The Legacy of Flatland

The following was written by Marie Ernster, practicum student from School of Library and Information Science

The field of mathematics was in a period of philosophical volatility in England in the 19th century. A huge debate raged in the area of geometry over whether they should allow non-Euclidean concepts to enter the pedagogy. Among the traditionalists, geometry represented a means of providing consistent models that would bring certainty to the universe. Non-Euclidean geometry threatened this certainty because it went against the established metrics of empiricism in mathematics. In exploring extra dimensionality through mathematics, this new paradigm would change the very foundation of how geometry could be used as a piece of evidence in the consistency of the universe.

In 1883 President of the British Association for the Advancement of Science, Arthur Cayley, addressed these

Edwin Abbott Abbott, Image from Wikipedia

concerns by pointing out that mathematics was pushing beyond its established boundaries, and his fellow mathematicians should proceed cautiously with their exploration in this new field. He understood that mathematicians would use geometry to explore beyond three dimensions, so he asked that they not leave their more traditional peers behind. One year later, under the pseudonym of “A Square,” Edwin Abbott Abbott (yes, two Abbotts) decided to take a different path from Cayley and explain non-Euclidean geometry in the ground-breaking work Flatland.

Abbott himself was an avid writer at this point in his life, while still working as headmaster for the City School of London until his retirement in 1889. He usually published English guides, such as How to Write Clearly and English Lessons for English People, as well as theological writings like Silanus the Christian and Philochristus. As headmaster, he made elementary knowledge of chemistry compulsory because he believed that students should have a reverence for science. Abbott understood that some of the fears of English mathematicians came from how the association between certainty and geometry made their very faith in Universal Truths shakable as well. After all, if the unassailable reality of geometry could be so affected, then what else could prove the certainty of their own lives? Well, Edwin Abbott Abbott took the proverbial hands of these people, and showed them how to maintain certainty despite these fears.

In the world of Flatland: a romance of many dimensions,  A Square describes a world that exists on an infinite plane; essentially, he lives on a huge piece of paper. A Square describes the basic mechanics of living in such a land: how they can see and navigate, how they know what shapes are and how to differentiate them, how the social structures based on sidedness works, and so on and so forth. But then, A Square meets a circle (the shape considered most important because of its near incalculable sidedness) unlike any circle he had ever met before because this circle was actually a sphere capable, to the eyes of the square, of reducing itself to a small point and then to complete invisibility. A Square eventually learns from the sphere that there are more dimensions than the two he uses to navigate his plane of existence. The gospel of the third dimension is radical to A Square, and near incomprehensible when he exists in his own plane because he has no vocabulary to adequately describe the concept of the third dimension. To make things even more difficult, the priestly circles who govern his world declare that any teaching of the third dimension would lead to imprisonment, or even death. As it goes, A Square ends his story imprisoned for the rest of his life for speaking about the third dimension because he couldn’t contain his excitement about this new paradigm of existence.

Considering the infighting amongst mathematicians at the time, it seems more calculated than cute of Abbott to publish this story under a pseudonym. After all, he uses Flatland to conceptualize the fourth dimension and more beyond that. But he wasn’t just critiquing the traditionalist dogma of mathematics; Abbott was attempting to show that non-Euclidean geometry was the next natural step in the evolution of mathematics—a means to find deeper, more certain truths about the universe than what Euclidean geometry could hope to achieve.

Beyond that, Abbott used Flatland to critique English culture at the time, especially the rigid social dogmas that restricted creative thought and expression. In the second edition of his story, Abbott added a preface under a new pseudonym (called the “Editor”) where he explained that women need greater consideration in wider culture. He uses the treatment of women in Flatland to demonstrate that the rigid social and educational control over women in England prevents them from contributing intellectually to the cultural discourse. The women of Flatland are vapid fools because this is the only option given to them.

Jumping almost a hundred years later, the 1980 Arion Press edition of Flatland found in the Sackner Archive provides an interesting tangibility to Flatland and its inhabitants. Printed on a single, accordion folded sheet of paper, this edition of Flatland provides unique type formatting and crisp illustrations to the story. It can be rather daunting to read a short story that comes with handling instructions, but that makes this copy all the more fascinating. The introduction in this edition is by Ray Bradbury, who presents a wholly literary perspective on the piece and its merits. Bradbury explains Abbott’s creation of Flatland as a process of building strange and silly ideas on top of each other, one after another. Abbott takes the serious and straightforward concept of mathematical geometry and turns it into a silly allegorical story about circles oppressing the creative intellectual growth of other shapes under their purview. Bradbury’s final note is that this book “won’t necessarily prevent us from being fools, but it may help us not to be absolute fools.” Flatland is a story about our own world and imperfect perspectives, presented through the whimsical lens of polygons and lines and points.

137 years later and Flatland still remains an interesting touchstone of debate and discussion about the mathematical concepts, feminist interpretations, and even genre definitions it encompasses. Even conventional genre labels cannot encompass the themes and ideas of a story about A Square living in a world of shapes. People debate whether it could technically be called science fiction when there isn’t anything all that scientific about it, or maybe literary culture as a whole should break down and call it “mathematical fiction,” even though such a label might only really exist for this story and the few pieces inspired by it.

Considering he never wrote another piece like it ever again, it seems as though Abbott expected his other works to become his greater legacy, or maybe he thought there could be no more to say about Flatland besides some minor corrections or clarifications from edition to edition. In fact, it is one of the shortest pieces he ever published. But the reality is Flatland: a romance of many dimensions became his most famous and enduring work because it presents a fantastical world so different and so similar to our own, with ideas that spark questions and debate to this day about intention and culture, that there could only ever be one


Special Note:

The Ruth and Marvin Sackner Archive of Concrete and Visual poetry has a treasure trove of materials yet to be uncovered as parts of it awaits processing in Special Collections & Archives.  The Arion Press edition in the Sackner Collection has not yet been processed, but it will soon be accessible from the Special Collections & Archives website.



Gilbert, Elliot L. “’Upward, Not Northward’: Flatland and the Quest for the New.” English Literature in Transition, 1880-1920, vol. 34, no. 4, Arizona State University, Department of English, 1991, pp. 391–404.

School of Mathematics and Statistics. “Edwin Abbott Abbott – Biography.” Maths History, University of St. Andrews, Feb. 2005,

Valente, K. G. “Transgression and Transcendence: Flatland as a Response to “A New Philosophy”.” Nineteenth-Century Contexts, vol. 26, no. 1, Taylor and Francis Ltd, 2004, pp. 61–77, doi:10.1080/08905490410001683309.

Different Editions of Flatland at Special Collections & Archives:

Flatland by Edwin Abbot Abbott, Introduction by Ray Bradbury, Printer’s Note by Andrew Hoyem, 18th American Edition, 1980

The Annotated Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott, Introduction and Notes by Ian Stewart, 2008

Flatland: a romance of many dimensions by Derek Beaulieu, Afterword by Marjorie Perloff, 2007

An Artist’s Perspective: Travel Diary of Stuart Travis

The following is written by our Workplace Learning Connection summer intern Cassady Jackson

Stuart Travis (1868-1942) was an American artist who was accepted into art school in France during the latter half of the 19th century. He was just nineteen years old when he made the journey alone from New York to Europe. In his travel diary, housed in Special Collections & Archives, he tells the story of his travels to France, and all of the things he saw and thought while he was there, or at least the things that he remembered to write down. 

Ink on paper drawing, men in ship’s smoking cabinet

He starts the diary during his voyage to London, England, aboard the USS Italy. Confined to the ship, he gives hour by hour updates as to what is happening aboard the ship and what the weather is like outside. He complains of the smell in the smoking room at night and counts down the hours until he falls seasick. He also illustrates many of his experiences. A personal favorite is the image he drew of himself standing near the door of the smoking room. The image captures the dimly lit cabin, and the way that his coat is blowing in the wind gives it a sort of eerie feeling. 

Once he arrives in what he refers to as ‘Queens’-land, alternatively known as London, he continues to tell the stories of what is happening around him. According to Travis, he knew the ship had reached London because those above deck had begun to ring the bells. No longer confined to the ship, the frequency of his stories begin to decrease to only one entry a day. While he was in London he stayed with an old woman, someone he states as being a comfort to him, and he writes long entries about what he sees on the street and what his room is like in London. 

Once he moves on to France, his entries become even shorter and further in between, but the stories become more interesting. His excitement about attending the academy is very apparent throughout his early entries in France. He loves the art he is doing, although he does often tell about his frustrations he has with each of his creations. He also despises drawing his own portrait. More specifically, he hates having to use a looking glass because it is, “impossible to paint through a looking glass,” and he puts off his portrait for other work.

Ink on paper drawing of one-man wrestling match

Between his art-related complaints, he describes what a typical day would look like for a young man and his friends, in and out of school. He tells how they critique each other’s art before class starts, and their professors listen in to see what they are thinking. They each had a favorite figure model, male or female, and were always excited when they got to work with them. He is surrounded by many personalities and talks openly of all of them. He observes that some of the models are very aloof and the professors are very snarky, that he hates tourists, and he loves mimes. One of the mimes, a classmate of his, is able to wrestle himself, performing while others gather around him and watch. Travis was so impressed that he illustrated the experience. 

Blank square meant for an illustration

Despite the excitement of his travels, Travis’s entries reveal some hints of homesickness. Many of the entries, especially those in the beginning and end, mention the number of letters he has written home. He says he has written dozens of letters to those back in America, but has yet to have one be returned. He hopes that if he continues to write to his family, one day one of the letters will be answered, but he never mentions whether or not anyone wrote back to him. The longer he stays in Europe, the less he writes in his diary as well. There are many empty sections of the journal, some that are dated, and some that are not. He also leaves room in some entries for an illustration of the day, but never gets around to filling them in. There are also days that he has written in the middle of the page, leaving room for the days before and after that he never got around to completing. These are actions maybe all of us have been guilty of in our own journaling.

The end of his diary leaves many questions as to what happened next in his life, even the end of the trip is not included. The very last entry is just a pencil drawing of a bird in a cage, hanging in his suite on the voyage home. This drawing feels as unfinished as Travis’ diary, as the majority of the images he included before it are in ink. This leaves one to wonder what could have happened to Travis after this diary project was abandoned. 

Pencil on paper drawing, birdcage in ship’s cabin

Fear not, some online searching reveals that Travis lived a long and successful life after this diary. He lived to be 74 years old, illustrated magazine covers for Vogue, and was a partner at a few museums. If you wish to walk in the shoes of a young artist in the last half of the 19th century, Stuart Travis’s diary is a compelling place to start.