Intuition

Learning Without Thinking

Harnessing Perceptual Discrimination

What’s a good eye?
You probably know someone who has one, for fashion, for photography, for antiques, for seeing a baseball. All of those skills are real, and they’re special. But what are they? What’s the eye doing in any one of those examples that makes it good? What’s it reading, exactly?
Take hitting a baseball. Players with a “good eye” are those who seem to have a sixth sense for the strike zone, who are somehow able to lay off pitches that come in a little too high or low, inside or outside, and swing only at those in the zone. Players, coaches, and scientists have all broken this ability down endlessly, so we can describe some of the crucial elements. Let’s begin with the basics of hitting. A major league fastball comes in at upward of 90 mph, from 60 feet, 6 inches away. The ball arrives at the plate in roughly 4/10 of a second, or 400 milliseconds. The brain needs about two thirds of that time—250 milliseconds—to make the decision whether to swing or not. In that time it needs to read the pitch: where it’s going, how fast, whether it’s going to sink or curve or rise as it approaches (most pitchers have a variety of pitches, all of which break across different planes). Research shows that the batter himself isn’t even aware whether he’s swinging or not until the ball is about 10 feet away—and by that point, it’s too late to make major adjustments, other than to hold up (maybe). A batter with a good eye makes an instantaneous—and almost always accurate—read.
What’s this snap judgment based on? Velocity is one variable, of course. The (trained) brain can make a rough estimate of that using the tiny change in the ball’s image over that first 250 milliseconds; stereoscopic vision evolved to compute, at incredible speed, all sorts of trajectories and certainly one coming toward our body. Still, how does the eye account for the spin of the ball, which alters the trajectory of the pitch? Hitters with a good eye have trouble describing that in any detail. Some talk about seeing a red dot, signaling a breaking ball, or a grayish blur, for a fastball; they say they focus only on the little patch in their field of vision where the pitcher’s hand releases the ball, which helps them judge its probable trajectory. Yet that release point can vary, too. “They may get a snapshot of the ball, plus something about the pitcher’s body language,” Steven Sloman, a cognitive scientist at Brown University, told me. “But we don’t entirely understand it.”
A batting coach can tinker with a player’s swing and mechanics, but no one can tell him how to see pitches better. That’s one reason major league baseball players get paid like major league baseball players. And it’s why we think of their visual acuity more as a gift than an expertise. We tell ourselves it’s all about reflexes, all in the fast-twitch fibers and brain synapses. They’re “naturals.” We make a clear distinction between this kind of ability and expertise of the academic kind. Expertise is a matter of learning—of accumulating knowledge, of studying and careful thinking, of creating. It’s built, not born. The culture itself makes the same distinction, too, between gifted athletes and productive scholars. Yet this distinction is also flawed in a fundamental way. And it blinds us to an aspect of learning that even scientists don’t yet entirely understand.
To flesh out this dimension and appreciate its importance, let’s compare baseball stars to an equally exotic group of competitors, known more for their intellectual prowess than their ability to hit line drives: chess players. On a good day, a chess grand master can defeat the world’s most advanced supercomputer, and this is no small thing. Every second, the computer can consider more than 200 million possible moves, and draw on a vast array of strategies developed by leading scientists and players. By contrast, a human player—even a grand master—considers about four move sequences per turn in any depth, playing out the likely series of parries and countermoves to follow. That’s four per turn, not per second. Depending on the amount of time allotted for each turn, the computer might search one billion more possibilities than its human opponent. And still, the grand master often wins. How?
The answer is not obvious. In a series of studies in the 1960s, a Dutch psychologist who was also himself a chess master, Adriaan de Groot, compared masters to novices and found no differences in the number of moves considered; the depth of each search, the series of countermoves played out, mentally; or the way players thought about the pieces (for instance, seeing the rook primarily as an attacking piece in some positions, and as a defensive one in others). If anything, the masters searched fewer moves than the novices. But they could do one thing the novices could not: memorize a chess position after seeing the board for less than five seconds. One look, and they could reconstruct the arrangement of the pieces precisely, as if they’d taken a mental snapshot.
In a follow-up study, a pair of researchers at Carnegie Mellon University—William G. Chase and Herbert A. Simon—showed that this skill had nothing to do with the capacity of the masters’ memory. Their short-term recall of things like numbers was no better than anyone else’s. Yet they saw the chessboard in more meaningful chunks than the novices did.* “The superior performance of stronger players derives from the ability of those players to encode the position into larger perceptual chunks, each consisting of a familiar configuration of pieces,” Chase and Simon concluded.
Grand masters have a good eye, too, just like baseball players, and they’re no more able to describe it. (If they could, it would quickly be programmed into the computer, and machines would rule the game.) It’s clear, though, that both ballplayers and grand masters are doing more than merely seeing or doing some rough analysis. Their eyes, and the visual systems in their brains, are extracting the most meaningful set of clues from a vast visual tapestry, and doing so instantaneously. I think of this ability in terms of infrared photography: You see hot spots of information, live information, and everything else is dark. All experts—in arts, sciences, IT, mechanics, baseball, chess, what have you—eventually develop this kind of infrared lens to some extent. Like chess and baseball prodigies, they do it through career-long experience, making mistakes, building intuition. The rest of us, however, don’t have a lifetime to invest in Chemistry 101 or music class. We’ll take the good eye—but need to do it on the cheap, quick and dirty.
• • •

When I was a kid, everyone’s notebooks and textbooks, every margin of every sheet of lined paper in sight, was covered with doodles: graffiti letters, caricatures, signatures, band logos, mazes, 3-D cubes. Everyone doodled, sometimes all class long, and the most common doodle of all was the squiggle:

Those squiggles have a snowflake quality; they all look the same and yet each has its own identity when you think about it. Not that many people have. The common squiggle is less interesting than any nonsense syllable, which at least contains meaningful letters. It’s virtually invisible, and in the late 1940s one young researcher recognized that quality as special. In some moment of playful or deep thinking, she decided that the humble squiggle was just the right tool to test a big idea.
Eleanor Gibson came of age as a researcher in the middle of the twentieth century, during what some call the stimulus-response, or S-R, era of psychology. Psychologists at the time were under the influence of behaviorism, which viewed learning as a pairing of a stimulus and response: the ringing of a bell before mealtime and salivation, in Ivan Pavlov’s famous experiment. Their theories were rooted in work with animals, and included so-called operant conditioning, which rewarded a correct behavior (navigating a maze) with a treat (a piece of cheese) and discouraged mistakes with mild electrical shocks. This S-R conception of learning viewed the sights, sounds, and smells streaming through the senses as not particularly meaningful on their own. The brain provided that meaning by seeing connections. Most of us learn early in life, for instance, that making eye contact brings social approval, and screaming less so. We learn that when the family dog barks one way, it’s registering excitement; another way, it senses danger. In the S-R world, learning was a matter of making those associations—between senses and behaviors, causes and effects.
Gibson was not a member of the S-R fraternity. After graduating from Smith College in 1931, she entered graduate studies at Yale University hoping to work under the legendary primatologist Robert Yerkes. Yerkes refused. “He wanted no women in his lab and made it extremely clear to me that I wasn’t wanted there,” Gibson said years later. She eventually found a place with Clark Hull, an influential behaviorist known for his work with rats in mazes, where she sharpened her grasp of experimental methods—and became convinced that there wasn’t much more left to learn about conditioned reflexes. Hull and his contemporaries had done some landmark experiments, but the S-R paradigm itself limited the types of questions a researcher could ask. If you were studying only stimuli and responses, that’s all you’d see. The field, Gibson believed, was completely overlooking something fundamental: discrimination. How the brain learns to detect minute differences in sights, sounds, or textures. Before linking different names to distinct people, for example, children have to be able to distinguish between the sounds of those names, between Ron and Don, Fluffy and Scruffy. That’s one of the first steps we take in making sense of the world. In hindsight, this seems an obvious point. Yet it took years for her to get anyone to listen.
In 1948, her husband—himself a prominent psychologist at Smith—got an offer from Cornell University, and the couple moved to Ithaca, New York. Gibson soon got the opportunity to study learning in young children, and that’s when she saw that her gut feeling about discrimination learning was correct. In some of her early studies at Cornell, she found that children between the ages of three and seven could learn to distinguish standard letters—like a “D” or a “V”—from misshapen ones, like:

These kids had no idea what the letters represented; they weren’t making associations between a stimulus and response. Still, they quickly developed a knack for detecting subtle differences in the figures they studied. And it was this work that led to the now classic doodle experiment, which Gibson conducted with her husband in 1949. The Gibsons called the doodles “nonsense scribbles,” and the purpose of the study was to test how quickly people could discriminate between similar ones. They brought thirty-two adults and children into their lab, one at a time, and showed each a single doodle on a flashcard:

The study had the feel of a card trick. After displaying the “target” doodle for five seconds, the experimenters slipped it into a deck of thirty-four similar flashcards. “Some of the items in the pack are exact replicas, tell me which ones,” they said, and then began showing each card, one at a time, for three seconds. In fact, the deck contained four exact replicas, and thirty near-replicas:

The skill the Gibsons were measuring is the same one we use to learn a new alphabet, at any age, whether Chinese characters, chemistry shorthand, or music notation. To read even a simple melody, you have to be able to distinguish an A from a B-flat on the clef. Mandarin is chicken scratch until you can discriminate between hundreds of similar figures. We’ve all made these distinctions expertly, most obviously when learning letters in our native tongue as young children. After that happens and we begin reading words and sentences—after we began “chunking,” in the same way the chess masters do—we forget how hard it was to learn all those letters in the first place, never mind linking them to their corresponding sounds and blending them together into words and ideas.
In their doodle experiment, the Gibsons gave the participants no feedback, no “you-got-its” or “try-agains.” They were interested purely in whether the eye was learning. And so it was. The adults in the experiment needed about three times through, on average, to score perfectly, identifying all four of the exact replicas without making a single error. The older children, between nine and eleven years old, needed five (to get close to perfect); the younger ones, between six and eight years old, needed seven. These people weren’t making S-R associations, in the way that psychologists assumed that most learning happened. Nor were their brains—as the English philosopher John Locke famously argued in the seventeenth century—empty vessels, passively accumulating sensations. No, their brains came equipped with evolved modules to make important, subtle discriminations, and to put those differing symbols into categories.
“Let us consider the possibility of rejecting Locke’s assumption altogether,” the Gibsons wrote. “Perhaps all knowledge comes through the senses in an even simpler way than John Locke was able to conceive—by way of variations, shadings, and subtleties of energy.”
That is, the brain doesn’t solely learn to perceive by picking up on tiny differences in what it sees, hears, smells, or feels. In this experiment and a series of subsequent ones—with mice, cats, children, and adults—Gibson showed that it also perceives to learn. It takes the differences it has detected between similar-looking notes or letters or figures, and uses those to help decipher new, previously unseen material. Once you’ve got middle-C nailed on the treble clef, you use it as a benchmark for nearby notes; when you nail the A an octave higher, you use that to read its neighbors; and so on. This “discrimination learning” builds on itself, the brain hoarding the benchmarks and signatures it eventually uses to read larger and larger chunks of information.
In 1969, Eleanor Gibson published Principles of Perceptual Learning and Development, a book that brought together all her work and established a new branch of psychology: perceptual learning. Perceptual learning, she wrote, “is not a passive absorption, but an active process, in the sense that exploring and searching for perception itself is active. We do not just see, we look; we do not just hear, we listen. Perceptual learning is self-regulated, in the sense that modification occurs without the necessity of external reinforcement. It is stimulus oriented, with the goal of extracting and reducing the information simulation. Discovery of distinctive features and structure in the world is fundamental in the achievement of this goal.”
This quote is so packed with information that we need to stop and read closely to catch it all.
Perceptual learning is active. Our eyes (or ears, or other senses) are searching for the right clues. Automatically, no external reinforcement or help required. We have to pay attention, of course, but we don’t need to turn it on or tune it in. It’s self-correcting—it tunes itself. The system works to find the most critical perceptual signatures and filter out the rest. Baseball players see only the flares of motion that are relevant to judging a pitch’s trajectory—nothing else. The masters in Chase and Simon’s chess study considered fewer moves than the novices, because they’d developed such a good eye that it instantly pared down their choices, making it easier to find the most effective parry. And these are just visual examples. Gibson’s conception of perceptual learning applied to all the senses, hearing, smell, taste, and feel, as well as vision.
Only in the past decade or so have scientists begun to exploit Gibson’s findings—for the benefit of the rest of us.
• • •

The flying conditions above Martha’s Vineyard can change on a dime. Even when clouds are sparse, a haze often settles over the island that, after nightfall, can disorient an inexperienced pilot. That’s apparently what happened just after 9:40 P.M. on July 16, 1999, when John Kennedy Jr. crashed his Piper Saratoga into the ocean seven miles offshore, killing himself, his wife, and her sister. “There was no horizon and no light,” said another pilot who’d flown over the island that night. “I turned left toward the Vineyard to see if it was visible but could see no lights of any kind nor any evidence of the island. I thought the island might have suffered a power failure.” The official investigation into the crash found that Kennedy had fifty-five hours of experience flying at night, and that he didn’t have an instrument rating at all. In pilot’s language, that means he was still learning and not yet certified to fly in zero visibility, using only the plane’s instrument panel as a guide.
The instruments on small aircraft traditionally include six main dials. One tracks altitude, another speed through the air. A third, the directional gyro, is like a compass; a fourth measures vertical speed (climb or descent). Two others depict a miniature airplane and show banking of the plane and its turning rate through space, respectively (newer models have five, no banking dial).
Learning to read any one of them is easy, even if you’ve never seen an instrument panel before. It’s harder, however, to read them all in one sweep and to make the right call on what they mean collectively. Are you descending? Are you level? This is tricky for amateur pilots to do on a clear day, never mind in zero visibility. Add in communicating with the tower via radio, reading aviation charts, checking fuel levels, preparing landing gear, and other vital tasks—it’s a multitasking adventure you don’t want to have, not without a lot of training.
This point was not lost on Philip Kellman, a cognitive scientist at Bryn Mawr College, when he was learning to fly in the 1980s. As he moved through his training, studying for aviation tests—practicing on instrument simulators, logging air time with instructors—it struck him that flying was mostly about perception and action. Reflexes. Once in the air, his instructors could see patterns that he could not. “Coming in for landing, an instructor may say to the student, ‘You’re too high!’ ” Kellman, who’s now at UCLA, told me. “The instructor is actually seeing an angle between the aircraft and the intended landing point, which is formed by the flight path and the ground. The student can’t see this at all. In many perceptual situations like this one, the novice is essentially blind to patterns that the expert has come to see at a glance.”
That glance took into account all of the instruments at once, as well as the view out the windshield. To hone that ability, it took hundreds of hours of flying time, and Kellman saw that the skill was not as straightforward as it seemed on the ground. Sometimes a dial would stick, or swing back and forth, creating a confusing picture. Were you level, as one dial indicated, or in a banking turn, like another suggested? Here’s how Kellman describes the experience of learning to read all this data at once with an instructor: “While flying in the clouds, the trainee in the left seat struggles as each gauge seems to have a mind of its own. One by one, he laboriously fixates on each one. After a few seconds on one gauge, he comprehends how it has strayed and corrects, perhaps with a jerk guaranteed to set up the next fluctuation. Yawning, the instructor in the right seat looks over at the panel and sees at a glance that the student has wandered off of the assigned altitude by two hundred feet but at least has not yet turned the plane upside down.”
Kellman is an expert in visual perception. This was his territory. He began to wonder if there was a quicker way for students to at least get a feel for the instrument panel before trying to do everything at once at a thousand feet. If you developed a gut instinct for the panel, then the experience in the air might not be so stressful. You’d know what the instruments were saying and could concentrate on other things, like communicating with the tower. The training shortcut Kellman developed is what he calls a perceptual learning module, or PLM. It’s a computer program that gives instrument panel lessons—a videogame, basically, but with a specific purpose. The student sees a display of the six dials and has to decide quickly what those dials are saying collectively. There are seven choices: “Straight & Level,” “Straight Climb,” “Descending Turn,” “Level Turn,” “Climbing Turn,” “Straight Descent,” and the worrisome “Instrument Conflict,” when one dial is stuck.

In a 1994 test run of the module, he and Mary K. Kaiser of the NASA Ames Research Center brought in ten beginners with zero training and four pilots with flying experience ranging from 500 to 2,500 hours. Each participant received a brief introduction to the instruments, and then the training began: nine sessions, twenty-four presentations on the same module, with short breaks in between. The participants saw, on the screen, an instrument panel, below which were the seven choices. If the participant chose the wrong answer—which novices tend to do at the beginning—the screen burped and provided the right one. The correct answer elicited a chime. Then the next screen popped up: another set of dials, with the same set of seven choices.
After one hour, even the experienced pilots had improved, becoming faster and more accurate in their reading. The novices’ scores took off: After one hour, they could read the panels as well as pilots with an average of one thousand flying hours. They’d built the same reading skill, at least on ground, in 1/1,000th of the time. Kellman and Kaiser performed a similar experiment with a module designed to improve visual navigation using aviation charts—and achieved similar results. “A striking outcome of both PLMs is that naïve subjects after training performed as accurately and reliably faster than pilots before training,” they wrote. “The large improvements attained after modest amounts of training in these aviation PLMs suggest that the approach has promise for accelerating the acquisition of skills in aviation and other training contexts.”
Those contexts include any field of study or expertise that involves making distinctions. Is that a rhombus or a trapezoid? An oak tree or a maple? The Chinese symbol for “family” or “house”? A positive sloping line or a negative sloping one? Computer PLMs as Kellman and others have designed them are visual, fast-paced, and focused on classifying images (do the elevated bumps in that rash show shingles, eczema, or psoriasis?) or problems rather than solving them outright (does that graph match x—3y = 8, or x + 12 y + 32?). The modules are intended to sharpen snap judgments—perceptual skills—so that you “know” what you’re looking at without having to explain why, at least not right away.
In effect, the PLMs build perceptual intuition—when they work. And they have, mostly, in several recent studies. In one, at the University of Virginia, researchers used a perceptual learning module to train medical students studying gallbladder removal. For most of the twentieth century, doctors had removed gallbladders by making a long cut in the abdomen and performing open surgery. But since the 1980s many doctors have been doing the surgery with a laparoscope, a slender tube that can be threaded into the abdominal cavity through a small incision. The scope is equipped with a tiny camera, and the surgeon must navigate through the cavity based on the images the scope transmits. All sorts of injuries can occur if the doctor misreads those images, and it usually takes hundreds of observed surgeries to master the skill. In the experiment, half the students practiced on a computer module that showed short videos from real surgeries and had to decide quickly which stage of the surgery was pictured. The other half—the control group—studied the same videos as they pleased, rewinding if they wanted. The practice session lasted about thirty minutes. On a final test, the perceptual learning group trounced their equally experienced peers, scoring four times higher.
Kellman has found that his PLMs can accelerate dermatology students’ ability to identify skin lesions and rashes, which come in enormous varieties and often look indistinguishable to the untrained eye. He and Sally Krasne at UCLA Medical School have found similar results in radiology, as well as in reading echocardiograms (ECGs). Working with other colleagues, Kellman has also achieved good results with a module that prompts chemistry students to categorize chemical bonds between molecules.
True, this is all advanced, technical stuff for people who’ve already done just fine in school. What about the kid watching the clock in math class, trying to figure out what on earth “slope” means or how to graph 3(x + 1) = y?
Here, too, perceptual modules have shown great promise. At a school in Santa Monica, Kellman tested a module that works just like the instrument panel trainer, only with equations and graphs. A graph of a line pops up on the computer screen, and below it are three equations to choose from (or an equation with three choices of graphs beneath; it alternates). Again, students have to work fast: make a choice and move on; make another choice, and another, through dozens of screens. With enough training, the student begins to feel the right answer, “and then they can figure out why it’s right afterwards, if they need to,” as Joe Wise, the high school teacher working with Kellman, told me.
Scientists have a lot more work to do before they figure out how, and for which subjects, PLMs are most effective. You can play computer games all you want, but you still have to fly the plane or operate on a living human being. It’s a supplement to experience, not a substitute. That’s one reason perceptual learning remains a backwater in psychology and education. It’s hardly a reason to ignore it, though. Perceptual learning is happening all the time, after all, and automatically—and it’s now clear that it can be exploited to speed up acquisition of specific skills.
• • •

The promise of this book was to describe techniques that could help us learn more effectively without demanding more effort. The goal is to find more leisure, not less. I’m now about to break that promise, but not shatter it into little pieces.
We’re going to make a slide show together.
I know, I know. But look: I once made my own flashcards in high school with old-fashioned paper and No. 2 pencils. It’s just as easy to create a PLM, right here, right now, to show how it can be done, and what it can and can’t do. I was determined to be as lazy as possible about this. I subcontracted the work. I hired my sixteen-year-old daughter to design the module for me, because I’m a busy professional writer, but also because, like many kids, she’s digitally fluent. She’s perfectly capable of making her own digital slide shows, PowerPoint presentations, or videos, downloading images off the Internet. And that’s what I told her to do.
I also poached the subject matter, or at least the idea. I decided to do exactly what Kornell and Bjork did in their interleaving study of painting styles described in the last chapter, with a few small changes. Those two used interleaving to teach students to distinguish individual styles among landscape artists. I changed that. My module would focus on famous artistic movements, like Impressionism. This wasn’t a random choice. My motives here were selfish: I’d been embarrassed on a recent visit to the Museum of Modern Art by how little I knew of art history. I recognized a piece here and there but had zero sense of the artistic and cultural currents running through them. Van Gogh’s Starry Night holds the eye with its swimming, blurred sky, but what did it mean for him, for his contemporaries, for the evolution of “modern” art? I sure didn’t know.
Fine. I didn’t have to know all that right away. I just wanted to know how to tell the difference between the pieces. I wanted a good eye. I could fill in the other stuff later.
What kind of perceptual module did I need? This took a little thinking but not much. I had my daughter choose a dozen artistic movements and download ten paintings from each. That was the raw material, 120 paintings. The movements she chose were (inhale, hold): Impressionism, Post-Impressionism, Romanticism, Expressionism, Abstract Expressionism, Abstract Impressionism, Dadaism, Constructivism, Minimalism, Suprematism, Futurism, and Fauvism. Got all that? You don’t have to. The point is that there are many distinctions to make, and I couldn’t make any of them. I came into the project with a thick pair of beginner’s goggles on: I knew Monet and Renoir were Impressionists, and that was about it.
Kornell and Bjork had presented their landscape paintings in mixed sets, and of course that’s what I had my daughter do, too. The order was random, not blocked by style. She made a PLM and rigged it just as Kellman did. A painting appears on the screen, with a choice of twelve styles below it. If I chose right, a bell rang and the check symbol flashed on the screen. If I guessed wrong, a black “X” appeared and the correct answer was highlighted.

I trained for as long as I could stand it in a single sitting: about ten minutes, maybe sixty screens. The first session was almost all guessing. As I said, I had a feel for the Impressionist pieces and nothing else. In the second ten-minute session I began to zero in on Minimalism and Futurism; baby steps. By session four I had Expressionism and Dadaism pretty well pegged. What were the distinguishing features, exactly? Couldn’t say. What was the meaning of the unnatural tones in the Fauvist pieces? No idea. I wasn’t stopping to find out. I was giving myself a few seconds on each slide, and moving on. This was perceptual learning, not art history.
Eventually I had to take a test on all this, and here, too, I borrowed from Kornell and Bjork. Remember, they’d tested participants at the end of their study on paintings (by the same artists) that they’d not studied. The idea is that, if you can spot Braque’s touch, then you ought to be able to peg any Braque. That was my goal, too. I wanted to reach a place where I could correctly ID a Dadaist piece, even if it was one I hadn’t studied in the PLM.

Henri Matisse

After a half dozen sessions, I took a test—no thinking allowed—and did well: thirty out of thirty-six correct, 80 percent. I was glancing at the paintings and hitting the button, fast. I learned nothing about art history, it’s true, not one whit about the cultural contexts of the pieces, the artistic statements, the uses of color or perspective. But I’ll say this: I now know a Fauvist from a Post-Impressionist painting, cold. Not bad for an hour’s work.
The biggest difference between my approach and Kornell and Bjork’s is that interleaving may involve more conscious deliberation. Perceptual modules tend to be faster-paced, working the visual (perceptual) systems as well as the cognitive, thinking ones. The two techniques are complementary, each one honing the other.
What I’ll remember most, though, was that it was fun, from start to finish—the way learning is supposed to be. Of course, I had no exam looming, no pressure to jack up my grades, no competition to prepare for. I’ve given this example only to illustrate that self-administered perceptual training is possible with minimal effort. Most important, I’ve used it to show that PLMs are meant for a certain kind of target: discriminating or classifying things that look the same to the untrained eye but are not. To me it’s absolutely worth the extra time if there’s one specific perceptual knot that’s giving you a migraine. The difference between sine, cosine, tangent, cotangent. Intervals and cadences in music. Between types of chemical bonds. Between financing strategies, or annual report numbers. Even between simple things, like whether the sum of two fractions (3/5 and 1/3) is greater or less than 1. Run through a bunch of examples—fast—and let the sensory areas of your brain do the rest.
This is no gimmick. In time, perceptual learning is going to transform training in many areas of study and expertise, and it’s easy enough to design modules to target material you want to build an instinct for quickly. Native trees, for example, or wildflowers. Different makes of fuel injectors. Baroque composers or French wines. Remember, all the senses hone themselves, not only vision. As a parent I often wish I’d known the dinosaurs better by sight (there are way more types than you might know, and categories, too), or had a bead on fish species before aquarium visits.
The best part is, as Eleanor Gibson said, perceptual learning is automatic, and self-correcting. You’re learning without thinking.

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