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Original Essays


by Thomas Banchoff
  1. Flatland: The Movie Edition: A Journey of Many Dimensions "The ultimate edition of the classic book." Providence Journal

    "[T]his classic story has been reinterpreted as a gloriously vivid movie that will excite both children and adults. This book completes the movie experience by providing the original book, the screenplay of the movie, and comments by the filmmakers." Discover Magazine

    "Flatland has [been] and always will be a fun and fascinating journey, showing us again how the world of mathematics can expand the mind and take the imagination to places where it didn't know it could play." Danica McKellar, actress and author of the bestselling Math Doesn't Suck

When I introduced Flatland: the Movie at its premiere showing for the mathematics community at the San Jose MathFest in 2007, I explained that my role was primarily to promote the film to mathematics teachers, the audience to which it was dedicated by the producer, director, and chief animator sharing the stage with me. We showed not only the film itself, but also the Extras, including interviews with the actors who provided the voices of the animated characters, and a short explanation of the geometry of four-dimensional space, edited from interviews with me in Austin, Texas, where the film was created. Afterwards, at a reception, someone asked the director if the person who gave the mathematical commentary was an actor or a professor. "He's an actor," was the reply, because all professors are in some real sense actors. I felt honored. I was honored to be asked to join the consultant board, because, as I said at the end of my interview, "Flatland" is my favorite book, and anything that introduces a new generation of readers to this 132 years old classic is welcome. Whether or not the viewers who appreciate the film go on to read the book is an unanswerable question. If they pick up on the challenge of the book, then that is the main point, and that is twofold. For one thing, the film and the book both present the dimensional analogy, a fundamental technique the lies at the basis of so many geometric ideas in mathematics: If we understand well what happens in zero, one, and two dimensions, then we are well on the way to understanding the third, and if we understand 0, 1, 2, and 3, then we can follow that momentum to the threshold of a fourth spatial dimension. Moreover, the fact that we will never understand the fourth dimension as well as we comprehend the third can be a source of humility and modesty in all our dealings with things beyond the reach of our immediate experience. That message, enunciated explicitly in the dedication of Flatland, is just as powerful today as it was when it was first written, by Edwin Abbott Abbott, a renowned Victorian head master and the author of more than fifty books, on school subjects, on Shakespeare, and on history and theology, including a fourteen-volume study of the Sacred Scriptures. The story of how he wrote this seminal book is sketched in my introduction to the Princeton Science Series edition of Flatland, and the relationship of the book to the movie version is the subject of my introduction to the new edition of that book, together with the filmscript adapted from it.

Since the premier, I have had the honor of introducing the film at the annual joint meeting of the Mathematical Association of America and the American Mathematical Society, where over 1200 participants attended a showing, and where many of them remained for a discussion of the possible uses of the film in classes at various levels. I personally have enjoyed showing the film to elementary and middle school students, as well as secondary school students and their teachers, and at the college level as well.

Let me describe my interaction with the creators of the film. Last spring, I got a call from Seth Caplan, who identified himself as the producer of this new film. He told me that he had contacted Steve Rasmussen, the president of Key Curriculum Press, about distribution questions, and that he had immediately suggested that I would be a good person for the consulting board they were in the process of forming. I immediately agreed to take part, and sometime after that, I received copies of a preliminary version of the film, without any music track and only rudimentary decoration, in particular without facial features on the Sphere. At the time I was teaching a First Year Seminar on "The Fourth Dimension" to a dozen freshmen at Brown University, and they were eager to make comments and suggestions as we watched the film in progress. Somehow our comments seemed to make a difference, as the creators of the film were dedicated to working further on the ending, and on some of the earlier scenes.

At the end of April, I went to Austin, Texas, to take part in the wedding of my younger daughter. I came a day early in order to participate in an interview, ultimately edited into the Extras on the DVD. The headquarters of the operation that was producing the film was not prepossessing. Basically it was one large room housing a number of pieces of computer equipment, and Dano Johnson seated at one of the consoles working on details of a scene. He explained how he worked to provide greater and greater elaboration of the main characters and also the background for the various scenes. Then I met Jeffrey Travis, listed as the director of the film, and we went to his home for the two-hour interview session (finally reduced to eight minutes). That was my last contact with the filmmakers until I saw the final finished version.

I should mention that I have been working on ancillary materials for use by teachers, in middle school, junior high and senior high schools, and by math educators. I have shown the film to groups of writers in text projects for secondary schools, and they are uniformly positive about the possible uses of the film and the materials in engaging students in geometric investigations. It is a great project, and I am very happy to be a part of it.

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Thomas Banchoff, a professor of mathematics at Brown University, is an authority on Edwin A. Abbott. spacer

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