Range, page 11
Each time he got stuck, Kepler unleashed a fusillade of analogies. Not just light, heat, odor, currents and boatmen, but optics of lenses, balance scales, a broom, magnets, a magnetic broom, orators gazing at a crowd, and more. He interrogated each one ruthlessly, every time alighting on new questions.
He eventually decided that celestial bodies pulled one another, and larger bodies had more pull. That led him to claim (correctly) that the moon influenced tides on Earth. Galileo, the embodiment of bold truths, mocked him for the ridiculous idea of “the moon’s dominion over the waters.”
Kepler’s intellectual wanderings traced a staggering journey, from planets imbued with souls and riding on interlocking crystalline spheres in perfect circles around the stationary Earth, to his illumination of the laws of planetary motion, which showed that the planets move in ellipses that are predictable based on their relation to the sun.
More important, Kepler invented astrophysics. He did not inherit an idea of universal physical forces. There was no concept of gravity as a force, and he had no notion of momentum that keeps the planets in motion. Analogies were all he had. He became the first discoverer of causal physical laws for phenomena in the heavens, and he realized it. “Ye physicists,” he wrote when he published his laws of planetary motion, “prick your ears, for now we are going to invade your territory.” The title of his magnum opus: A New Astronomy Based upon Causes.
In an age when alchemy was still a common approach to natural phenomena, Kepler filled the universe with invisible forces acting all around us, and helped usher in the Scientific Revolution. His fastidious documentation of every meandering path his brain blazed is one of the great records of a mind undergoing creative transformation. It is a truism to say that Kepler thought outside the box. But what he really did, whenever he was stuck, was to think entirely outside the domain. He left a brightly lit trail of his favorite tools for doing that, the ones that allowed him to cast outside eyes upon wisdom his peers simply accepted. “I especially love analogies,” he wrote, “my most faithful masters, acquainted with all the secrets of nature. . . . One should make great use of them.”
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Mention Kepler if you want to get Northwestern University psychologist Dedre Gentner excited. She gesticulates. Her tortoiseshell glasses bob up and down. She is probably the world’s foremost authority on analogical thinking. Deep analogical thinking is the practice of recognizing conceptual similarities in multiple domains or scenarios that may seem to have little in common on the surface. It is a powerful tool for solving wicked problems, and Kepler was an analogy addict, so Gentner is naturally very fond of him. When she mentions a trivial historical detail about him that might be misunderstood by modern readers, she suggests that maybe it’s best not to publish it as it might make him look bad, though he has been dead for nearly four hundred years.
“In my opinion,” Gentner told me, “our ability to think relationally is one of the reasons we’re running the planet. Relations are really hard for other species.” Analogical thinking takes the new and makes it familiar, or takes the familiar and puts it in a new light, and allows humans to reason through problems they have never seen in unfamiliar contexts. It also allows us to understand that which we cannot see at all. Students might learn about the motion of molecules by analogy to billiard-ball collisions; principles of electricity can be understood with analogies to water flow through plumbing. Concepts from biology serve as analogies to inform the cutting edge of artificial intelligence: “neural networks” that learn how to identify images from examples (when you search cat pictures, for instance) were conceived as akin to the neurons of the brain, and “genetic algorithms” are conceptually based on evolution by natural selection—solutions are tried, evaluated, and the more successful solutions pass on properties to the next round of solutions, ad infinitum. It is the furthest extension of the type of thinking that was foreign to Luria’s premodern villagers, whose problem solving depended on direct experience.
Kepler was facing a problem not just new to himself, but to all humanity. There was no experience database to draw on. To investigate whether he should be the first ever to propose “action at a distance” in the heavens (a mysterious power invisibly traversing space and then appearing at its target), he turned to analogy (odor, heat, light) to consider whether it was conceptually possible. He followed that up with a litany of distant analogies (magnets, boats) to think through the problem.
Most problems, of course, are not new, so we can rely on what Gentner calls “surface” analogies from our own experience. “Most of the time, if you’re reminded of things that are similar on the surface, they’re going to be relationally similar as well,” she explained. Remember how you fixed the clogged bathtub drain in the old apartment? That will probably come to mind when the kitchen sink is clogged in the new one.
But the idea that surface analogies that pop to mind work for novel problems is a “kind world” hypothesis, Gentner told me. Like kind learning environments, a kind world is based on repeating patterns. “It’s perfectly fine,” she said, “if you stay in the same village or the same savannah all your life.” The current world is not so kind; it requires thinking that cannot fall back on previous experience. Like math students, we need to be able to pick a strategy for problems we have never seen before. “In the life we lead today,” Gentner told me, “we need to be reminded of things that are only abstractly or relationally similar. And the more creative you want to be, the more important that is.”
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In the course of studying problem solving in the 1930s, Karl Duncker posed one of the most famous hypothetical problems in all of cognitive psychology. It goes like this:
Suppose you are a doctor faced with a patient who has a malignant stomach tumor. It is impossible to operate on this patient, but unless the tumor is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumor. If the rays reach the tumor all at once at a sufficiently high intensity, the tumor will be destroyed. Unfortunately, at this intensity the healthy tissue that the rays pass through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but they will not affect the tumor either. What type of procedure might be used to destroy the tumor with the rays, and at the same time avoid destroying the healthy tissue?
It’s on you to excise the tumor and save the patient, but the rays are either too powerful or too weak. How can you solve this? While you’re thinking, a little story to pass the time: There once was a general who needed to capture a fortress in the middle of a country from a brutal dictator. If the general could get all of his troops to the fortress at the same time, they would have no problem taking it. Plenty of roads that the troops could travel radiated out from the fort like wheel spokes, but they were strewn with mines, so only small groups of soldiers could safely traverse any one road. The general came up with a plan. He divided the army into small groups, and each group traveled a different road leading to the fortress. They synchronized their watches, and made sure to converge on the fortress at the same time via their separate roads. The plan worked. The general captured the fortress and overthrew the dictator.
Have you saved the patient yet? Just one last story while you’re still thinking: Years ago, a small-town fire chief arrived at a woodshed fire, concerned that it would spread to a nearby house if it was not extinguished quickly. There was no hydrant nearby, but the shed was next to a lake, so there was plenty of water. Dozens of neighbors were already taking turns with buckets throwing water on the shed, but they weren’t making any progress. The neighbors were surprised when the fire chief yelled at them to stop, and to all go fill their buckets in the lake. When they returned, the chief arranged them in a circle around the shed, and on the count of three had them all throw their water at once. The fire was immediately dampened, and soon thereafter extinguished. The town gave the fire chief a pay raise as a reward for quick thinking.
Are you done saving your patient? Don’t feel bad, almost no one solves it. At least not at first, and then nearly everyone solves it. Only about 10 percent of people solve “Duncker’s radiation problem” initially. Presented with both the radiation problem and the fortress story, about 30 percent solve it and save the patient. Given both of those plus the fire chief story, half solve it. Given the fortress and the fire chief stories and then told to use them to help solve the radiation problem, 80 percent save the patient.
The answer is that you (the doctor) could direct multiple low-intensity rays at the tumor from different directions, leaving healthy tissue intact, but converging at the tumor site with enough collective intensity to destroy it. Just like how the general divided up troops and directed them to converge at the fortress, and how the fire chief arranged neighbors with their buckets around the burning shed so that their water would converge on the fire simultaneously.
Those results are from a series of 1980s analogical thinking studies. Really, don’t feel bad if you didn’t get it. In a real experiment you would have taken more time, and whether you got it or not is unimportant. The important part is what it shows about problem solving. A gift of a single analogy from a different domain tripled the proportion of solvers who got the radiation problem. Two analogies from disparate domains gave an even bigger boost. The impact of the fortress story alone was as large as if solvers were just straight out told this guiding principle: “If you need a large force to accomplish some purpose, but are prevented from applying such a force directly, many smaller forces applied simultaneously from different directions may work just as well.”
The scientists who did that work expected that analogies would be fuel for problem solving, but they were surprised that most solvers working on the radiation problem did not find clues in the fortress story until they were directed to do so. “One might well have supposed,” the scientists wrote, that “being in a psychology experiment would have led virtually all subjects to consider how the first part [of the study] might be related to the second.”
Human intuition, it appears, is not very well engineered to make use of the best tools when faced with what the researchers called “ill-defined” problems. Our experience-based instincts are set up well for Tiger domains, the kind world Gentner described, where problems and solutions repeat.
An experiment on Stanford international relations students during the Cold War provided a cautionary tale about relying on kind-world reasoning—that is, drawing only on the first analogy that feels familiar. The students were told that a small, fictional democratic country was under threat from a totalitarian neighbor, and they had to decide how the United States should respond. Some students were given descriptions that likened the situation to World War II (refugees in boxcars; a president “from New York, the same state as FDR”; a meeting in “Winston Churchill Hall”). For others, it was likened to Vietnam, (a president “from Texas, the same state as LBJ,” and refugees in boats). The international relations students who were reminded of World War II were far more likely to choose to go to war; the students reminded of Vietnam opted for nonmilitary diplomacy. That phenomenon has been documented all over the place. College football coaches rated the same player’s potential very differently depending on what former player he was likened to in an introductory description, even with all other information kept exactly the same.
With the difficult radiation problem, the most successful strategy employed multiple situations that were not at all alike on the surface, but held deep structural similarities. Most problem solvers are not like Kepler. They will stay inside of the problem at hand, focused on the internal details, and perhaps summon other medical knowledge, since it is on the surface a medical problem. They will not intuitively turn to distant analogies to probe solutions. They should, though, and they should make sure some of those analogies are, on the surface, far removed from the current problem. In a wicked world, relying upon experience from a single domain is not only limiting, it can be disastrous.
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The trouble with using no more than a single analogy, particularly one from a very similar situation, is that it does not help battle the natural impulse to employ the “inside view,” a term coined by psychologists Daniel Kahneman and Amos Tversky. We take the inside view when we make judgments based narrowly on the details of a particular project that are right in front of us.
Kahneman had a personal experience with the dangers of the inside view when he assembled a team to write a high school curriculum on the science of decision making. After a full year of weekly meetings, he surveyed the entire team to find out how long everyone thought the project would take. The lowest estimate was one and a half years, the highest two and a half years. Kahneman then asked a team member named Seymour, a distinguished curriculum expert who had seen the process with other teams, how this one compared.
Seymour thought for a while. Moments earlier, he had estimated it would take about two more years. Faced with Kahneman’s question about other teams, he said he had never even thought to compare this instance to separate projects, but that about 40 percent of the teams he’d seen never finished at all, and not a single one he could think of took less than seven years.
Kahneman’s group was not willing to spend six more years on a curriculum project that might fail. They spent a few minutes debating the new opinion, and decided to forge ahead trusting the about-two-years wisdom of the group. Eight years later, they finished, by which point Kahneman was not even on the team or living in the country, and the agency that asked for the curriculum was no longer interested.
Our natural inclination to take the inside view can be defeated by following analogies to the “outside view.” The outside view probes for deep structural similarities to the current problem in different ones. The outside view is deeply counterintuitive because it requires a decision maker to ignore unique surface features of the current project, on which they are the expert, and instead look outside for structurally similar analogies. It requires a mindset switch from narrow to broad.
For a unique 2012 experiment, University of Sydney business strategy professor Dan Lovallo—who had conducted inside-view research with Kahneman—and a pair of economists theorized that starting out by making loads of diverse analogies, Kepler style, would naturally lead to the outside view and improve decisions. They recruited investors from large private equity firms who consider a huge number of potential projects in a variety of domains. The researchers thought the investors’ work might naturally lend itself to the outside view.
The private equity investors were told to assess a real project they were currently working on with a detailed description of the steps to success, and to predict the project’s return on investment. They were then asked to write down a batch of other investment projects they knew of with broad conceptual similarity to theirs—for instance, other examples of a business owner looking to sell, or a start-up with a technologically risky product. They were instructed to estimate the return for each of those examples too.
In the end, the investors estimated that the return on their own project would be about 50 percent higher than the outside projects they had identified as conceptually similar. When given the chance at the end to rethink and revise, they slashed their own initial estimate. “They were sort of shocked,” Lovallo told me, “and the senior people were the most shocked.” The investors initially judged their own projects, where they knew all the details, completely differently from similar projects to which they were outsiders.
This is a widespread phenomenon. If you’re asked to predict whether a particular horse will win a race or a particular politician will win an election, the more internal details you learn about any particular scenario—physical qualities of the specific horse, the background and strategy of the particular politician—the more likely you are to say that the scenario you are investigating will occur.
Psychologists have shown repeatedly that the more internal details an individual can be made to consider, the more extreme their judgment becomes. For the venture capitalists, they knew more details about their own project, and judged that it would be an extreme success, until they were forced to consider other projects with broad conceptual similarities. In another example, students rated a university a lot better if they were told about a few specific science departments that were ranked in the top ten nationally than if they were simply told that every science department at the university was ranked among the top ten. In one famous study, participants judged an individual as more likely to die from “heart disease, cancer, or other natural causes” than from “natural causes.” Focusing narrowly on many fine details specific to a problem at hand feels like the exact right thing to do, when it is often exactly wrong.
Bent Flyvbjerg, chair of Major Programme Management at Oxford University’s business school, has shown that around 90 percent of major infrastructure projects worldwide go over budget (by an average of 28 percent) in part because managers focus on the details of their project and become overly optimistic. Project managers can become like Kahneman’s curriculum-building team, which decided that thanks to its roster of experts it would certainly not encounter the same delays as did other groups. Flyvbjerg studied a project to build a tram system in Scotland, in which an outside consulting team actually went through an analogy process akin to what the private equity investors were instructed to do. They ignored specifics of the project at hand and focused on others with structural similarities. The consulting team saw that the project group had made a rigorous analysis using all of the details of the work to be done. And yet, using analogies to separate projects, the consulting team concluded that the cost projection of £320 million (more than $400 million) was probably a massive underestimate. When the tram opened three years late, it was headed toward £1 billion. After that, other UK infrastructure projects began implementing outside-view approaches, essentially forcing managers to make analogies to many outside projects of the past.
