In the Light of What We Know Read Free

process of integration of the parts, which takes place, as some scientists and physicians understand it, in the optic nerves long before any transmission reaches the brain. The otherwise dizzying abundance of information that hits the retina is distilled in this tract of fibers behind the eye into a sign that our intelligence can absorb. When we see a strip of letters, a billboard slogan, for example, we cannot help but read the word; we do not see each letter separately, but rather, instantly, we grasp the whole word and, moreover, its meaning. As I stood there, on that June morning in Oxford, my friend’s mother’s face offered no sign of resemblance to Zafar, as if their respective faces were words written in different languages.
    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.
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    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