a white T-shirt despite the time of year, while the second wore an open leather jacket, ineffectively obscuring some of the excess weight around his torso. The tall man in the white T-shirt, so obviously the alpha male of the pair, fixed his attention on my friend. A quizzical expression spread across the man’s face.

Do you speak English? he asked Zafar.

Zafar looked at him, turned his head toward the shorter man, and then turned back to the alpha male, before replying in the haughtiest Englishman’s accent, affected to perfection: Terribly sorry. Not a word. Good day.

Zafar touched my elbow and we both turned and walked on. After a few steps, I asked him under my breath, What the hell was that about? When Zafar replied, he told me that from where I had been standing, I could not have seen what he saw.

Which was? I asked.

The shoulder of the man in the T-shirt, he said.

What? That the sleeves had been rolled up to the shoulder?