Soaps in Sanskrit
This may sound a bit abstruse and remote, so let me suggest an analogy. Imagine the challenge of writing out a clear explanation of the meaning of the contemporary term “soap digest rack” in the ancient Indian language of Sanskrit. The key constraint is that you are restricted to using pure Sanskrit as it was in its heyday, and are not allowed to introduce even one single new word into the language.
In order to get across the meaning of “soap digest rack” in detail, you would have to explain, for starters, the notions of electricity and electromagnetic waves, of TV cameras and transmitters and TV sets, of TV shows and advertising, the notion of washing machines and rivalries between detergent companies, the idea of daily episodes of predictable hackneyed melodramas broadcast into the homes of millions of people, the image of viewers addicted to endlessly circling plots, the concept of a grocery store, of a checkout stand, of magazines, of display racks, and on and on… Each of the words “soap”, “digest”, and “rack” would wind up being expanded into a chain of ancient Sanskrit words thousands of times longer than itself. Your final text would fill up hundreds of pages in order to get across the meaning of this three-word phrase for a modern banality.
Likewise, Gödel’s string KG, which we conventionally express in supercondensed form through phrases such as “I am not provable in
PM
”, would, if written out in pure
PM
notation, be monstrously long — and yet despite its formidable size, we understand precisely what it says. How is that possible? It is a result of its condensability. KG is not a random sequence of
PM
symbols, but a formula possessing a great deal of structure. Just as the billions of cells comprising a heart are so extremely organized that they can be summarized in the single word “pump”, so the myriad symbols in KG can be summarized in a few well-chosen English words.
To return to the Sanskrit challenge, imagine that I changed the rules, allowing you to define new Sanskrit words and to employ them in the definitions of yet further new Sanskrit words. Thus “electricity” could be defined and used in the description of TV cameras and televisions and washing machines, and “TV program” could be used in the definition of “soap opera”, and so forth. If abbreviations could thus be piled on abbreviations in an unlimited fashion, then it is likely that instead of producing a book-length Sanskrit explanation of “soap digest rack”, you would need only a few pages, perhaps even less. Of course, in all this, you would have radically changed the Sanskrit language, carrying it forwards in time a few thousand years, but that is how languages always progress. And that is also the way the human mind works — by the compounding of old ideas into new structures that become new ideas that can themselves be used in compounds, and round and round endlessly, growing ever more remote from the basic earthbound imagery that is each language’s soil.
Winding Up the Debriefing
In my allegory, both the Klüdgerot and the Alfbert supposedly have the ability to read pure
PM
strings — strings that contain no abbreviations whatsoever. Since at one level (the level perceived by the Klüdgerot) these strings talk about themselves, they are like Gödel’s KG, and this means that such strings are, for want of a better term, infinitely huge (for all practical purposes, anyway). This means that any attempt to read them as statements about numbers will never yield anything comprehensible at all, and so the Alfbert’s ability, as described, is a total impossibility. But so is the Klüdgerot’s, since they too are overwhelmed by an endless sea of symbols. The only hope for either the Alfbert or the Klüdgerot is to notice that certain patterns are used over and over again in the sea of symbols, and to give these patterns names, thus compressing the string into something more manageable, and then carrying this process of patternfinding and compression out at the new, shorter level, and each time compressing further and further and further until finally the whole string collapses down into just one simple idea: “I am not edible” (or, translating out of the allegory, “I am not provable”).
Bertrand Russell never imagined this kind of a level-shift when he thought about the strings of
PM
. He was trapped by the understandable preconception that statements about whole numbers, no matter how long or complicated they might get, would always retain the familiar flavor of standard number-theoretical statements such as “There are infinitely many primes” or “There are only three pure powers in the Fibonacci sequence.” It never occurred to him that some statements could have such intricate hierarchical structures that the number-theoretical ideas they would express would no longer feel like ideas about numbers. As I observed in Chapter 11, a dog does not imagine or understand that certain large arrays of colored dots can be so structured that they are no longer just huge sets of colored dots but become pictures of people, houses, dogs, and many other things. The higher level takes perceptual precedence over the lower level, and in the process becomes the “more real” of the two. The lower level gets forgotten, lost in the shuffle.
Such an upwards level-shift is a profound perceptual change, and when it takes place in an unfamiliar, abstract setting, such as the world of strings of
Principia Mathematica,
it can sound very improbable, even though when it takes place in a familiar setting (such as a TV screen), it is trivially obvious.
My allegory was written in order to illustrate a
downwards
level-shift that is seen as very improbable. The Klüdgerot see only high-level meanings like “I am edible” in certain enormous
PM
strings, and they supposedly cannot imagine any lower-level meaning
also
residing in those strings. To us who know the original intent of the strings of symbols in
Principia Mathematica,
this sounds like an inexplicably rigid prejudice, yet when it comes to understanding our own nature, the tables are quite turned, for a very similar rigid prejudice in favor of high-level (and only high-level) perception turns out to pervade and even to define “the human condition”.
Trapped at the High Level
For us conscious, self-aware, “I”-driven humans, it is almost impossible to imagine moving down, down, down to the neuronal level of our brains, and slowing down, down, down, so that we can see (or at least can imagine) each and every chemical squirting in each and every synaptic cleft — a gigantic shift in perspective that would seem to instantly drain brain activity of all symbolic quality. No meanings would remain down there, no sticky semantic juice — just astronomical numbers of meaningless, inanimate molecules, squirting meaninglessly away, all the livelong, lifeless day.
Your typical human brain, being blissfully ignorant of its minute physical components and their arcanely mathematizable mode of microscopic functioning, and thriving instead at the infinitely remote level of soap operas, spring sales, super skivaganzas, SUV’s, SAT’s, SOB’s, Santa Claus, splashtacular scuba specials, snorkels, snowballs, sex scandals (and let’s not forget sleazeballs), makes up as plausible a story as it can about its own nature, in which the starring role, rather than being played by the cerebral cortex, the hippocampus, the amygdala, the cerebellum, or any other weirdly named and gooey physical structure, is played instead by an anatomically invisible, murky thing called “I”, aided and abetted by other shadowy players known as “ideas”, “thoughts”, “memories”, “beliefs”, “hopes”, “fears” “intentions”, “desires”, “love”, “hate”, “rivalry”, “jealousy”, “empathy”, “honesty”, and on and on — and in the soft, ethereal, neurology-free world of
these
players, your typical human brain perceives its very own “I” as a pusher and a mover, never entertaining for a moment the idea that its star player might merely be a useful shorthand standing for a myriad of infinitesimal entities and the invisible chemical transactions taking place among them, by the billions — nay, the millions of billions — every single second.
The human condition is thus profoundly analogous to the Klüdgerotic condition: neither species can see or even imagine the lower levels of a reality that is nonetheless central to its existence.
First Key Ingredient of Strangeness
Why does an “I” symbol never develop in a video feedback system, no matter how swirly or intricate or deeply nested are the shapes that appear on its screen? The answer is simple: a video system, no matter how many pixels or colors it has,
develops no symbols at all,
because a video system does not
perceive
anything. Nowhere along the cyclic pathway of a video loop are there any symbols to be triggered — no concepts, no categories, no meanings — not a tad more than in the shrill screech of an audio feedback loop. A video feedback system does not attribute to the strange emergent galactic shapes on its screen any kind of causal power to make anything happen. Indeed, it doesn’t attribute anything to anything, because, lacking all symbols, a video system can’t and doesn’t ever
think
about anything!
What makes a strange loop appear in a brain and not in a video feedback system, then, is an
ability
— the ability to think — which is, in effect, a one-syllable word standing for the possession of a sufficiently large repertoire of triggerable symbols. Just as the richness of whole numbers gave
PM
the power to represent phenomena of unlimited complexity and thus to twist back and engulf itself via Gödel’s construction, so our extensible repertoires of symbols give our brains the power to represent phenomena of unlimited complexity and thus to twist back and to engulf themselves via a strange loop.
Second Key Ingredient of Strangeness
But there is a flip side to all this, a second key ingredient that makes the loop in a human brain qualify as “strange”, makes an “I” come seemingly out of nowhere. This flip side is, ironically, an
inability
— namely, our Klüdgerotic inability to peer below the level of our symbols. It is our inability to see, feel, or sense in any way the constant, frenetic churning and roiling of micro-stuff, all the unfelt bubbling and boiling that underlies our thinking. This, our innate blindness to the world of the tiny, forces us to hallucinate a profound schism between the goal-lacking material world of balls and sticks and sounds and lights, on the one hand, and a goalpervaded abstract world of hopes and beliefs and joys and fears, on the other, in which radically different sorts of causality seem to reign.
When we symbol-possessing humans watch a video feedback system, we naturally pay attention to the eye-catching shapes on the screen and are seduced into giving them fanciful labels like “helical corridor” or “galaxy”, but still we know that ultimately they consist of nothing but pixels, and that whatever patterns appear before our eyes do so thanks solely to the local logic of pixels. This simple and clear realization strips those fancy fractalic gestalts of any apparent life or autonomy of their own. We are not tempted to attribute desires or hopes, let alone consciousness, to the screen’s swirly shapes — no more than we are tempted to perceive fluffy cotton-balls in the sky as renditions of an artist’s profile or the stoning of a martyr.
And yet when it comes to perceiving ourselves, we tell a different story. Things are far murkier when we speak of ourselves than when we speak of video feedback, because we have no direct access to any analogue, inside our brains, to pixels and their local logic. Intellectually knowing that our brains are dense networks of neurons doesn’t make us familiar with our brains at that level, no more than knowing that French poems are made of letters of the roman alphabet makes us experts on French poetry. We are creatures that congenitally cannot focus on the micromachinery that makes our minds tick — and unfortunately, we cannot just saunter down to the corner drugstore and pick up a cheap pair of glasses to remedy the defect.
One might suspect neuroscientists, as opposed to lay people, to be so familiar with the low-level hardware of the brain that they have come to understand just how to think about such mysteries as consciousness and free will. And yet often it turns out to be quite the opposite: many neuroscientists’ great familiarity with the low-level aspects of the brain makes them skeptical that consciousness and free will could ever be explained in physical terms at all. So baffled are they by what strikes them as an unbridgeable chasm between mind and matter that they abandon all efforts to see how consciousness and selves could come out of physical processes, and instead they throw in the towel and become dualists. It’s a shame to see scientists punt in this fashion, but it happens all too often. The moral of the story is that being a professional neuroscientist is not by any means synonymous with understanding the brain deeply — no more than being a professional physicist is synonymous with understanding hurricanes deeply. Indeed, sometimes being mired down in gobs of detailed knowledge is the exact thing that blocks deep understanding.
Our innate human inability to peer below a certain level inside our cranium makes our inner analogue to the swirling galaxy on a TV screen — the vast swirling galaxy of “I”-ness — strike us as an undeniable
locus of causality,
rather than a mere passive epiphenomenon coming out of lower levels (such as a video-feedback galaxy). So taken in are we by the perceived hard sphericity of that “marble” in our minds that we attribute to it a reality as great as that of anything we know. And because of the locking-in of the “I”-symbol that inevitably takes place over years and years in the feedback loop of human self-perception, causality gets turned around and “I” seems to be in the driver’s seat.
In summary, the combination of these two ingredients — one an ability and the other an inability — gives rise to the strange loop of selfhood, a trap into which we humans all fall, every last one of us, willy-nilly. Although it begins as innocently as a humble toilet’s float-ball mechanism or an audio or video feedback loop, where no counterintuitive type of causality is posited anywhere, human self-perception inevitably ends up positing an emergent entity that exerts an upside-down causality on the world, leading to the intense reinforcement of and the final, invincible, immutable locking-in of this belief. The end result is often the vehement denial of the possibility of any alternative point of view at all.