by R J Andrews
Like a train running down its tracks clickety-clack clickety-clack the minutia of moment-to-moment experience feels like one long sequence. But what if the train track runs in a big circle? Consider any span of life and you notice recurring phenomena. A new sunrise every day. A new moon every month. A new harvest every year. Of course, we know now that all these natural cycles are created by incomprehensibly large circles in space. We perceive cycles because Earth rotates and revolves.
Right-handedness influences the direction of text. Chiseled letters, hammered by the dominant right hand, were naturally inscribed right to left. This method left a lasting mark on ancient right-left written languages such as Hebrew. Ink's invention necessitated a switch so that the pen-holding right hand did not smudge wet ink.
As hunter-gatherers, our lives revolved around the cycles of birth, life, and death. At night we looked to the stars and tracked their progression. The agricultural revolution extended our understanding of time—time is a circle—to the lives of crops and livestock. An early agriculturist's experience was not that different from the life of their parents. Unlike the last few hundred years of history, there was little discernible change between generations. All noticeable changes came from natural cycles. The health of the community depended on our ability to manage these cycles. Every spring, the rebirth of crops and new baby animals strengthened communities. If you master the circle of time, then you can rule your world.
In [South American] Aymaran culture, the past is ahead because it is already known and can therefore be seen. The future, in contrast, is unknown and can’t be seen; therefore, it is located behind the speaker.
JAMES GEARY, 2011
Today, we can splice linear and circular time together by imagining a spiral. Its coils capture the essence of moving around in a circle and moving forward along a line. Like a Babylonian ziggurat, the tower spirals around as it climbs. Unfortunately, showing a Slinky-spiral form in static 2-D does not convey the visual metaphor well. Even rotating a spiral on screen somehow is not the same as rotating it in our heads. Abstracting a spiral to zig-zag lines or a sinusoidal curve may be a good compromise if we can bear over-emphasized turning points.
[Australian Aboriginal] Pormpuraawans arrange time according to cardinal directions: east to west. That is, time flows from left to right when one is facing south, from right to left when one is facing north, toward the body when one is facing east, and away from the body when one is facing west.
BORODITSKY AND GABY, 2010
A different visual metaphor for time highlights individual spans of time. It minimizes the continuity stressed by the timeline and time cycle. More and more, we appreciate the idiom that time is money. Today we spend, invest, and budget our time. We are careful how we use it because we only have so much and it will eventually run out. Time is a thing you give, lose, and expect to be thanked for.
Henry Gantt developed a waterfall method in the 1910s to manage schedules. The Gantt chart was refined through its use in WWI to coordinate production for American armed forces. Polish researcher Karol Adamiecki had already invented a similar method in the 1890s, called the harmonograf.
Time as valuable currency revives the first metaphor of this chapter. Time as money, like other objects, gets counted. In today's world, our digital calendars help schedule time in minute increments. It is as if we each manage our time like Ebenezer Scrooge manages the coins in his counting house, carefully dolling out every twelfth of an hour.
Today, the work of chemist and Nobel laureate Ilya Prigogine can help us think of time in yet one more way, an irreversible performance. The whole universe is a stage, and all matter are its actors. The actors move about the stage with energy and the play unfolds with their unpredictable interaction. We could never give all of them, all of the matter in the universe, perfect directions for how to return to exactly where they were at the start. That would require an impossible amount of precision. As complexity expert César Hidalgo summarized, “There is no past, although there was a past. In our universe, there is no past, and no future, but only a present that is being calculated at every instant.”
What is the world? What is reality? In the end reality is just a flow of data. Physics, biology, economics, it's all just a flow of data.
YUVAL NOAH HARARI, 2017
CHAPTER
5
WORLD BUILDING
The Grid, a digital frontier. I tried to picture clusters of information as they moved through the computer. What do they look like? Ships, motorcycles? Were the circuits like freeways? I kept dreaming of a world I thought I'd never see. And then, one day… I got in.
KEVIN FLYNN, TRON: LEGACY
To see data, we must build a visual world for it to inhabit. The metaphors we use to count objects, measure distance, and experience time are the foundations for building these worlds. To choose the rules of these worlds is to choose how data gets spatially encoded. Further design decisions flow once we position data.
Spatial Diagrams
Think of the number line as a virtual world. Compared to the one we inhabit, it is rather simple. Yet, the number line is a self-contained world. It has order, rules, and constraints. Like a tabletop aquarium, any number line is a product of, and exists within, our world. Both the number line and fish tank are also distinct domains we get to play in. When we invoke visual metaphors to visualize data, it is like we are imagining an aquarium for the data to swim in. How big should it be? What does its terrain look like? Will the data look interesting in this world?
One might say that the world is hardly more ancient than the art of making the world.
PAUL VALÉRY, 1871–1945
Numbered worlds were most whimsically related by schoolmaster Edwin Abbott in 1884. In his Lineland, points move back and forth, unable to imagine the higher-dimensional world of geometric shapes. Shapes exist on a plane called Flatland. There, number lines cross to form a two-dimensional grid. Flatland is inhabited by triangles, circles and the square protagonist (named A. Square). These flat characters struggle to comprehend the three-dimensional Spaceland of spheres and cubes.
Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows.…
EDWIN ABBOTT, 1884
In Unflattening, comics educator Nick Sousanis uses Abbott's Flatland to show how dimensional extension can elevate us above the confines of limited perspectives:
World building is essential to any storytelling adventure. When I recall my favorite childhood stories I am transported to Alice's Wonderland, Dorothy's Oz, or Wendy's Neverland. These stories have relatively simple plots. Find your way home. Get the prize. Defeat the villain. The light narrative burden clears plenty of room for complex, colorful, and compelling world building.
Like Abbott's spheres and cubes, we too inhabit a Spaceland. Our original look at the world is with our own eyes. They give a thoroughly unique perspective. From our self-centered vantage point, we perceive direction and distance relative to our body. Things are to the right or left of me, below or above me, close to or distant from me.
What do we make of our contemporary interactive maps' post-Copernican, egocentric orientation, which places you—not the earth, not the sun, not Jerusalem or Mecca—at the center? What happens when we hold in our hands manipulable maps that render space as something seamlessly traversable, rational, and exploitable?
SHANNON MATTERN, 2015
Even though we are vertically oriented creatures, our motion is often abstracted to a flat, 2-D plane. We live in a world represented by the marriage of two number lines: forward-back and left-right. Most of our spaces are flat because it takes a lot of energy to raise our bodies against the force of gravity. The vertical dimension is only seriously considered during specific activities. We think about going up and down when we scale a hill
, ride an elevator, or climb to cruising altitude. Despite our higher dimensionality, we frequently think about our own physical reality as a kind of Flatland.
Imagine walking across the neighborhood to dinner. Part of your mental vision might include some kind of avatar moving about an overhead map. Mobile web maps reinforce this view. They dynamically reposition the entire virtual Earth so that you stay at the center of the screen. You are the star of the show. This out-of-body perspective fuses our personal vantage point with a more objective frame of reference.
The crowning achievement of memory is the model of the world we carry in our heads, a kind of diorama that closely resembles reality and allows us to respond to events in real time … we are all born cartographers who draw mental maps.…
ABBY SMITH RUMSEY, 2016
A map represents on a flat surface, especially geographic features, from Latin word mappa which originally meant table napkin.
The front-back-left-right perspective is meaningful only to the unique viewer. In contrast, a north-south-east-west grid is useful to anyone who traverses its plane. Latitude and longitude's objectivity transports our personal experience from relativity to the 2-D virtual world. In either case, how we think about our multidimensional world is not so multidimensional after all.
The first maps and global directionality were of celestial bodies, not land features.
The geographic map is populated with a variety of simple marks. Points, lines, and shapes represent roads, buildings, land, vehicles, and you. Each flat map is a projection of the globe designed for a particular use case. Each map projection is a tool designed for a specific purpose. All map projections are distorted because they warp the surface of Earth's oblate spheroid to lie flat on a map's 2-D plane. Projections straddle trade-offs between area, shape, direction, bearing, distance, and scale.
There are appropriate and inappropriate map projection choices. It all depends on what part of Earth you want to show, and for what purpose. However projected, physical geography is reduced to Flatland's two-dimensions. Map grids are created by crossing two axes, two distance-number lines. They elegantly mirror our embodied conception of the world around us.
René Descartes advanced his ideas about analytic geometry, algebra to describe shapes, using only a single axis. Others, like Frans van Schooten, were responsible for pushing the Cartesian approach into additional dimensions, giving us the paired-axis Cartesian plane.
The perpendicular distance-number lines of longitude and latitude mimic the physical world and connect physical geography to the Cartesian plane. The geographic map is a gateway to exploring an endless variety of 2-D virtual worlds. Replace the longitude-latitude axes with other dimensions, such as time and performance, and the same grid can be used to explore more abstract territories. A familiar grid variant places time on the horizontal axis. This abstract grid shows us what would be difficult to appreciate otherwise. It lets us see how a value, like population, changes over the years in a way impossible without a picture. All grids are virtual worlds we interpret and navigate.
A mapping is a correspondence. It associates each element of a given set with one element of a second set
When you define the horizontal (x) and vertical (y) axes of a 2-D plane, you are world-building. Virtual environments are invoked so data can be positioned. Just as map roads and buildings demand a virtual geography, all data must have a spatial home if they are to be seen. It is like set-design for play actors. The show cannot go on without a stage. Some of these environments, like the stock market price (y) over time (x), are quite familiar. Other worlds require careful introduction. Most of these virtual worlds will build somehow on our familiarity with the number line and its conceptual extension, the timeline.
Descartes cemented the convention of using the beginning of the alphabet (abc) for known constants and the end (xyz) for unknown variables. It has been speculated that x is the most prominent variable in Descartes's La Géométrie (1637) because it is the least commonly used letter. Terry Moore argued that x is the result of Spanish scholars using the Greek (Chi) as a phonetic stand-in for the sh sound of the Arabic word (al-shalan), which means “the unknown thing.”
Like 2-D web maps, data worlds are not reality. They are useful virtual models of reality. It is easy to lose yourself in these virtual worlds, but we have not yet been completely consumed by them. We still look toward the horizon and picture what is on the other side of the next hill.
Ancient Romans adopted Greek orthogonal city grids. The Cardo Maximus was the main north-south street in the city; it was full of shops and considered the axis, or hinge (cardo), of the city. Today, we still call the north-south-east-west directional hinges the cardinal directions.
Off the Grid
Rectangular maps and charts are everywhere. Yet, Cartesian x-y axes are only one way to build worlds for data. Polar coordinates put the focus of the world on a central axis, or pole, and extend vectors away from that anchor. The polar world has two dimensions, just like its squBre cousin. But their meaning is asymmetrical compared to the rectangular grid. Cartesian axes are balanced in rectangular harmony.
Polar coordinates' nested circles and radiating rays are not so interchangeable. They strike a different kind of perpendicularity. Each polar axis has a differentiated ability to convey information.
Vectors are perfectly shown with the angle-magnitude dimensions of polar coordinates, but these axes can do even more. Polar charts reflect basic ways we perceive the world. They channel an outlook from a definite perspective and they reflect our cyclical appreciation of time. Furthermore, polar charts often have a compact form factor, which makes them easy additions to many graphic compositions.
Clocks runs clockwise because they mimic the directional path of a sundial's shadow in the northern hemisphere.
The pie chart shows part-to-whole ratios. It works well for a few categories. Our mind's eye contrasts pie chart divisions against invisible 25, 50, and 75 percent portions of the circle. These reference points are reinforced by our familiarity with clock faces. Pie charts are criticized for their inability to display comparisons effectively. Indeed, they are not capable of comparing too many divisions. All things being equal, data is usually better displayed with a bar chart, but things are often not equal.
Pie chart slices are conventionally ordered by size, with the biggest starting at the top 12:00 position and proceeding clockwise until the smallest piece ends back at 11:59. An alternate ordering also places the largest slice clockwise from 12:00, but the second largest slice counterclockwise from 12:00, giving both a chance to be compared against the invisible horizontal reference line that runs from 9:00 to 3:00.
Pie charts continue to perform on thematic maps. There, they serve triple duty. First, they encode position as marks on a greater reference plane; second, they encode magnitude with circle area size, and, third, they encode a simple ratio with the angular division of the pie. Polar coordinates make virtual a worldview that appreciates distance from the center. The tribal, and polarizing, us-versus-them attitude reflects a past reality where we did not yet have a global sense of geography. In some ways, the self-centeredness of polar coordinates is more natural. We stand upright at the center of our own personal world and turn about to look out at what is near and far. In the evolutionary extreme, polar coordinates hurtle us right back to a life jumping through the branches around the trunk of our home tree. Imagine an evolutionary ancestor's mental map of the world. The world is anchored to the safety of the tree. Distance is tracked from the tree. Direction is mapped around the tree, perhaps anchored by the position of the warming sun. The world extends cylindrically from the forest floor to the heavenly sky.
To look is a territorial activity.
JAMES P. CARSE, 1986
Much later, we lived in walled cities. The physical boundary protected the community from the dangers of wild animals and ravagers of the outside world. The early city, or polis, was safety. Its center was sacred, and often m
arked with a temple altar or vertical obelisk. For its inhabitants, their city was the center of their world. Unlike the ancient tree-jumpers, early city-dwellers were already losing interest in the vertical dimension. Our love of polar coordinates is more deeply rooted than we can imagine.
None of these things exist outside the stories that people invent and tell one another. There are no gods in the universe, no nations, no money, no human rights, no laws, and no justice outside the common imagination of human beings.
YUVAL NOAH HARARI SAPIENS, 2015
As we move about the globe, different perspectives help us enhance the environments we build for data. Cartesian and polar systems are readily available codes for positioning data. Both virtual microcosms mirror physical environments. Their familiarity helps audiences navigate and interpret their way through information.
The curved surface of the globe stitches together Cartesian and polar coordinates into a conceptual harmony. A perfect polar system is seen at the poles, while zooming into where anyone actually lives shows a rectangular grid.