Mind in Motion

by Barbara Tversky

  Then we had a change of perspective and an insight. You probably realized that putting a capital J under the grapefruit half forms an umbrella. This feat required mental construction, albeit simple mental construction, not as complicated as imagining structures from Lego or Tinker Toys. Applying a series of mental transformations to solve geometric analogies is also a mental construction task, a 2D one, akin to mental drawing. If mental drawing is internalized physical drawing, then drawing order should account for transformation order. And it did. We asked another group to imagine drawing a simple object, for example, a cane. Then we asked them to tell us their drawing order; it compared nicely with the transformation order. Drawing has built-in constraints. If you’re drawing, you first need to decide where to put your pencil on the page, that is, where to place the object; that’s move. Then you need to decide what direction to begin drawing, that is, how the object you are drawing is oriented; that’s rotate or reflect. Next, you need to decide how far to draw, that is, how large the object is. That’s remove or add half or size. After you’ve drawn the object, you can shade it or add a small part. With that, mental construction, in this case, drawing, accounted for the perplexing order of performing the mental gymnastics needed to solve geometric analogies. And simultaneously revealed the origins of some of the marvelous creativity of the mind. Imagining elaborate scenes is like internalized drawing.

  ANIMATING IMAGES: STEP-BY-STEP

  Step-by-step mental construction is an amazing feat our minds can perform to create an endless array of objects in the mind and to alter them and their configurations and actions. The very gifted among us, choreographers, topologists, engineers, Ping-Pong players, seem to be able to mentally animate those changes, that is, to imagine transformations in parts, shape, and location as they happen. Bodies dancing or diving; mechanical systems like pumps or brakes. It might seem that way, but closer examination suggests otherwise.

  We ordinary folk need to imagine motion whenever we cross the street as a car is approaching; do we have enough time to cross—or will the driver slow down? A complicated judgment, part spatial, part social, and the cost of error is high. Sadly, both pedestrians and drivers are reliably unreliable in these judgments despite extensive practice. According to the National Safety Council, approximately forty thousand people died in traffic in the United States in 2016. Almost six thousand were pedestrians. Of course, not all deaths were due to unreliable judgments, either by pedestrians or by drivers, but misjudgments are likely to have contributed to many.

  Baseball outfielders ought to be expert in mental animation, in imagining the path of a fly ball as they dash to catch it. They are indeed pretty good at it, or they wouldn’t have lasted on the team, but they don’t seem to mentally animate the trajectory. That is, the brain doesn’t seem to have an algorithm that accurately computes the ball’s trajectory. Rather, outfielders seem to have developed heuristics, or approximations, for estimating what direction and how far they need to run to catch the ball. The estimations are modified “on the fly” as outfielders are running. Frisbee-catching dogs, and presumably Frisbee-catching people, seem to do the same.

  The paths of fly balls or oncoming vehicles are single objects in motion. Perhaps we are better at imagining mechanical systems in action. Alas, those are difficult for most people as well. People animate them step-by-step, sometimes with great effort. Take pulley systems; they run smoothly and continuously. You pull on the rope, the rope turns the pulleys, and the weight attached to the rope rises. Now suppose you see a static diagram of a set of pulleys and have to answer which way each pulley rotates. If you are watching the pulley system in action, you can immediately see whether each pulley is going clockwise or counterclockwise. But most people can’t mentally animate a pulley system from a diagram of the system. To decide which way each pulley is rotating from a diagram, they animate each pulley step-by-step, discretely. What’s perhaps even more interesting, there’s a bias to begin at the conceptual beginning, with the person pulling on the rope, even when beginning at the “end” with the weight would be faster and more efficient for the last pulley.

  Mental animation, like mental drawing, seems to be conceptually driven and step-by-step rather than a smooth and continuous analog transition.

  SPATIAL ABILITIES

  I was once asked to write a book on spatial ability: what it’s good for, do you have it, and how to get it. I replied that it would be either a very brief book or a long, tedious one. Here’s a summary of the brief book. Spatial ability is good for football, basketball, sharpshooting, Go, hockey, science, math, engineering, design, art, fashion, stage sets, choreography, carpentry, and surgery, just for starters. You probably have it if you did the mental rotation tasks easily. Otherwise, practice; it works.

  Now a slightly longer version, hopefully not yet tedious. First to dispel a pop psych myth: people don’t split into verbal or visual thinkers. Verbal and visual thinking skills are pretty much (note: I said pretty much) independent. You can be good at both or bad at both or good at one and bad at the other. Next, like verbal ability, spatial ability isn’t unitary, it has many flavors.

  Finally, like musical ability and athletic ability, and just about every other ability, some fortunate people seem to come into the world with it, but the rest of us can work hard and get better. Studies of twins show—no surprise here—both genetic and environmental influences on spatial ability. Even those who come into the world blessed with abilities have to work hard to excel. No amount of musical ability can make someone an instant violin virtuoso, no amount of athletic ability can make someone instantly into a soaring high jumper, no amount of spatial ability can turn someone instantly into a Frank Lloyd Wright or an Einstein. Expertise as well as abilities can be quite specialized, as anyone who has built a baseball team or a symphony orchestra or a design team knows. Sports provide an elegant lesson: both what you come into the world with and what you do with those qualities matter. To be an elite high jumper or shortstop or quarterback, you need special physical characteristics and the talent and the training. All of the above.

  Measuring spatial abilities

  Spatial ability is intimately tied to spatial transformations and other forms of spatial reasoning. Although there are no standardized measures of spatial ability, versions of mental rotation are widely used. So are other measures of mental spatial manipulations, like geometric analogies or imagining how to fold a flat diagram into a box or which way a part of a mechanical system moves. Some of these tasks are shown in Figure 4.5.

  FIGURE 4.5. Four kinds of spatial reasoning tasks. Answers: 1. A, 2. A, 3. C, 4. D.

  Other measures use jigsaw puzzles or finding a simple geometric figure like a triangle hidden in a larger intricate one. Some rely on understanding the spatial world. Here’s one. People are shown a picture of a tilted but empty water glass and asked to draw a line showing the top of the water in the glass. Some people mistakenly draw the line parallel to the tilted bottom of the glass instead of parallel to the ground. The trick for this one is using the right reference frame, using the world, which is not in the picture, as a reference frame rather than the glass, which is in the picture.

  The different measures of spatial ability go together to some extent, that is, people who do well on one tend to do well on another—but not always—and the lack of standard measures can make it difficult to compare across studies or draw generalizations. Rather than a single spatial ability, there seem to be many spatial abilities. Naturally, there have been many attempts to make sense of the various spatial abilities, to develop a taxonomy, but none has proved satisfactory—yet. On reflection, this is not surprising. It wouldn’t be easy to come up with a taxonomy of sports or music or literary abilities.

  We can’t escape the gender question. Yes, males perform somewhat better on mental rotation tasks. And slightly better on the tilted-glass problem. Playing fast action video games, the kind boys are more likely to play, improves performance. As does other kinds of
training, which reduces the differences in mental rotation. So does removing time pressure, but neither seems to eliminate the male advantage entirely. However, plenty of women surpass plenty of men in these tasks, and as we saw, they can be solved in different ways.

  Women, however, aren’t about to be undone. Women excel at recognizing objects and object locations. Perhaps even more important, women, from infancy, recognize faces and facial expressions better than men. Again, the differences aren’t large, and there’s considerable overlap in the distributions, that is, there are plenty of men who surpass women.

  What is spatial ability good for?

  One very impressive endeavor, Project Talent, followed a sample of four hundred thousand (!) US high school students for eleven years. Students’ spatial skills were assessed using variations of the test you just saw. Their verbal and math skills were also assessed using standardized measures. Naturally, math skills were important for success in science, technology, engineering, and math (fondly referred to as STEM), but spatial skills gave an extra boost. That is, when students were equally high in math skills, those with superior spatial skills were more likely to reach higher educational goals and careers in STEM fields. The spatial-STEM connection receives further support from the twin research, which shows moderate correlations between specific spatial skills and mastery of certain mathematical concepts. Other research shows common brain underpinnings for some spatial skills and some mathematical skills.

  Laboratory experiments support the STEM–spatial thinking connections. Many studies have shown that people excelling in spatial skills also excel in understanding explanations of assembly procedures and mechanical systems. People with good spatial skills are also better at creating visual and even verbal explanations of assembly procedures and the actions of STEM systems.

  But spatial skills should be important for many other talents and occupations beyond STEM. Choreography, all sorts of sports and coaching all sorts of sports, all sorts of design, art, carpentry, board games like Go and chess, surgery, filmmaking; the list is long. Which skills for which activities? There are bits and pieces of tantalizing data. There seem to be some people who excel at visualizing spatial transformations, and others, at visualizing intricacies of objects. And of course, some are pretty good at both. Mathematicians and physicists seem to be especially adept at spatial transformation of objects and artists especially adept at visualizing details of objects. Designers seem to be pretty good at both.

  To add to the puzzles, none of the popular tests of spatial ability predicts navigational abilities. What does predict way-finding abilities is self-report, that is, our own ratings of our navigational abilities. For navigation, too, there are small but persistent gender differences, more in style than ability. Women tend to prefer routes for navigation and for giving directions; men tend to rely more on cardinal directions.

  Acquiring spatial skills

  For years, I taught an honors program in psychology, an elite group of students who went on to stunning careers in many fields, not just psychology. One year we carpooled to the Exploratorium, a wonderful science museum with excellent hands-on psychology demonstrations. This was in ancient times before mobile phones and navigation systems—we relied on paper maps. I sketched one for the carpool drivers. One of the student drivers said, “I don’t do maps.” I wrote out verbal directions; they worked. One of my colleagues, a distinguished member of the National Academy of Sciences, lived not far from me. I told that person about a shortcut that had opened up to drive to campus. The reply: “Please don’t confuse me.” Very smart people can have trouble thinking spatially. We notice when people are brilliantly articulate or the opposite, but only in unusual circumstances do we discover that someone has trouble thinking spatially.

  Not only can spatial skills be developed, but according to no less than a committee of the National Academy of Sciences, they must be developed. Spatial skills are fundamental to so many professions, tasks, and activities. Reading, writing, and arithmetic are proverbially taught in schools, but what about understanding and creating maps, graphs, assembly and operation instructions, and visual explanations of not just science and math but also literature, history, social sciences, and more?

  Enhancing spatial skills is a no-brainer: acquiring spatial skills is fun! For kids—and their caretakers—all sorts of spatial play: puzzles, construction toys like Lego and Tinker Toys, board games like Chutes and Ladders, computer games like Tetris. Even often dismissed computer games, action ones like Grand Theft Auto, can have benefits; they improve allocation of attention and perceptual speed.

  Wrestling places high demands on spatial thinking to get out of complex holds. Learning and practicing wrestling turns out to improve spatial skills. It wouldn’t be surprising if other sports that demand spatial thinking also improve spatial skills. It is known that expertise in various sports correlates with various spatial tasks. But those data don’t tell us whether the sports improved spatial abilities or those with better spatial skills do better in sports. The causality is not clear, but it is likely that it goes both ways: some spatial skills are needed to excel in athletics and attaining expertise boosts spatial skills.

  Parents, teachers, and caretakers can do much more than provide opportunities, sports, toys, games, and more. Crucially, they can enrich the experiences with spatial talk. Calling attention to spatial details and spatial relations and comparisons, to similarities, differences, symmetries, analogies. Querying the child about those relations, similarities, differences, symmetries, and analogies. Using gestures: pointing to details, using back-and-forth gestures for comparisons: similarities, differences, and analogies. Playing the opposites game: in/out; up/down; forward/backward; over/under; inside/outside. Using gestures, even whole-body movements, for those concepts. Naming shapes, describing their characteristics using the P words, parallel, perpendicular, perimeter, the D words, diagonal and diameter, and others, area, circumference, radius. Guessing games: which is taller, wider, closer? Measuring almost anything. Lining up shoes or blocks or toy cars by size. Drawing. Asking or, better yet, working with children—and adults—to create visual-spatial representations, perhaps starting with heights of people and things, then maps, then how something works or how to do something, continuing to a multitude of concepts, on paper or with any objects that are at hand. Bar graphs of books read or glasses of milk consumed, networks of family relations. Wonderful art projects. There are so many opportunities in everyday life: the shapes and sizes of everything; the ways bodies twist and move; the patterns of spots on butterflies and giraffes, of windows on buildings; the speeds of ants and dogs and cars; shadows; all sorts of fastenings: buckles, hinges, keys and locks, snaps, zippers, knots, screws, and lids.

  Of course, these activities aren’t just for kids. A painstaking analysis of over two hundred studies showed that spatial thinking skills can be improved in anyone by many different training techniques. That the effects of training were long-lasting and, in many cases, transferred to other spatial skills, skills that were not directly trained. Hopeful and encouraging findings.

  SCOPE OF SPATIAL ABILITIES

  We have a bit of a quandary here. We now know that there are many spatial abilities and that some of them seem to hang together. We also know that training improves various spatial skills and that training one skill can improve performance on another. But we still don’t have a taxonomy of spatial skills.

  Let’s zoom out now and consider the range of spatial abilities. They seem to fall on a continuum from seeing to doing, from perceiving to acting. There is the talent many artists and designers have for seeing—and often producing—fine details of the visual world, catching slight asymmetries in faces, the proportions and layerings of bodies and landscapes, the tilt of a head and the curve of a road, in depth. There are judgments and comparisons: Which is taller? Wider? Farther? There is that talent athletes in team sports need, keeping track of moving things—the players on each team and the ball or Frisbee.
Which is faster? Higher? Then there are the various imaginings in the mind. Imagining what an object will look like under various transformations like rotating or folding or stretching, imaging what the playing field will be like, imaging the trajectory of a moving object, skills tied to seeing but adding motion in imagination. Now we slide into skills that involve actions of the body in space as well as perception: imagining navigating, wrestling holds, broad jumps, violin sonatas, gymnastics tricks, knitting, or knotting, The continuum: seeing, imagining, doing.

  That continuum from perception to action is really a spiral, an upward one. The perceiving helps the imagining, the imagining helps the doing, the doing helps the perceiving. To use another metaphor, they bootstrap each other. You draw the curve of a smile or a body or a hill as you see it; you look again at the world and at your drawing, and you adjust. And adjust until you are so practiced at seeing and drawing that you do it right the first time. As a result, you probably see the world more clearly. You practice tossing the Frisbee to where you imagine your teammate (or your dog) will be until you get that right. That tight connection between perceiving and doing is a hallmark of spatial thinking. It’s not just doing and perceiving, it’s doing and knowing. Remember that making circular gestures with the hand helps mental rotation. And that drawing lines and dots with the hands to make a schematic map helps people understand and remember environments. The spiral is enriched: perceiving and acting and knowing.