I Am a Strange Loop

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?

Although nobody planned it that way, most of us wind up emerging from adolescence with a deeply nuanced sense of what is real, with shades of gray all over the place. (However, I have known, and probably you have too, reader, a few adults for whom every issue that strikes me as subtle seems to them to be totally black-and-white — no messy shades of gray at all to deal with. That must make life easy!) Actually, to suggest that for most of us life is filled with “shades of gray” is far too simple, because that phrase conjures up the image of a straightforward one-dimensional continuum with many degrees of grayness running between white and black, while in fact the story is much more multidimensional than that.

All of this is disturbing, because the word “real”, like so many words, seems to imply a sharp, clear-cut dichotomy. Surely it ought to be the case that some things simply are real while other things simply are not real. Surely there should be nothing that is partly real — that wouldn’t make sense! And yet, though we try very hard to force the world to match this ideal black-and-white dichotomy, things unfortunately get terribly blurry.

The Many-faceted Intellectual Grounding of Reality

That marble over there in that little cardboard box on my desk is certainly real because I see the cardboard box sitting there and because I can go over and open it and can squeeze the marble, hefting it and feeling its solidity. I hope that makes sense to you.

The upper edge of that 75-foot-tall Shell sign near the freeway exit is real, I am convinced, because every road sign is a solid object and every solid object has a top; also because I can see the sign’s bottom edge and its sides and so, by analogy, I can imagine seeing its top; also because, even though I’ll certainly never touch it, I could at least theoretically climb up to it or be lowered down onto it from a helicopter. Then again, the sign could topple in an earthquake and I could rush over to it and touch what had once been its upper edge, and so forth.

Antarctica, too, is real because, although I’ve never been there and almost surely will never go there, I’ve seen hundreds of photos of it, I’ve seen photos of the whole earth from space including all of Antarctica, and also I once met someone who told me he went there, and on and on.

Why do I believe what certain people tell me more than I believe what others tell me? Why do I believe in (some) photos as evidence of reality? Why do I trust certain photos in certain books? Why do I trust certain newspapers, and why only up to a certain point? Why do I not trust all newspapers equally? Why do I not trust all book publishers equally? Why do I not trust all authors equally?

Through many types of abstraction and analogy-making and inductive reasoning, and through many long and tortuous chains of citations of all sorts of authorities (which constitute an indispensable pillar supporting every adult’s belief system, despite the insistence of high-school teachers who year after year teach that “arguments by authority” are spurious and are convinced that they ought to be believed because they are, after all, authority figures), we build up an intricate, interlocked set of beliefs as to what exists “out there” — and then, once again, that set of beliefs folds back, inevitably and seamlessly, to apply to our own selves.

Just as we believe in other peoples’ kidneys and brains (thanks almost entirely to arguments from analogy and authority), so we come to believe in our own kidneys and brains. Just as we believe in everyone else’s mortality (again, thanks primarily to arguments from analogy and authority), so we come, eventually, to believe in our own mortality, as well as in the reality of the obituary notices about us that will appear in local papers even though we know we will never be able to flip those pages and read those notices.

What makes for our sense of utter sureness about such abstract things? It comes firstly from the reliability of our internal symbols to directly mirror the concrete environment (e.g., we purchase a cup of coffee and instantly, somewhere inside our cranium, God only knows where, there springs into existence a physical record reflecting this coffee, tracking where it is on the table or in our hand, constantly updating its color, bitterness level, warmth, and how much there is left of it). It comes secondly from the reliability of our thinking mechanisms to tell us about more abstract entities that we cannot directly perceive (e.g., the role of Napoleon in French history, the impact of Wagner on late-romantic French composers, or the unsolvability by radicals, such as Evariste Galois, of the quintic equation). All of this more abstract stuff is rooted in the constant reinforcement, moment by moment, of the symbols that are haphazardly triggered out of dormancy by events in the world that we perceive first-hand. These immediate mental events constitute the bedrock underlying our broader sense of reality.

Inevitably, what seems realest to us is what gets activated most often. Our hangnails are incredibly real to us (by coincidence, I found myself idly picking at a hangnail while I was reworking this paragraph), whereas to most of us, the English village of Nether Wallop and the high Himalayan country of Bhutan, not to mention the slowly swirling spiral galaxy in Andromeda, are considerably less real, even though our intellectual selves might wish to insist that since the latter are much bigger and longer-lasting than our hangnails, they ought therefore to be far realer to us than our hangnails are. We can say this to ourselves till we’re blue in the face, but few of us act as if we really believed it. A slight slippage of subterranean stone that obliterates 20,000 people in some far-off land, the ceaseless plundering of virgin jungles in the Amazon basin, a swarm of helpless stars being swallowed up one after another by a ravenous black hole, even an ongoing collision between two huge galaxies each of which contains a hundred billion stars — such colossal events are so abstract to someone like me that they can’t even touch the sense of urgency and importance, and thus the reality, of some measly little hangnail on my left hand’s pinky.

We are all egocentric, and what is realest to each of us, in the end, is ourself. The realest things of all are my knee, my nose, my anger, my hunger, my toothache, my sideache, my sadness, my joy, my love for math, my abstraction ceiling, and so forth. What all these things have in common, what binds them together, is the concept of “my”, which comes out of the concept of “I” or “me”, and therefore, although it is less concrete than a nose or even a toothache, this “I” thing is what ultimately seems to each of us to constitute the most solid rock of undeniability of all. Could it possibly be an illusion? Or if not a total illusion, could it possibly be less real and less solid than we think it is? Could an “I” be more like an elusive, receding, shimmering rainbow than like a tangible, heftable, transportable pot of gold?

No Luck, No Soap, No Dice

One day, many years ago, I wanted to pull out all the envelopes from a small cardboard box lying on the floor of my study and stick them as a group into one of my desk drawers. Accordingly, I picked up the box, reached into it, clasped my right hand around the pack of envelopes inside it (about a hundred in number), and squeezed tightly down on them in order to pull them all out of the box as a unit. Nothing at all surprising in any of this. But all of a sudden I felt, between my thumb and fingers, something very surprising. Oddly enough, there was a marble sitting (or floating?) right in the middle of that flimsy little cardboard box!

Like most Americans of my generation, I had held marbles hundreds of times, and I knew without any doubt what I was feeling. Like you, dear reader, I was an “old marble hand”. But how had a marble somehow found its way into this box that I usually kept on my desk? At the time I didn’t have any kids, so that couldn’t be the explanation. And anyway, how could it be hovering in the very middle of the box, rather than sitting at the bottom? Why wasn’t gravity working?

I peered in between the envelopes, looking for a small, smooth, colored glass sphere. No luck. Then I fumbled about with my fingers between the envelopes, feeling for it. Again no soap. But then, as soon as I grasped the whole set of envelopes as before, there it was again, as solid as ever! Where was this little devil of a marble