Read Surfaces and Essences: Analogy as the Fuel and Fire of Thinking Online
Authors: Douglas Hofstadter,Emmanuel Sander
This indeed is one of the wellsprings of creativity — namely, the ability to make certain crucial leaps that at first seem surprising but that come to make eminent sense after the fact. Even if conceptual slippage is the most ordinary mental phenomenon, there are contexts where it is subtle, rare, and anything but straightforward. Discovery via conceptual slippage gave rise to many of the greatest ideas in history, including scientific discoveries (which we will discuss in more detail in
Chapter 8
). As the above outline shows, the present chapter has many ambitions; we shall take them one at a time, starting with the notion of abstraction.
Abstraction comes in different varieties. Here we will focus on the variety that we will call “generalizing abstraction”. We will say that category A is
more abstract
than category B if B is a subcategory of A — that is, if anything that belongs to category B also belongs to category A. For example,
coffee
4
is more abstract than
coffee
3
, because all
coffee
3
’s (basically, after-dinner drinks including tea but not wine) are also
coffee
4
’s (basically any light thing ordered at all), and moreover a
diabolo menthe
and a Coke belong to
coffee
4
but not to
coffee
3
. For much the same reason,
coffee
3
is more abstract than
coffee
2
, which in turn is more abstract than
coffee
1
.
The notion of abstraction (from now on, we’ll omit the modifier “generalizing”, since that’s the only type of abstraction that we’ll be concerned with) applies to classical categories of things occurring in nature (thus the category
bird
is more abstract than the category
sparrow
) as well as to categories of human-made objects (the category
furniture
is more abstract than the category
chair
), and also, of course, to categories of actions (
moving
is more abstract than
walking
) and to categories named by adjectives (red is more abstract than
scarlet
, and
colored
is more abstract than
red).
It also applies to categories named by idiomatic phrases, proverbs, or fables (thus,
little misdeeds lead to big misdeeds
is a more abstract category than
little thefts lead to big thefts
, and
better safe than sorry
is a more abstract category than
an ounce of prevention is worth a pound of cure
), and last but not least, it applies to categories that are not lexicalized at all, like those that were examined in the previous chapter.
In short, one category is more abstract than another when it includes the latter category as a special case. The existence in our minds of categories enjoying several different levels of abstraction makes it possible to take different perspectives on a single entity. Sometimes, for instance, a particular entity will be seen as a
sparrow
, and other times as a
bird
.
If we lacked the ability to abstract, our lives would resemble that of Ireneo Funes, the main character in Jorge Luis Borges’ short story “Funes, the Memorious”, for whom a fall from a horse had the devastating consequence that “Funes not only remembered every leaf on every tree of every wood, but… he was almost incapable of general, platonic ideas. It was not only difficult for him to understand that the generic term
dog
embraced so many unlike specimens of differing sizes and differing forms; he was disturbed by the fact that a dog at three-fourteen (seen in profile) should have the same name as the dog at three-fifteen (seen from the front).” In contrast to Funes, the standard human mind has not only the ability but the proclivity to abstract, in order to deal with the world’s vast diversity. It pulls together into a single category items that it sees as similar, and it further organizes its categories according to their levels of generality. We see the dog at 3:15 as being the same as the dog at 3:14, we consider that
dogs
and
cats
are the same as each other in that they are all
animals
, and so on.
Any situation can be categorized in an essentially limitless number of different fashions. Thus one can use many different words to label a situation, and also many different idioms or proverbs. An old piano might be a
musical instrument
to a music teacher, a
piece of furniture
to movers, a
dust trap
to the person who does the weekly dusting, and a
status symbol
to those who proudly display it in the middle of their living room. A tomato might be a
fruit
in a botany course and a
vegetable
in a cooking course. And there are times when a given situation can spontaneously evoke completely opposite and thus contradictory concepts in the minds of different observers; the very same situation can bring to mind the category
all that glitters is not gold
for one person and the category
where there’s smoke there’s fire
for another.
A given situation can be labeled at many different levels of abstraction because sometimes we wish to
make distinctions
and other times we wish to
see commonalities.
While dining, one naturally wishes to keep track of which glass is one’s own and which is one’s neighbor’s, but while washing them, one will blithely ignore that difference. A refrigerator and a piano have very different purposes, but for movers, they are both simply
big heavy objects.
When one is bringing up children, one wants all of them to be involved in
activities
; for one child this might mean acting, for another it might mean judo, and taking flute lessons, for a third. Indeed, what better way to distinguish two things than to assign them to different categories? For example, the distinction between an eagle and a swallow, or between a barn swallow and a cliff swallow, depends on the existence of distinct categories in the mind of the categorizer. But on the other hand, the barn swallow and the cliff swallow can both be seen as
swallows
, and the swallow and the eagle can both be seen as
birds.
This idea of highlighting a commonality uniting two things, just as valid and useful as the idea of drawing a distinction between them, depends on the existence of a common category to which they both belong.
Our ability to categorize things in many different ways determines how adaptable we are. Indeed, we often shift our perceptions of mundane situations with great speed and fluency, although such reperceptions tend to seem so bland that they usually go unnoticed. And yet such cases reveal the remarkable suppleness of everyday human intelligence, as a small example will now show.
You open the cupboard and pull out a glass. To do this, you had to recognize that the object was indeed a glass. This seems as simple as simple gets: any object has its intrinsic conceptual box, these boxes are called “categories”, and categorization is simply the placing of each object in its proper box, end of story. But perhaps it’s not quite the whole story, after all…
You don’t know me. In fact, I don’t know myself either; I’m unconscious. But whatever. Here’s my story. I was produced on July 11, 2005 in a French factory. From my birth onwards, I have been categorized left and right. So in no particular order, here’s what I have been:
artifact, industrial product, commodity produced in the European Union, consumer article, fragile object, glass, item of dishware, drinking glass, water glass, transparent object, recyclable object.
When I was being shipped to the store, I became a
piece of freight
and also a
piece of merchandise
, and while I was sitting on the shelf, I was an
item for sale.
Since my designer seems not to have been super-inspired that day, I remained on the shelf for several months, and the clerks variously reclassified me as an
unsold object
, a
casting error
, an
unsellable object
, and then a
dust-gatherer
, at which point I was declared a
discounted item.
My drastically slashed price finally allowed me to find an owner, and thus I became a
purchase.
Mr. Martin, who certainly is no great shakes in the creativity department, is nonetheless forever shunting me back and forth between categories, and he does so without realizing it in the least. When he’s thirsty, he never confuses me
with the plates, bowls, cups, or mugs (let alone the silverware!); indeed, for him I’m not even a piece of dishware or a glass — all I am is a
glass for cold drinks.
I can thus relish being the host for water, soft drinks, and milk, but I’m never given the chance to welcome wine into my person — that role is granted only to a certain special elite that occupies the shelf just above mine. One time, though, a confused guest actually promoted me to the swanky status of
wineglass
, and as such I did a rather commendable job, if I don’t say so myself, even though I’m not as sophisticated as my cupboard-neighbors. Usually, after having done my duty, I wind up in the dishwasher, and during that brief stay, no one cares that I’m a
glass;
I’m just
dishware
and that’s that. My peripatetic life has occasionally given me the chance to be categorized in some rather extreme fashions. Thus the lady of the house has more than once employed me as a
spider carrier
and quite often as a
knickknack holder.
One time when the family went on vacation, I did duty as a
toothbrush holder
for an entire month, and the next year I was recruited to serve as a
sugar bowl.
I’ve also done stints as a
home for tadpoles
(this after the Martin children had been playing in the woods), and as a
vase
(a couple of times when the kids had picked some wildflowers for their mother). I was once even a
piece of construction material
, when the kids decided to make a tower using me and some of my peers. Alas, they forgot that I was a
fragile object
and things came to an abrupt and unhappy end when the tower fell down. Luckily, though, since I’m a
recyclable object
, a new life is awaiting me just around the corner, rich in undreamt-of new categorizations.
Categorization pervades every facet of our existence and is never fixed, even in the most mundane of circumstances. Our mini-saga has just demonstrated this, as did our various portraits in
Chapter 1
of the 60-kilogram mosquito-attracting mirror-symmetric insomniac object known as “Ann”, and as do innumerable other examples. Being moved from one categorical “box” to another, often by being slid up or down the rungs of an abstraction ladder, is the inevitable fate of all objects, actions, and situations.
Some readers might nonetheless feel tempted to think that, despite the incessant bouncing back and forth of our story’s unconscious narrator from one category to another, it still has just one true and permanent identy — namely, it is a
glass.
But to think that way is to fall into the trap of Plato’s “objectivist” vision, according to which objects have one and only one true identity. That is a naïve vision.
It’s nonetheless true that psychological studies have identified certain types of “default” categorizations, usually called
basic-level
categories. For example, people tend to find it more natural to call an object a “chair” than an “armchair” or a “piece of furniture”, and likewise they prefer “glass” over “water glass” or “piece of dishware”, and this experimentally confirmed intuition might reinforce one’s intuition that each object really does have a “true identity” in terms of its
genuine
category. But at any moment, an entity is what its categorization says it is, and that’s all. Some objects are of course more
glass
-like while others are more
chair
-like, and they become
glasses
in those contexts when “glass” is the word that they tend to evoke in human minds, but in other contexts they become members of other categories. Thus, as we just saw, a
glass
-like object can become
dishware, artifact, commodity, spider carrier, knickknack holder
, and so forth.
(Incidentally, when we write “The glass was categorized as a knickknack holder”, we are in fact using sloppy language and we should, in principle, say something more like this: “The entity that in many contexts is categorized as a
glass
has, in this case, been categorized as a
knickknack holder.”
That, however, would be heavy and pedantic, so we refrain from such precision.)
The fact that “our friend the glass” has a clearly dominant category in our minds (the category
glass
, obviously) may make it harder to accept the idea that it doesn’t have one single fixed identity. The same could be said of most artifacts (objects made by people with a certain narrow purpose in mind). That narrow purpose will dominate our perception of the object’s identity, making us feel that it is indeed the object’s true and sole identity.
But playing the game of “musical categories”, as we did above, shows that things are not that simple. To be more concrete, let us come back to the just-mentioned case of Ann and ask: Is she first and foremost a human being? A woman? A lawyer? A living being? A mother? An animal? Everyone would agree that Ann is “all of the above”, and, depending on the state of mind of the person (or the mosquito) perceiving her, she will be more
one
than
another
of them. Who or what, though, would decide whether Ann is intrinsically more a
living being
, more a
human being
, or more a
woman
? And why would there have to be a “winner” among these diverse viewpoints?