I Am a Strange Loop

Another way of thinking about “how real X is to you” is how much you would trust a newspaper article that took for granted the existence of X (for example, a living dinosaur, a sighting of Hitler, insects discovered on Mars, a perpetual-motion machine, UFO abductions, God’s omniscience, out-ofbody experiences, alternate universes, superstrings, quarks, Bigfoot, Big Brother, the Big Bang, Atlantis, the gold in Fort Knox, the South Pole, cold fusion, Einstein’s tongue, Holden Caulfield’s brain, Bill Gates’ checkbook, or the proverbial twenty-mile “wall” for marathon runners). If you stop reading an article the moment you see X’s existence being taken for granted, then it would seem that you consider X’s “reality” highly dubious.

Pick any of the concepts mentioned above. Almost surely, there are plenty of people who believe fervently in it, others who believe in it just a little, others not at all (whether out of ignorance, cynicism, poor education, or excellent education). Some of these concepts, we are repeatedly told by authorities, are not real, and yet we hear about them over and over again in television shows, books, and newspapers, and so we are left with a curious blurry sense as to whether they do exist, or could exist, or might exist. Others, we are told by authorities, are absolutely real, but somehow we never see them. Others we are told were real but are real no longer, and that places them in a kind of limbo as far as reality is concerned. Yet others we are told are real but are utterly beyond our capacity to imagine. Others are said to be real, but only metaphorically or only approximately so — and so on. Sorting all this out is not in the least easy.

Concrete Walls and Abstract Ceilings

To be more concrete about all this, how real is the marathoners’ twenty-mile wall, mentioned above? If you’re a marathoner, you almost surely have a well-worked-out set of thoughts about it. Perhaps you have experienced it personally, or know people who have. Or perhaps you think the notion is greatly exaggerated. I’ve never hit the wall myself, but then my longest run ever was only fifteen miles. What I know is that “they say” that most runners, if they haven’t trained properly, will bang up against a brutal wall at around twenty miles, in which their body, having used up all of its glycogen, starts burning fat instead (I’ve heard it described as “your body eating its own muscles”). It comes out of the blue and is extremely painful (“like an elephant falling out of a tree onto my shoulders”, said marathoner Dick Beardsley), and many runners simply cannot go any further at that point, and drop out. But is this a universal phenomenon? Is it the same for all people? Do some marathoners never experience it at all? And even if it is scientifically explicable, is it as real and as palpable a phenomenon as a concrete wall into which one bangs?

When I entered math graduate school at Berkeley in 1966, I had the self-image of being quite a math whiz. After all, as an undergraduate math major at Stanford, not only had I coasted through most of my courses without too much work, but I had done lots of original research, and on graduating I was awarded the citation “with Distinction” by the Math Department. I was expecting to become a mathematician and to do great things. Well, at Berkeley two courses were required of all first-year students — abstract algebra and topology — and so I took them. To my shock, both were very hard for me — like nothing I’d ever encountered before. I got good grades in them but only by memorizing and then regurgitating ideas on the finals. For the entire year, my head kept on hurting from a severe lack of imagery such as I had never before experienced. It was like climbing a very high peak and getting piercing headaches as the air grows ever thinner. Abstraction piled on abstraction and the further I plowed, the slower my pace, and the less I grasped. Finally, after a year and a half, I recognized the situation’s hopelessness, and with a flood of bitter tears and a crushing loss of self-confidence, I jettisoned my dream of myself as a mathematician and bailed out of the field forever. This hated, rigid “abstraction ceiling” against which I had metaphorically banged my head without any advance warning was a searingly painful, life-changing trauma. And so… how concrete, how genuine, how real a thing was this abstract “abstraction ceiling”? As real as a marathoner’s wall? As real as a wooden joist against which my skull could audibly crash? What is really real?