Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (13 page)

Very similar examples are provided by Corentin, who says, “You can stop, Mom, your hair’s all cooked now” (meaning it’s now dry), or Ethan who observes, “I broke the book” (meaning he’s torn it), or Tiffany who declares, “I want to get my nails permed” (meaning she wants a manicure), or little Alexia, who asks, “Mom, can you glue my button back on?” (of course meaning “sew it back on”), and last but not least by Joane, who poses the classic conundrum, “Do buses eat gas?”

In each of the cases shown above, one can ask if the child actually was making an error. The key question is, what would constitute an error? If Danny knows the word “drink” but it simply doesn’t come to mind, and if he realizes that “to eat” isn’t really what he means to say, then saying “I want to eat water” would be an error. But if he has the feeling that what he said is perfectly fine, and if he would be surprised to hear the nursery-school teacher correct him, then we’d say that his statement was correct, at least from his own point of view. Most likely Camille, who “undressed the banana”, Ethan, who “broke the book”, and Alexia, who wanted the button to be “glued back on”, had little or no idea of the existence of the verbs “to peel”, “to tear”, and “to sew”. From their viewpoint, what they were saying was correct, because their concepts of
undressing, breaking
, and
gluing
were more inclusive than those concepts are in the mind of an adult, and they could thus be applied to situations having a wider range of diversity. For example, Ethan could almost certainly have said, given the proper conditions, “the curtains are broken”, “I broke a loaf of bread”, or “they broke the house”.

On the other hand, it’s very unlikely, even in our society, filled as it is to the brim with technological gadgets, that Joane (“Come on, Mommy, turn your eyes on!”) would be familiar with the verb “to turn on” and yet unfamiliar with the verb “to open”. Likewise, it’s extremely unlikely that Jules (“They turned off the rain!”) knows the verb “to turn off” but is unaware of the verb “to stop”. And so we ask: are these children making errors, or not?

The line between what is and what is not an error is less precise than one might think. What these children are doing is making semantic approximations, stretching their personal concepts in a way that adults would not feel comfortable doing, because the concepts
to turn on, to turn off, to open
, and
to close
in these children’s minds have not yet reached their adult forms — no more than (to switch from verbs to nouns momentarily) the categories
horse
and
cat
had reached their relatively stable adult stages in the mind of little Abby when, at age three, she saw some greyhounds and called them “horses”, and soon thereafter saw a chihuahua and called it a “cat”. The concepts silently hidden behind these words will continue to develop in the minds of all these children, just as will the category
mother
in Tim’s mind.

The utterances made by such children are not terribly different from the semantic approximations of adults who say “I broke my DVD” instead of “I scratched it”, or “I broke my head getting out of the car” instead of “I banged it”; it’s just that adults’ concepts are a little bit more sophisticated than children’s. And then (sticking with the
verb “to break” for a moment) there are many usages that are often labeled “metaphorical”, such as “to break bread”, “to break one’s fast”, “to break one’s silence”, “to break one’s brain”, “to break somebody’s neck”, “to break the ice”, “to break wind”, “to break ground”, “to break the news”, “to break someone’s heart”, “to break a habit”, “to break away”, “to break a code”, “to break the law”, “to break a world record”, and on and on. Such usages are obviously built upon analogical extensions of the verb “to break” that go way beyond anything that a child does who says “the book is broken”.

Our tale of children’s usage of verbs hasn’t “turned off” yet. Let’s look at little Joane’s use of the verb “Come on!” (“Come on, Mommy, turn your eyes on!”). This usage is undeniably a correct one, and it reveals a deep understanding of the situation that this two-year-old is in. What does “Come on” mean? Firstly, it’s a verb that indicates that the speaker wants some change to come about, and it’s directed at another person who the speaker feels would be able to make that change happen. Secondly, it’s spoken as a kind of urging — stronger than and less polite than “please”, almost reaching the intensity of “I insist”. Thirdly, although it’s an imperative based on the verb “to come”, it has nothing to do with physical motion. In fact, “Come on!” is such a frozen expression that one might even argue that it is no longer a genuine verb but more of an interjection, rather like “Hey!” After all, no one would reply to the exhortation “Come on!” by saying “Okay, I’m coming on!” But grammar aside, we are dealing with a subtle word choice made by a toddler. She clearly had put her finger on the situation’s essence — namely, she wanted her mother to open her eyes — and that desire led to an eager hope that she could achieve this goal by whining.

To put it in another way, already at the tender age of two, Joane had understood that there is a certain class of situations in life that match and that evoke the label “Come on!” This mental category of
Come on!
situations had gained a solid toehold in her mind. One of the situations belonging to this category was the current one, with her napping mother. To put it succinctly, then, we are saying that
Come on!
situations constitute a mental category that is every bit as real and as important as categories such as
eyes, truck
, and
Mommy
, which refer to physical entities in the world. The acquisition of the abstract category of
Come on!
situations by a two-year-old child is a small cognitive miracle and is thus an excellent challenge for anyone who has the goal of deeply understanding human thought.

We might equally well focus on the choice of the verb “gotta” by Lenni (“Gotta nurse the truck!”). This two-year-old boy has understood the essence of situations that are labeled with the pseudo-word “gotta” — namely, something is needed in a hurry, there’s no time to lose, and so on. It’s very likely that Lenni thinks that “gotta” is just one single word (which is why we didn’t write “got to” or “I’ve got to” or “we’ve got to”, etc.), and this would suggest that he hasn’t fully understood that it is a verb, even if in different circumstances he might say, “You don’t gotta do it” or “I gotted to do it”, and other variants, which are clearly attempts to use it as a verb. So once again we observe a case of a high degree of abstraction carried out by a human being who belongs to the category
toddler
.

Here are a couple of other childish pearls that do not involve verbs. Six-year-old Talia announced, “Dad, we have to get some deodorant for the refrigerator!” (since it reeked of seafood), and her two-and-a-half-year-old cousin Hannah, having just licked all the chocolate off her Eskimo Pie, exclaimed with delight, “Look, now the ice cream is naked!”

Even with nouns that denote the most ordinary and concrete of objects, there remain many subtleties. Lenni said, “Gotta nurse the truck!”, but what truck was he speaking of? There was no truck in the apartment; there was just a broken toy. Was that object really a truck? Well, yes and no. Lenni knows perfectly well that the trucks he sees on highways are hugely bigger than
his
truck, but for him those are distant abstractions; he’s never even touched one. By contrast, his little toy truck is a physical object that drives down the invisible highways on the floor of his apartment. In that sense, this toy is, for Lenni, just as central a member of the category
truck
as are those “real” trucks that drive down the “real” highways — indeed, for him, it’s probably more central than those are. Ironically, for Lenni, it’s
real
trucks that are metaphorical.

Earlier we suggested that there is a strong resemblance between the concrete perceptions of a small child and the abstract mental leaps made by a sophisticated physicist. We wish now to illustrate this thesis by means of a concrete example.

In 1610, Galileo Galilei, having just constructed his first telescope, turned it toward the heavens and peered at various celestial bodies. Recall that at that time, the distinction between planets and stars, which today is quite sharp, was still blurry. Certain celestial lights seemed to wander against a backdrop formed by others, but the reason for this movement was not at all clear. Galileo’s choice to focus on Jupiter did not mean he knew what it was; it was probably because Jupiter was one of the brightest and thus most inviting objects in the sky to look at.

Galileo’s first surprise was that in his telescope Jupiter appeared not as a mere point but as a small circle, which suggested that this “point of light” might well be a solid object with a definite size. Galileo had certainly had the experience of seeing someone with a lantern approaching him. From afar, the lantern seems to be just a dot without size, but then, little by little, the dot acquires a diameter. By analogy with this familiar phenomenon, Galileo could thus imagine that Jupiter, up till then just a dot of light, was in fact a physical object, much like the objects he knew all around him. A second surprise was that against the background of this small white circle he observed some tiny black points, and moreover — a third surprise — these tiny points moved across the circle in a straight line, some taking a few hours, others a few days. Furthermore, whenever one of these points reached the edge of the white circle, it would change color, becoming white against the backdrop of the blackness of space, and would continue moving along the same straight line, then it would slow down, stop, and reverse tracks; when it returned to the edge of the white circle, it would disappear totally, and after a while would reappear on the far side of the white circle.

We won’t go into great detail about Galileo’s epoch-making discovery; we want, rather, to focus on the way in which the great scientist interpreted what he was observing through his telescope. He decided that Jupiter was a roughly spherical object around which other, smaller objects were rotating perfectly periodically (with periods ranging from about two days to about fifteen days, depending on which dot he was paying attention to). Galileo knew that the Earth was round and that the Moon rotated around it in a periodic fashion, with a period of about thirty days. All these factors added up and suddenly something clicked in his mind. All at once, Galileo was “seeing” a second Earth in the sky, accompanied by several Moons. We put “seeing” in quotation marks to remind readers of the fact that the key moment of “perception” was Galileo’s act of interpretation, since the light stimuli arriving at his eyes hadn’t changed in the slightest. The analogy between the Moon and a spot of light (or a black point, depending on where the dot was with respect to the white circle of Jupiter itself) was a stroke of genius — a “vision” of a visionary, so to speak.

Not everyone would have seen what Galileo saw, even if they had been given a telescope, even if they had observed the celestial lights over several weeks, and even if they had focused on Jupiter in particular. The reason is that until that moment, the word “Moon” had been applied to only one object, and the fantasy of “pluralizing” that object was well beyond the imagination of anyone alive at that time (and if someone original had the audacity to think such a thought, that was sufficient to bring about their swift demise: it suffices to recall the case of poor Giordano Bruno, who was burned at the stake in Rome in 1600 for his fantasies about worlds like our own spread throughout space). Moreover, Galileo’s daring act of pluralization was the fruit of an analogy that might have seemed laughable to most people — after all, it was an analogy between the entire world, on the one hand (since for most people back then, the terms “Earth” and “world” were synonyms), and on the other hand, an infinitesimal dot of light. This analogy, which might seem far-fetched, nonetheless led to the pluralization of the Earth, since it began by taking Jupiter to be another Earth, and it was rapidly followed by the pluralization of the Moon, which naturally led to the lowercasing of the initial “M”. The concept of
moon
had been born, and from that moment on it was possible to imagine one or more moons circling around any celestial body, even around moons themselves.

What Galileo envisioned, in hypothesizing that some small objects in the heavens were rotating around a larger object, was a replica, on an unknown scale, of numerous earthbound situations that were familiar to him, in which one or more objects rotated around a central object. Galileo’s stroke of genius was to bank seriously on the daring heliocentric hypothesis of Copernicus and to think to himself that the sky, far from being merely a pretty two-dimensional mural whose purpose was solely to make human life more pleasant, was a genuine
place
that is completely independent of humanity, similar to the places he knew on Earth but much vaster, and as such, capable of housing entities having unknown sizes, and capable of being the site of their movement. In fact, Galileo was completely ignorant of the size of Jupiter and its moons; of course he could imagine a sphere roughly the Earth’s size, but doing so would be no more than
guesswork, since all he had access to was a set of tiny points. For all he knew, Jupiter might be no larger than the town of Padova, in which he was doing his stargazing, or it might be a hundred times larger than the Earth. Galileo’s analogy was an analogy created (or rather, perceived) between something vast and concrete (the Earth and the Moon) and something else that was extremely tiny and immaterial (a circle and some points), but which was nonetheless imaginable as another vast and concrete thing.

Is this profound vision of Galileo’s all that different from the vision of the child who sees a very small toy as being a member of the category
truck
, whose other members are so enormous that they are almost inconceivable to the child? One thing is certain — namely, that in both cases, there is a very small object that is imagined as being a very large object, and in both cases, the perceiver uses familiar phenomena in order to understand what is not familiar.