Info We Trust

by R J Andrews

  The rod, equal to sixteen feet, was the basic unit of land measure in the early 1500s. Since the king's foot was not practically available for every measurement across the land, an alternative solution was proposed by Jacob Köbel: Sixteen men should be lined up, heel to toe, and the length of that line would be used to measure the rod, which could further be divided into sixteen equal lengths to determine the foot. It was an early modern example of the mean (average).

  Zero also takes on new meaning with length. A wall-mounted measuring stick used to track a growing child's height gives zero the smallest possible height, not a lack of height. Zero is no longer constrained to just emptiness; it can also be the ultimate smallness. Length can also be divided, just as the assembly-number metaphor split whole objects into fractional parts. But assemblies only allow for wholes to be divided into equal parts. The length metaphor is able to do more because lines are continuous. Length's measuring stick shows that for every physical segment of length, there is a number. Length supports a continuity of fractional parts that assembly cannot.

  Rational numbers are produced from the quotient of integers, such as ½ or ¾.

  Irrational numbers, such as √2 and π, are not supported by the assembly metaphor because it is not possible to produce irrational numbers by simply dividing one integer by another.

  Travel distance is a particular type of length that we encounter in everyday life. Sure, travel distance is usually much longer than object length. We measure the length of a garden wall in meters and the distance to the next town in kilometers. Otherwise, measured length and distance traveled seem metaphorically identical; they are not. See, it does not matter what end of the wall you begin measuring from, the length of the measurement will be just as useful. Travel, however, incorporates the value properties of length's measuring stick and then adds more meaning to the number: Distance gives numbers direction.

  In Oz, Dorothy travels away from Munchkinland and toward the Emerald City. Travel implies an orientation and a destination. The distance-number metaphor combines the magnitudes of line segment length with the direction of motion along a path. Together, they connect mathematics to our experience of physical space. Together, magnitude and direction give us vectors.

  Travel distance is one example of a broader spatial schema. The source-path-goal schema moves an entity from a source of motion and toward a destination goal. We describe paths traveled using words like along, through, and across. This spatial language is sometimes called “fictive motion.” It can help us understand and describe parts of our world that do not actually move. A fence runs alongside the road that goes up the hill. Of course, neither the fence nor road move at all.

  Personification is a general category that covers a very wide range of metaphors, each picking out different aspects of a person or ways of looking at a person. … they allow us to make sense of phenomena in the world in human terms—terms that we can understand on the basis of our own motivations, goals, actions, and characteristics.

  LAKOFF AND JOHNSON, 1980

  Fictive motion is one of the ways we describe meaning when we see information. Data takes on a personality that moves about the page: A trend reaches its peak and lines meet at a point. The way we talk about charts makes it sound like they are flea circuses inhabited by imaginary beings moving about the grid.

  Science interests me precisely because of my efforts to escape anthropomorphic knowledge; at the same time, however, I’m convinced that our imagination can only be anthropomorphic.

  ITALO CALVINO, 1985

  The distance-number metaphor also gives zero more meaning. When we first considered objects, zero was emptiness, absence, or destruction. Zero was the group of nothing. Then, the measuring stick helped us extend our thinking to zero as the ultimate smallness. Distance implies a departure point. Now, zero is the name of the origin of travel. Zero can finally scream out of the void. It has become a real place. Zero is the point-location at the start of the number line.

  Travel along a path gives a relatable home to zero and then proceeds forward. The directional nature of travel allows us to also consider going backward on a return trip. Negative magnitude, impossible to imagine with a bunch of bricks, can now be seen. To negate is to move against the direction of the path. Existence below zero simply describes progress in the opposite direction. The entire number line can be pivoted, or reflected, around zero to balance the environment. Negative numbers extend our basic experience of physical reality so that we can do even more with mathematics.

  We use the same language to talk about the number line as we do geographic space: “4.9 is near 5. The result is around 40. Count backward from 20. Count to 100, starting at 20. Name all the numbers from 2 to 10.”

  LAKOFF AND NÚÑEZ, 2000

  Time after Time

  We use the number line to understand all sorts of phenomena. Perhaps most helpful is the way its linearity has become conflated with time: the past, the future, and the space in-between that we inhabit right now. Space and time have always been mixed-up linguistically, light-years ahead of Einstein's space-time continuum. How exactly do we see time?

  Sixty's many factors (2*30, 3*20, 4*15, 5*12, 6*10) offered a pre-fraction world several ways to slice a whole, which is why there are 60 minutes in an hour and 360 degrees in a circle.

  Time is space.

  Space is time.

  In the near future,

  perhaps at two o’clock.

  Turn after the light, but

  before the statue.

  We are so spellbound by our voyage through time that it is easy to forget that we have not always been along for the ride. Our linear comprehension of time is rooted in the limits of our embodied experience of the world. The evolutionary story goes something like the following: Eyes evolved to hunt for specific objects in the environment. But the most sensitive photoreceptors detect only a small portion of the entire field of vision. Narrow slices of the environment arrive to our mind in the order that we direct our focus. Moment to moment, we move our eyes and send new slices to the mind. The holistic, three-dimensional image of the world you think you see is actually a psychological trick of the brain. It is the product of combining a sequence of narrow, two-dimensional flashes.

  The depiction of time: The process begins with metaphor. Once the metaphor is established, the images quickly follow.

  KRISTEN LIPPINCOTT, 1999

  Perception of time is not linear. In our mind, time speeds up the farther into the future we go. One year from today definitely feels closer than two years away. On the other hand, 10 years from today feels about the same as 11 years away. Both periods are one year apart, but we perceive them differently.

  DONA WONG, 2010

  Your ancestors’ eyes darted about the landscape to find food and detect predators. Today, the analogous hunt is for the perfect piece of fruit at the grocer. Stand still in front of a display of apples. Your visual search across the bin of apples is experienced as a temporal journey, even though neither you nor the fruit ever move. The sequential cascade of images arrives across the sequential passage of time. As our eyes dart around we begin to anticipate what might come next. We begin to have foresight about the future.

  Western readers naturally begin scanning pages at the top left and move diagonally to the bottom right according to the pull of “reading gravity” first described by newspaper graphics pioneer Edmund Arnold. Eye-tracking tests confirm the top left corner is where to put the most important information.

  Our ancestors did not just stand still, of course. Like us, they moved around. And as we move around, especially with forward-facing predator eyes, we experience time through our motion. Time, like space, is a dimension that we move through. Time is travel over a landscape. Time becomes associated with distance. A change in time is a change in distance. The passage of time is linear motion over a landscape. The number line is naturally extended to conceptualize time as distance. We are at a point in time, hurtling into the future fro
m the past. Our personal mental image puts us, in this current moment, at the zero-origin, with past events behind our forward motion and future events ahead of it. Like someone looking out the back window of a car, we see the past receding in the distance, blind to what's to come.

  Time travel is only science fiction when it happens suddenly.

  MICHAEL BIERUT, 2005

  Our motion through space became conflated with motion through time. Across evolution, our identity and concept of self strengthened. We all became time travelers who remember the past, expect the future, and move through time together, at the constant speed of reality, one second per second. And then, a curious flip can occur. As the self strengthens, we no longer move through time. Time moves through us. Time becomes objectified, even personified, and it does not sit still. Time becomes a moving object that hurtles toward us. The time will come, then the time arrives, and then it is gone. Because time moves, it has a front, which takes a face, just like us. We face the future just as the future faces us.

  The statement We’re looking ahead to the following weeks seems to be metaphorically inconsistent. Something that follows should be behind, not ahead. However, this phrase works because it combines two temporal frames of reference: From our perspective, we are looking forward and ahead. From the future's perspective, the “following weeks” are the far future that is following the near future, with the entire future train barreling toward us.

  As we reflect on our life, we might play with the number line's origin point. Our own life anchors a personal timeline as we count our age from birth. Our timeline extends through the current point of progress and into an uncertain future. Thinking about our own number line helps us build relationships with a continuum of versions of our self across time. It helps us recognize that the current moment is not all there is. We have an origin and a destination.

  Then I reflected that everything happens to a man precisely precisely now. Centuries of centuries and only in the present do things happen; countless men in the air, on the face of the earth and the sea, and all that really is happening is happening to me.…

  JORGE LUIS BORGES, 1941

  To reflect on your experiences is to converse with your past self. To make plans for the future is to make an agreement with your future self. You make little bargains with your future. Do not eat all the food today; save some for tomorrow. Practical and symbolic sacrifices helped us plan and improve. Paradoxically, youth represents both the past and the future. In the past you were young, but the potential of today's youth inherits the future. We can have clearer conversations across time as we learn to manage our multiple temporalities.

  The human awakening to time is so important that it became immortalized as one of the creation myths of Genesis. Adam and Eve eat from the tree of knowledge and learn of their own impending doom. A personal relationship with time is a relationship with one's own mortality. To know time is to know that the state you exist in today will not persist forever.

  The year zero does not exist in the Anno Domini system of the current Gregorian calendar. The year 1 BC is immediately followed by AD 1. The Scythian monk Dionysius Exiguus (c. 470–544) is credited with inventing the Anno Domini era. He is also the first known medieval Latin writer to use a precursor for the concept of the number zero, which would not reach Europe broadly for hundreds of years.

  Detach the timeline's origin from your personal existence. Now, you can entertain more creative possibilities for how to see time, and how time can help us see. Removing the self uncouples the number line from our personal life and sets it free to look for other sensible origins. The origin could be any date within the continuum of our world. Perhaps we select a historic event like the birth of a religious hero or the Big Bang's birth of the universe itself. Every timeline suggests a beginning and end, whether personal, historic, or cosmic.

  Chronostatic time is relative time, determined by looking at relationships to other events.

  Chronometric time is absolute time, usually described by year, a global constant progression of time.

  We can also step outside of a single time continuity to play with many timelines at once. If we gauge distance as the time elapsed since birth, then the timeline can be repurposed to represent age instead of dates. Asynchronous lives can be reimagined as contemporary and compared using this new context.

  The time-is-distance metaphor was essential for the Newton-Leibniz conception of calculus, which begins by considering the change of distance over a change in time:

  [f (x + δ) – f (x)] / [δ] Taking the ratio of distance to time makes perfect sense if you already consider time to be a type of distance.

  The timeline is a marvelous extension of the number line. Timelines adapt arithmetic properties to show differences, helping us see spans of time. The number line's continuous property allows us to imagine immeasurably small slices of time. Its directionality can help us reorient what the past and future mean to any particular perspective. The timeline can even help us weave different continuities together. It is so useful and so powerful that we forget that the timeline is but one visual way of seeing time.

  Any Time You Want

  Beyond movement, other sequential activities reinforce the linearity of time. Counting objects and constructing shelters step by step further anchor us in linear time. Wherever sequential alphabets gained power, cultures became more transfixed by linear time. Change the order of the letters, and you get a new meaning: canoe is never mistaken for its anagram ocean. Map is not the same as its levidrome Pam. Linear time in our mind moves forward because we move forward. Linear time on the page moves from left to right because we read from left to right.

  In all these cases, every point of view is correct. It all depends upon what you consider to be moving. What does all this mean for design? What is natural depends upon point of view, the choice of metaphor, and therefore, the culture.

  DON NORMAN, 2013

  Just because the Latin alphabet is read left-to-right does not mean that reading has always been so. Before Gutenberg gave us cheap books, people did not read much. But if they did, there was a good chance that it would have been on a vertical scroll. Verticalness is fundamental to our perspective as creatures defined by an upright posture. Today, time progresses as we scroll down web pages. You advance toward the future as you read toward the bottom of an article. We can sense this weakly in English when we talk about a family heirloom being handed down to the next generation.

  Screens orient navigation with a moving-window or moving-page metaphor.

  By contrast, in static infographics where the reader does not move content, such as in a printed newspaper, the most recent time is often at the top. This suggests the murkiness of the past: Sit in a boat today and look down into the water of time, where less light is able to shine on older events. So, vertical time's direction might depend on whether the reader interacts with the content. In either case, vertical time orientation should be reinforced.

  A man who explains necessarily makes intelligible that which is not known by comparing it with what is known.

  HUI TZU, c. 370–310 BC

  Chinese Mandarin words are different from the words of Western languages. Chinese is not made up of sequential phonetic alphabet characters and so does not demand any particular lateral reading. Its traditional vertical orientation still impacts how the Chinese language orients time. The past is up and the future is down: June is above July. July is under June.

  While the Indo-Aryans and Semites found economical ways to translate the sounds of the voice into abstract letters, the Chinese transformed the mental ideas into concrete images.

  LEONARD SHLAIN, 1998

  Even more important than how its characters are arranged is how Chinese words are composed. Each character is an ideogram because each holistically represents an idea without indicating the sound used to say it. They can then be poetically combined to create ideogrammatic metaphors. For example, tomorrow , combines the ideograms for day , m
oon , and date . The result is a written language that, relative to Western written languages, emphasizes synthesis more than sequence. The Mandarin language does not include past, present, or future tenses. There is no need to conjugate verbs. The entire essence of time is less linear. This perspective has preserved more appreciation in China for another ancient way of thinking about time: in circles.

  The cosmic clock: If time was conceived as the precise measure of an ordered succession of states, it should come as no surprise to find that its first criterion of measurement in every known civilization should have been the movement of the stars (which is both movement and return, in other words a ‘constant periodical appearance’).

  UMBERTO ECO, 1999