I Am a Strange Loop

As the above excursion has shown, strange loops in mathematical logic have very surprising properties, including what appears to be a kind of upside-down causality. But this is by no means the first time in this book that we have encountered upside-down causality. The notion cropped up in our discussion of the careenium and of human brains. We concluded that evolution tailored human beings to be perceiving entities — entities that filter the world into macroscopic categories. We are consequently fated to describe what goes on about us, including what other people do and what we ourselves do, not in terms of the underlying particle physics (which lies many orders of magnitude removed from our everyday perceptions and our familiar categories), but in terms of such abstract and ill-defined high-level patterns as mothers and fathers, friends and lovers, grocery stores and checkout stands, soap operas and beer commercials, crackpots and geniuses, religions and stereotypes, comedies and tragedies, obsessions and phobias, and of course beliefs and desires, hopes and fears, dreads and dreams, ambitions and jealousies, devotions and hatreds, and so many other abstract patterns that are a million metaphorical miles from the microworld of physical causality.

There is thus a curious upside-downness to our normal human way of perceiving the world: we are built to perceive “big stuff” rather than “small stuff”, even though the domain of the tiny seems to be where the actual motors driving reality reside. The fact that our minds see only the high level while completely ignoring the low level is reminiscent of the possibilities of high-level vision that Gödel revealed to us. He found a way of taking a colossally long PM formula (KG or any cousin) and reading it in a concise, easily comprehensible fashion (“KG has no proof in PM”) instead of reading it as the low-level numerical assertion that a certain gargantuan integer possesses a certain esoteric recursively defined number-theoretical property (non-primness). Whereas the standard low-level reading of a PM string is right there on the surface for anyone to see, it took a genius to imagine that a high-level reading might exist in parallel with it.

By contrast, in the case of a creature that thinks with a brain (or with a careenium), reading its own brain activity at a high level is natural and trivial (for instance, “I remember how terrified I was that time when Grandma took me to see The Wizard of Oz”), whereas the low-level activities that underwrite the high level (numberless neurotransmitters hopping like crazy across synaptic gaps, or simms silently bashing by the billions into each other) are utterly hidden, unsuspected, invisible. A creature that thinks knows next to nothing of the substrate allowing its thinking to happen, but nonetheless it knows all about its symbolic interpretation of the world, and knows very intimately something it calls “I”.

Stuck, for Better or Worse, with “I”

It would be a rare thinker indeed that would discount its everyday, familiar symbols and its ever-present sense of “I”, and would make the bold speculation that somewhere physically inside its cranium (or its careenium), there might be an esoteric, hidden, lower level, populated by some kind of invisible churnings that have nothing to do with its symbols (or simmballs), but which somehow must involve myriads of microscopic units that, most mysteriously, lack all symbolic quality.

When you think about human life this way, it seems rather curious that we become aware of our brains in high-level, non-physical terms (like hopes and beliefs) long before becoming aware of them on low-level neural terms. (In fact, most people never come into contact at all with their brains at that level.) Had things happened in an analogous fashion in the case of Principia Mathematica, then recognition of the high-level Gödelian meaning of certain formulas of PM would have long preceded recognition of their far more basic Russellian meanings, which is an inconceivable scenario. In any case, we humans evolved to perceive and describe ourselves in high-level mentalistic terms (“I hope to read Eugene Onegin next summer”) and not in low-level physicalistic terms (imagine an unimaginably long list of the states of all the neurons responsible for your hoping to read Eugene Onegin next summer), although humanity is collectively making small bits of headway toward the latter.

Proceeding Slowly Towards the Bottom Level