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 lower-casing 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.
And what about the analogy that we are drawing between what Galileo did and what the small child does — is this, too, not just a leap between one scale of sizes and another? Isn’t the small cognitive leap by the child, which links a silent, odorless plastic toy truck on the floor with a loud, smoke-belching truck on the highway, simply a small-scale version of the sophisticated cognitive leap by Galileo, which linked the Earth under his feet with the imagined, distant Jupiter, and which linked our familiar Moon with the imagined, distant Jovian moons? Could it in fact be the case that the tiny child’s act of calling an everyday object by its standard name is a close cousin of the genius’s act of creating a new concept that revolutionizes human life? For the time being, we won’t press the point, but we’ve planted the seed. To go further will require that we look more closely at the subtlety of the most ordinary categories.
Analogies in the Corridors and Behind the Scenes
Some years back, the senior author of this book went to Italy for a sabbatical year. When he arrived, he had a decent command of Italian but, like everyone in such a situation, he made plenty of mistakes — sometimes subtle, sometimes not — most of which were based on unconsciously drawn analogies to his native culture and language. The research institute where his office was located was a building in which some three hundred people worked — professors, researchers, students, writers, secretaries, administrators, technicians, cafeteria workers, and so forth. During his first few weeks, he met several dozen people, whose names he instantly forgot but whom he would continually bump into in the wide, austere corridors of the building, each time he ventured out of his small office. What to say to all these friendly folks who instantly recognized the newly arrived foreigner, the professore americano, and who greeted him warmly (or at least politely) whenever their paths crossed in the hallways? And what to say to the people he saw every day but whom he had never actually met?
His initial assumption, coming from his native culture, was that the proper thing to say to anyone and everyone was “Ciao!”, even if it was someone that he wasn’t sure he’d ever seen before. This was an innocent assumption based on the American way of saying “Hi”, and perhaps it seemed charming to those who received such spontaneous greetings and who were naturally inclined to humor their sender because of his status as a foreign guest, but il professore soon noticed that his monosyllabic choice did not coincide with that of the majority of the native speakers of Italian whom he ran into. To be sure, there were a handful of people who said “Ciao” to him, but these were his closest colleagues whom he knew well. Otherwise, though, the people in the halls tended to say either “Salve” or “Buongiorno” to him. It took him a while to figure out the levels of formality that were linked to these two forms of greeting, but in the end he devised a fairly clear rule of thumb for himself to guide him in his hallway greetings. Basically you say “Ciao” to people with whom you are on a first-name basis; you say “Salve” to people you see from time to time and whom you recognize (or think you recognize); and finally, you say “Buongiorno” to people you’re not sure you recognize, and also to people whom you would prefer to keep at arm’s length.
Once he had formulated this rule of thumb and had gotten it more or less confirmed by native Italian-speaking confidants (who, in truth, had never really thought about it and who were therefore not all that sure of what they were saying), he tried to put his new insight into practice, which meant that every time he ran into someone in a corridor, he had to make an instant triage: “First-name basis? ⇒ Ciao. Know them a little bit? ⇒ Salve. Not sure who it is? ⇒ Buongiorno.” He rapidly discovered that this was a cognitive challenge that was not in the least trivial. Fortunately, in each of these three greeting-categories, there were one or two individuals who served as prototypes, and using these people as starting points, he began to feel his way in the obscure corridors of acquaintanceship. “Hmm… This fellow who’s approaching me, I know him roughly as well as I know that tall curly-haired administrator” — and zing! — he whipped out a “Salve”. Around several central individuals constituting the nuclei of the three categories, there started to form mental clouds that spread out as time passed. The strategy worked pretty well, and after a few months, il professore was handling the challenge fluently as he strode through the corridors of what, at the outset, had been a mysterious maze.
This is a concrete example of how new categories form — in this case, those of ciao situations, salve situations, and buongiorno situations — thanks to the use of analogies at every step of the way. And it also allows us to stress another key point — namely, that behind the scenes of even such a simple-seeming thing as uttering an interjection, there is a complex cognitive process that depends on subtle categories.
Let’s take an example in English that has many points in common with the one just described. On certain occasions one says simply “Thanks” to convey one’s
gratitude to someone; on other occasions, one says “Thank you” or “Thank you very much” or “Thanks a lot”; indeed, there is a whole range of thanking possibilities, including such familiar phrases as “Many thanks”, “Thanks ever so much”, “Thanks for everything”, “Thanks a million”, “How can I ever thank you?”, “I can’t thank you enough”, and so on. Obviously there isn’t one exact and perfect choice for each thanking occasion, but on the other hand, certain situations will very naturally evoke just one of these expressions, and some of these expressions would be wildly out of place in certain circumstances. In short, although there isn’t a one-to-one correspondence between situations and expressions, a good choice by a native speaker is far from being a random act, far from being a mere toss of dice. When one is a child, one observes thousands of occasions in which adults use one or another of these phrases without thinking about it for a split second, and pretty soon one starts to do just that oneself. Sometimes adults will smile a little, which conveys the sense that one is probably slightly off-target, while other times one can tell, watching others’ reactions, that one has hit the bull’s-eye. Thus bit by bit, one refines one’s feel for the range of applicability of each of these important and frequent phrases. However, one will probably have no memory whatsoever of the many pathways that collectively led one to one’s current status of grandmaster in the day-to-day arts of greeting and thanking.
And what holds for these seemingly trivial acts holds as well for the labels that one pins on all aspects of reality, including verbs (as we already illustrated in the case of children), adjectives, adverbs, conjunctions (as we shall shortly see), and so forth.
“Office” or “Study”?
If one pays attention to the words that are spontaneously uttered in the most mundane of conversations, one will run into many surprises that reveal something of the processes underlying these choices (if indeed “choice” is the mot juste here, since words generally bubble up so automatically that they do not feel like choices one has made). Here we’ll take an example involving Kellie and Dick, two friends who came from Boston to the house of the above-mentioned professore a number of years after he had returned to the United States, and who visited for a few days. As it happened, Kellie and Dick both used the term “your office” to designate the standard workplace of their host, while he himself would always call it “my study”. After he had put up with this cognitive dissonance for a couple of days, it occurred to him to ask them, “How come the two of you always go around talking about my ‘office’ when you both know perfectly well that I always call it my ‘study’?”
This question caught the Bostonians by surprise, but they quickly hit upon an answer to it, and it was almost surely the answer. They said, “In our Boston house, the place where we work [they had a small public-relations firm that they ran from their house] is on the third floor — our house’s top floor — and we always call it our ‘office’. It’s the place where we have our computer, printer, and photocopy machine, all our filing cabinets, and all the slides and videos we’ve made over the course of the three decades we’ve been doing this. And for you it’s the same thing: your work area is on the second floor — the top floor of your house — and it’s where you have all the stuff that you rely on for your work: your computer, printer, and photocopy machine, your filing cabinets, your books, and so forth. To us the analogy is blatant, crystal-clear. It just jumps out at us, no need to think at all. So to us, your workplace is your office, clear as clear can be. That’s the whole story.”
After some reflection on the matter, their host answered, “Aha! I think I see what’s going on here. When I was a kid in California, my father had what he called his ‘study’, which was on the second floor — once again the top floor — of our house. It was the spot where he had lots of papers, books, slide rules, filing cabinets, a mechanical calculator, and so forth. Every day I would see him working there, and it left a vivid impression on me. And also, at the university, on the campus, he had an office, where he had many more books, and he often worked down there as well, but the difference between his study and his office was crystal-clear for me. And today, I too have both a study at home and an office on the campus here in Indiana. But I would never confuse the two of them. So that’s how I see things.”
And on this note the exchange between friends closed, but there are important lessons that can be drawn from it. First of all, what’s clear is that all parties concerned had depended unconsciously on analogies they had made to very familiar situations. These analogies involved slight “slippages” (third floor instead of second floor; slides and videos instead of books; public-relations work instead of academic work; calculator instead of computer; etc.), but at the same time they respected and preserved a more important essence — namely, both sides of each analogy involved the standard daily workplace, which was separated from the rest of the house and was the storage area for professional material, and so forth. In each case, one sees how the choice of the word to apply to the workplace came from an analogy made to one single familiar situation, rather than what one might have thought a priori, which is that assigning an entity to a general category like office would depend on the fact that the rich and abstract category office had been built up from thousands of different examples encountered over the course of a lifetime. And yet no connection to such a general category took place in this case. Each of the three people, although they all had rich and abstract concepts at their disposal, completely ignored them and instead made a concrete and down-to-earth analogy to a single familiar situation. The numberless prototypical instances of the concept office, such as executives’ offices, dentists’ offices, doctors’ offices, lawyers’ offices, and so forth, had nothing to do with what went on in Kellie’s and Dick’s minds. All that mattered was that primordial image of office from their own house. This is reminiscent of little Tim’s primordial concept of Mommy. Even though the concept mother has been enormously enriched for Tim as an adult, there’s no doubt that his own mother has remained over the decades a potential source for analogies; she never got melted down and lost in the abstract concept of mother.
As a postscript to this episode, we might add that the Bostonians, during a visit to their friend’s home a year later, occasionally used the term “your attic” when referring to his study. Surprised once again by this word choice, he asked them about it, and they explained that they often used the term “attic” in talking about their office in Boston. For them, in this context, the word “attic” had nothing whatsoever to do with a typical messy and dusty attic in a typical house; quite to the contrary, they were thinking of a room at the opposite end of the messiness spectrum — a very clean space in their house, constantly in use on a daily basis. And thus, once again, we see an extremely down-to-earth analogy linking the new place to just one single familiar place rather than to a generic category in which many places are blurred together.
If Kellie and Dick had discovered a truly prototypical attic in their friend’s house, full of cobwebs, ancient checkbooks, huge old wooden trunks shipped from abroad, discarded amateurish paintings, and such things, the word “attic” would certainly have sprung to mind because each of them has in their memory not only the concept our own attic but also the concept typical attic, which allows them to envisage a standard attic, if need be. For example, if Kellie were reading a mystery novel and she came across the sentence, “Trembling, the aged aunt slowly groped her way up the steep and narrow stairway towards the attic to look for the golden statuette, but after three quarters of an hour she hadn’t yet come down”, the chance is next to zero that this description would evoke in Kellie’s mind an image of her Boston house’s attic.
This example of the host’s study, designated first by his visitors as “your office” and later as “your attic”, shows how we are guided by unconscious analogies towards labels that seem to pinpoint just what we want to say. It illustrates why there is no boundary line — indeed, no distinction — between c
ategorization and the making of analogies.
The Structure of Categories and of Conceptual Space
The anecdote we’ve just related shows that a concept (such as those designated by the terms “attic”, “truck”, “to open”, “to melt”, “to nurse”, “come on!”, “ciao”, and so forth) can have specific and very distinct instances. Indeed, if we ask you to think of a golfer, you might conjure up the image of an anonymous middle-aged lady riding, on a Sunday morning, down some anonymous fairway on a golf cart. But it’s more likely that you would conjure up the image of a famous golfer such as Tiger Woods swinging a five-iron, or perhaps you would recall a golf pro you once took lessons from. Instances of the category golfer abound, and around each of these specific and concrete instances there is a halo that extends far out. For example, around Tiger Woods, one can imagine seeing him not only making (or missing) a long putt on a tricky green, but also teeing off with great power, hitting out of the rough, and getting out of a sand trap, not to mention appearing in various airport ads and on television, and so forth. Moreover, in this cloud surrounding Tiger Woods, any golf aficionado will surely find a number of Woods’ famous predecessors, such as Jack Nicklaus, Arnold Palmer, Sam Snead, Ben Hogan, and others. Anyone familiar with golf will evoke such images without any trouble at all. And so, what does the concept of golfer amount to?
It might seem, a priori, that asking about the nature of the concept golfer is a minuscule question in comparison with the huge question, “What is human thought all about?”, but the fact is that it is no smaller. In any case, our modest musings about the concept golfer are bringing to the fore the obvious fact that concepts are densely stitched together through relationships of similarity and context. The concept of golfer is quite closely linked to that of minigolfer, and less closely to such concepts as tennis player, runner, bicycle racer, and so forth. Among these connections, some are very close while others are so distant that they barely exist (for example, there will be practically no relation at all between the notions of golfer and sumo wrestler in anyone’s mind, aside from the fact that both are types of athletes).
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