I Am a Strange Loop

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.