Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (41 page)
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Authors: Douglas Hofstadter,Emmanuel Sander
To be sure, we don’t want to suggest that an event has just
one
abstract structure. Speaking,
a posteriori
, of “the” abstract structure of an event gives the impression that there was and is only one correct way to perceive it and to have a memory of it get triggered, which is not the case; any of various distinct conceptual skeletons might get attached to a given situation, depending on the frame of mind one is in when it is encountered.
The wide variety of potential encodings of
Danny at the Grand Canyon
means that many extremely different situations, possibly encountered much later in life, could induce that old memory to bubble up from dormancy. Such situations would thereby become members of the category
Danny at the Grand Canyon
, or, to propose a more generic name for it,
trivial side show more fascinating than the main event.
Let’s look at a few scenarios that might trigger such remindings:
A French family is taking a vacation in Italy’s famed Cinque Terre region, on the Ligurian coast, where five small towns hug a rugged coastline. After finding a bed-and-breakfast place in the countryside, the parents are eager to set off and explore the towns, but the children, delighted by their discovery of a family of grasshoppers in the garden, refuse to budge.
A four-year-old girl has just received a lovely Christmas present, but she’s paying no attention to it, concentrating instead on the sparkling wrapping paper.
In the cathedral-like main room of Cairo’s Egyptian Museum, a boy is totally ignoring the tiny three-inch ivory statue of Kheops, which is the focus of all the guides and crowds; rather, his eye is caught by the cracked paint covering the vast room’s high walls, in which he thinks he can make out the shapes of gigantic dragons and other fantastic monsters.
A young mother is more absorbed in the photos of her baby than in the baby itself.
A neurologist gives a talk to which she brings her ten-year-old niece, visiting for a few days. After the talk, the little girl says, “I liked your speech a lot, but I have just one question about it.” The neurologist is delighted and even wonders if her niece is some kind of prodigy. Then the girl goes on, “When you thanked a bunch of people at the end and you mentioned someone named Janet, were you talking about my mom?”
A graphic artist is reading a famous novel but is paying less attention to the plot than to the typesetting and page layout.
Two intensely motivated scholars spend all their days and nights in a tiny cramped office working on a specialized treatise, when all of Paris, with its magnificent monuments, museums, cafés, and restaurants, is out there, just begging to be explored.
Two co-authors are frittering away every day and evening of their Parisian vacation visiting museums and monuments and munching on
pâtisseries
, when instead they could find a secluded spot and sit down and jointly create a masterpiece.
A mosquito hovering about Albert Einstein’s body sees it as nothing more than a warm object filled with liquid sustenance.
Doug and Carol don’t in the least appreciate the exquisite marvels of the tiny ants and delicate leaves on the sandy soil, but instead, aping the mob of awestruck philistines around them, they merely gawk at some random hole in the ground.
Each of these scenarios has its own unique kind of resemblance to the story of Danny at the Grand Canyon. Although a certain essence is shared by all of them, there are a few, especially the first one, that are extremely similar to the original episode, despite differing in many superficial aspects, while others, especially those toward the end, enjoy a far more abstract connection. Readers will have different personal judgments about how forced or natural each analogy is, depending on how they encode these scenarios. There is no objective way of ranking these episodes in order of their degree of resemblance to the episode of Danny in the Grand Canyon, because similarity is not only subjective (encodings can vary wildly from one person to the other) but also multidimensional (many aspects of a situation play roles in its encoding). Still, these anecdotes will allow us to illustrate the variety of encodings that can analogically trigger memories of the episode of Danny at the Grand Canyon.
Thus, a relatively superficial encoding such as “children who are more interested in playing with insects than in savoring a famous tourist spot” will suffice to connect the episode of the family taking their vacation in the Cinque Terre with the Grand Canyon episode. On the other hand, the analogy involving the little girl who is more interested in the wrapping paper than in her gift is based on a rather more abstract similarity, because her story involves no insects and no famous tourist destination. This time, the shared gist is the lack of interest paid to something that is supposedly fascinating to any child (a gift) in contrast with the preferential treatment afforded something that is presumably devoid of interest (wrapping paper).
The third episode brings in the new idea of size inversion. The phenomenon that is supposedly universally interesting — the statuette — is now tiny, while the supposedly boring phenomenon — the cracks in the paint on the walls — is huge. For the two episodes to be analogous, this difference has to be transcended by an encoding that stresses the contrast between an entity that is conventionally considered important and another that is conventionally considered trivial, no matter what their sizes are.
As for the mother who is absorbed in the photos of her baby while paying little attention to the baby itself, the irony here comes from the fact that paying more attention to the photos than to the baby seems to suggest more interest in a copy than
in the original, more interest in inanimate objects than in a living being, more interest in the past than in the present, and more interest in what is frozen than in what is changing; these priorities constitute stark contrasts with conventional priorities, thus abstractly linking this scenario with that of Danny at the Grand Canyon.
The conceptual skeleton implicitly abstracted from the story of the child who attends her aunt’s lecture matches that of the scenario of Danny at the Grand Canyon provided that one’s perception goes up a notch in abstraction. Here there are no physical entities or places on which to base the mapping. The key thing is the contrast between a child’s superficial (indeed,
childish
) interest in a person’s name mentioned only fleetingly during a technical talk and the abstruse neurological ideas that all members of the audience were, at least theoretically, deeply engrossed in.
The case of the graphic artist who is more interested in the typesetting than in the novel is similar in some ways to the case of the child who prefers the wrapping paper to the gift, but there is a difference of scale. The child is neither an expert in nor a huge fan of wrapping paper, while the graphic artist is a specialist in letterforms and words and their placement on the page. This anecdote is related to the two that follow it (those involving the two scholars and the two co-authors), which form a matched pair of episodes that bring out particularly clearly the subjective nature of people’s points of view on a situation (Paris, in this case). The connection to the episode of Danny at the Grand Canyon is clearer when one reads these three stories at a yet higher level of abstraction than would be suggested by this section’s title (“A Trivial Side Show that is More Fascinating than the Main Event”), because here it would seem that the linking idea is
each person sees things in their own fashion
.
It’s not so much Danny’s fascination with a trivial side show instead of with a spectacular geographical spot known the world over that links that episode by analogy to the two Paris episodes in our list; what matters is simply that to Danny, an ant and a leaf are every bit as interesting as the Grand Canyon is to adults. From Danny’s point of view, the ants and leaves have every bit as much going for them as the Grand Canyon does. The notions of
trivial side show
and
main event
, which are central to the notion of
a trivial side show that is more fascinating than the main event
, have to be relativized and seen simply as natural consequences of a particular individual’s idiosyncratic point of view. Indeed, for some people, the stereotypical attractions of Paris — monuments, museums, cafés, restaurants — constitute the core meaning of that city, whereas for other people, completely different kinds of things dominate their perception of Paris. Likewise, ants and leaves are just as interesting to little Danny as the Grand Canyon is to adults; indeed, from his point of view, the meaningless pattern of red and orange hues that his parents are ogling doesn’t hold a candle to the exquisite ants and leaves. It’s at this abstract level of encoding of
Danny at the Grand Canyon
and of the two Parisian anecdotes that the identity of all three episodes emerges most clearly and naturally.
As for the final two scenarios in our list, they too involve the same basic idea — what is central and crucial for one being can be peripheral and trivial for others. The mosquito doesn’t understand Einstein’s genius one whit and is limited to its far more down-to-earth refueling interests; in this regard, this particular mosquito is no different
from any other member of its species, and nobody is surprised or amused by its irreverent behavior when it lands on Albert Einstein. For the mosquito, the crux of the situation is that this nameless object is a warm vessel filled with fuel, and we all understand that that is the only way the mosquito is capable of relating to Einstein.
This scenario in fact leads easily to a new set of variations on a theme. Thus one can imagine a dog that goes along one night into the countryside with some astronomy students but is indifferent to the beauty of the starry sky. The intrinsic inability of the mosquito or the dog to appreciate what is exceptional in the situation right in front of their eyes brings to mind a familiar proverb: “It’s casting pearls before swine.” (Note that, through a deft analogical sleight of hand, Einstein has just been transmuted into a set of pearls, and a mosquito into a herd of pigs.) Indeed, such an encoding of the situation, once it’s been made, casts the original story in a new light — namely, taking Danny at age one to the Grand Canyon is a member of the category
casting pearls before swine.
At first, this analogy may seem harsh, but on reflection, it makes perfect sense and clearly it is not singling out Danny for criticism in any way. Once the idea is out on the table, it seems a quite natural one, and yet it took many years and the writing of this book for us to discover this proverb-based way of perceiving the event. This shows how difficult it can be to transcend one’s first spontaneous encoding of an event.
The final scenario in the list implicitly takes the point of view of a hypothetical Danny who has the same interests as a typical one-year-old but who is also miraculously endowed with the critical faculties of an adult and who sees a huge hole in the ground as singularly uninviting to the gaze, especially given that botanical and entomological marvels are right there in front of his eyes. It’s of interest to note that even if this final anecdote shares all the superficial attributes of the original episode of Danny at the Grand Canyon (Danny himself, his parents Doug and Carol, the ants, the Grand Canyon, Doug and Carol’s fascination for the Grand Canyon, and so forth), it is also the most distant from the original episode, in the sense that in order to see the analogy between the two stories, one has to encode them in a “relativist” fashion, based on the idea that the received wisdoms of a given society might well strike some of the society’s members as absurd. Only in this fashion can one overcome the natural resistance to letting actors play opposite roles to those they played in the initial anecdote.
As is hopefully clear from our analysis, the way an event is
unconsciously interpreted
(the choice of cues that will enable remindings to take place far in the future) should not be confused with the much larger set of
perceived facts
about the situation. What matters is the
perspective taken
on the perceived facts: which dimensions are used in encoding the event, and the amount of abstraction along each dimension — how the event is
distilled
, in short. Thus if, in the Grand Canyon episode, one saw only ants and leaves and a toddler looking at them, then one would be stuck at an extreme level of literality, and the range of possible events that might remind one of this episode will be reduced to practically nothing. If one opens up one’s point of view to the slightly broader idea that there are some insects and a child who finds them interesting, that encoding will allow slightly more distant memories to be triggered, such as that of the family on vacation in the Cinque Terre, but even so, the set of possible retrievals remains very sparse.
When one goes yet further and perceives a person who is concentrating on something trivial and ordinary instead of something grand and extraordinary that is right there before their eyes, then one has taken a large step in the abstraction of one’s encoding. At that point, the set of potential remindings becomes much wider (it’s only at this level of abstraction that the episode of Dick at Karnak is seen as analogous). And nothing keeps us from making yet more abstract perceptions of the situation, letting us see Danny, for example, as a person whose passions are at odds with all the standard clichés. This perception might suggest an analogy likening little Danny to sad, outcast poets who, from their youth onwards, are eternally misunderstood by society. This analogy may strike some readers as an absurdity, and in some ways it is one (here we are touching on the previous chapter’s ideas about the gradual impoverishment of the essence of an event as one glides ever higher in the abstraction spectrum), but be that as it may, it illustrates the wide variety of possible encodings of a single situation, and it is these encodings, unconsciously carried out, that will determine the remindings that might, in principle, occur at unpredictable moments of the foggy future.