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Even sketchy likenesses can be readily recognized by the uninitiated. Likenesses have been creatively integrated into more abstract representations of quantitative data by Neurath and his Vienna Circle and later colleagues in the form of isotypes Neurath, Isotypes turn bars into depictions, for example, the number of airplanes in an army or yearly production of corn by a country is represented by a proportional column or row of schematic airplanes or corn plants. Just as likenesses can facilitate comprehension and memory, they can also interfere. Because depictions are specific and concrete, including them when they are not essential to the meaning of a diagram can inhibit generalization, to sets of cases not depicted.

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By contrast, glyphs, because they are abstractions, can encourage generalization. Capturing the objects in the world and their spatial arrays in diagrams is compelling and has some communicative value, but it can interfere or even conflict with the generalizations or abstractions diagrams are meant to convey. The typical water cycle diagram includes mountains, snow, lakes, sky, and clouds. On the one hand, these diagrams intend to teach the cycle of evaporation of surface water, formation of clouds, and precipitation.

They use arrows to indicate the directions of evaporation and precipitation. On the other hand, they also want to show the water cycle on the geography of the world. As a consequence, the arrows ascend and descend everywhere, so that the cyclicity is obscured.

In producing diagrams, for example, of a pond ecology, when groups work in pairs, the compelling iconicity evident in individual productions often disappears Schwartz, Diagrams produced by dyads become more abstract, most likely because the irrelevant or distracting iconicity is idiosyncratic and the abstractions shared. The conflict between visualizing the world and visualizing the general phenomena that occur in the world is especially evident when diagrams are used to convey the invisible such as evaporation and gravity.

With all the challenges of conveying the visible, conveying the invisible, time, forces, values, and the like presents even more challenges. Glyphs are ideal for visually conveying the invisible. They are not iconic, they do not depict the visible world, so they do not confuse or distract, yet they share many of the advantages of visual communication over purely symbolic communication, notably rapid access to meaning. We turn now to many examples of using glyphs to visually convey invisible and abstract concepts.

We shift now from the complex and representative to the simple and abstract. Probably the simplest mark that can be made on the page is a dot, a mark of zero dimensions. On a map of the United States, New York City can be represented as a point, or the route from New York to Chicago as a line, or the entire city can be represented as a region, containing points and lines indicating, for example, roads, subway stops, and subway lines. Like many other spatial distinctions, this set of distinctions has parallels in language and gesture, parallels that suggest the distinctions are conceptual and widely applicable.

Regarding an entity in zero, one, two, or three dimensions has implications for thought. She waited at the station, rode on the train, rose in the elevator. She arrived at 2, on time, and was in the meeting until dinner. She was at ease, on best behavior, in a receptive mood. Visual expressions of dimensionality are common in diagrams, as they abstract and express key conceptual components. Dots, lines, and regions abound in diagrams. Dots and lines, nodes and links or edges are the building blocks of route maps.

They also form a toolkit for a related set of abstractions, networks of all kinds. To uncover the basic visual and verbal vocabularies of route maps, students outside a dormitory were asked if they knew how to get to a nearby fast food restaurant. If they did, they were asked either to draw a map or to write directions to get there.

Notably, although the sketch maps could have been analog, they were not; turns were simplified to right angles and roads were either straight or curved. Short distances with many turns were lengthened to show the turns, and long distances with no actions were shortened. Thus, the route maps not only categorized continuous aspects of the world, they also distorted them. Interestingly, the verbal directions were similarly schematized.

Distances were specified only by the bounding landmarks; turns were specified only by the direction of the turn, not the degree. These close parallels between disparate modes of communication suggest that the same conceptual structure for routes underlies all of them. They were asked to supplement the toolkits if needed. In spite of that suggestion, very few students added elements; they succeeded in using the toolkits to create a variety of new directions.

Although the semantics vocabularies and syntax rules of combing semantic elements of route maps and route directions were similar, their pragmatics differs. Route maps cannot omit connections; they must be complete. Why do directions that are so simplified and distorted work so well? Because they are used in a context, and the context disambiguates Tversky, This is another general characteristic of diagrams; they are designed to be used by a specific set of users in a specific context. The success of the visual and verbal toolkits for creating route maps and route directions has a number of implications.

It suggests that maps and verbal directions could be automatically translated from one to the other. It is encouraging for finding similar visual and verbal intertranslatable vocabularies for other domains, such as circuit diagrams or musical notation or even domains that are not as well structured domains such as assembly instructions, chemistry, and design.

Finally, it shows that certain simple visual elements have meanings that are spontaneously produced and interpreted in a context. Some of these visual elements have greater generality. Lines are naturally produced and interpreted as paths connecting entities or landmarks that are represented as dots. Hence their widespread use, from social networks, connections among people, to computer networks, connections among computers or components of computers, and more.

So are dots and bars. Graph lines connect dots representing entities with particular values on dimensions represented by the lines. The line indicates that the entities are related, that they share a common dimension, but have different values on that dimension. In graphs, bars indicate that all the instances inside are the same and different from instances contained in other bars.

Because lines connect and bars contain and separate, students were expected to favor trend descriptions for data presented as lines and favor discrete comparisons for data presented as bars, especially for the graphs without content. More surprisingly, the visual forms had large effects on interpretations of graphs with content, in spite of contrary content.

Mirror results were obtained in production tasks, where students were provided with a description, trend, or discrete comparison, and asked to produce an appropriate graph. More students produced line graphs when given trend descriptions and bar graphs when given discrete comparisons, as before, in spite of contrary content. The meanings of the visual vocabulary, lines or bars, then, had a stronger effect on interpretations and productions than the conceptual character of the data.

Because glyphs such as lines, dots, boxes, and arrows, induce their own meanings, they are likely to enhance diagrammatic communication when their natural meanings are consistent with the intended meaning and to interfere with diagrammatic communication when the natural meanings conflict with the intended meanings. This interaction was evident in the case of bar and line graphs for discrete and continuous variables, where the interpretations of the visual glyphs trumped the underlying structure of the data when they conflicted.

Mismatches between the natural interpretations of lines as paths or connections and the intended interpretations in diagrams turn out to underlie difficulties understanding and producing certain information systems designs. A central component of information system design is a LAN or local area network, common in computer systems in every institution. All of the components in a LAN are interconnected so that each can directly transmit and receive information from each other. A natural way to represent that interconnectivity would be lines between all pairs of components.

For large systems, this would quickly lead to a cluttered, indecipherable diagram. To insure legibility, a LAN is diagramed as if a clothesline, a horizontal line, with all the interconnected components hanging from it. However, when students in information design are asked to generate all the shortest paths between components from diagrams containing a LAN, many make errors. A common error demonstrates a strong bias from the line glyph.

Here, again, the visual trumps the conceptual and misleads. In one experiment, information about the locations of people over time was presented either as tables with place and time as columns or rows and dots representing people as entries or as tables with lines connecting individuals from place to place over time.

Because lines connect, one might expect that the lines would help to keep track of movements of each individual. In one task, participants were asked to draw as many inferences as they could from the diagrams; in another they were asked to verify whether a wide range of inferences was true of the diagrams. At the end of the experiment, they were asked which interface they preferred for particular inferences. Overall, participants performed better with dots than with lines both in quantity of inferences drawn and in speed and accuracy of verification. However, and consonant with expectations, there was one exception, one kind of inference where dots lost their advantage, inferences about the sequence of locations of individuals.

For temporal sequence, lines were as effective and as preferred as dots. Nevertheless, the lines interfered with generating and verifying other inferences. In another experiment, participants were asked to generate diagrams that would represent the locations of individuals over time. As for preferences, participants preferred the visualizations with dots over those with lines except for temporal sequences.

These findings suggest that popular visualizations that rely heavily on lines, such as parallel coordinates e. Arrows are asymmetric lines. As a consequence, arrows suggest asymmetric relationships. Arrows enjoy several natural correspondences that provide a basis for extracting meaning. Arrows in the world fly in the direction of the arrowhead. The diagonals at the head of an arrow converge to a point.

Studies of both comprehension and production of arrows show that arrows are naturally interpreted as asymmetric relationships. Half of each kind of the diagram included arrows, half did not. For the diagrams without arrows, students gave structural descriptions, that is, they provided the spatial relations of the parts of the systems. The second study provided a description, either structural or functional, of one of the systems and asked students to produce a diagram.

Students produced diagrams with labeled parts from the structural descriptions but produced diagrams with arrows from the functional descriptions. Both interpretation and production, then, showed that arrows suggest asymmetric temporal or causal relations. One of the benefits of arrows can also cause difficulties; they have many possible meanings. Their ambiguity can cause misconceptions and confusion.

Arrows are used to label or focus attention; to convey sequence; to indicate temporal or causal relations; to show motion or forces; and more. How many meanings? Some have proposed around seven e. Circles , with or without arrows, can be viewed as another variant on a line, one that repeats with no beginning and no end. As such, circles have been used to visualize cycles, processes that repeat with no beginning and no end.

The common etymology of the two words, circle and cycle, is one sign of the close relationship between the visual and the conceptual. However, the analogies, like many analogies, are only partial. Circles are the same at every point, with no natural divisions and no natural direction. Yet when we talk about cycles, we talk about them as discrete sequences of steps, sometimes with a natural beginning.

Hence, cycles are often visualized as circles with boxes, text, or pictograms conveying each stage of the process. They did this easily. Both cycles and linear processes had four stages. Unsurprisingly, most students portrayed the linear processes in lines, but, more surprisingly, most portrayed the cyclical processes as lines as well, without any return to the beginning. There is strong resistance to producing circular diagrams for cycles, even among college students. In the final study, participants were provided with a linear or circular diagram of four stages of a cycle, and asked which they thought was better.

This is the first case we have found where production and preference do not match, though production lags comprehension in other domains, notably, language acquisition. Why do people prefer circular diagrams of cycles but produce linear ones? We speculate that linear thinking is easier than circular; that is, it is easier to think of events as having a beginning, a middle, and an end, a forward progression in time, than it is to think of events as returning to where they started and beginning all over again, without end.

Events occur in time, time marches relentlessly forward, and does not bend back on itself. Each day is a new day, each seed a new seed; it is not that a specific flower emanates from a seed and then transforms back into one. Thinking in circles requires abstraction, it is not thinking about the individual case, but rather thinking about the processes underlying all the cases. What is more, the sense in which things return to where they started is different in different cases.

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Every day has a morning, noon, and night, but each morning, noon, and night is unique. A cell divides into two, and then each of those cells undergoes cell division. For clothing and dishes, however, the very same articles of clothing and the very same dishes undergo washing, drying, putting away each time. Earlier, we saw that people interpret bars as containers, separating their contents from everything else.

Boxes are an ancient noniconic depictive device, evident explicitly in stained glass windows, but even prior to that, in Roman wall frescoes. Frames accentuate a more elementary way of visually indicating conceptual relatedness, grouping by proximity, for example, the spaces between words. Framing a picture is a way of saying that what is inside the picture has a different status from what is outside the picture. Comics, of course, use frames liberally, to divide events in time or views in space. Comics artists sometimes violate that for effect, deliberately making their characters pop out of the frame or break the fourth wall, sometimes talking directly to the reader.

The visual trope of popping out of the frame makes the dual levels clear, probably even to children: The story is in the frames, the commentary outside e. Speech balloons and thought bubbles are a special kind of frame, reserved for speech or thought; as for other frames, they serve to separate what is inside from what is outside. Boxes and frames serving these ends abound in diagrams, in flow charts, decision trees, networks, and more.

As was evident from the visual toolkit for routes, glyphs can be combined to create complex diagrams that express complex thoughts and systems. Networks of lines and nodes, more abstractly, concepts and connections between concepts, are so complete and frequent that they constitute a major type of diagram. Others types of diagrams include the following: hierarchies, a kind of network with a unique beginning and layers of asymmetric relations, such as taxonomies and organization charts; flow charts consisting of nodes and links representing temporal organizations of processes and outcomes; decision trees, also composed of nodes and links, where each node is a choice.

These organized sets of glyphs and space constituting diagrammatic types appear to match, to naturally map, conceptual organizations of concepts and relations. Note that many of these visual complex combinations of glyphs, for example, bar and line graphs, social and computer networks, decision and evolutionary trees, have no pictorial information whatsoever, yet they inherit all the advantages of being visual. They enable human application of visuospatial memory and reasoning skills to abstract domains.

The aim of most of the diagrams discussed thus far is to convey certain information clearly in ways that are easily apprehended, from route directions to data presentations to scientific explanations. Another important role for visualizations of thought is to clarify and develop thought. This kind of visualization is called a sketch because it is usually more tentative and vague than a diagram. Sketches in early phases of design even of physical objects, like products and buildings, are frequently just glyphs, lines and blobs, with no specific shapes, sizes, or distances e.

Designers use their sketches in a kind of conversation: They sketch, reexamine the sketch, and revise Schon, They are intentionally ambiguous. Ambiguity in sketches, just like ambiguity in poetry, encourages a multitude of interpretations and reinterpretations. Diagrams and other forms of visual narratives are enhanced by the inclusion of a rich assortment of schematic visual forms such as dots, lines, arrows, circles, and boxes, whose meanings derive from and are constrained by their Gestalt or mathematical properties within the confines of a context.

The meanings they support, entities, relations, asymmetric relations, processes, and collections, are abstract, so apply to many domains. They encourage the kind of abstractions needed for inference, analogy, generalization, transfer, and insight. They have analogs in other means of recording and communicating ideas, in language and in gesture, suggesting that they are elements of thought. There are other abstract visual devices, infrequent in diagrams, but common in graphic novels and comics, lines suggesting motion, sound, fear, sweat, emotions, and more e.

Some of these, like the lines, boxes, and arrows discussed above, have meanings suggested by their forms. Others, like hearts for love, are more symbolic. The concepts conveyed by the diagrammatic schematic forms are not as readily depictable as objects or even actions. Among the properties of lines is that they connect, just as relationships, abstract or concrete, connect. Among the properties of boxes is that they contain one set of things and separate those from other things.

What is in the box creates a category, leaving open the basis for categorization to the creator or interpreter. The box implies that the things in the box are more related or similar to each other than to things out of the box. The box might contain a spatial region, a temporal slice, a set of objects. These mappings of meaning, the transfer of a few of the possible features from the object represented to the representing glyph, are partial and variable.

The consequence is variability of meaning, allowing ambiguity and misconception. A case in point is uses of arrows, which map asymmetric relations. But there are a multitude of asymmetric relations, temporal order, causal order, movement path, and more. The concepts suggested by glyphs have parallels in language and gesture with the same tradeoffs between abstraction and ambiguity. Think of words, notably spatial ones that parallel glyphs, like relationship or region or point. A romantic relationship? A mathematical relationship? Here, context will likely disambiguate, but not on all occasions.

There is good reason why spatial concepts, whether diagrammatic or linguistic or gestural, have multiple meanings; they allow expression of kinds of meanings that apply to many domains. Much has been said on what depictions do well: make elements, relations, and transformations of thought visible, apply human skills in visuospatial reasoning to abstract domains, encourage abstraction, enable inference, transfer, and insight, promote collaboration. But many concepts essential to thought and innovation are not visible.

A key significance of glyphs is that they can visualize the invisible, entities, relations, forces, networks, trees, and more. The page is flat, as is the visual information captured by the retina.

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Reasoning from 3D diagrams is far more difficult than reasoning from 2D diagrams whether depictive e. Language, visual search, and reasoning are sequential and limited, so that continuous animations of explanatory information can cause difficulties e. Ability matters.

Spatial ability is not a unitary factor, and some aspects of spatial thinking, especially performing mental transformations and integrating figures, matter for some situations and others for others e. Different spatial, and undoubtedly conceptual, abilities are needed for different kinds of tasks and inferences that involve diagrams. Expertise matters. It can trade off with ability. As noted, diagrams, like language, are incomplete and can be abstract, requiring filling in, bridging inferences.

Domains include implicit or explicit knowledge that allows bridging, encouraging correct interpretations and discouraging incorrect ones. The significance of domain knowledge was illustrated in route maps and holds a fortiori in more technical domains e. Working memory matters. Although, as advertised, external representations relieve working memory, they do not eliminate it. Typically, diagrams are used for comprehension, inference, and insight. All involve integrating or transforming the information in diagrams, processes that take place in the mind, in working memory. Structure matters. When diagrams are cluttered with information, finding and integrating the relevant information takes working memory capacity.

Schematization, that is, removing irrelevant details, exaggerating, perhaps distorting, relevant ones, even adding relevant but invisible information, can facilitate information processing in a variety of ways. Aerial photographs make poor driving maps. Schematization can reduce irrelevancies that can clutter, thereby allowing attention to focus on important features, increasing both speed and accuracy of information processing e.

Sequencing matters. Conveying sequential information, important in history, science, engineering, and everyday life, poses special challenges. Time lines of historical events are another common successful example. Depicting each step separately and connecting them, often using frames and arrows, is another popular solution, from Egyptian tomb paintings showing the making of bread to Lego instructions.

Both separating and connecting require careful design. People segment continuous organized action sequences into meaningful units that connect perception and action, by changes in scene, actor, action, and object e. Animations are attractive because they appear to conform to the Congruity Principle: They use change in time to show change in time, a mentally congruent relation Tversky, However, as we have just seen, the mind often segments continuous processes into steps e.

The segmentation of routes by turns and object assembly by actions provide illustrative examples. Even more than in static diagrams, visualizing the invisible, causes, forces, and the like, is difficult in animations. And, indeed, a broad range of kinds of animations for a broad range of content have not proved to be superior to static graphics e. Depictions and language differ in many ways, some discussed earlier, among them, expressiveness, abstraction, constraints, accessibility to meaning e.

As we have seen, many meanings may be easier to convey through diagrams, but diagrams can also mislead. Here, comparing three "unstable" examples of frozen action stimuli with aesthetic artworks that imply movement reminded me the historical innovators in science and art who aspired to bring movement to still pictures e. One section, on the Tai-chi tao symbol, has stayed in my mind. He further asks whether the properties and descriptive modes applicable to a surface specified in our ontology of the external world are the same as those that our internal perceptual ontology specifies.

While the questions may seem simple, his approach to them was original and quite stimulating. I simply could not see the changes between the b and c sequences mentioned in the caption. Under the image it states that there was an addition of a thin demarcating bead along the perimeter of the main surface discontinuity to perceptually enhance the discontinuity feature. I suspect this is due to inadequate contrast in the printing or the small size of the graphics. The last chapter of the book, which celebrates the contributions of the late John Willats to the field, added an incredibly human dimension to the book.

I was delighted the editor decided to include it, and must admit I read this chapter first. Jan J. The tribute brought to mind that vision is not a dry, academic topic confined to research agendas. Rather, as those of us who study it know well, it is something we experience so fully we are compelled to learn more about it. Indeed, it is because what we see "happens to us" that studies of visual cognition are tantalizing, thought provoking, and evocative.

In summary, the volume combines interdisciplinary expertise in an examination of conscious qualitative states in perception. Its primary theme is the co-presence and interaction of diverse types of spaces in vision, like the optical space of psychophysics and of neural elaboration, the qualitative space of phenomenal appearances, and its relation with the pictorial space of art. The essays agree that these qualitatively distinct "spaces" follow different rules of organization, although they co-exist.

Essay after essay affirms that Visual Thought is a high quality book, one that expands visual thought beyond science and philosophy. Kress, Gunther R.

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Liebsch, Dimitri ed. Maar, Christa — Hubert Burda eds. McKim, Robert H. Mitchell, William J. Mitchell, W. University of Reading: Dept. Price, H. Read, Rupert — Jerry Goodenough eds. Sachs-Hombach, Klaus ed. Tufte, Edward R. Walton, Kendall L. Wartenberg, Thomas E. West, Thomas G. Lewis, Yazdani, Masoud — Philip Barker eds. Block, Ned ed. Dondis, Donis A. Kepes, Gyorgy ed. Press, Talbot, Daniel ed.