A shape is a graphical representation of an object’s form
or its external boundary, outline, or external surface.
— Wikipedia, retrieved May 13, 2026
Most of the time, we grow up with an understanding of “shape” without needing to have it articulated. For some of us, or our children or grandchildren, that sense is reinforced by the simple yet elegant, Tupperware Shape-O, originally released in 1969. If you’ve ever wandered around in bare feet, picking up toys after the kids were in bed, and accidentally stepped on one of those ten yellow pieces, you may also have a very visceral feel for “shape.”
What doesn’t come so naturally, however, is the connection of shape to mathematics — to geometry at the simplest level — which is implicit in the epigraph (above) from Wikipedia. Those ten yellow pieces in the Shape-O are 3-dimensional, and yet the actual shapes, the graphical representations in Wikipedia’s phrasing, are 2-dimensional: triangle, circle, pentagon, star, cross, square, hexagon, quadrant, oval, trapezoid. They are flat shapes that just happen to have easy-to-grip sides for little fingers.
So what (if they’re not Platonic solids)?
Metaphorical connections between stories and geometry are ubiquitous. For theater-goers, movie and television viewers, and readers, the most familiar phrases are probably dramatic arc, narrative arc, and story arc, all three used interchangeably in those genres today. The implication of “arc” is less of a portion of the circumference of a circle and more of a curving path or trajectory of, for example, the Sun moving across the sky. To the extent one can determine from casual exploration on Google-branded tools — Search, Books, the Books Ngram Viewer, and Scholar — all three phrases have traces of pre-web usage. But story arc, which came into widespread usage in the 1990s, now far exceeds the other two in indexed results: about 6,230,000 hits on Search as of this writing. Compare that to the slightly earlier use of narrative arc in the 1980s, now lagging behind on Search with 1,390,000 hits.
Ironically, dramatic arc is by far the oldest of the three, yet has only 282,000 hits on Search. It originated in 1863 with the playwright Gustav Freytag and his Pyramid, which is self-explanatory in any of its thousands of images online. Here is one:
This is perhaps best thought of as an open shape, definitely 2-dimensional; and since we have moved into the realm of metaphor, we can easily allow it informally as a graphical representation of dramatic structure.
One of the best-known examples of the story-geometry connection was created by the writer Kurt Vonnegut in a now-vanished, mid-1940s master’s thesis in anthropology at the University of Chicago. As he recounts in his autobiography, Palm Sunday, he literally graphed stories, including Cinderella and Kafka’s The Metamorphosis (Vonnegut, 1981, pp. 312-316, emphasis added):
The fundamental idea is that stories have shapes which can be drawn on graph paper, and that the shape of a given society’s stories is at least as interesting as the shape of its pots or spearheads.
Examples include a horizontal line, sinusoids, step-functions, and one that rolls off asymptote-like to negative infinity. The anthropologists at Chicago famously rejected the thesis “because it was so simple and looked like too much fun.” Vonnegut had the last laugh, however, when a six-decades-later video of him speaking at Case Western Reserve University in 2004 went viral after it was eventually posted on YouTube. Here is an excerpt of the full lecture (available online), in which he draws story shapes:
This link begins at the directly relevant portion (37:35-50:18), prefaced by his statement that “I have had a technical education… and I have tried to bring scientific thinking to literary criticism, and there’s been very little gratitude for this.” His characteristic humor notwithstanding, this is arguably the first serious attempt to suggest that stories could have shapes with distinctive, meaningful geometric features.
Stories and Shapemaking
The four Google search tools (see above) indicate that by the 1990s stories and shape had become inextricably linked, exemplified by this list of endings for the phrase “stories give shape to…”:
– the present
– our self-understanding
– that which has no shape
– politics
– lives
– events and emotions
– memory
– children’s desires
– a collective consciousness
– personal meanings
– cultures
Some of the contexts are self-evident, for example, “politics” and “children’s desires.” Others not so much: “the present” is from a book of literary criticism (Theroux, 1972) on the writings of V. S. Naipaul that considers how the colonial history of Trinidad has affected the modern society in which he grew up and about which he wrote a century and a half later.
Despite this variety, the dominant phrasing leads back to a single source, the first chapter of Diving Deep and Surfacing: Women Writers on Spiritual Quest by theologian Carol P. Christ (1980, emphasis added):
In a very real sense, there is no experience without stories. There is a dialectic between stories and experience. Stories give shape to experience, experience gives rise to stories.
If you wanted a compelling tagline for narrative sensemaking, this could be it. There have been pre-/post-pended variants of it, for example, “traditional stories give shape to experience” (Bearne, 1992) and “stories give shape to experience and allow us to go through life unblind” (Alex Tizon in Banaszynski, 2002). But when you search on that original five-word phrase with the databases of Google, the Hathi Trust/Library of Congress, and the Internet Archive, the overwhelming majority of hits directly quote Carol Christ. In fact, her phrase has become so elemental that it now often appears in prominent sources without attribution (for example, Ferrante, 2019). It has effectively been vernacularized.
”Historical forms: narratives and stories”
This quoted phrase is from What Is History Teaching? Language, Ideas and Meaning in Learning about the Past by historian Chris Husbands (1996, Ch. 4, p. 44). It is worth quoting an excerpt from one paragraph at length to set a larger historical context for narratives, stories, and shapes (pp. 45-46, emphasis added):
Narrative shapes are built into the way we think about the past…. At their most basic, narrative shapes differentiate history from chronicle. Chronicles record events in unconnected and jumbled ways; histories sort events and organize them around ideas and labels in ways which give them meaning. Some of these narrative shapes are on the grand scale: they relate the rise, the consolidation and the fall of great empires over many centuries; there is a narrative of the rise and then the decline and fall of the Roman Empire; there is a narrative of the development of democracy in Britain…. We use narrative shapes on smaller scales too, where we use different words: we give a narrative shape to the French Revolution, to the First World War, to the sinking of the Lusitania. We give a narrative shape to individuals’ lives, where we call them “biographies” and we select experiences from those lives to give shape, to give identity to the subject of the biography…. In all these cases we are using story to give a shape to experiences as a way of understanding them.
The operative words here — events and labels, meaning and understanding — lead directly to the new metaphor discussed in the subsequent post on Narrative Landscapes, Part II.
Endnote
This post is intentionally sandwiched between the two Parts of Narrative Landscapes: the extant Part I: The emperor has no clothes that fit; and the upcoming Part II: The emperor goes bespoke. It started life as a simple footnote on the tone-setting epigraph at the beginning of Part II. Then, as its scope grew, it wanted to become a succession of footnotes on a scattering of epigraphs. Then an endnote, or even an appendix to Part II itself. This evolutionary pressure reached its maximum — hopefully an optimum — when it was finally obvious that a separate post was needed to map out why the shape of stories is important in the lead-up to Part II.
References
Banaszynski, J. (2002, March 15) Why We Need Stories. Nieman Reports. (https://niemanreports.org/why-we-need-stories/). Retrieved Oct 17 2023.
Bearne, E. (1992) Myth and Legend: The Oldest Language?, pp. 143-152, in Styles, M., Bearne, E., and Watson, V., eds., After Alice: Exploring Children’s Literature. Cassell & Co., Ltd., London, 195 pp.
Christ, C. (1980) Diving Deep and Surfacing: Women Writers on Spiritual Quest. Beacon Press, Boston, 159 pp.
Ferrante, E. (2019, May 17) Elena Ferrante: A Power of Our Own. The New York Times (https://www.nytimes.com/2019/05/17/opinion/elena-ferrante-on-women-power.html). Retrieved Oct 18 2023.
Husbands, C. (1996) What Is History Teaching? Language, Ideas and Meaning in Learning about the Past. Open University Press, Buckingham, 148 pp.
Theroux, P. (1972) V.S. Naipaul: An Introduction to His Work. Africana Publishing Corporation, New York, 144 pp.
Vonnegut, K. (1981) Palm Sunday: An Autobiographical Collage. Delacorte Press, New York, 330 pp.