by James Geary
An advisor to the King of Liang338 warned the monarch of Hui Tzu’s use of analogical reasoning. “Hui Tzu is very good at using analogies when putting forth his views,” the advisor said. “If your Majesty would stop him from using analogies, he will be at a loss what to say.”
“Very well, I will do that,” the King said.
When he received Hui Tzu the following day, the King said to him: “If you have anything to say, I wish you would say it plainly and not resort to analogies.”
Hui Tzu said, “Suppose there is a man here who does not know what a tan is, and you say to him, ‘A tan is like a tan.’ Would he understand?”
“No,” the King said.
“Then were you to say to him, ‘A tan is like a bow, but has a strip of bamboo in place of the string.’ Would he understand?”
“Yes, he would,” the King replied.
“A man who explains necessarily makes intelligible that which is not known by comparing it with what is known,” Hui Tzu said.
Lewis called this type of analogy—the type that compares the unknown with the known—a “master’s metaphor339,” or metaphor as teaching tool. Like Langer, Lewis argued that master metaphors are essential to communicate any kind of innovative, original thinking.
In the case of the Flalansfere, Lewis argued, we could dispense with the analogy only if we could directly study or even imagine a four-dimensional world. But we can’t. For those of us not conversant with the highly specialized vocabulary of theoretical physics, analogy is our only access to the Flalansfere. “Our thought is independent of the metaphors we employ340, in so far as these metaphors are optional,” Lewis wrote, “that is, in so far as we are able to have the same idea without them.” But when it comes to understanding and communicating the great, bewildering truths of science, there are no ideas but in analogies.
Our analogical abilities start early. To pinpoint the onset of analogical reasoning, researchers told children a story about a genie341 who moved precious jewels from one bottle to another by rolling up his magic carpet into a tube and bowling the jewels through it. They then presented the children with two bowls (one containing some balls and the other empty), an aluminum walking cane, a large sheet of heavy paper, scissors, tape, paper clips, and rubber bands. The children had to use these tools to come up with as many ways as possible to get the balls into the empty bowl.
Only about 10 percent of the children between the ages of four and six thought of rolling up the paper and using it as the genie used his magic carpet, even after researchers suggested to them that something in the story might help. All the children aged ten to twelve came up with this solution, though some needed a helpful nudge. The study suggests that analogical reasoning takes hold in early adolescence, around the same time kids become able to understand more complex conceptual metaphors.
The timing may be more than coincidence since analogies, like complex conceptual metaphors, typically involve sources and targets drawn from very distant domains. And, just as the appropriate set of associated commonplaces must be in place in order to understand a complex conceptual metaphor, you must know something of an analogy’s source if you are to understand how it informs, or misinforms, the target.
The theoretical physicist Richard Feynman was such a lauded lecturer in large part because, like Hui Tzu, he was skilled in finding the right analogies to illustrate his explanations of extremely abstract—and extremely difficult—concepts. He once compared a drop of water magnified 2,000 times to “a kind of teeming342 . . . like a crowd at a football game as seen from a very great distance.” That description has all the precision of good physics and good poetry.
To convey the operation of electromagnetic fields343, Feynman used the master metaphor of two corks floating in a pool of water. If you move one cork around in the water, you immediately notice that the other one moves, too. Looking only at the two corks, Feynman explained, a naïve physicist might be forgiven for thinking there was some kind of interaction between the corks that caused the one to move in response to the other.
The second cork, however, is not moved directly by the first cork but by the movement of the water. “If we jiggle the cork . . . waves travel away,” Feynman explained, “so that by jiggling, there is an influence very much farther out, an oscillatory influence. That cannot be understood by the direct interaction. Therefore the idea of direct interaction must be replaced with the existence of the water, or in the electrical case, with what we call the electromagnetic field.”
Note, though, that in science as in every area where the combinatory play of metaphor applies, analogy comes only after the facts. To know that the tale of two corks is an accurate comparison, Feynman must already have known how electromagnetic fields operate, just as in order to know the meaning of “Man is a wolf” you must already be familiar with that lean and hungry look. As Hungarian-born mathematician George Pólya put it, “When you have satisfied yourself that the theorem is true344, you start proving it.”
This is exactly how discovery works, according to David Deutsch, a theoretical physicist at Oxford University. The process starts with a problem, a conflict between two ideas or theories, he says. The first step in solving the problem is to tweak the existing theories so they fit. Failing that, you introduce another theory that resolves the incompatibility.
Assuming you do this successfully, Deutsch says, the outcome is, “You don’t understand the resulting theory. It solves the theoretical problems, but you can’t see what it means. You don’t understand how that could be a description of the actual world, or what the world would have to be like for that to be true. Then you think of an analogy.”
Deutsch cites the theory of continental drift as an example. As early as the sixteenth century, natural philosophers had observed that the shapes of the continents, particularly Africa and South America, seemed as if they would fit snugly together. But until the early twentieth century, no one had come up with a plausible mechanism by which a single land mass could have fragmented and drifted apart. Finally, in the 1960s, the theory of plate tectonics provided the answer.
But, Deutsch points out, having the correct theory is not the full story. We still need to know what the theory says about reality, what plate tectonics means for the actual history of Earth. This is where analogy comes in handy.
“Maybe the Earth is like a rice pudding,” Deutsch says of the analogical reasoning that followed the plate tectonics theory, “hard and brittle on top but pliable and liquid underneath. Sometimes, the surface skin ruptures and pulls apart. The metaphor is useful because it answers the question of how something can be. It makes the theory easier to understand because it is similar to something else.”
If analogies are useful in understanding what the world is like according to plate tectonics theory, they are essential in understanding the most abstract, least directly observable sciences, such as Deutsch’s specialty, quantum physics.
In the quantum world, Feynman observed, things “do not behave like waves345, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen . . . So we have to learn about them in a sort of abstract or imaginative fashion.” This abstract, imaginative fashion is analogy, the only way we learn about anything of which we can have no direct experience, whether it’s the behavior of subatomic particles or the content of other people’s experience.
The philosopher Thomas Nagel posed the curious question, What is it like to be a bat? To the extent that an organism has conscious mental states, he argued, “there is something it is like to be that organism.346” Every conscious organism must have private, directly apprehended mental states that define “what it is like” to be that organism. Known as “qualia,” these subjective characteristics of experience include qualities like the pain of a stubbed toe or the redness of a red, red rose.
Nagel wanted to know what it is like to be a bat because bats are so different from us. They percei
ve the world primarily through echolocation, bouncing sound waves off objects in the environment to determine their size, shape, and motion. This is nothing like how we perceive the world, so there is little in our direct experience to suggest what it must be like to be a bat. A bat’s qualia are inaccessible to us.
Nagel concluded from this thought experiment that we can never know what it is like to be a bat and, therefore, that there are facts we can neither comprehend nor express in language. “I want to know what it is like for a bat to be a bat347,” he wrote. “Yet if I try to imagine this, I am restricted to the resources of my own mind, and those resources are inadequate to the task.”
Our resources are indeed inadequate to the task of directly knowing the quality of a bat’s experience, just as they are inadequate to the task of directly knowing the dimensions of the Flalansfere or the quality of the pain someone else feels when he stubs his toe. We can never know what it is to be a bat.
But metaphor can always tell us what it is like, by providing the right analogy from our own experience. Indeed, the fact that we cannot pose such questions—What is it like to be a bat? What is a four-dimensional universe like? What must the earth be like if the plate tectonics theory is true?—without using the word “like” suggests analogy’s central role in understanding these most recalcitrant, recondite aspects of the world.
So, what is it like to be a bat? It is like pinpointing the location of a fluttering scarf while walking blindfolded through the Grand Canyon using as a guide only the echo of your own voice reverberating from the canyon walls.
What is it like for two particles to be in a state of quantum entanglement, in which a change to one particle effects an immediate and corresponding change to the other particle even though a vast physical distance separates both? It is like one person, in Peoria, instantly catching cold when another person, on Pluto, sneezes.
In a speech about the role of analogy in science, another physicist, J. Robert Oppenheimer, said this:
We cannot, coming into something new348, deal with it except on the basis of the familiar and the old-fashioned . . . We cannot learn to be surprised or astonished at something unless we have a view of how it ought to be; and that view is almost certainly an analogy. We cannot learn that we have made a mistake unless we can make a mistake; and our mistake is almost always in the form of an analogy to some other piece of experience.
Scientific analogies must be empirically verifiable to be of use. It is possible to test whether the earth is like a rice pudding, for instance, in ways that it is not possible to test whether my love is like a red, red rose. Experiment leads to more and better information, which leads to more and better analogies. Finally, after sufficient testing and modification, the new and improved analogy becomes a scientific model, a useful conceptual description of a concrete physical reality.
But Deutsch warns against prematurely invoking metaphor. As Oppenheimer pointed out, analogies are always flawed because one thing is never exactly like some other thing. Analogy can never be accepted as proof, because one theory is never correct merely because it’s like some other theory that happens to be correct. “Metaphor is useful to understand deep meaning, but only after the theory,” Deutsch says. “Before the theory, metaphor is misleading and can be a powerful source of error because we can’t know which aspects of the analogy are right or wrong.”
In science, metaphor tells you what things are like, not what they are. After analogy, Deutsch says, the final step in the discovery process is “to understand the thing in its own right, not metaphorically. Once you do this, you can dispense with the metaphor and understand the world as it actually is.”
In The Structure of Scientific Revolutions, Thomas Kuhn noted that metaphor “plays an essential role349 in establishing a link between scientific language and the world.” He noted, too, that those links are not set in stone: “Theory change, in particular, is accompanied by a change in some of the relevant metaphors and in the corresponding parts of the network of similarities through which terms attach to nature.” Thus, the danger of an analogy like the Flalansfere, according to C. S. Lewis, is not that it may be incorrect but that people may forget it is an analogy.
“I too play with symbols350,” the mathematician and astronomer Johannes Kepler wrote, anticipating Einstein’s analogy of scientific creativity, “but I play in such a way that I do not forget that I am playing. For nothing is proved by symbols . . . unless by sure reasons it can be demonstrated that they are not merely symbolic but are descriptions of the ways in which the two things are connected and of the causes of this connexion.”
Metaphors, once forgotten or ignored, are easily mistaken for objective facts. If that happens in science, analogies congeal into dogmas, losing the elasticity that made them useful in the first place. Science is like a rice pudding: firm and fully formed on top but pliable and in constant motion underneath.
John Stuart Mill, one of the nineteenth century’s few philosophical fans of metaphorical thinking, said that a metaphor “is not to be considered as an argument351, but as an assertion that an argument exists.” Lewis would surely have agreed. Metaphor and analogy prove nothing, but they are the only ways we have of showing what the world must be like when scientific proofs are true. For Lewis, that meant we must never lose sight of the fact that metaphors are metaphors, models of things rather than the things themselves.
“We are never less the slaves of metaphor352 than when we are making metaphor, or hearing it new made,” Lewis wrote in “Bluspels and Flalansferes.” “When we are thinking hard of Flatlanders, and at the same time fully aware that they are a metaphor, we are in a situation almost infinitely superior to that of the man who talks of the Flalansferes and thinks that he is being literal and straightforward . . . If our thinking is ever true353, then the metaphors by which we think must have been good metaphors.”
Metaphor and Parables and Proverbs
Mighty Darn Good Lies
A few years ago, a Spanish artist gave my wife and me one of his prints, a thank-you gift for putting him up at our house for a couple of nights. We really liked the vivacity and cheerfulness of the work, which we hung in the living room in a spot previously occupied by a clutch of black-and-white drawings. The print brightened up that whole corner of the room. But even as our new acquisition cast the living room in an entirely new light, it occasioned other, somewhat darker thoughts.
The black outlines of dust on the wall where the old frames hung were now clearly visible, like the chalk lines around the corpse at a murder scene. We would have to paint over those, I thought.
And that section of plaster near the corner of the ceiling—where the damage occurred the night our daughter Hendrikje was sick and the humidifier water spilled across the floor of her room upstairs, trickling down along this wall—we would have to do something about that, too. It looked too much as if that part of the room had some kind of strange dermatological condition.
And that gash in the ceiling where a chunk of plaster collapsed years ago: Why the hell haven’t we fixed that?
And, while we’re at it, I’m sick and tired of constantly stumbling over the lip of the stairs where the carpet is worn away. Let’s get new carpets for the whole stairway.
With our recent acquisition barely in place, the list of essential home improvements suddenly seemed endless. Yes, before our enthusiasm for the print had even cooled, we had succumbed to the dreaded “Diderot effect.”
The Diderot effect is named after eighteenth-century French philosopher Denis Diderot, who spent twenty-five years editing the massive Encyclopaedia, one of the founding documents of the Enlightenment. Diderot is also the author of a charming essay called “Regrets on Parting with My Old Dressing Gown,” in which he describes how the gift of a beautiful scarlet dressing gown plunges him into debt and turns his life upside down.
Initially pleased with the unexpected gift, Diderot describes how he soon came to rue the day he received his new garment. Compared to
his elegant new dressing gown, the rest of his possessions seemed tawdry. His old straw chair, for example, just wouldn’t do. So he replaced it with an armchair covered in Moroccan leather. And the rickety old desk that groaned under his papers? That was out, too, and in came an expensive new writing table. Even the beloved prints that hung on his walls had to make way for newer, more costly works.
Diderot spent far more than he could afford on upgrading his accommodations, realizing too late that his opulent robe was actually a poisoned chalice. “I was absolute master of my old dressing gown354,” Diderot wrote in his essay, the subtitle of which is “A Warning to Those with More Taste than Money,” “but I have become a slave to my new one . . . Beware of the contamination of sudden wealth. Let my example be a lesson to you. The poor man may take his ease without thinking of appearances, but the rich man is always under a strain.”
“Regrets on Parting with My Old Dressing Gown” is a delightful essay. It is also an excellent example of parable, or metaphor in story form.
Like metaphors, parables have double meanings. Diderot’s essay is about the financial catastrophe occasioned by his receipt of a beautiful scarlet dressing gown. But it is also about how any of life’s little upgrades—new cars, new dresses, new lovers—can initiate a dizzying and potentially ruinous spiral of desire for more and better acquisitions.
Parables come in a variety of forms. An allegory, like Bunyan’s Pilgrim’s Progress or Dante’s Divine Comedy, is a theatrical parable with lots of different characters. A fable is simply a parable starring animals. A myth is nothing more than an epic parable. Edwin Paxton Hood, a late nineteenth-century English preacher popular on both sides of the Atlantic despite what the New York Times described as “an unpleasant peculiarity in his voice355 and a somewhat eccentric mannerism,” provided the best definition:
