MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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Flatland: A Romance of Many Dimensions (1884)
Edwin Abbott Abbott
Highly Rated!
Note: This work of mathematical fiction is recommended by Alex for literati.

This is the classic example of mathematical fiction in which the author helps us to think about the meaning of "dimension" through fictional example: a visit to a world with only two spatial dimensions.

One of the genres used in this Website is is “didactic”. I classify works of fiction as “didactic” if the intention of the author is to use the fiction to teach mathematics. For example, Enzensberger’s “Der Zahlenteufel” is didactic because the story does not really matter at all; the purpose of that novel is to interest the reader in the real mathematics that it discusses. The idea is that many readers who have trouble with abstract mathematical thinking will understand it better if it is included in a story and given some sort of fictional “reality”.

Many people do have trouble conceiving of higher dimensional geometry, and a reference to Flatland is now commonly used by people who are trying to help others understand this difficult concept. It does seem to help people to imagine creatures living and thinking in a two-dimensional universe and to imagine how they would perceive the three-dimensional objects that are familiar to us. So, people certainly use Flatland as a didactic work of mathematical fiction.

However, I do not think Edwin Abbott Abbott was using math that way. It was not his goal to make the math more understandable and believable by including it in a story. Quite the opposite, in fact. I think Abbott thought of math as something that people would already understand and wanted to use that math to discuss certain non-mathematical ideas that were important to him. Moreover, he hoped that by using mathematics (a topic most people agree upon), he would be able to generate some agreement in discussing something more controversial. In particular, I think that what he really wanted to write about was not mathematics but the relationships between people and the relationship between people and the supernatural.

Consider this: the main character, “a square”, of Flatland has had an experience with something from beyond his own universe, something he cannot see entirely but can only glimpse in pieces. This has changed his view of his reality, changed his view of his relationship with the other creatures of Flatland, and he wants to share that information.

Now, notice that because of his strangely repetitive name (“Abbott Abbott”), the author of Flatland could also describe himself as “A Squared”=“A^2". Abbott was a theologian. He presumably also believed that he could perceive God’s existence, but not entirely, only in pieces. And although some of his ideas seem to reflect an old fashioned bias to modern readers (e.g. that the females in Flatland are line segments while the males are polygons) he was actually somewhat progressive for his day. His view of the relationships between people was also rather introspective for Victorian England.

Consequently, I believe that the role of mathematics in Flatland was to provide Abbott with a language (the language of geometry) through which he could discuss non-mathematical ideas with the readers that he otherwise could not quite put into words.

One difference between my professional area of expertise (mathematics) and my hobby (literature) is that there is much more agreement in the former than the latter. This is one reason that people like to use mathematical language to discuss controversial non-mathematical topics. (They hope that the listener will be swayed by the supposed “objectivity” of mathematics.) But, for this very same reason, I think it is likely that people will entirely disagree with my analysis of Flatland and the author’s intentions. Do you think I'm right or am I completely missing the point? Please let me know your opinion on this question.

Note: The entire text of Flatland is currently available for free in an electronic (ASCII) format from the Gutenberg Project at ibiblio.org. Note for 2002: The book has been rereleased with annotations by Ian Stewart. The new version is reviewed in the AMS Notices by AK Dewdney.

Note that this book has inspired many direct sequels. See Flatterland, An Episode of Flatland, A Message Found in a Copy of Flatland, Sphereland and Spaceland.

Contributed by Anonymous

Brilliant book but some details are lacking within Flatland's societal infrastructure. Abbott, for example, describes the greeting process of flatlanders as "feeling" but his depictions of Flatland inhabitants are merely geometrical shapes with no appendages (arms, legs) with which to feel. Left out details such as this are distracting to the reader. Had Abbott addressed these issues, the book would have been more convincing and intriguing.

Contributed by Dave Luer

My girlfreind is a geometry teacher in Jersey. We went to high school together and we both remember seeing the movie called "Flatland" and it was based on the book. The problem is, she hasn't been able to find a copy of it anywhere. Her birthday is coming up, and I'd really like to find it. Any suggestions on where to look? Thanks! Dave

Perhaps you're thinking of the 1965 animated version made at Harvard University, featuring the voice of Dudley Moore and directed by Eric Martin?!? At least, that's the only candidate I can think of. Believe it or not, that version is still for sale from the DER. (Unfortunately, it's not cheap. But nobody ever said that romance would be, eh?)

Contributed by Fred McIntyre

(April 2005) I was first introduced to Flatland by E. A. Abbott in a college philosophy class, in 1977. I fell in love with it. (I am also a mathemetician.) It inspired what has become to me a delightful investigation of higher dimensions.

Contributed by Sonja Dezman

Flatland is not comparable to anything else. It is unique! I think that every mathematician should read it. What bothered me was the position that women have in this story. They are presented as stupid, unable to learn and think, or make choices of their own. After reading the story I found out more about the role of women in the time that Flatland was written. It makes sense now. It is worth reading it because of two things (not only one): The mathematics that is used and the way women are presented.

Contributed by Jim Napolitano

An intriguing and provocative work which I will use in a math text cluster in my 11th Grade International Baccalaurate Math SL classroom. It is a great bridge between previous classes and new concepts/thinking at the start of Junior Year, particularly as a spur to discussing social issues using this geometric vehicle. Note: It's also available for free at http://downlode.org/etext/index.html

[Added October 2006] It appears that "Flatland the Movie" (starring Martin Sheen) is in the works. Some have suggested that it is just a joke (oh, come on...it's not THAT bad), but the trailer available at flatlandthemovie.com is rather entertaining.

Contributed by Tina Chang

This is the best description of dimensions I've ever seen.

Contributed by B-Square

While promoting a film I'm involved in, I ran across your webpage where you keep a list of mathematical fiction, and thought you might like to know about this current film adaptation of Edwin Abbott's Flatland.

Flatland: The Film, directed by Ladd P. Ehlinger Jr.

It's currently in prerelease and has so far received good reviews at places like Scifi.com and Filmthreat.com

You can find trailers and clips at the film's webpage: http://www.flatlandthefilm.com/

We'd be honored if you would include us on your Flatland page!

Thank you,

R. Perrin Ehlinger (aka B-Square)

Yes, it's true. You can read about two different projects at FlatlandTheFilm.com and FlatlandTheMovie.com. I'm sure someone will get a wonderful term paper out of comparing and contrasting the two movies.

Contributed by "William E. Emba"

By the way, you may want to mention that FLATLAND was originally published under the pseudonym "A. Square". As Stewart points out, this was presumably an inside joke on Abbott's part, what with his middle name being the same as his last name.

Contributed by James Bashkin

I think that all people, not just mathematicians, should read this book. It is really tremendous, offering a good story, and pretty self-contained world, and lots of help understanding projections, etc., without ever appearing to be a math textbook. I wrote about it and Flatterland on my own fiction site (I found Flatterland a bit difficult after a while, and haven't finished it yet, but enjoyed the beginning). I bought the DVD (Flatland-the movie I think it is called) but haven't watched it yet.

Contributed by Robert W. Franson

A very clever novel, and I still find it thought-provoking.

Contributed by Mark R. Leeper

There are four film versions of FLATLAND listed in the IMDB. Two came out in 2007 and I reviewed them both: one and two.

Thanks, Mark! (NB When visiting the IMDB link above, take note that there is also an unrelated TV series with the same title.)

Contributed by Marcus L. Rowland

I'm the author of a Flatland Role Playing Game published in PDF and sold in aid of Doctors Without Borders. Any publicity you feel able to give it would be appreciated.

Vijay and I agreed that "Geometric Regional Novel" by Gert Jonke is not sufficiently mathematical to justify having its own entry in this database. However, since it is similar to Flatland in some ways, I will post Vijay's summary of that book here for those who might be interested in it:

Contributed by Vijay Fafat

Geometric Regional Novel by Gert Jonke is another book that is similar to Flatland in some ways.

An odd but charming book which desrcibes a strange, very static, grey world nestled in some corner of thought. In measured, clipped tones, the narrator describes the contours of the geometric village, with its Village Square, its bylanes, its bridge, the bridge keeper, the artist and his pyramidal tent, the blacksmith and his house, the regimented routines of the village officials, the sleeping positions of people, the door frames and door styles, the trees, the irrigation system, dairy farming, folk songs, etc etc. Geometric drawings supplement the descriptions in various places.

However, unlike “Flatland”, this is really not a mathematical novel, as such, beyond the geometric mood it sets. It is intended as a very subtle satire. As the back cover of the book describes it:

“[The book is] An innovative satire on the process by which bureacracy and official regimentation insidiously pervade society. In a dead-pan, pseudo-scientific tone, the nameless narrator takes us on a tour of a bizarre village whose inhabitants lead such habitual, regulated lives that they resemble elements in a mathematical equation."

Buy this work of mathematical fiction and read reviews at amazon.com. Amazon.com logo
(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to Flatland: A Romance of Many Dimensions
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Romance of Mathematics: Being the Original Researches of a Lady Professor of Girtham College... by Peter Hampson Ditchfield
  2. Sphereland: A Fantasy About Curved Spaces and an Expanding Universe by Dionys Burger
  3. Inquirendo Island by Hudor Genone
  4. The Next Dimension by Vladimir Karapetoff
  5. An Episode of Flatland by Charles H. Hinton
  6. Brave New World by Aldous Huxley
  7. Message Found in a Copy of Flatland by Rudy Rucker
  8. Journey into Geometries by Marta Sved
  9. Plane People by Wallace West
  10. The Time Machine by Herbert George Wells
Ratings for Flatland: A Romance of Many Dimensions:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
3.83/5 (37 votes)
..
Literary Quality:
3.26/5 (39 votes)
..

Categories:
GenreScience Fiction, Didactic,
MotifHigher/Lower Dimensions,
TopicGeometry/Topology/Trigonometry,
MediumNovels, Films, Available Free Online,

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Your Help Needed: Some site visitors remember reading works of mathematical fiction that neither they nor I can identify. It is time to crowdsource this problem and ask for your help! You would help a neighbor find a missing pet...can't you also help a fellow site visitor find some missing works of mathematical fiction? Please take a look and let us know if you have seen these missing stories anywhere!.

(Maintained by Alex Kasman, College of Charleston)