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The Visual Display of Data

The computer has provided a revolutionary tool to represent information visually. Its power is clearly demonstrated by the captivating power of today's video games. While usually describing a narrative of mayhem and destruction, the stunningly seductive rendering of 3D imagery in video games draws the gamer into new visual worlds. It also has the power to bring forward data from multiple dimensions to render information.

One of the most stunning multidimensional graphical representations of human folly was created 141 years ago by Charles Joseph Minard, a French engineer and general inspector of bridges and roads. Sometimes called the "best statistical graphic ever produced," and a work that "defies the pen of the historian," Minard drew a flow-map depicting the tragic fate of Napoleon's Grand Army in the disastrous 1812 Russian campaign. Using pen and ink, Minard captured on the two-dimensional page no fewer than six dimensions of descriptive data.

Edward Tufte, an information designer who, for over three decades, has cultivated the art and science of making sense of data, has eloquently described Minard's map.

The thick band in the middle describes the size of Napoleon's army, 422,000 men strong, when he began the invasion of Russia in June of 1812 from the Polish-Russian border near the Niemen River. As the army advances, the line's thickness reflects its size, narrowing to reflect the attrition suffered during the advance on Moscow. By the time the army reached Moscow (right most side of the drawing), it had been reduced to 100,000 men, one-quarter of its initial size. The lower black line depicts the retreat of Napoleon's army, and the catastrophic effect of the bleak Russian winter. The line of retreat is linked to both dates and temperature at the bottom of the graphic. The harsh cold reduced the army to a mere 10,000 men by the time it re-crossed into Poland. In addition to the main army, Minard characterizes the actions of auxiliary troops who move to protect the advancing army's main flanks.

Minard's map is a tour de force of data representation, an escape from flatland. He conveys a central reality about the world: Things that are interesting are multidimensional. Minard captures and plots six variables: the size of the army (1); the army's location on a two-dimensional surface (2, 3); direction of the army's movement (4); the temperature on various dates during the retreat from Moscow (5, 6).

The truth is nearly everything is multidimensional. Consider giving directions. Telling someone how to get from Logan airport to Cambridge at different times of the day requires the traveler to juggle information in four dimensions.

Since the first image was scrawled on a rock 6,000 years ago the representation of ideas has challenged our intellect and tools. Conveying information is a cognitive task. Doing so on a computer screen is thinking visually. As Tufte reminds us, bad design is stupidity made visible. It d'esn't take much, unfortunately, to find examples of this fact.

The computer screen is a temptress. On the one hand, it can bring static images to life through 3D animation. On the other hand, it has about one-fifteenth the resolution of good paper images, such as nice topographic maps. It would take about 15 computer screens to render a page-size topographic map in similar detail.

With approximately 8,000 characters per page in a directory or catalog, there are 350 characters per square inch. On a monitor you're lucky to have 3,000 characters available to you from the whole screen. That's 37.5 percent of the working space. This puts clarity of thought and content that matters at a premium. That's what will engage those looking at the screen to stay around.

Why d'es this matter? Because we are asking our students to learn more and more from a monitor. Getting clear thoughts across on the printed page has always been a challenge. Doing it with a computer is harder, even with the unique attributes it has over the static page. But clear thinking visually is not just good teaching, it can be a matter of life and death.

The Challenger disaster, for instance, could have been avoided if the visual representation of quantitative data had been clear. The engineers knew there was a problem nearly 12 hours before the launch and voted to postpone it. But when challenged to justify their argument, the contractors presented tables and charts, none of which brought the essential point to light: the causal relationship between temperature and O-ring damage at launches.

The sad fact is that had the data been ordered by temperature, it would have shown a direct correlation with O-ring damage. The Challenger launch temperature was six standard deviations outside the range for which they had actual engineering data. It was, as they say, a disaster waiting to happen.

As we move toward teaching with visual media, we need to remember that visual literacy involves just as much understanding of quantitative data as it d'es artistic expression. Our students must learn reasoning through visual argument as well as verbal expression. Thinking clearly is as much a visual quality as it is a verbal quality worth striving for.


Re-Visions of Minard

Edward Tufte, The Visual Display of Quantitative Information, Graphics Press, Cheshire, Conn., Second Edition, 2001.

Seth M. Powsner and Edward R. Tufte, "Graphical Summary of Patient Status," The Lancet 344 (August 6, 1994), 386-389.

Card, S. K., MacKinley, J. D. & Schneiderman, B. (1999), Readings in Information Visualization: Using Vision to Think, Morgan Kaufmann Publishers Inc., San Francisco, Calif.

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