Humans are hungry for pie charts

There has long been division over the use of pie charts in relation to reporting data but that hasn’t dulled their popularity. It is rare that we see a report or study presented to us that doesn’t include one or more pie chats in them. Sometimes these represent the data well and sometimes they simply confuse the results. Good data visualisation should be easy t understand at a glance and get the intended message across to its audience. So why the insistence on using pie charts? We found this article to be an interesting look into the human attraction to the circle.

Ever since Scottish engineer William Playfair devised the pie chart in his Statistical Breviary (1801) this popular statistical graphic has been praised for its intuitive readability (think of slicing up a cake in ratios), and vehemently criticised for its lack of accuracy. Leland Wilkinson said it best in regards to this dichotomy when he wrote that pie charts “have been reviled by statisticians (unjustifiably) and adored by managers (unjustifiably)”.

William Playfair, Statistical Representation of the United States of America (1805)

William Playfair, Statistical Representation of the United States of America (1805). One of the earliest uses of the modern pie chart, a visualization model that William Playfair is credited with inventing. The chart shows a breakdown of the square mileage of the United States in 1805. Below the pie chart one can read: “This newly invented method is intended to show the proportions between the divisions in a striking manner.”

It’s hard to pinpoint when exactly the wave of criticism started, but back in 1914 American engineer Willard C. Brinton in his Graphic Methods for Presenting Facts already voiced a disapproval so prevalent today. On page 6 of his seminal book on information design, Brinton says the pie chart is “used probably more widely than any other form to show component parts”, however, he immediately denounces it for not being a “desirable form of presentation”. As Briton recognises further down in the page, in contrast to the stacked bar chart, the “easy reading” of the pie chart is “largely due to habit”.

A representation of a “circle with sectors”

A representation of a “circle with sectors” [pie chart] featured in page 6 of Graphic Methods for Presenting Facts (1914). It depicts the “disposition of a family income of from $900 to $1000”

In 1983, American statistician Edward Tufte, one of the most forceful voices against the pie chart, went as far as calling the graphical method “dumb”. In The Visual Display of Quantitative Information, Tufte argues that “the only worse design than a pie chart is several of them”, and he further explains that due to the chart’s “low density and failure to order numbers along a visual dimension”, they “should never be used.”

A similar distaste for the chart is evident in a quote commonly credited to American mathematician John Wilder Tukey (1915–2000):

“There is no data that can be displayed in a pie chart that cannot be displayed better in some other type of chart.”

But it’s not all doom and gloom for this humble diagram. Pie charts, and its more recent variant, the donut chart, can certainly be effective in some cases, particularly in conveying part-to-whole relationships. An example would be plotting the outcomes of a survey where users have to provide simple “yes” or “no” answers, which invariably reflects a given percentage in relation to the whole (100%). Many studies over the past decades have validated this important use case where pie charts seem to prevail as more successful.

Walter Crosby Eells was the first one to look at the efficacy of pie charts in comparison to bar charts in a study from 1926. The results showed that pie charts were as easy to read as bar charts and furthermore, “as the number of components in the chart increased, bars become less efficient encoding the data.”  Eells’ study also revealed an interesting insight that will become more explicit in a few paragraphs. Out of the 96 study participants, 71 preferred the pie chart and only 25 preferred the bar equivalent. In subsequent studies, respectively by Croxton,  Simkin and Hastie, Spence and Lewandowsky, and Hollands and Spence, pie charts proved to be advantageous at mapping part-to-whole relationships particularly with a small number of segments, and less so at depicting changes over time.

An image from Eells’s 1926 study.

An image from Eells’s 1926 study. Participants were asked to estimate segment proportions between a group of pie charts (left) and bar charts (right).

However, despite its implicit benefits, the tone of criticism towards pie charts has been louder, and more acute, in recent times. In the past decade alone, many authors, scholars and researchers have condemned the chart, despite, or perhaps due to, its widespread reach. Some have stated that “pies are bad” and therefore we should “save the pies for dessert”, or in a more passionate cry, proclaimed the “death to pie charts”.

While condemnation for the chart is accurate in certain cases, it doesn’t answer the most interesting question: why, despite some shortcomings in data display, are pie charts so popular? As Eells noticed early on in his 1926 study, humans show a strong preference, or dare we say attraction, for pie charts. What are the reasons for such a widespread appeal? In order to answer this question we have to consider the multidimensional nature of its underlying visual motif.

In the following paragraphs I will expand on two important explanations that underpin the broad adoption of the pie chart:

  1. Historical explanation: the universal, cultural significance of the sectioned circle motif.
  2. Evolutionary explanation: the perceptual bias and innate proclivity for radiating lines and circular shapes.

Historical Explanation

Humans are innate image makers and image enjoyers. Millennia before written language, humans employed images to communicate and express themselves, as well as to record and recall events. The earliest signs of this fascination date back to the Upper Paleolithic period, possibly as far back as 35,000 BC, in the form of petroglyphs and pictographs created by hunter-gatherers across Europe, Asia, and Africa. Among the most common geometric figures drawn by prehistoric humans are spirals, concentric and sectioned circles, found everywhere from modern-day Gabon, Africa, to Utah, United States.

The three oldest archetypes of the circle diagram: spiral, concentric rings, and sectioned circle.

The three oldest archetypes of the circle diagram: spiral, concentric rings, and sectioned circle.

 

Variations of the wheel motif.


Numerous petroglyphs (rock carvings) found across the globe showcasing variations of the wheel motif.

The sectioned circle motif has had multiple meanings through the millennia for different societies and civilisations. Its prevalence was so overwhelming in prehistoric societies, particularly as a religious symbol, that scholars believe it was meant to represent the sun. Bronze Age Europe was filled with artifacts and engravings showing a cross within a circle, many associated with paganism. This motif, known as the sun cross, solar wheel, or wheel of the year, frequently represented the four quadrants or seasons of a year, with variations of the sun cross dividing the circle into eight equal areas instead of four, representing the midpoints of the seasons. One of its most popular manifestations today is in the modern astronomical symbol for Earth, a popular visual metaphor to symbolise the division of continents, meridians and parallels in our globe.

World Map

Peter Apian, World map (ca. 16th century). A map of Europe, the Middle East, and Africa with estimates of the circumference and diameters of the globe written in the bars that divide the chart in four quadrants.

A famous representation of the sectioned circle motif is the medieval abstraction of Earth known as the T-O map. Introduced by the Spanish monk Isidore of Seville in his groundbreaking Etymologies, first published in the early seventh century and distributed throughout the European Middle Ages until the Renaissance, the T-O map provides a simple view of the known world and became a dictating force in medieval European cartography.

Four versions of the popular T-O map.

Four versions of the popular T-O map. Surrounding the circle of the inhabitable world is the river of salt known as Mare Oceanum. The main T shape in the map represents three rivers: the Don and the nile at the top (the horizontal line) and the Mediterranean (the vertical leg). The three rivers divide Asia (top), Europe (bottom left), and Africa (bottom right).

Another popular medieval diagram that embraced the sectioned circle came to be known as anemographic, or wind chart. Such graphics were used to depict the various wind directions (sometimes up to 32) and compass points, in multiple languages and with occasional illustrations. The example below is a chart of the twelve directional winds, taken from a section of an early textbook by the English mathematician Thomas Blundeville.

Juxtaposition of a medieval wind chart (1613)

Juxtaposition of a medieval wind chart (1613) by Thomas Blundeville, with wind names in English, Greek and Latin, and a modern-day pie chart (2008) by Nicholas Feltron, plotting various data for an average day of the author, such as number of emails sent, miles run, or cups of coffee consumed.

One of the most enduring manifestations of the circle — and of human invention — has undoubtedly been the wheel. Initially used by potters in ancient Mesopotamia around 4500 BC, the wheel was soon embraced by chariot makers in Sumer, Central Europe, Egypt, and ultimately China. Wheeled vehicles enabled major advances in agriculture, transportation, and the military, and became a major catalyst for the progress of human civilization. The wheel also became the ultimate embodiment of the circle’s generative force, associated over the ages with ideas of movement, rotation, transformation, cyclicality, and periodicity.

The phrases “the circle of life” and “the wheel of life” express the notion of movement through a cycle from birth to death. One might even bring something “full circle” when ending exactly where one started. For centuries, such ideas of cyclicality had corresponding visual signifiers, some imbued with spiritual and religious significance. The wheel of life of Tibetan Buddhism, known as bhavacakra, is a visual representation of the cycle of birth, life, and death, with the main six sections of the wheel standing for the six realms of Samsara (continuous movement), respectively: heaven or God realm, demon realm, human realm, animal realm, hungry ghost realm and hell realm. At the very core of the wheel of life, there’s normally a pig, snake and bird representing ignorance, anger and desire.

The Wheel of Life

The Wheel of Life

In Buddhism, as well as other Indian religions such as Hinduism and Jainism, we find another symbolic wheel: the Wheel of the Dharma, or dharmachakra. Found on the flag of India and as the national emblem of Sri Lanka, the dharmachakra represents the teachings of Buddha, with the eight spokes of the wheel standing for the tenets of Buddhist belief or the Eightfold Path (Right View, Right Resolve, Right Speech, Right Actions, Right Occupation, Right Effort, Right Mindfulness, and Right Concentration).

The Dharmachakra at Konark Sun temple

The Dharmachakra at Konark Sun temple in Odisha, Odisa, Orissa, India, c. 1200 CE.

Different variations and abstractions of Dharmachakra.

Different variations and abstractions of Dharmachakra.

Finally, we can witness the wheel symbol, as well as other circular marks, in early ideograms and system of letters. Archaeologist Denise Schmandt-Besserat has long studied the evolution of written language and the emergence of the cuneiform script, the oldest writing system, invented in Sumer around 3500 BC. She has looked particularly closely at the main predecessor of the cuneiform, which dates back as far as 8000 BC. It was a system of small clay tokens used to record transactions. These tokens represented anything from a sheep to a portion of grain. In an effort to make sense of their numerous forms and inscriptions, Schmandt-Besserat identified eighteen primary typologies of clay tokens as the prototypes of subsequent numerical notations that endured in the cuneiform script. Of these eighteen types, no less than nine exhibited some circular shape or motif, making the circle a fundamental construct in the earliest known proto-writing system. Circular shapes appear today in almost every modern-day alphabet as a primary graphical component of characters and accents, from the Ge’ez script of Ethiopia and Eritrea to the Hangul alphabet of South Korea.

Fifty-two tokens, representative of 12 categories of token types, compiled by archaeologist Denise Schmandt-Besserat.

In the previous paragraphs we saw how humans have embraced the sectioned circle, or the wheel motif, throughout centuries and associated it with different concepts, either to represent Earth, a sheep, or the teachings of Buddha. Thousands of years before any of us were exposed to the work of William Playfair and the modern-day pie chart, its underlying visual motif was already everywhere. Every time we look at a contemporary version of this popular chart, in a newspaper or business annual report, we’re carrying a long, millennial tradition of interpreting and attributing meaning to such a graphical construct. The final question is why did the sectioned circle became such a prevalent motif, with the pie chart being one of its more recent manifestations? In the following paragraphs we will look at a set of perceptual biases that could help explain such a phenomenon.

Evolutionary Explanation

In his book The Vision Revolution, Mark Changizi provides a possible explanation for our primordial fascination with wheel symbols. Changizi explains that most classic geometric illusions possess diagonal “spoke” lines, perhaps because when we observe these, our brain “interprets those lines as motion streaks due to forward motion.” You could certainly think of countless examples of visual phenomena that convey a similar sense of forward motion, including perspective drawings, the illusion seen while you drive down a highway as trees and road lines appear to converge in the middle, or even science fiction renditions of spacecraft traveling at warp speed, as popularised by Star Trek. Why is forward motion important? Changizi provides a short explanation: “First, it is the most common motion that we, and most animals, engage in. Second, we run the risk of colliding with whatever objects we approach. Perceiving the present is crucial for quick and agile forward movement, and particularly for not getting seriously hurt.”

Figure 13 featured in the book The Vision Revolution. As the author explains: “(A) a forward-movement image, where the blur lines are directed outward, away from the direction of motion. The radial blur lines you see in photographs also occur in the retina; (B) the pattern of contours in the visual field during the forward movement in the image in (a); (C) an even more abstract version of (a) and (b) — a generic set of radiating lines.”

This cognitive trigger, together with the pattern’s ubiquity in nature — from scallop shells and palm leaves to the radiating sun — could explain the allure of the numerous drawings and charts, found in both art and science, that display converging diagonal lines.

The ubiquitousness of the radiating line pattern in Nature. We can see it in plants, shells, starfish, sea urchins, and diatoms (single-celled alga).

Over time, humans have appropriated this radiating principle in many of their artifacts, from large-scale church domes to turbo engines, from tires to umbrellas. Today, when someone looks at a pie chart they are recognising a visual pattern they see everywhere, everyday, in both the natural world and our man-made culture. They are recognising a graphical arrangement that our ancestors have been exposed to for countless generations.

From left to right: A Victorian lithograph of a type of starfish called Asteria echinites (1982) by Jean Vincent Félix; photograph of the dome of the Cathedral of Zamora, Spain (ca. 1151–74) by David Stephenson; photograph of the eight-legged, one-piece wagonwheel design of the rake of an F / A-18 fighter jet (1994) by Jim Ross (NASA).

The “spoke” line motif is so prevalent in art and design that it’s impossible to mention every example ever created. As the English artist Walter Crane observed, “If there can be said to be one principle more than another, the perception and expression of which gives an artist’s work in design peculiar vitality, it is this principle of radiating line.” Even in the domain of contemporary data visualisation, the pie chart is far from being the only model that incorporates the radiating line motif.

Cara Barer, 1996 (2007). Barer transforms books into art by sculpting them, dyeing them, and then photographing them in their new state.

Different modern-day data visualization

Different modern-day data visualisation examples that explore the radiating line construct. From left to right: Valerio Pellegrini, La febbre del Sabato sera (2014), Valerio Pellegrini AFRICA — Big Change / Big Chance (2014), Oliver Uberti, Lifelines (2013).

We might have a strong predisposition for radiating lines. Yet, when such a pattern is combined with another highly enticing shape, the circle, it’s the ultimate perceptual attraction. This sensorial recipe is to our eyes what sugar and salt are to our mouth. An irresistible combination.

I’ve spent some time trying to understand the multitude of visual archetypes of the circle, as well as its diverse cultural associations, such as perfectionunitymovement, and infinity. In The Book of Circles: Visualising Spheres of Knowledge I provided three possible explanations for our propensity towards circular shapes (the book goes into detail about each account).

1. Humans prefer curves
At five months of age, before they utter a word or scribble a drawing, infants already show a clear visual preference for contoured lines over straight ones. In a seminal paper published in 2006, cognitive psychologists Moshe Bar and Maital Neta conducted an experiment in which fourteen participants were shown 140 pairs of letters, patterns, and everyday objects, differing only in the curvature of their contour (see illustration below). The results: participants showed a strong preference for curved items in all categories. The same pair of scientists conducted another study one year later, this time by mapping the cognitive response. Sharp-cornered objects caused much greater amygdala activation than rounded objects. In other words, angular shapes tend to trigger fear and therefore aversion and dislike, while contoured objects evoke safety.

Examples of visual stimuli used in Moshe Bar and Maital Neta’s 2006 experiment. From left to right: (A) Arial regular typeface versus Arial rounded; (B) a square-faced watch versus a round-faced watch; (C) an angular sofa versus a curvy sofa.

2. Circles = Happiness
In 1978 psychologist John N. Bassili conducted an experiment in which he painted the faces and necks of participants black and then applied one hundred luminescent dots. Participants were then asked to assume different expressions, such as “happy,” “sad,” “surprised,” and “angry.” In the final video recording, with only the luminescent dots visible, the outcome was quite revealing: while expressions of anger showed acute downward V shapes (angled eyebrows, cheeks, and chin), expressions of happiness were conveyed by expansive, outward curved patterns (arched cheeks, eyes, and mouth). In other words, happy faces resembled an expansive circle, while angry faces resembled a downward triangle.

3. Eyes  circles
Our eyeballs not only create a natural circular frame for our visual field, but also a spherical distortion of reality. The spherical geometry of our visual field is normally called non-Euclidean. In a non-Euclidean space there are no true straight, parallel lines, as they tend to always converge toward the periphery. You can think of it in a similar way to the alteration of the world captured by a fish-eye lens or a crystal ball. As I hypothesised in the book, perhaps the brain prefers forms and contours that have a better fit within such a conditioned field of view. This could well explain the almost hypnotic effect of concentric circles, one of the oldest configurations of the circle and the subject of numerous optical illusions.

Illustrations and optical illusions analogous to the ones presented by Mark Changizi in his book The Vision Revolution. From left to right: (A) an orthogonal grid based on Euclidean geometry; (B) the same grid in a non-Euclidean space, similar to the spherical geometry of our visual field; (C) two simple vertical lines representing an abstract door seen from afar; (D) the same vertical lines appearing to bow out when a set of radiating lines are placed in the background to provide a sense of forward motion.

Now that we understand our natural proclivity for curves and circles, it’s not surprising that someone in the long past used this shape in combination with radiating lines. The enclosing of the primal “spoke” line motif within a circular frame led to numerous associations over the centuries, as we saw in the beginning of this article. More recently, the work of Scottish engineer William Playfair opened the door to a new set of graphical possibilities in data display including the exploded pie chart, commonly known as rose chart or polar area diagram, popularised by English social reformer Florence Nightingale in her famous “Diagram of the Causes of Mortality in the Army in the East” (1858).

Collection of spoke line patterns. From left to right: (A) motion streaks typical of our visual field when we are moving at a fast speed; (B) abstract pattern of the forward-motion effect, which appears as a set of converging lines with a central vanishing point; (C) typical wheel model, also known as the sun cross, an ancestral symbol used by numerous cultures across space and time; (D) typical pie chart, which assigns a numerical proportion to each slice, conveyed by its angle and area; (E) variant of the pie chart, known as a polar area diagram, where slices have the same angle but vary in length from the core.

Conclusion

We might think of the pie chart as a fairly recent invention, with arguably more flaws than benefits, in regards to the statistical portrayal of data. However, if we look deep into history we realise this popular chart is only a recent manifestation of an ancient visual motif that carried meaning to numerous civilisations over space and time. A graphical construct of radiating lines enclosed by a circle, this motif is also a powerful perceptual recipe. If we look deep into ourselves we uncover a strong proclivity for such a visual pattern, despite the final message it might carry. As one of the oldest archetypes of the circular diagram, the sectioned circle will certainly outlast all of us, and indifferent to criticism, I suspect, so will the pie chart.

Original source taken from Usejournal.com and the author Manuel Lima

Wednesday, August 1, 2018 In: Hot Topics, Newsletters, Whitepapers Comments (None)

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