Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (51 page)

There is also the phenomenon of a lunar eclipse. Slowly, slowly, some dark shape moves across the face of the moon. It is eerie and mysterious, and most people probably don’t realize exactly what is going on. The truth is, it is just an enormous magnification of what would happen if, in a pitch-dark room, you were to turn on a flashlight and shine it at a suspended ping-pong ball and then were to slowly pass an orange between the source of light and the dangling little ball. Of course the beam of light would be blocked by the orange, and the ping-pong ball would grow much darker; and if, by chance, there were some highly motivated and curious ants poised on the side
of the orange that was facing the ping-pong ball, they would in theory be able to stare across the room and observe the darkening of that dangling little ball. Now just blow this picture up by a factor of a hundred million or so. The orange and the ping-pong ball are now floating in the blackness of space, the sun is of course the flashlight, and the ants are human observers. We don’t need to spell this out, but what is interesting is that an enlargement on a monumental scale seems to change the nature of the phenomenon entirely. Most people no longer have an intuition for what is going on; it feels cosmic and alien, possibly even filled with prophetic meanings.

Also somewhat disorienting, although more familiar, is the shadow cast by oneself or by other people when the source of light is very low, near the horizon, as at sunset; in such cases, a person’s shadow can easily stretch out 100 feet or more across the ground. If at night you are walking down a sidewalk and a shaft of light is streaming from a far-off streetlight behind you, you can detect someone else as they approach you from behind even when they are still a long way off. This, too, is a kind of magnification of the usual phenomenon — an extreme horizontal stretching — and it, too, feels somewhat strange and eerie.

Eclipses and elongated shadows show that an act as simple as a change of size or proportion can stretch the boundaries of a familiar category. Of course the conceptual boundaries can be stretched much further by exploring other dimensions of change. For instance, one’s concept of
shadow
grows richer and deeper when one liberates oneself from the idea that what matters is the blockage of the passage of sunlight. The same phenomenon — exactly the same! — works with moonlight, firelight, lamplight, light emitted by a flashlight, by a television screen, by a cell phone, by a cigarette lighter, or even by a lowly glowworm. Collectively, this provides a significant generalization of the concept of
shadow
, but one can go considerably further, to be sure.

The two photographs on the following page show a lovely old oak tree in two different seasons. They look very similar and yet there is something crucially different. In both of them, the tree appears to be casting a dark shadow, but a careful look reveals that there is more to the story. In the first photo, the shadow is clearly “made of” the absence of sunlight, so to speak, but in the second photo, the day is overcast and there is no sharp source of light above the tree. Therefore, the tree can’t be casting a “light shadow”. Rather, the white covering on the ground surrounding the tree is
snow
, while the dark patch directly underneath it is the result of a
lack
of snow. What we are seeing is thus a “snow shadow” cast by the same tree, but on a winter’s day. The stream of snow that fell vertically from the sky, perhaps a few hours or days earlier, is the analogue to the ceaselessly falling vertical stream of sunlight in the summer photo. But despite all these differences, the two photos are so strikingly similar that it feels as if one is looking at
exactly the same phenomenon.
And indeed, in an important sense, one is doing just that. And that’s why “snow shadow” is just the right term for what we see here.

A more established and standard term is “rain shadow”. You might at first guess that this term refers to the dry patch on the ground underneath a bridge, an awning, a table, or an umbrella during a heavy downpour — and indeed, why not use the phrase “rain shadow” in that very natural way? — but in geography, it is a technical term with a rather different meaning. Like a lunar eclipse, a rain shadow is a physical phenomenon on a far larger scale than that of everyday shadows, and it also involves a change of medium, as does the concept of
snow shadow
, and in some ways it also resembles the very long shadows on sidewalks, described above.

To illustrate the idea concretely, let’s turn to the state of Oregon. The western third of the state is famous for its rainy weather, due to its proximity to the Pacific Ocean, and of course to the fact that weather patterns generally move eastwards. However, about a third of the way across the state, the Cascade mountain range, running north–south, forms an impenetrable barrier to rain-carrying clouds, and therefore, for the next couple of hundred miles eastwards of the Cascades, there is a vast barren desert — a stark contrast to the lush Willamette Valley just west of the Cascades. The absence of rain for those hundreds of miles is known as a “rain shadow”, and just such a shadow is cast by the Cascade Range. The analogue of the downward stream of falling snow or of sunlight is the eastward-flowing stream of rainstorms that suddenly hits the obstacle of the mountains, and whose passage is thereby blocked. Like the greatly elongated late-afternoon or nighttime shadows on a sidewalk, a rain shadow is far longer than the height of the object that is casting it.

What we are exploring is a set of close analogues to the primordial notion of
shadow
that, despite their simplicity, give rise to a much broader category than is usually attached to the word. The core of the
generalized shadow
idea (
shadow
₂
) is that there is a stream or beam of stuff, for want of a better word (we might call it the “medium”) whose straight, linear flow is interrupted by an obstacle, and as a result, beyond that obstacle there is a perceptible absence of the stuff (
i.e.
, of the medium). Irrelevant are: the nature of the medium itself, the speed of the stream, the physical dimensions of the stream and of the obstacle, and the time it takes to create the effect. A sunlight shadow is virtually instantaneous, a snow shadow takes a few minutes or perhaps an hour to appear clearly, depending on the intensity of the storm, and a rain shadow is a phenomenon whose existence has to do with the frequency of rainstorms taking place over a period of years.

The concept of
shadow
can be further extended in numerous fashions. Imagine a large truck driving down a freeway, and going much more slowly than most of the vehicles sharing the road. It is thus being passed continually, both on its left and its right, by faster vehicles. In other words, a constant stream of vehicles (analogous to falling snowflakes) is coming up on the truck from behind. Those in other lanes simply pass by it unimpededly, but those in the truck’s own lane cannot do so, as it is “opaque” to them. If they want to pass it, they have to change lanes and go around it, and only after getting somewhat ahead of it can they return to the lane they started in. For that reason, directly
ahead
of the truck, in its own lane, there are no vehicles at all for a couple of truck-lengths or so. Thus in the medium of traffic flow on a freeway, a slow-moving truck always casts a noticeable downroad “vehicular shadow”.

In physics experiments in the nineteenth century using long cathode-ray tubes made of glass, a beam of electrons emitted at one end of the tube was powerfully attracted by a strong positive charge at the tube’s far end. Physicists didn’t really know
anything about the nature of this beam, however, and so to find out, they tried interfering with the high-speed stream of unknown entities inside the tube by blocking its flow in different ways, thus creating various kinds of “shadows” at the downstream end of the tube. Of course they knew that they were not dealing with a stream of light but with a stream of mysterious microscopic and invisible entities, and that the notion of
shadow
was thus necessarily being extended analogically, and yet to the physicists who did these experiments, such a conceptual extension did not feel forced or abstract, but natural and simple.

Some shadows are far more shadowy than the rather physical ones we have just discussed. For instance, we can easily understand the sentence “World War II cast a decades-long shadow on the birth rates of many nations.” Here we once again have a kind of abstractly moving stream — that of humanity propagating itself down through the years — and the obstacle that this abstract stream hit was war, which inflicted an immense death toll on young men, thus knocking them out of the reproductive stream. The “shadow” consisting of their absence was then felt in many countries. Eventually, after a generation or two, birth rates gradually started to recover, just as in front of the slow truck on the freeway, the downroad shadow that it casts is not infinitely long, but only a couple of truck-lengths or so. Notice how very abstract, in this case, are both the “stream” and the “obstacle” blocking it — and yet, in spite of this high degree of abstraction, the mechanism giving rise to the “shadow” is the same, so much so that it is easy to see the connection of this shadow cast by World War II to the downroad “traffic shadow” cast by the slowly-moving truck.

Consider next the following sentence, ominously foreshadowing World War II, which was taken from an obituary of the famous Hungarian–American physicist Edward Teller: “As both émigré and physicist, Dr. Teller was aware of the Nazis’ lengthening shadow.” What does this mean? It is reminiscent of the earlier-mentioned very long shadows cast down sidewalks by people walking as the sunset draws near, the people in this case being the Nazis. But the sentence from the obituary does not conjure up in our minds a source of light or an obstacle; rather, we are merely being invited to recall, in a very general way, how an elongated shadow, at the time of a setting sun, can reveal the existence of an ominous threat sneaking up on one from behind, long before it actually materializes. And of course shadows are dark, and as the sun goes down they grow both longer and darker, which increases the sense of somber foreboding.

Then there are the perennial stories of children who have to “grow up in the shadow” of their world-famous father or mother, or of people who suffer calamities and emerge from them “only a shadow of their former self”. In these two phrases, as in the case of “the Nazis’ lengthening shadow”, the physical mechanism that gives rise to everyday shadows is very much in the background, and all that is retained of shadowness is, in the first case, the idea of a “dark zone” where there is such a profound absence of “light” (presumably “underneath” the parent) that it can conceal the presence of even a significant object such as a child, thus causing great suffering, and in the second case, the idea that a shadow is far more ethereal and less substantial than the
object that casts it. Depending on one’s view of what a shadow “really” is, one may think that these metaphors are finally allowing us to put our finger on the essence of shadowness — or conversely, one may think that these metaphors are merely facile borrowings of some of the more obvious and superficial trappings of shadowness.

Those of us who grew up near the sea have spent countless hours watching waves sweeping in toward land, rising up and turning into whitecaps, then breaking in a loud and violent fashion as they crash onto the beach. Indeed, for many people, the idea of waves in water is synonymous with the deafening crash and dazzling spray of breakers. However, water waves can also roll for hundreds of miles across the open sea without ever breaking at all (these are often called “swells”), and this gives a somewhat different image of the meaning of the word “wave” — and one that, as it turns out, has been far more fertile in its generalizations over the past two millennia.

For those who grew up inland, another kind of wave is familiar: “O beautiful for spacious skies, for amber waves of grain…”, and then again, “The wavin’ wheat can sure smell sweet, when the wind comes right behind the rain…” Instantly responding to the breeze, tall stalks sway back and forth, with, at times, entire fields undulating nearly in unison. No wonder such waves are celebrated in song.