Moving right along, Tim will soon handle cases that are even more abstract, such as “Marie Curie is the mother of radioactivity”, “The American revolution is the mother of the French revolution”, “The American revolution is the mother of the Daughters of the American Revolution”, “Judaism is the mother of Christianity”, “Alchemy is the mother of chemistry”, “Censorship is the mother of metaphor” (Jorge Luis Borges), “Leisure is the mother of philosophy” (Thomas Hobbes), and “Death is the mother of beauty” (a quote from Wallace Stevens, and also the title of a detailed study of the role of metaphor in thought by cognitive scientist Mark Turner).
And we can go yet further, to the idea of Nature as the mother of all living creatures (“Mother Nature”), or the idea of Mother Superior in a convent, or the idea of den mother for a Cub Scout pack, or the idea of a company that has a mother company from which it sprang at some earlier point, or the idea of the mother board in a computer, and so forth. A mother in a park, a mother in a soap opera, an adoptive mother, a den mother, a mother doll, a mother bee, a mother cell, a mother board, a mother drop of water, a mother deity, a mother company, the mother lode… Given that some mothers, such as Tim’s mommy Sue, are certainly “real mothers”, while others, like the mother board, are just as certainly “metaphorical mothers”, the goal of drawing a sharp, objective boundary between the two distinct subcategories seems as if it might well be within reach. However, as we have shown with our list of blurry examples, such as the person in a novel, the doll mother, and the adoptive mother, that hope is but a beckoning mirage.
On the Categories and Analogies of Children
The story we’ve just told illustrates a central theme of our book — namely, that each category (in this book we use this term synonymously with the term “concept”) is the outcome of a long series of spontaneous analogies, and that the categorization of the elements in a situation takes place exclusively through analogies, however trivial they might seem to an adult. A crucial part of this thesis is that analogies created between a freshly perceived stimulus (such as the mother of a little girl in the park, as seen by Tim) and a relatively new and sparse mental category that has only one single member (such as Tim’s category Mommy) are no different from analogies created between a perceived stimulus (once again, take the same woman in the park) and a highly developed mental category to which thousands of analogies have already contributed (think of the very rich category mother in the mind of an adult).
This last statement is among the most important in our book, yet on first sight it might seem dubious. Is it really plausible that the very same mechanisms underlie the act whereby a two-year-old spots a Saint Bernard and exclaims “Sheep!” and the act whereby a physicist of great genius discovers a subtle and revelatory mapping between two highly abstract situations? Perhaps it seems implausible at first glance, but we hope to have made it convincing by the end of the book.
In the meantime, to facilitate building a pathway that will get us to this goal, we’ll set up some intermediary bridges. Toward this end, it will be useful for us to take a look at a number of statements made by children, for these statements reveal hidden analogies that underlie their word choices. And so, without further ado, here is a small sampler of children’s sentences, many of which were collected by developmental psychologist Karine Duvignau in her work with parents who were observing their children at home.
Camille, age two, proudly announces: “I undressed the banana!”
She talks about the banana as she would talk about a person or a doll, seeing the peel as an article of clothing that she has removed from it. The banana has thus been “laid bare” (a near neighbor of what Camille said).
Joane, age two, says to her mother: “Come on, Mommy, turn your eyes on!”
Here a little girl speaks to her mother as if she were dealing with an electrical device having an on–off switch.
Lenni, age two, says about a broken toy: “Gotta nurse the truck!”
Here, as in the case of Camille, we see a personification of an inanimate object. The truck is “sick” and so the child wants to help it “get well”.
Talia, three years old, says: “Dentists patch people’s teeth.”
This represents the flip side of the coin, where the child speaks of something alive as if it were an inanimate object (as we just saw Joane do as well).
Jules, three years old, exclaims: “They turned off the rain!”
For Jules, rain is like a television set or a lamp that a person or people can turn on or off with a switch.
Danny, aged five, says to his nursery-school teacher: “I want to eat some water.”
In this case, Danny was not speaking his native language but one he was just starting to learn, so he reached out and grabbed the nearest word he knew.
Talia, aged six, says to her mother, “Are you going to go scold the neighbors today?”
The night before, the upstairs neighbors had held a very noisy party, and her mother had told Talia that the next morning she would go knock on their door and complain about their noisemaking. In using the word “scold”, Talia was unconsciously revealing her egalitarian value system: any person, whether it’s an adult or a child, may sometimes have to be scolded.
Tom, aged eight, asks: “Dad, how long does a guinea pig last?”
While it’s true that Tom talks here about his guinea pig in a most materialistic manner, the tenderness with which he treats his pet shows unmistakably that his category entity of limited duration is much broader in scope than that of most adults.
At the same age, Tom asks his parents, “How do you cook water?”
This question gets uttered when Tom has generously decided to fix some coffee for his parents one morning, but isn’t sure how to start. The distinctions between such kitchen-bound concepts as to heat up, to boil, to cook, and to fix are not yet very clear in his mind, but since he announces to anyone who’ll listen that he aspires to be a chef in a top-flight restaurant someday, it’s to be hoped that this blur won’t last too long.
Once again Tom, still eight, says to his uncle, “You know, your cigarette is melting.”
This is stated when Tom’s uncle is so involved in a conversation that he seems unaware that his cigarette is slowly being consumed in the ashtray. Although Tom knows cigarettes are not for consumption by children, here he links them with certain foods that he knows well, such as ice cream and candy, which can melt.
Tom tips over a wineglass, goes to get a sponge, and chirps, “Here, I’ll erase it!”
Part of the tablecloth has just been colored dark, much as paper is colored by pencils or a blackboard is colored by chalk, and so to Tom it makes sense that the sponge will act as an eraser, eliminating all traces of the spilled liquid.
Mica, age twelve, asks his mother, “Mom, could you please roll up your hair?”
He wants to take a snapshot of her and what he means is, “Could you please put your hair up in a bun?”, but his thought comes out in a more picturesque way.
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?”
Impressive Heights of Abstraction by Children
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 w
e’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.
Shining Light on the Moon
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.
Surfaces and Essences Page 8