Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (61 page)

But let’s jump upwards from
consumer goods
, further broadening our vision of the possibilities of random murder. One could stand on a lonely hill with a rifle and fire on random people in the streets below. One could strap explosives around one’s waist and board a crowded bus or walk into a nightclub or a busy marketplace.

From Tylenol murders to various types of terrorist acts, we have moved upwards in abstraction, maintaining only the conceptual skeleton of
random murder.
Each leap upwards in abstraction corresponds to creating a wider ring of possibilities around a common core, moving gradually outwards in semantic distance from the original event. This is the quintessential human way of imagining novelties — starting with small variants, then working one’s way outwards to more and more radical ones, the discovery of which is much less likely. As is always the case when the answer to a riddle is given, abstraction seems very simple if one displays its fruits in front of an observer’s eyes, but that impression is deceptive. If the pathway meandering through the space of categories seems like child’s play, that is an illusion. When you have to make the leaps yourself, each one presents an obstacle, and few people will get far in the endeavor. The best proof of the difficulty of this kind of progressive abstraction is its rarity.

In the end, how far did the FDA go? It did not impose any requirements on how fruits and vegetables were sold, nor on other types of buyable goods, and so today, one still finds such items on the shelves of stores exactly as they were back in the pre-Tylenol-murder days — without protection. Why did the FDA stop at the level of medicines, and not go any further? Why did it arbitrarily draw the line here?

The reason is that the type of rising-abstraction semantic pathway that we sketched out above cannot be followed at will, and cannot be taught in schools as a sure-fire creativity technique. The number of ways a given object, action, or situation can be categorized is gigantic (recall Mr. Martin’s wineglass, tadpole home, and spider holder), and the vast majority of potential categories are simply not available to the conscious mind, even to a mind actively looking for new ways to categorize something. However, there are circumstances in which a useful discovery can be the fruit of a simple-seeming upwards leap. In such cases, the seeming ease of an act of mental agility not only is esthetically pleasing but also lets one escape from mental ruts and see things in a genuinely novel fashion.

“Thinking outside the box” — who has not heard this mantra chanted dozens of times? It purports to reveal the key mechanism of creative thought. It suggests that whenever we have a mental block, whenever we get stuck in a rut, whenever we find ourselves trapped in a box canyon, whenever we have painted ourselves into a corner, whenever we are getting nowhere fast, whenever our wheels are spinning, whenever we are “pedaling in sauerkraut”, as they say in French, why then, if we merely know this appealing sound bite, it will come to our aid like a loyal St. Bernard dog, lifting us up

out of our foggy, unproductive mindset. Like a genie in a lamp, the magic recipe of
thinking outside the box
will liberate us from our cul-de-sac thinking and will open up fantastic new vistas. There is even an electricians’ union whose motto is “Trained to Think Outside the Box!”, which sounds to us like a contradiction in terms (unless by “the box” they mean “the fuse box”). Or then again, as another advertising slogan put it a while back, whenever things looks hopeless, just “Think Different!” This notion that creative thinking involves avoiding the beaten path will surely not catch anyone off guard, but unfortunately it is no more insightful than stating that what makes opium induce sleep is its “dormitive virtue”. Yet it is amazing how humble are the conceptual slippages that have sparked intellectual revolutions, sometimes small, sometimes large, sometimes on a tiny level, sometimes on a global level. Indeed, creative insight depends surprisingly often on very small but subtle conceptual slippages.

This solution is hardly the stuff of genius, but it is nonetheless a clever idea whose origin is worth looking at. It consists in the conceptual leap from
pulling
the cork to
pushing
the cork — actions that are essentially diametric opposites. And yet, what allowed Jillian to make this directional slippage is an act of recategorization — namely, she glided from the concrete, physical idea of
pulling the cork out
to the more general idea of
accessing the wine
, or to put it more abstractly, she glided from the narrow, physical idea of
pulling out what is blocking access
to the broader but more goal-focused idea of
gaining access to what is desired.
This is clearly an act of abstraction. In this situation,
pulling out
is a member of the category
gaining access
, and the recategorization allowed Jillian to imagine other ways in which she might gain access to the beverage. Jillian’s mental move is reminiscent of that strange ambiguity, mentioned earlier, of the English verb “to grow”, which can be used to describe not only changes where something increases but also changes where something decreases. And thus Jillian escaped from her box canyon by imagining the idea of
reverse pulling
, which amounts to pushing.

Such a mental slippage resulted from a new encoding of the situation, seeing it in a more abstract fashion than at the outset. Jillian realized that her primary goal was not to pull the cork out of the bottle but to get some wine; with this goal clearly in mind, she could reperceive the obstacle that was between her and the wine, and so she vaguely mused to herself, “If I can somehow
slide
this cork, whether inwards or outwards, it will slip out of the bottleneck, and that will give me the access I seek.” The seemingly
paradoxical aspect of Jillian’s picnic dilemma is that the act of abstraction, which drastically reduced the attention she was paying to certain concrete aspects of her mental representation of the situation and which was thus a
cognitive impoverishment
, turned out to be the key step in finding a solution.

This phenomenon is connected to the fact that one is never able, in a single moment, to think of all the properties of an object (or of an action or situation). Rather, one is usually trapped by the more specific, concrete, and salient aspects of the entity in question, for those are what most obviously distinguish one category from others. For example, seeing the challenge of opening a wine bottle as a
pulling
of its cork tends to make less salient the idea that the cork is
pushable.
However, by the act of simplifying and thus perceptually
impoverishing
the situation, replacing the initial category by a more abstract one, the representation of the situation is paradoxically
enriched
by revealing characteristics that had previously been hidden. That, in a word, is the paradox.

The apparent simplicity of this creative strategy of
enriching one’s perception by engaging in an impoverishing act of abstraction
does not preclude it from being a powerful mechanism. It allows one to transcend an irrelevant point of view that has led to a dead end, which is the result of an unfruitful initial categorization of the desired goal.

The just-described phenomenon of recategorization can be seen in a psychological experiment known as the “candle problem”, invented in the 1940s by the German gestalt psychologist Karl Duncker, in which subjects are given the challenge to attach a candle to the wall. Aside from the candle, they have at their disposition a full matchbook and a full box of thumbtacks. The insight that yields the solution involves emptying the thumbtack box and then using some thumbtacks to affix it to the wall, after which the candle can be placed on top of it. Since the box is filled at the start, the challenge is subtle and not too many subjects find the solution. However, it is rendered easier, though by no means trivial, if at the start the box is empty and the thumbtacks are simply lying around on a table.

The main challenge in this problem is that of categorizing the thumbtack box not merely as a
container
but also as a potential
stand.
When the thumbtacks are contained in it, the box is spontaneously and naturally perceived as a
thumbtack box
, and that is seen as its sole identity. At a more abstract level, one can perceive it anew, as a
box
, whose central function remains that of containing things. To reach the solution, a still higher level of abstraction is necessary: that of perceiving this same object as a
stand.
Of course, at this level of abstraction, any number of objects can be so perceived, including tables, chairs, shelves, drawers, and so on. In any case, the empty thumbtack box thus recategorized can be used in a new manner.

Discoveries of great import can result from just this kind of mental slippage. For example, if the old “Eureka!” legend can be trusted, Archimedes’ discovery of the “principle of Archimedes” in hydrostatics came from just such a shift in categorization. The historical accuracy of the tale may be questionable, but in any case it epitomizes
both the subtlety and the richness of adopting a more abstract viewpoint concerning an object one is looking at, even if it involves ignoring nearly everything that one normally associates with it.

Archimedes made an analogy between the crown and his body, noting that either one, when fully submerged, would displace a volume of water equal to its volume. Now if one names various categories to which a crown belongs, one comes up with such things as
symbol of royalty, made of precious metal, worn on head
, and so on. These have little if anything in common with categories that come to mind in thinking of a human body. Only when one rises to a highly rarefied level of abstraction — all the way to the category
object endowed with volume
— does the analogical connection appear explicitly. One has to ignore many facts, such as that a human body is alive, in order to map it onto a crown, which is not alive. Here, then, is a case where an analogy depends on a categorization far more abstract than anything that springs to mind spontaneously. The creative act in this story thus resides in the ability to relate entities that are extremely different in every way except one, which allows the discovery to be made.

The preceding discussion might give the impression that we are trying to portray creativity as the natural outcome of meticulous searching for commonalities among situations that, on first glance, would seem to have little or nothing in common. Unfortunately, though, even if we are exploring the mechanisms underlying creativity, we cannot pass along a recipe for genius, because a
deliberate
process of search for features linking two situations plays little or no role in the matter. The process of abstraction here described does not emerge from systematic, conscious search. Indeed, it often surprises the discoverer as much as it would surprise an observer.

When leaps are made at a very high level of abstraction, small though they may be, they can give rise to highly important discoveries, as the Archimedes story shows. This is certainly part of the explanation of the mystery of creative discovery, but it would be
misleading to see it as a recipe, for in general, it is only
after the fact
that two seemingly distant situations strike an average person as being analogous, and the common traits that give rise to an abstract analogy linking them may have been hidden by unconscious presuppositions, tending to make the sought-after generalization very hard to find.

There is a well-known recent invention that came out of one simple abstraction and resulted in a major revolution. In the early 1980s, communicating with computers was not easy. Aside from a tiny coterie of people who had worked at or visited a handful of advanced and little-known research centers in the preceding decade, no one had ever seen or used a mouse. Everything was done by typing symbols on the keyboard. One had to explain to the machine, using arcane strings of symbols expressing commands, what one wanted it to do, and it would then execute those instructions. All human–machine interaction was conducted via such a “command language”. A human would order the machine to do something, and the computer would obediently carry out the order, as long as the command was syntactically well-formed.