Douglas Hofstadter - I Am a Strange Loop

I could list hundreds of things that take place on computer screens, but few people ever think about the fact that all of this is happening courtesy of addition and multiplication of integers way down at the hardware level. But that is exactly what’s happening. We don’t call computers computers for nothing, after all! They are, in fact, computing sums and products of integers expressed in binary notation. And in that sense, Gödel’s world-dazzling, Russell-crushing, Hilbert-toppling vision of 1931 has become such a commonplace in our downloading, upgrading, gigabyte culture that although we are all swimming in it all the time, hardly anyone is in the least aware of it. Just about the only trace of the original insight that remains visible, or rather, “audible”, around us is the very word “computer”. That term tips you off, if you bother to think about it, to the fact that underneath all the colorful pictures, seductive games, and lightning-fast Web searches, there is nothing going on but integer arithmetic. What a hilarious joke!

Actually, it’s more ambiguous than that, and for all the same reasons as I elaborated in Chapter 11. Wherever there is a pattern, it can be seen either as itself or as standing for anything to which it is isomorphic. Words that apply to Pomponnette’s straying also apply, as it happens, to Aurélie’s straying, and neither interpretation is truer than the other, even if one of them was the originally intended one. Likewise, an operation on an integer that is written out in binary notation (for instance, the conversion of “0000000011001111” into “1100111100000000”) that one person might describe as multiplication by 256 might be described by another observer as a left-shift by eight bits, and by another observer as the transfer of a color from one pixel to its neighbor, and by someone else as the deletion of an alphanumeric character in a file. As long as each one is a correct description of what’s happening, none of them is privileged. The reason we call computers “computers”, then, is historic. They originated as integer-calculation machines, and they are still of course validly describable as such — but we now realize, as Kurt Gödel first did back in 1931, that such devices can be equally validly perceived and talked about in terms that are fantastically different from what their originators intended.

Universal Beings

We human beings, too, are universal machines of a different sort: our neural hardware can copy arbitrary patterns, even if evolution never had any grand plan for this kind of “representational universality” to come about. Through our senses and then our symbols, we can internalize external phenomena of many sorts. For example, as we watch ripples spreading on a pond, our symbols echo their circular shapes, abstract them, and can replay the essence of those shapes much later. I say “the essence” because some — in fact most — detail is lost; as you know very well, we retain not all levels of what we encounter but only those that our hardware, through the pressures of natural selection, came to consider the most important. I also have to make clear (although I hope no reader would fall into such a trap) that when I say that our symbols “internalize” or “copy” external patterns, I don’t mean that when we watch ripples on a pond, or when we “replay” a memory of such a scene (or of many such scenes blurred together), there literally are circular patterns spreading out on some horizontal surface inside our brains. I mean that a host of structures are jointly activated that are connected with the concepts of water, wetness, ponds, horizontal surfaces, circularity, expansion, things bobbing up and down, and so forth. I am not talking about a movie screen inside the head!

Representational universality also means that we can import ideas and happenings without having to be direct witnesses to them. For example, as I mentioned in Chapter 11, humans (but not most other animals) can easily process the two-dimensional arrays of pixels on a television screen and can see those ever-changing arrays as coding for distant or fictitious three-dimensional situations evolving over time.

On a skiing vacation in the Sierra Nevada, far away from home, my children and I took advantage of the “doggie cam” at the Bloomington kennel where we had boarded our golden retriever Ollie, and thanks to the World Wide Web, we were treated to a jerky sequence of stills of a couple of dozen dogs meandering haphazardly in a fenced-in play area outdoors, looking a bit like particles undergoing random Brownian motion, and although each pooch was rendered by a pretty small array of pixels, we could often recognize our Ollie by subtle features such as the angle of his tail. For some reason, the kids and I found this act of visual eavesdropping on Ollie quite hilarious, and although we could easily describe this droll scene to our human friends, and although I would bet a considerable sum that these few lines of text have vividly evoked in your mind both the canine scene at the kennel and the human scene at the ski resort, we all realized that there was not a hope in hell that we could ever explain to Ollie himself that we had been “spying” on him from thousands of miles away. Ollie would never know, and could never know.

Why not? Because Ollie is a dog, and dogs’ brains are not universal. They cannot absorb ideas like “jerky still photo”, “24-hour webcam”, “spying on dogs playing in the kennel”, or even, for that matter, “2,000 miles away”. This is a huge and fundamental breach between humans and dogs — indeed, between humans and all other species. It is this that sets us apart, makes us unique, and, in the end, gives us what we call “souls”.

In the world of living things, the magic threshold of representational universality is crossed whenever a system’s repertoire of symbols becomes extensible without any obvious limit. This threshold was crossed on the species level somewhere along the way from earlier primates to ourselves. Systems above this counterpart to the Gödel–Turing threshold — let’s call them “beings”, for short — have the capacity to model inside themselves other beings that they run into — to slap together quick-and-dirty models of beings that they encounter only briefly, to refine such coarse models over time, even to invent imaginary beings from whole cloth. (Beings with a propensity to invent other beings are often informally called “novelists”.)

Once beyond the magic threshold, universal beings seem inevitably to become ravenously thirsty for tastes of the interiority of other universal beings. This is why we have movies, soap operas, television news, blogs, webcams, gossip columnists, People magazine, and The Weekly World News, among others. People yearn to get inside other people’s heads, to “see out” from inside other crania, to gobble up other people’s experiences.

Although I have been depicting it somewhat cynically, representational universality and the nearly insatiable hunger that it creates for vicarious experiences is but a stone’s throw away from empathy, which I see as the most admirable quality of humanity. To “be” someone else in a profound way is not merely to see the world intellectually as they see it and to feel rooted in the places and times that molded them as they grew up; it goes much further than that. It is to adopt their values, to take on their desires, to live their hopes, to feel their yearnings, to share their dreams, to shudder at their dreads, to participate in their life, to merge with their soul.

Being Visited

One morning not long ago I woke up with the memory of my father richly pulsating inside my cranium. For a shining moment my dreaming mind seemed to have brought him back to life in the most vivid fashion, even though “he” had had to float in the rarefied medium of my brain’s stage. It felt, nonetheless, like he was really back again for a short while, and then, sadly, all at once he just went poof. How is this bittersweet kind of experience, so familiar to every adult human being, to be understood? What degree of reality do these software beings that inhabit us have? Why did I put “he” in quotation marks, a few lines up? Why the caution, why the hedging?