Info We Trust

by R J Andrews

  Bar charts can have horizontal or vertical orientations. The dominant horizontal metaphor is that of progress towards a goal, often a target of 100% completion. Horizontal bars, like the number line, convey travel away from an origin baseline. They are like runners on a straight dash or miners cutting tunnels into the sheer side of a mountain. Horizontal progress bars are one of the most often experienced data visualizations. Horizontal bars also make great companions to the horizontal text of category titles. However you lay your bar, remember that its journey, how far it has come, is more meaningful if you can see where it began.

  Pierre E. Levasseur referred to vertical bar charts, in 1885, as columns of stacked facts.

  A different conceptual meaning is conveyed if the horizontal bar chart is rotated to create columns. The dominant visual metaphor for the vertical bar chart is a stack of stuff. Each column represents a total number of things, items that are often not actually stackable in the real world. A row of columns can show time progressing to the right. Like the horizontal bar chart, each vertical column must extend all the way to zero or it will lose its meaning. You would not be able to appreciate the height of a stack of stuff if you were only allowed to see its top.

  Suppose the money received by a man in trade were all in guineas, and that every evening he made a single pile of all the guineas received during the day, each pile would represent a day … so that by this plain operation, time, proportion, and amount, would all be physically combined.

  WILLIAM PLAYFAIR, 1786

  As long as visual comparisons are of the more-or-less variety (e.g., 18 versus 13), not the multiplicative x-times more (e.g., 18 versus 1), we are pretty good at reading linear comparisons for what they are. A pair of bars, one longer than the other, whose lengths are encoded with values, one larger than the other, has a good shot at being decoded by the reader accurately.

  Jacques Barbeu-Dubourg's 1753 Chronographique was an annotated timeline of history on a 54-foot continuous scroll, including names and descriptive events, grouped thematically, with symbols denoting character and profession. Howard Wainer described that Barbeu-Dubourg “believed that by wedding the methods of geography to the data of chronology he could make the latter as accessible as the former.”

  Both horizontal and vertical bar charts encode numeric magnitude with length, a one-dimensional size encoding. But bars and columns must be drawn in two dimensions so that they can be seen. So, the bar widths are held constant, only their lengths change. Sizing only one dimension requires that the encoded-value be one of the two positional axes, even when we work in polar coordinates.

  Using only a single dimension to convey importance is not always satisfactory because it constrains design. We can layer more data into our story with other methods. It is time to reach for more.

  Area of Influence

  The 1-D length of lines, bars, and columns can be exchanged for the 2-D area of shapes. This can be an appealing trade. Shapes are often better fits for design because shapes have a more even aspect ratio. Circles and squares are more compact than long lines. Shapes are also more freely scattered about the page. Unlike a bar chart, shapes do not have to be anchored to any position baseline. Compactness and freedom combine to allow more information to be packed into a design. Shapes spread around can layer more meaning onto a canvas. For example, the geographic map of Columbia County at left locates cities while circle size tells you how many people lived in each one in 2010. Two axes, x-y or longitude-latitude, encode position while sized marks add a third dimension of meaning.

  Mere 1-D length, compared to 2-D area, also misses an opportunity to reflect the dimensionality of the real world. A list of numbers is one-dimensional, but its associated units often allude to something more in the real world. The area of a plot of land, a single number, is seen in our head as a two-dimensional field. The weight of an animal, also a single number, comes from the amount of matter the animal has, something we experience in the real world as a complex 3-D shape. Money is an abstract idea. It is best compared in the single dimension of the bar chart. But in real life, money can be seen as the 1-D height of a stack of bills, 2-D area of a sheet of bills that just rolled-off a mint's printing press, or 3-D volume of a pallet of currency waiting to be robbed from a bank vault in a Hollywood heist film.

  We use 2-D size to layer more meaning into a data story and reflect the physicality of the real world. To gain these benefits we must consider the total graphic design. We do not encode in isolation, but across an entire graphic composition. How do we expect the reader to decode meaning from size?

  Small dots indicate points in space, even though points actually have no form at all. Points on the 2-D plane exist where two lines intersect. By themselves, points have no area. They have only positions. But if we want to see points in space, we have to mark them somehow. Just as we gave 1-D bars a constant width so we could see their length, we need to mark points. A small dot does the trick.

  [Euclid] gave his famous definition of a point: “A point is that which has no parts, or which has no magnitude.” … Euclid's notion of a point only becomes clear when one reads beyond the definition and sees how points are related to lines and planes and circles and spheres. A point has no existence by itself.

  FREEMAN J. DYSON, 1988

  All locations around a circle's edge are equally far away from the center point. Unlike other shapes, the circle has no orientation. It has no sharp corners. There is nothing distracting about the circle. We like circles because they are almost formless.

  To help layer more data onto each point position, it is natural to enlarge each dot to represent a value. Bigger circles attract more attention, so they must be more important. It is considered best practice to encode the data value in the circle by sizing its area, not its diameter. Our eye sees all of the 2-D circle's pixels, not just the pixels across its 1-D diameter. So we relate each of the circle's pixels, its entire area, to the data value. This creates a power relationship between a set of data values and the radius (r) of their associated circles because the area of a circle equals πr2.

  Unfortunately, even with the recommended encoding of area, it turns out that we are not particularly skilled at decoding quantitative values from circle areas. Circles engulf many pixels in increasingly larger rings that get added on to represent higher and higher values. It is easy to underestimate a circle's area that is storing a relatively large value. For example, each ring depicted here has the same area as the inner circle. See how quickly they thin. Imperfect decoding of circle area makes us aware of area encoding limitations. Do not encumber your reader with the task of discerning precise values from circle areas. Instead, use circles when they can enhance a design by enabling rough comparisons. To convey precise values, augment circle area encoding by directly labeling them with the encoded value.

  If two-dimensional area is problematic, decoding values from three-dimensional volumes is impossible. Spheres and cubes are no good on 2-D screens and sheets of paper. Too much of any volume just cannot be seen at any single time. Each vantage hides more than it shows. For example, how could we even begin to know how much more volume is packed into the larger of these two spheres?

  The argument against encoding data in volumes goes on. Surprisingly, we do not actually see 3-D. Every instance of sight is 2-D and, quickly over time, we build 3-D models of the world in our mind. Most of what lets us build our mental model of the world is missing from the 2-D page. The page lacks natural depth cues such as lighting, shadows, and nearby familiar objects, which we use for size comparison. Stereoscopic two-eye perspective and the different views we get by moving through the environment are also real-world aids missing from our experience of the 2-D page. In the real world we can concentrate our eyes on objects near and far and learn about their distance as they come in and out of focus. It is impossible to replicate these non-pictorial experiential cues on the canvas.

  Finally, recall that a column of data values is one-dimensional, no matter wha
t real world physical thing it represents. We may stretch this 1-D data into a 2-D area, but extending a single value into 3-D is a dimension too far. Did you guess that the larger sphere has triple the volume of the smaller? No chart is more easily mocked than a 3-D chart. Not only does it make data decoding ugly, but critics will always be able to snicker that 1-D data could have been more easily and more accurately presented in a 1-D bar chart. Do not wade into 3-D representation of numbers unless you are prepared to mount a strong defense.

  Imagine you were being chased through a hedge maze by a psychotic axewielding maniac. Wouldn't it be nice to have a 2-D overhead view to complement your rich multidimensional experience?

  The circle is an amiable introduction to why encoding data with size is troublesome, and why 3-D shapes are best to avoid. With each dimension added to form, the visual impact of the data becomes compressed. Below is one more comparison between dimensions. The gist of both the 1-D bar chart and 2-D area plot is created by grouping the same set of marks into different forms. See how rearranging the same parts into different wholes changes the nature of the comparisons made.

  Most of us must undertake a mental exercise to relate a given figure of density to a meaningful experiential context.

  ALBERT BIDERMAN, 1963

  Assembling smaller shapes into bigger patterns can enable a variety of multi-layered data storytelling. By showing all the parts that make the whole, you reveal something more about its makeup. By creating an array of marks, you also have a set of miniature canvases on which you can encode even more data detail.

  The 1-D linear comparison of the stacked bar chart puts the difference between the total values at center stage. On the one hand, the 2-D packed circle comparison can only help us see that one group is bigger than the other, but leaves us guessing by how much. On the other hand, packed circles are ready to be positioned wherever we want, while bars should remain anchored to the same baseline. Trade-offs in size encoding abound. The ability to make precise comparisons must be evaluated against everything else the design needs.

  CHAPTER

  7

  TRUE COLORS

  Man lives with what he sees, but he only sees what he wants to see. Try different types of people in the midst of any landscape. A philosopher will only vaguely see phenomena; a geologist, crystallized, confused, ruined and pulverized epochs; a soldier, opportunities and obstacles … They all experience a certain arrangement of colors; but each one immediately transforms them into symbols.…

  PAUL VALÉRY, 1871–1945

  The Grey

  Eyespots are tiny light sensors. They help single-cell organisms like green algae get into position for optimal photosynthesis. Primitive biology is able to detect the intensity of light, and we can still accomplish a lot by swimming between black and white. Today, the human eye has millions of photoreceptor cells called rods. Like their eyespot forerunners, rods sense lightness. Concentrated on the periphery of the back of our eye, they have little to do with our modern color vision.

  Light detection generally begins with the absorption of a photon, which causes the electron of a molecule to attain a higher, and unstable, energy level. Return from this higher energy level begins a cascading chain of electron transfers.

  Alone at night in the woods, listen for clues about what nocturnal predator might be staring at you. The fear of being prey is manifest by darkness. The original experiential duality is symbolized by the Chinese yin and yang, literally dark and light. Our oldest visual archetype is rooted in life's daily journey. Through the mysterious night, into the revelation of the sun, and then back into night. Metaphoric light is the antidote to darkness because it lets you see what is going on. With light, real predators are detected, and imagined predators vanish. The sun's warming rays are the source of energy for life on Earth. No wonder so many ancient religions worshipped the sun. No wonder so much symbolic light shines throughout religious texts.

  Eyespots to eyeballs:

  A layer of retina cells

  recessed into a cavity with a pinhole opening to allow directional sensitivity. A transparent lid covered this hole to filter light and keep out parasitic invaders.

  The cornea split in two. The inner layer became a lens that could be manipulated by tiny muscles to better focus light.

  The archetypal colors, black and white, can distinguish two groups. But we can also segment them into shades of grey to do even more. This is like increasing how many flashlights shine against a white wall in a dark room, increasing the ratio of white to black in a paint mixture, or increasing the number of pinholes in a screen. Black has a lightness of 0 percent and white has a lightness of 100 percent. The continuous spectrum between black and white can be keyed to a single dimension of data by stretching a set of greys across a number line. As with area, easily encoded numbers are not always easily decoded. The way we make sense of different lightness is mostly relative. When we compare two shades, we can discern that one is darker than the other, but only if they are located near one another. Too much distance removes too much context, and distorts the comparison.

  The contrast ratio between foreground and background can be calculated to avoid reducing readability. The ratio compares the relative luminance value for each color, with darkest black = 0 and lightest white = 1

  Qualitative palettes identify named categorical groups.

  Sequential spectrums highlight values at one extreme with a “more ink for more numbers” metaphor.

  Diverging palettes highlight values at both extremes, a pair of sequential spectrums.

  The background color behind the encoded lightness spectrum matters a lot. The background determines contrast and gives context. Data values of higher interest, usually higher magnitudes, should be more salient. They receive higher contrast. Alternatively, both high and low extremes may deserve attention. Then, greys can appear to diverge by choosing a background with an average lightness. Now, middle values will have the lowest contrast and shrink from notice. Today, digital screens have removed the printing constraints that made full color expensive. Greyscale is a stylistic choice. Still, the minimalism of black and white helps focus design. It avoids the busyness and distraction that the freedom of the full color palette can introduce.

  Greyscale allows us to isolate a single dimension of color, lightness, to see how to relate data and color. Quantitative values can be mapped to color spectrums. Background and nearby context is essential to appearance. We must be intentional in how we design sequential and diverging palettes. But who wants to live in austere, desaturated minimalism all the time? And working with color's other dimensions can help us increase the total number of discernible categories. These grey-scale lessons can accompany us as we step out of the proverbial blackand-white Kansas farmhouse and into the wonderful world of color.

  The sequence from dark to light is lightness. Brightness soecufically refers to the absolute brightness of a light source. In color theory, measured position along the black-to-white spectrum may be referred to as intensity (light power) or luminance (intensity relative to the eye's spectral response). Tone mapping helps keep lightness consistent across different formats. In the HSV color model, value characterizes a range for each hue from black to most-saturated. The simplest value scale is greyscale. Tint lightens and desaturates by mixing with white. Shade darkens and greys by mixing with black.

  Species of Wheels

  The world is full of colors that convey categorical, or qualitative, meaning. Some, like the stop-go palette of a trafic light, are more universal than others, like the uniform colors of two competing football teams. A handful of very different colors can convey category groups. They must be very different because the goal of a qualitative palette is to make categories visually distinct from each other. The color wheel sweeps through color hues. Or, perhaps it is better to say a color wheel. You see, connecting the world of color to only a single model is like connecting the globe to only a single map projection. Many color models exist for di
fferent purposes, for different technology, and from across the history of always-progressing color science.

  Primates, including humans, are pretty good at seeing color. The popular theory why is that our color vision evolved to help us pick out colorful ripe fruit from surrounding foliage. Predators, like cats, do not need color vision to catch their prey. Grazers, like cows, do not need color vision to keep eating grass.

  Birds, who need vision to fly, exceed our vision capabilities in many ways. Across avians we find three eyelids, binocular vision, nocturnal vision, oil droplets for haze, large relative eye size, asymmetric focus between eyes, a second fovea for sideways viewing, and UV-sensitivity.