And that’s it, we no longer need to leave our armchairs. At the same time that technologies are allowing us to move farther and farther, other technologies are bringing the world nearer and closer, to wherever we happen to be. Letters, eons ago only for the wealthy, now instantaneous and always at our fingertips (a mixed blessing), enhanced by video and sound, replacing telephones, once an astounding resource. Now our bodies don’t have to move at all; we can travel the world with smartphones, augmented reality, virtual reality. If we need to move, and physicians advise us to do so, we can move our feet on the treadmill in the gym, without going farther than getting to the gym. From the treadmill, we can enter a virtual world of our choosing, Machu Picchu without climbing, Bangkok without traffic, Beijing without pollution. Or we may prefer a social experience, chatting virtually with friends at a distant party or conferencing virtually with dispersed work colleagues. If, that is, we have the devices and high-speed internet that can take us anywhere virtually—it’s just another way of moving. High-speed internet or high-speed jets? Yet experiences in augmented and virtual reality are enhanced by actual action. And actual sensation, so when we virtually visit Machu Picchu, we can feel the stones underfoot and smell the rarified air. All that without altitude sickness.
We’ve enhanced moving our bodies in space. We’ve also enhanced perception and action by hands. Many of us wouldn’t have lasted long in this world without glasses. Glasses, telescopes, microscopes enhance seeing, allowing us to see farther, almost to the end of the universe and the beginning of time. They allow us to see smaller, almost to the most fundamental minute particles that compose everything in the universe. Of course, those particles are constantly in motion; astrophysicists go into caves deep in the earth to catch them. Microphones and hearing aids enhance hearing. Prosthetic arms and hands, robots, and apparatuses of other sorts augment actions by hand. Too many to list, and more and more accumulating.
Enhancing the mind
Even more important than enhancements of the world and enhancements of action and perception are enhancements of the mind. Teaching. Cooperating. Educating. These depend crucially on social interactions, and begin very early in life. They need nothing more than other human beings, though they are even more effective with books and toys and more. Sticks and stones work too. There’s imitation, a phenomenon often laughable in small children. Chimps and bonobos imitate, too; that’s how they learn from each other. One chimp figures out a clever way to crack nuts and the others imitate. Different tribes of chimps develop different methods. Interestingly, chimps will imitate another successful chimp, but they will not imitate a machine that accomplishes the same goal in the same way.
But chimps don’t teach each other. People do. The foundations are put in place early in life, in games. Games like patty-cake involve more than imitation, they involve timing, synchrony, and alternation—turn-taking, like conversation. Those games are cooperative, they entail attending to each other, working together, and joint attention to the task. In humans, but notably not in apes, teaching and cooperating are enhanced by caretakers who show and guide. Gesture has a large role in guiding and teaching. Language comes to bootstrap those interactions, especially in Western cultures, but the naming game itself depends on joint attention and gesture, pointing, if not by the hand, by the eyes. There’s so much more to say, but that would be another book.
THINKING
We spend our lives in space, acting in space, moving in space. For the most part, it’s our feet that move our bodies in space. The paths of our feet as we move from place to place in the world leave traces on the ground and traces in our minds. Well-trodden paths get thicker. They make routes that can be turned into maps. The paths and places form networks, like the networks of neurons in the brain, blood vessels in the body, rivers on earth, information in computer systems, and power in governments. Frequented places become neighborhoods or hubs and they get thicker. Their boxes accumulate more actions. Sometimes one box takes charge, the brain, the heart, the president, and the network becomes a tree, with a single root. The patterns are patterns in time as well as in space, rhythmic points and lines, repetitions, orders, cycles. There’s no separating time and space. Assembly lines, knitting, music, tennis games, cleaning the house. Sequences of punctuated actions, paths and places in time and space. They create the forms that are used to represent ideas and relations between ideas.
Now let’s move to hands. For the most part, it’s the hands that do the acting on objects, with remarkable agility. They touch, twist, raise, push, pull, put together, take apart, reach, organize, throw, scatter, mix, flip, rearrange, sort, construct, deconstruct, and act on objects in a thousand more ways. At the same time, our eyes glance, scrutinize, inspect, go back and forth. Pay attention to those verbs. They’re the same ones we use to talk about thinking. Thinking is mental actions on mental objects—ideas—rather than physical actions on physical objects. All inside the mind. Now we move to gesture. Gestures are physical actions, but not on physical objects. Gestures are actions on invisible objects, on ideas, ideas that exist only in the minds of the person gesturing or the conversation partner, if there is one. I trust you remember the bottom line on gesture: gesturing helps thinking. If thinking is internalized action, then externalizing actions on thought as gestures that perform miniatures of the actions should help the thinking. It does. Our own thinking, and that of others.
The same is true for graphics of all forms, sketches, charts, graphs, diagrams, models, pebbles, cocktail napkins. They externalize thought and thereby promote thought. Taking ideas that are in the mind out of the mind and putting them into the world in front of our eyes helps our own thinking and that of others. Putting thought into the world is key to collaboration, to working together, to the joint action that is core to human society, and to survival.
Both gesture and graphics abstract. They abbreviate, truncate, schematize, generalize. Gestures don’t capture entire actions, only thumbnails of them. Much like the words for action. Lift doesn’t say how an object is lifted, with a finger or a hand or two hands or eight hands. Or a machine, a fork lift. Whether you lift a crumb from the floor or a piano, it’s the same word. Gestures can actually be more specific, showing, if useful, how something is lifted. A sketch map schematizes a route; there’s so much missing from sketch maps, and what’s there gets simplified and distorted.
Gestures, in common with diagrams and other graphics, abstract thought in other ways. Gestures can create overall schemas in space. They set a stage for ideas. Here’s one that’s frequent because it’s so very useful: compare and contrast. One hand puts one set of imaginary things on one side of the body, the other hand places another set of imaginary things on the other side. On the one hand, on the other. Columns and rows on a page, imaginary ones in the air. Then point back and forth as you go through the comparison. Each place now represents a separate set of ideas. You show it; you don’t have to say it. Here’s another: set up an order, along a horizontal line. Could be a sequence of events in time, could be a sequence of preferences for movies, restaurants, or baseball teams. Now a circle, showing events that repeat. Now a vertical line, going upward. Could be temperature or achievements or power or mood. Forms again. Am I describing diagrams on a page or gestures in the air? Both. Both gestures and graphics put thought in the world, arrange thought, and abstract thought. Both gestures and graphics put checkers on a checkerboard to play in a game of thought, ideas on a stage to perform in a theater of thought.
All those patterns and forms we’ve collected. The ones our feet create moving in the world: points and paths and boxes and networks and trees and circles. The ones our hands create in designing the world: boxes and lines and circles again, rows and columns and symmetries and repetitions and one-to-one correspondences. We put those on a page to use them to represent many kinds of ideas and many kinds of relations between ideas. They become maps and tables and charts and diagrams. They organize the thoughts in our mind, show them to ot
hers, and help us generate more thoughts. There are so many more forms and patterns in math, in physics, in biology, in chemistry, in engineering, in art. Patterns in space, forms in space that are the foundation for each of them. They get formed and transformed, rotated, translated, taken apart and put together. Arches and crystals and Bucky balls and Mobius strips.
THE DESIGNED WORLD SPEAKS A SPATIAL LANGUAGE
So much information emanates from the spatial forms and patterns that we create and that surround us. They are informative in and of themselves. They tell us what they are and how to interact with them. They also express abstractions, the kind that go into logic or math or computer science: linear orders in bookshelves and assembly lines, categories and hierarchies of categories in kitchen cabinets and drawers of clothing and supermarket shelves, one-to-one correspondences in table settings, symmetries and repetitions in buildings. Rooms are organized by themes: stuff for cooking in the kitchen, stuff for personal care in the bathrooms, stuff for socializing and relaxing in the living room. Those organizations were not created by nature; they were created by and for human actions, by conscious minds. They were created for a purpose. The rows and columns of shelves and windows and buildings form regular patterns that are good gestalts. They’re tables and graphs. They bring the eye, inviting a search for their meanings, for the reasons the arrangements were created. Typically, we can figure them out. As can children, each person in the family gets a plate and silverware—and a treat, the plates stacked in categories on shelves, beds and pillows in the bedroom, towels and bathtubs in the bathroom. We use the same organizations in our minds, in our homes, and on the streets.
There’s another layer on the streets. The streets are organized the ways our homes and supermarkets are, in boxes, lines, rows, columns, orders, and more. But the streets go further; they are marked and labeled, sometimes, like diagrams, with words, but so often not. The whole world has become like a string of basketball courts, golf courses, soccer fields, and baseball diamonds. Lines of various colors and styles indicate pedestrian crossing lanes, bus lanes, bike lanes, car lanes, one-way streets, turning lanes, parking places for cars, motorcycles, bikes. The different functions are clearly marked: crossing lanes are zebra-striped, bike lanes are green, parking places are pairs of diagonal or parallel lines, slots to fit your car into. Car-sized boxes. There are arrows drawn on lanes that tell you you cannot turn or you must turn. There are bicycles painted on the ground to tell you to keep your car or feet out of the bike lanes. Dare not drive across a double yellow line. Those lines, for parking and turning and crossing and no crossing, have legal status. The laws are inscribed lines on the streets. Laws also appear in signs of different shapes and colors, hexagon for stop and triangle for yield, no U-turn with an icon and one-way streets with an arrow. Stop lights, red on top to halt, green on the bottom to go. Curious, laws that are not in words but in lines on the streets and signs along them.
The world is diagrammed. We’ve fastened our collective minds onto the world. The diagram in the world is information; it tells you where you are and what kinds of things are around you. It tells you where and when you can go, and where and when you cannot go. What you can do and what you cannot do. It controls, directs, and enables the ways you move and act in the world. Enter here, exit there. That way, people won’t bump into each other. Cross at the zebra stripes or when the light is green; put recyclables in the green trash can, a slit for paper, a circle for cans. It’s labeled, just like the fruit you buy in the supermarket, placed in lines and bins of appropriate shapes that are adorned with colors and symbols that are instructions for actions. The designed world is a diagram that reveals its meanings through place and marks in space and guides our action. The view from above is a map. The view from within tells us where people can walk, where cars and buses and bikes can go, when to stop and when to go, where to park, where to enter, and where to exit. The patterns on our bookshelves and in cabinets and table settings and on building facades express abstract ideas: categories, hierarchies, repetitions, one-to-one correspondences, linear orders. We organize the world the way we organize our minds and our lives.
The patterns created by our actions, lines and rows and columns and stacks, are not random, not like the leaves strewn on the ground or the sand rolling in the dunes or the trees scattered in the forests. They are regular and tidy, parallel and perpendicular, symmetric and repetitive. They enclose and separate; they are scaffolds for the things in the world. They didn’t happen by chance, they must have been put there for a reason. We can read the reasons, sometimes without trying, and use that information to guide our thoughts and our actions.
The forms and patterns on the ground are made by actions of our feet. Places and paths and circles and more. The forms and patterns on buildings and on tables and on computer screens are made by actions of our hands. Rows and columns and stacks and orders and embeddings and symmetries and more. The forms and patterns are good gestalts that attract the eye and inform the mind. We detach the actions and the patterns from whatever made them and use them to represent something else, so many things, they’re extraordinarily useful actions and patterns. On a page or in the air. In the world. The gestures we draw with our hands in the air abstract the actions that created the forms and patterns. They turn real actions on real objects into schematic actions on imaginary objects, ideas. They become actions on thought, any kind of thought. The diagrams we draw with our hands on the page abstract the patterns that we use to arrange objects in the world. We use them to arrange thoughts on a page, creating tools for thought that benefit thought. For everyone. And it all begins with our action in space. A spiral going ever upward. Spraction: actions in space create abstractions.
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The Nine Laws of Cognition
First Law of Cognition: There are no benefits without costs.
Second Law of Cognition: Action molds perception.
Third Law of Cognition: Feeling comes first.
Fourth Law of Cognition: The mind can override perception.
Fifth Law of Cognition: Cognition mirrors perception.
Sixth Law of Cognition: Spatial thinking is the foundation of abstract thought.
Seventh Law of Cognition: The mind fills in missing information.
Eighth Law of Cognition: When thought overflows the mind, the mind puts it into the world.
Ninth Law of Cognition: We organize the stuff in the world the way we organize the stuff in the mind.
BARBARA TVERSKY is an emerita professor of psychology at Stanford University and a professor of psychology at Teachers College at Columbia University. She is also the president of the Association for Psychological Science. Tversky has published over two hundred scholarly articles about memory, spatial thinking, design, and creativity and regularly speaks about embodied cognition at interdisciplinary conferences and workshops around the world. She has had the joy and privilege of collaborating not only with psychologists but also with linguists, scientists, philosophers, computer scientists, designers, artists, and more. She lives in New York.
Figure Credits
Figure 1.1. Source: OpenStax College, Anatomy & Physiology. OpenStax CNX. July 30, 2014. Retrieved from http://cnx.org/contents/[email protected]
Figure 3.1. Source: Tversky, B., & Hard, B. M. (2009). Embodied and disembodied cognition: Spatial perspective-taking. Cognition, 110(1), 124–129.
Figure 4.3. Source: Adapted from Kosslyn, S. M. (1980). Image and mind. Cambridge, MA: Harvard University Press.
Figure 4.4. Source: From Novick, L. R., & Tversky, B. (1987). Cognitive constraints on ordering operations: The case of geometric analogies. Journal of Experimental Psychology: General, 116(1), 50–67.
Figure 4.5. Source: Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 ye
ars of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817.
Figure 5.1. Source: Guidonian hand from a manuscript from Mantua, last quarter of fifteenth century (Oxford University MS Canon. Liturgy 216. f.168 recto) (Bodleian Library, University of Oxford).
Figure 8.1. Source: Photo by Scott Catron. May 14, 2006. Retrieved from https://commons.wikimedia.org/wiki/File:HuntSceneNMC.JPG
Figure 8.2. Courtesy of Professor Pilar Utrilla. Utrilla, P., Mazo, C., Sopena, M. C., Martínez-Bea, M., & Domingo, R. (2009). A paleolithic map from 13,660 calBP: Engraved stone blocks from the Late Magdalenian in Abauntz Cave (Navarra, Spain). Journal of Human Evolution, 57(2), 99–111.
Figure 8.3. Source: British Museum, Department of British and Mediaeval Antiquities and Ethnography, Handbook to the Ethnographical Collections (Oxford, England: Trustees, British Museum, 1910), 170. https://www.flickr.com/photos/internetarchivebookimages/14783361945/
Figure 8.4. Source: “Map” in Encyclopaedia Britannica (11th ed., Vol. XVII, p. 638). Retrieved from https://commons.wikimedia.org/wiki/File:EB_1911_Map_Fig_10.png
Figure 8.5. Source: Snow, J. (1855). On the mode of communication of cholera (2nd ed.). London, England: John Churchill. Retrieved from http://matrix.msu.edu/~johnsnow/images/online_companion/chapter_images/fig12-5.jpg
Figure 8.6. Source: Intitut Royal des Sciences naturelles de Belgique, Bruxelles.
Figure 8.8. Courtesy of Mark Wexler (1993).
Figure 8.9. Source: Swetz, F. (2012). Mathematical expeditions: Exploring word problems across the ages. Baltimore, MD: Johns Hopkins Press. Photograph by Jon Bodsworth between 2001 and 2011.
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