Douglas Hofstadter - I Am a Strange Loop

The preceding situation might strike you as being very contrived, thus leaving you with the impression that seeing one romantic situation as “coding” for another is a fragile and unlikely possibility. But nothing could be further from the truth. If two people are romantically involved (or even if they aren’t, but at least one of them feels there’s a potential spark), then almost any conversation between them about any romance whatsoever, no matter who it involves, stands a good chance of being heard by one or both of them as putting a spotlight on their own situation. Such boomeranging-back is almost inevitable because romances, even very good ones, are filled with uncertainty and yearning. We are always on the lookout for clues or insights into our romantic lives, and analogies are among the greatest sources of clues and insights. Therefore, to notice an analogy between ourselves and another couple that is occupying center stage in our conversation is pretty much a piece of cake handed to us on a silver platter. The crucial question is whether it tastes good or not.

The Latent Ambiguity of the Village Baker’s Remarks

Indirect reference of the sort just discussed is often artistically exploited in literature, where, because of a strong analogy that readers easily perceive between Situations A and B, lines uttered by characters in Situation A can easily be heard as applying equally well to Situation B. Sometimes the characters in Situation A are completely unaware of Situation B, which can make for a humorous effect, whereas other times the characters in Situation A are simultaneously characters in Situation B, but aren’t aware of (or aren’t thinking about) the analogy linking the two situations they are in. The latter creates a great sense of irony, of course.

Since I recently saw a lovely example of this, I can’t resist telling you about it. It happens at the end of the 1938 film by Marcel Pagnol, La Femme du boulanger. Towards his wife Aurélie, who ran off with a local shepherd only to slink guiltily home three days later, Aimable, the drollynamed village baker, is all sweetness and light — but toward his cat Pomponnette, who, as it happens, also ran off and abandoned her mate Pompon three days earlier and who also came back on the same day as did Aurélie (all of this happening totally by coincidence, of course), Aimable is absolutely merciless. Taking the side of the injured Pompon (some might say “identifying with him”), Aimable rips Pomponnette to shreds with his accusatory words, and all of this happens right in front of the just-returned Aurélie, using excoriating phrases that viewers might well have expected him to use towards Aurélie. As if this were not enough, Aurélie consumes the heart-shaped bread that Aimable had prepared for himself for dinner (he had no inkling that she would return), while at the very same time, Pomponnette the straying kittycat, wearing a collar with a huge heart on it, is consuming the food just laid out for her mate Pompon.

Does Aimable the baker actually perceive the screamingly obvious analogy? Or could he be so kind and forgiving a soul that he doesn’t see Aurélie and Pomponnette as two peas in a pod, and could the deliciously double-edged bile that we hear him savagely (but justifiedly) dumping on the cat be innocently single-edged to him?

Whichever may be the case, I urge you to go out and see the film; it’s a poignant masterpiece. And if by some strange chance your very own sweetheart, sitting at your side and savoring the movie with you, has just returned to the nest after une toute petite amourette with some third party, just imagine how she or he is going to start squirming when that last scene arrives! But why on earth would someone outside the movie feel the sting of a volley of stern rebukes made by someone inside the movie? Ah, well… analogy has force in proportion to its precision and its visibility.

Chantal and the Piggybacked Levels of Meaning

Let’s now explore an analogy whose two sides are more different than two cookies or two lovers, more different even than a straying wife and a straying cat. It’s an analogy that comes up, albeit implicitly, when we are watching a video on our TV — let’s say, a show about a French baker, his wife, his friends, and his cats. The point is that we are not really watching the cavortings of people and cats — not literally, anyway. To say that we are doing so is a useful shorthand, since what we are actually seeing is a myriad of pixels that are copying, in a perfect lockstep-synchronized fashion, dynamically shifting patterns of color splotches that once were scattered off some animate and inanimate objects in a long-ago-and-faraway French village. We are watching a million or so dots that “code” for those people’s actions, but luckily the code is very easy for us to decode — so totally effortless, in fact, that we are sucked in by the mapping, by the isomorphism (the screen/scene analogy, if you will), and we find ourselves “teleported” to some remote place and time where we seem to be seeing events happening just as they normally do; we feel it is annoyingly nitpicky to make fine distinctions about whether we are “really” watching those events or not. (Are we really talking to each other if we talk by phone?)

It is all too easy to forget that moths, flies, dogs, cats, neonates, television cameras, and other small-souled beings do not perceive a television screen as we do. Although it’s hard for us to imagine, they see the pixels in a raw, uninterpreted fashion, and thus to them a TV screen is as drained of long-ago-and-far-away meanings as is, to you or me, a pile of fall leaves, a Jackson Pollock painting, or a newspaper article in Malagasy (my apologies to you if you speak Malagasy; in that case, please replace it by Icelandic — and don’t tell me that you speak that language, too!). “Reading” a TV screen at the representational level is intellectually far beyond such creatures, even if for most humans it is essentially second nature already by age two or so.

A dog gazing vacantly at a television screen, unable to make out any imagery, unaware even that any imagery is intended, is thus not unlike Lord Russell staring blankly at a formula of his beloved system PM and seeing only its “easy” (arithmetical) meaning, while the other meaning, the mapping-mediated meaning due to Gödel, lies intellectually beyond him, utterly inaccessible, utterly undreamt-of. Or perhaps you think this comparison is unfair to Sir Bertrand, and in a way I agree, so let me try to make it a little more realistic and more generous.

Instead of a dog that, when placed in front of a TV screen, sees only pixels rather than people, imagine little three-year-old Chantal Duplessix, who is watching La Femme du boulanger with her parents. All three are native speakers of French, so there’s no language barrier. Just like her maman and papa, Chantal sees right through the pixels to the events in the village, and when that wonderful final scene arrives and Aimable rakes the cat over the coals, Chantal laughs and laughs at Aimable’s fury — but she doesn’t suspect for a moment that there is another reading of his words. She’s too young to get the analogy between Aurélie and Pomponnette, and so for her there is only one meaning there. Filmmaker Pagnol’s analogy-mediated meaning, which takes for granted the “simple” (although dog-eluding) mapping of pixels to remote events and thus piggybacks on it, is effortlessly perceived by her parents, but for the time being, it lies intellectually beyond Chantal, and is utterly inaccessible to her. In a few years, of course, things will be different — Chantal will have learned how to pick up on analogies between all sorts of complex situations — but that’s how things are now.