by R J Andrews
The polar and rectangular mental maps we already use to explore the physical world are repurposed to explore all kinds of data. Cartesian and polar coordinates are easy. They are easy to understand, and easy to implement. They ask you to simply snap data variable to axis, then sit back and relax as data pop into place. And that is wonderful, but it is also only a partial conception of how we can position data. What if these ready-made systems are not the best visual home for your data?
You Can Relate
We carry around a lot of experiential knowledge in our heads. Some of it is spatial. Our ability to traverse places that are familiar is naturally stored on a mental map. But onboard geographic knowledge is not what makes people special. Other animals, some with built-in magnetic systems, are superior wayfinders. Eels, shorebirds, bats, and even ants, all navigate staggeringly immense journeys.
What is truly special about humans is our ability to absorb, store, and transmit information that has little to do with geography. We are obsessed with invisible abstraction, long historical arcs of power, personal and professional relationships, and emotions whose essence escapes numerical capture. The abstract worlds we inhabit are what make people marvelous. Must we ground abstract information in maps that stem from the geographic world? Both Cartesian and polar systems help creators and readers, but perhaps there is a better way to show invisible worlds. What other microcosms might surpass these encoding systems?
Vertical power relationships have persisted through thousands of years of history. From Egyptian pharaohs to the medieval church to today's CEO, humans understand that power is stacked. Today, our conception of hierarchy is divorced from lived physical reality. Yet, we can still see vertical power's origin with a vision of a predator above its kill. The powerful are on top. This visual metaphor shapes how we imagine the power dynamics of society. Vertical power encoding logic is on display in the design of the org chart.
Information always invites us to realize it into better forms. It does not always map well to any standard linear or circular diagram. Perhaps your mind pictures it in a different way, just as the corporation is reflected in the tapered shape of the pyramid. Take a moment to pause and engage with your mind's eye. How does my mind already picture this information? If I were to pencil a sketch of what my mind already sees, what would it look like?
Data that does not map to familiar spatial encodings often have something to do with relationships. Relationships are documented by their nodes and whether these nodes link to one another. Then, qualities about the nodes and relationships can be added. Node-link network graphs reflect this particular data structure well. But like a table of text, these graphs often come up short showing anything of interest.
Too many network graphs are burdened with too many connections. A network hairball only reveals that the network has many connections. Respect the limits of display density. Then, network graphs may help discover groups, connecting paths, and associated nodes.
Network positions are fluid. If you remake a network graph, then its nodes may appear in a new location, as long as the same relationships are preserved. This is different from the geographic map, where the same city will always appear at the same latitude and longitude. For example, consider the chemical bonds of the caffeine molecule (C8H10N4O2). The entire molecular network can be rotated because the relationship links are still maintained. You may never see the same network the same way twice. Caffeine is still caffeine, wherever the nodes get drawn.
Topology comprises geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.
This freedom of positioning can be problematic. We yearn to catalog, categorize, and fix things in space. Recall how we extend existing familiar concepts to learn new knowledge. If we recognize something new as belonging to an existing category, then we can project our existing category knowledge to the new thing. Consistent positioning gives us something familiar to compare new things against. Unreliable, always-changing network positions take away the opportunity for a spatial baseline reference. Changing positions reduces our ability to visually compare the new to the familiar. The spatial freedom of network graphs also runs against how our mind actually pictures relationships. The mind may not see networks as tied to any geography, or even a numeric scheme. The mind may also not be able to picture many relationships at once. But, the mind's way of thinking about relationships often has some kind of meaningful order. You do not change the cubbyholes mentally reserved for your high school friends with those reserved for your family members. You anchor classes of relationships according to some kind of schema. Just as power relationships were likened to physical domination that put the subjugated below the powerful, conceptual rules can be unearthed to help position network graphs. Positional logic boosts context and helps keep design consistent for later reference. The chaos of the ever-morphing network graph can be tamed if we build it a more meaningful world.
A testament to our fondness for spatial information, the memory palace technique, also called method of loci, helped ancient orators deliver long speeches from memory by associating conceptual chunks with objects located in an imaginary architectural space.
Our first set of visual metaphors traces an evolution of human cognition: outward facing polar diagrams, geographic maps, time-lines, number lines, and the spatial freedom of network graphs. They all began with how we understand our own physical reality and then advanced toward abstract visions of invisible worlds.
One idea, say Playfair invented the bar chart, might be associated with an imaginary deck of cards placed on an imaginary table in the middle of the imaginary entrance hall. Chunks can be retrieved as needed by mentally “walking” through the space and recognizing objects. Sometimes, these spaces reflected real places already familiar to orators. Often, they were constructed (and expanded with additions) to perfectly accommodate memories.
We have introduced these different positioning schema one by one. But they need not be isolated in practice. They are at the ready for you to smash together into new spatial schema. It is up to you to craft the most effective virtual world for your data to inhabit and your audience to explore.
The used-future world of Star Wars helps create the magic, but it is not the main event.
We are now more familiar with how our physical reality is linked to different conceptual frames, especially how we think about numbers. We have a sense that these perspectives can help us build better worlds for data. Better worlds fit how we already think about things so that it is easier to learn something new. But world building is not the endgame. We build worlds so that we have a place to layer meaning. We build worlds so that we can see data.
CHAPTER
6
INFUSE MEANING
That was an instance of the charts meaning something for everyone, that they excluded nobody, that they allowed several layers of understanding.
MARIE NEURATH, 1898–1986
How do we convey meaning inside visual worlds? Well, there is a universe of possibility to consider. Position, so crucial to world building, is also one of the strongest conduits of meaning. It is joined by many other factors, such as color and size, to provide a multifaceted creative toolbox for linking visual cues to nonvisual concepts.
The canvas, printed page or digital screen, gives us only two dimensions to play with. Each dimension comes with a significant amount of baggage. Some ubiquitous visual metaphors, such as time goes to the right and good goes up, are natural to even data-illiterate audiences. They pack meaning into the Cartesian grid before we even get a chance to do anything with it. Once we know these biases, we can incorporate them into our design to ease audience's reading.
Upwards
The direction of up is usually relative to gravity's downward pull. Our upright posture was critical to our ability to scan the horizon, become the greatest endurance runners on the planet, and free hands for other tasks. Higher altitudes evoke the positivity of the mythological t
ree home, whose axis stretches against gravity, from downtrodden animalistic roots up to angelic heavens.
The vertical dimension has been associated with emotionally reading a person's body language, looking someone up and down. The horizontal dimension, associated with scanning the horizon, has been associated with the focus of the hunt.
Today, we live in a rectangular world. Buildings rise perpendicular to the horizon. They help tune our senses to detect even small deviations from a perfectly vertical line. Upright orientation has also impacted how we think about a myriad of abstract concepts. When we are happy we actually stand taller, things look up, and our spirits soar. When sad, we slouch, feel depressed, and our spirits sink. Consider these other vertically oriented dualities of good and bad:
HEALTH MORE VIRTUE RATIONAL PRESTIGE CONTROL
Peak health.
Income went up.
Upright morals.
High-minded
Lofty position.
Control over.
Top shape.
Prices soared.
High standards.
intellectual.
Rise to the top.
Height of power.
Fell ill.
Stocks fell.
Beneath me.
Rise above your
Fell in status.
Low man on the
Dropped dead.
Turn heat down.
Low-down.
emotions.
Bottom of ladder.
totem pole.
SICKNESS
LESS
DEPRAVITY
EMOTIONAL
TRIVIAL
SUBJECTED
In 1980, linguist-philosophers George Lakoff and Mark Johnson introduced these and many other primary concepts in Metaphors We Live By. It revealed how our own spatialization helps us make sense of abstract and invisible worlds. Topside positive connotation is nearly universal across a spectrum of social categories. For data stories, the top of any visual canvas naturally communicates positive emotion.
Piling more deaths downward invokes the down is bad conceptual metaphor.
On the one hand, the vertical y-axis is traditionally associated with the dependent variable. This means the vertical dimension is where a lot of the excitement happens. The horizontal x-axis, on the other hand, is the independent workhorse of the story. It keeps steady time like a metronome while the response gets to go up and down on the vertical y-axis. Both directions are critical to data stories.
We can choose to design against spatial biases in pursuit of more novel storytelling. But this may increase the risk of confusing the message. Creative experiments are laudable, but only when we recognize the responsibility that comes with going against conventions. They may need compelling design and added explanation to be successful. Deploy planar axes judiciously. You only get two and they each wield enormous power.
Onward
The horizontal x-axis is associated with time, just as metaphoric linear time stretches over the horizon. The x-axis is called independent because it often holds values that are not affected by circumstance. Independent values are self-governing. The x-axis often represents the regular frequency of data collection. We record the high temperature every single day, no matter how hot or cold it is. As the timeline introduction stated, we attribute the direction of time to how we read and write. We usually proceed through time to the right. Its vertical flow can go up or down. Western future is rarely on the left.
The principles:
Smooth, flat, horizontal shapes give us a sense of stability and calm. I associate horizontal shapes with the surface of the earth or the horizon line… We humans are most stable when we are horizontal, because we can't fall down. Shapes that lie horizontal look secure because they won't fall on us, either.
Vertical shapes are more exciting and more active. Vertical shapes rebel against the earth's gravity. They imply energy and a reaching toward heights or the heavens… These structures require a great deal of energy to build—to become vertical. They will release a great deal of energy if they fall. Vertical structures are monuments to kinetic energy of the past and the future, and to potential energy of the present.
MOLLY BANG, 2000
The archetypal display of time is the x-axis time-series chart. It tracks a value as it fluctuates up and down through time. There is a practical limit to how quickly data is sampled. We do not actually measure anything continuously. Smaller divisions of time can always be measured. So we choose a data-collection frequency that is precise enough. Showing a phenomenon with a continuous line mirrors our own uninterrupted experience of time, even though we record actual data at discrete moments. We see time-series data as an uninterrupted flow that proceeds to the right, just as we imagine the adventures of a storybook hero like Alice, whose journey progresses to the right as we turn the pages. Time-series charts consider the data's temporal density, value variability, and completeness. We must match the qualities of our data to the way we already perceive time. Visualization expert William Cleveland categorized ways of showing time by how each helps better show the data:
This data shows a measure of the disturbance level of the Earth's magnetic field. Learn its backstory in the endnotes.
Another way to achieve continuous flow is to use a summary curve. They are generally constructed with some type of moving average. In this way, they differ from a mathematical trend, which uses a formula to fit a single straight line to the data. A smoothing summary curve may benefit data that is too noisy. However, not showing the noise of all the data points can suggest a cleaner story than is actually there. Also, be careful that the summary line does not conceal significant gaps in the data. If you connect sparse points you might suggest more data than is actually available. It is better to leave gaps empty or straddle them with a dashed line.
The dashed line gives us a way to express the idea that something is not concrete. Something impermanent. It may be temporary; it may not currently exist (it will in the future or it did in the past); or it may be invisible or hidden. One way or the other, it represents what it is—not solid.
CONNIE MALAMED, 2012
Even seemingly simple line charts can confuse or, in very poor designs, lead to faulty decoding. Data journalist Dona Wong advocates that axis scales should be segmented into the familiar multiples people already use when thinking about numbers. We often count in fives or tens, but elections sometimes come in four-year cycles. Time should be in days, weeks, months, or years. Line charts 60 do not need to have a baseline at zero, but their baseline 20 should not confuse. Extend axes to zero rather than stopping at a baseline that is close to zero. A zero baseline may be emphasized as heavier, a non-zero baseline should have the same weight as other grid lines.
Ratio scales… have a meaningful zero point. Weight, height, speed, and so on, are examples of ratio variables. If one car is traveling at 100 mph and another one is at 50, you can say that the first one is going 50 miles faster than the second, and you can also say that it's going twice as fast.
ALBERTO CAIRO, 2016
100°F is not twice as hot as 50°F because temperature zero points are arbitrary. 0°F was originally keyed to the temperature of brine by the inventor of the first modern thermometer, Daniel Gabriel Fahrenheit.
Sizing Up
We already had a glimpse of the power of size. Recall that big things are important because a bigger object takes up more of your visual field. Bigger things demand notice. When objects are collected into groups, the largest group commands more attention. A taller pile of things has more things in it. More products, more land, more people, more money, and even more time: We can convey all flavors of more with larger size.
The International System Of Typographic Picture Education, or Isotype, is a method of pictorial statistics developed by Otto and Marie Neurath. It used a single symbol to represent a fixed quantity. Greater quantities are shown by the repetition of that symbol, rather than scaling the size of a si
ngle symbol.
The basic metaphorical linkage between physical size and numeric magnitude seems easy enough. However, the way you actually make shapes bigger with data in order to show more is trickier than meets the eye. We are pretty good at decoding linear position along the number line; four looks twice as far from zero as two does. However, decoding the same numbers in two dimensions, with sized areas, is fraught with pitfalls.
When we encode values in spatial dimensions, we must admit and reconcile the dimensionality of our data. A single column of number values is one-dimensional, no matter what the data is a measurement of in the real world. If our only task is to show values, then we can locate each one on the one-dimensional number line and call it quits. Points on a line are, of course, just positions. Each point has the same size, no matter how large the value it represents. Mere position misses the opportunity to distinguish values using the visual weight of more ink, or more pixels. Harness the visual importance of size by connecting each point back to its baseline. Now, value is also represented by length. If we increase the connector's thickness, then we increase the visual impact of each value's length. The steadfast bar chart appears. Voila.
In order for each bar length to encode the value it represents, it must encompass the entirety of the value, all the way from zero. Truncate a bar with a non-zero baseline and its size ceases to have meaning. It is perfectly fine to leave the data as points if you want to focus on a narrow range of positions, but, once you introduce the physicality of length, you have to show it all. Otherwise, the length is worse than meaningless; it is misleading.