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A richly illustrated compendium probes the colorful history of the circle

The Book of Circles: Visualizing Spheres of Knowledge

Manuel Lima
Princeton Architectural Press
272 pp.
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One of the most arresting images in Manuel Lima’s new study of visual culture, The Book of Circles, is also one of the simplest: a red and green serpent, looped on a bed of black script, swallowing its own tail. This is no drawn-from-life depiction of animal behavior but a figure in an alchemical manuscript dating from 1478: a vivid rendering of the ouroboros, an ancient symbol of perpetuity and a highlight in the colorful history of the circle. Lima’s aim is not so much to tell this history as to show it. And, by all accounts, he succeeds.

Many of the almost 300 illustrations found in this compendium open up portals to other worlds. Among them, we find one of the earliest pie charts, created in 1805 to visualize the area of different states in America; a yet-to-be-deciphered disk, produced in 1700 B.C.E. on the island of Crete, showing a parade of symbols spiraling outward from the center; a finely detailed Korean star chart, based on a stone engraving from 1395; and a so-called “rose chart” created in 2011 that depicts wind direction and speed in New York City during the second half of the 20th century.

The images come from different times and places and afford glimpses into different systems of knowledge and preoccupations. What unites them is their reliance on the same elemental shape.

This shape—the circle—leads many lives, and Lima explores them all. One is as a form found throughout the natural world—for example, in tree rings, celestial bodies, liposomes, and the human eye. Another is as a recurring motif in the built world, figuring in the layout of Stonehenge, the domes of cathedrals, and the plans of modern cities. Still another is as a framework for visualizing data. In addition to the familiar pie chart, Lima’s book showcases radar plots, sunburst diagrams, and charming volvelles, not to mention radial charts and biomorphic Voronoi diagrams.

As Lima emphasizes in the introduction, circles are also potent symbols. In addition to conveying the notion of perpetuity, circles have been regularly called upon to represent perfection, unity, and movement.

Lima’s book roundly demonstrates that humans are drawn to circles. It’s natural, then, that his introduction dwells on the question of why. Pulling from work in the cognitive sciences, Lima considers three possible explanations.


San Francisco–based artist Klari Reis creates colorful petri dishes that explore the intersections of art and science.

He begins by positing that angular shapes—thorns, teeth, jagged rocks, and the like—suggest threats. Curvilinear shapes, by contrast, suggest safety. Another potential reason for our affinity for circles is that humans express positive emotions curvilinearly, with arcing smiles and rounded cheeks. We thus cannot help but see round things as benevolent. Lima’s final hypothesis is that because our field of vision has a circular frame, we are drawn to forms that echo this frame. All these explanations have a strong “just so” flavor, of course, but it’s hard to imagine answers to such a big question that would not.

One shortcoming is that not all the uses of circles in Lima’s catalog seem especially deep or well motivated. He exhibits a number of specimens from the past decade or so of “data viz” culture—a culture that has, by the looks of it, enthusiastically embraced circular forms. Yet in some of these examples, the circle appears to be an arbitrary—even distracting—choice.

Several visualizations arrange countries around the center of a circle—for example, depicting data about those countries on concentric bands. This invites engagement—one has to turn the image (or one’s head) to figure out what is going on—but what does this circular layout illuminate?

Lima’s book might have been stronger had it paid a bit less attention to inventive show ponies and a bit more to humbler, more timeless uses of circles—the workhorses, if you like. Despite being discussed reverentially in the introduction, there is only one image of a Euler diagram (cousin to the Venn), and uses of circles to represent cycles are surprisingly scarce.

The Book of Circles is, above all, a wide-ranging exploration of an elemental shape in its guises as a form, symbol, motif, and more. The book joins Lima’s previous work, The Book of Trees, as an important study of one of our most human of impulses: to give abstractions visible form. This ancient and universal impulse will no doubt continue in perpetuity. We can hope that so, too, will insightful efforts—like Lima’s—to document and understand it.

About the author

The reviewer is at the Department of Psychology, University of Chicago, Chicago, IL 60637, USA.