yellowpigs.net

I already had a pretty good (though vague) idea of what I wanted to do when I got to California in May. I wanted to, as I wrote in my thesis proposal, ``write a thesis which combines mathematics and creative writing, a thesis which makes math accessible to a general reader and presents math as fun''. I didn't know exactly how I wanted to accomplish this, but I wanted to try to change the way math is perceived.

During the summer I considered some of the many myths of mathematics that I have heard, among them that math is more difficult than other subjects, math is dull, math is just about numbers, and that math's importance comes from being applied to sciences. At the same time I wondered why the idea of a mathematics and creative writing thesis seems so strange to people. I tried to find examples of mathematical fiction and recreational math writing. ``Why are there so few books in this category?'' I wondered. Well, the answer is, in one sense, pretty obvious: how large an audience is there for reading mathematics? Why don't people just sit down and read math?

So that's what I decided to do: sit down and read math. I read Edwin Abbott's classic Flatland and Dionys Burger's sequel Sphereland. I read almost the complete works of Lewis Carroll - Lewis Carroll being a wonderful example of an author and a mathematician. I read A Mathematical Mystery Tour by A.K. Dewdney, The Number Devil, a children's book by Hans Magnus Enzensberger, and two anthologies of mathematical short stories edited by Clifton Fadiman. I read books by Martin Gardner, Douglas Hofstadter, Theoni Pappas, Ivars Peterson, and Ian Stewart; I read biographies of mathematicians and Lewis Carroll, books of math puzzles, and old class notes.

Finally, I was ready to write something. But what? Some sort of an adventure like Alice in Wonderland, only with a curious girl who learns math from a yellow pig. I decided to write a five chapter short story. Each chapter would have creative writing episodes with some math. Immediately following each chapter would be a more mathematical explanation of the implications of Alice's travels.

In the first chapter I planned to primarily cover geometry while introducing the characters of Alice and the Yellow Pig. The second chapter, part of which is set in the Golden Garden, is a small subsection of number theory, including a discussion of p, e, f, primes, and the Chinese Remainder Theorem. The third chapter is about combinatorics, graph theory, and groups. In the fourth chapter, Alice and the Pig see a mathematical art gallery in which Alice learns more about geometry and topology. The fifth chapter finds Alice on the other side of a looking glass in Logicland, a world of probability, game theory, and symbolic logic. The story ends with Alice wondering about dreams and reality. I wrote a rough draft of this story in three months and have spent the last month attempting to revise it. The most current version can be found on the web at http://www.simons-rock.edu/~ sara/thesis/.

That more or less sums up what I've been doing for the past six months. I feel that I have gotten a lot accomplished and am mostly happy with it, though I really only like the middle three chapters. I like the Yellow Pig as a character and am starting to like Alice. I ended up changing my model in some ways. The main difference is that instead of adopting something like the dual chapters of Gödel, Escher, and Bach, I have incorporated almost all of the math directly into the story. I think I like this better, but I am not sure.

I have a lot left to do. The story portion of my thesis is far from complete. It's awkward, choppy, and often inconsistent. It's missing diagrams (drawn as the Pig would draw them), some transitions, and the mathematical appendices to the chapters have yet to really be considered. I need to decide how much math I want there to be compared to the amount of creative story. I also have a lot to discuss in introduction and conclusion.

One question that needs to be answered is: Who is the audience for my story? I see the story as potentially useful for those with an interest in math and the desire to learn something beyond classroom textbook mathematics. I also hope to make the text accessible enough that someone with little background and interest in math can learn to appreciate it.

References

[1]

Abbott, Edwin A. Flatland: A Romance of Many Dimensions. New York, NY: HarperCollins, 1994. (A classic example of mathematical fiction and a great introduction to the concept of dimensionality based on analogy.)

[2]

Anderson, John T. and C. Stanley Ogilvy. Excursions in Number Theory. New York, NY: Dover Publications, 1966. (This is a fairly basic introduction to number theory, discussing, among other topics, induction, primes, congruences, Fibonacci numbers, unique factorization, Pythagorean triples, continued fractions, the golden ratio, and Pascal's triangle.)

[3]

Battista, Michael T. The Mathematical Miseducation of America's Youth. http://www.pdkintl.org/kappan/kbat9902.htm. (A detailed article discussing the lack of math skills and education.)

[4]

Bogomolny, Alexander. Pythagorean Theorem and its many proofs. http://www.cut-the-knot.com/pythagoras/. (Dozens of proofs of the Pythagorean Theorem.)

[5]

Burger, Dionys. Sphereland. New York, NY: HarperCollins, 1994. (A sequel to Flatland. Inspirational words from Isaac Asimov's introduction: ``Fear not, however. It contains no difficult mathematics and it won't sprain your understanding. [It is] a pleasant fantasy. You will have no sensation of `learning' whatsoever, but you will learn just the same.'')

[6]

Buskes, Gerard and Arnoud van Rooij. Topological Spaces: From Distance to Neighborhood. New York, NY: Springer-Verlag, 1997. (An undergraduate topology textbook.)

[7]

Carroll, Lewis. The Complete Works of Lewis Carroll. New York, NY: Barnes and Noble Books, 1994. (Not actually the complete works of Carroll, but pretty close. I especially enjoyed Sylvie & Bruno)

[8]

Chung, Fan and Ron Graham. Erdos on Graphs: His Legacy of Unsolved Problems. Wellesley, MA: A K Peters, 1998. (A bibliographical and mathematical tribute to Erdos.)

[9]

Coxeter, H.S.M., Emmer, Penrose, and Teuber, Ed. M.C. Escher: Art and Science. Amsterdam, Netherlands: Elsevier Science Publishers B.V., 1988. (A collection of essays about mathematical ideas in Escher's art.)

[10]

Dewdney, A. K. A Mathematical Mystery Tour. New York, NY: John Wiley & Sons, 1999. (This is a journey and dialogue in mathematics, full of good stuff about Pythagoras and Lagrange. I was most impressed by the chapter ``Horping Zooks'', and the way in which it presented group theory using nonsense words.)

[11]

Enzensberger, Hans Magnus. The Number Devil: A Mathematical Adventure. New York, NY: Metropolitan Books, 1997. (It's a children's book so it's on a pretty basic level. There are a lot of gaps and I don't feel that the terminology is precise enough, but it's a good story even without the math, and I think it could motivate readers to want to learn more math. This book is probably the best example I've found of what I want to create.)

[12]

Fadiman, Clifton, Ed. Fantasia Mathematica. New York, NY: Springer-Verlag, 1997. (A collection of mathematical stories including Aldous Huxley's ``Young Archimedes'', Robert A Heinlein's ``And He Built a Crooked House'', Martin Gardner's ``No-Side Professor'', William Hazlett Upson's ``A. Botts and the Moebius Strip'', Martin Gardner's ``The Island of Five Colors'', and Bruce Elliott's ``The Last Magician''. Most of these are based on ideas from topology and geometry.)

[13]

Fadiman, Clifton, Ed. The Mathematical Magpie. New York, NY: Springer-Verlag, 1997. (More stories, including Miles J. Breuer's ``The Appendix and the Spectacles'', Mark Clifton's ``Star, Bright'', J.L. Synge's ``Euclid and the Bright Boy'', Lewis Carroll's ``The Purse of Fortunatus'', and John Reese's ``The Symbolic Logic of Murder''.)

[14]

Frucht, William, Ed. Imaginary Numbers: An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings. New York, NY: John Wiley & Son's, 1999. (A more recent collection of science fiction. Themes include symmetry, infinity, probability, and logic. Stories include Rudy Rucker's ``A New Golden Age'', Raymond Smullyan's ``How Kazir Won His Wife'', Martin Gardner's ``The Church of the Fourth Dimension'', Stanislaw Lem's ``The Extraordinary Hotel, or the Thousand and First Journey of Ion the Quiet'', and excerpts from Lewis Carroll's A Tangled Tale, Douglas Hofstadter's Gödel, Escher, Bach, and Edwin Abbott's Flatland.)

[15]

Gardner, Martin. Aha! Gotcha. New York, NY: Scientific American, 1975. (Paradoxes and puzzles presented as a series of cute comics with more detailed text explanations. Of particular interest are Hilbert's Hotel, Cantor and infinities, Gödel's Incompleteness Theorem, and paradoxes.)

[16]

Gardner, Martin. Aha! Insight. New York, NY: Scientific American, 1978. (More of the same, though I think I found more material in this one. Topics touch upon the pigeonhole principle, coin problems, turtles walking toward the center of a square, Euclid's cubes, modular arithmetic and Josephus, and the Chinese Remainder Theorem.)

[17]

Gardner, Martin, Ed. The Annotated Alice. New York, NY: Random House, 1998. (The full text of Alice and Through the Looking Glass, with Gardner's extensive notes on mathematics, chess, and Carroll's life.)

[18]

Gardner, Martin. The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Other Word Plays. New York, NY: Springer-Verlag, 1996. (This book didn't have as much information as I had hoped, or rather not too much of it was new to me. I did learn that Lewis Carroll had a fascination with the number 42 and that Donald Knuth did some work with the game of doublets. Most of the book is about Carroll's puzzles, including the monkey puzzle, the quest for anagrams, the genre of crossing river problems, connected graphs, chess puzzles, and doublets.)

[19]

Gardner, Martin. Visitors from Oz: The Wild Adventures of Dorothy, the Scarecrow, and the Tin Woodman. New York, NY: St. Martin's Press, 1998. (Gardner describes the travels of Dorothy and her friends through a Klein bottle to Mount Olympus, Wonderland, a world inhabited by balls, and contemporary Manhattan. It is not a mathematical piece, but it was an entertaining example of a modern fantasy.)

[20]

Hoffman, Paul. The Man Who Loved Only Numbers. New York, NY: Hyperion, 1998. (A biography of Paul Erdös. I found it too mathematically oversimplified, and I don't think it presented a well-rounded enough picture of Erdös. But it tells the story of his rather interesting life and contains a lot of his vocabulary and quotes. Anyone who would choose ``Finally I am becoming stupider no more'' for an epitaph must have had a lot of good things to say.)

[21]

Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid. New York, NY: Vintage Books, 1989. (It's a Hofstadter classic. Originally I was considering adopting his style of presenting short sketches between Carrollian characters and then delving further into the topics they discuss. I am now modeling my story more on Enzensberger's form.)

[22]

Hofstadter, Douglas R. Metamagical Themas: Questing for the Essence of Mind and Pattern. New York, NY: Basic Books, 1985. (More Hofstadter, taken from his column in Scientific American. Chapter topics include self-referential sentences, LISP, and game theory.)

[23]

Knott, Dr. Ron. Fibonacci Numbers, the Golden Section, and the Golden String. http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html. (Tons of information on Fibonacci and the Golden section. The first two links about Fibonacci and the Golden section in nature were particularly useful as were the ones on art.)

[24]

Kasman, Alex. Mathematical Fiction. http://math.cofc.edu/faculty/kasman/MATHFICT/default.html. (A wonderful list of mathematical fiction.)

[25]

King, Jerry P. The Art of Mathematics. New York, NY: Ballantine Books, 1993. (I found this book both interesting and annoying. King makes what I think are invalid generalizations about the educational system, and then he doesn't bother to support them. He divides people into two categories: those who can do math and those who can't. He also discusses the schism between pure and applied math.)

[26]

Lang, Serge. Undergraduate Algebra. New York, NY: Springer-Verlag, 1990. (A textbook of undergraduate algebra.)

[27]

Locher, J.L., et al. M.C. Escher: His Life and Complete Graphic Work. New York, NY: Harry N Abrams, 1982. (A readable tribute to Escher's life and art.)

[28]

The Math Forum. Mathematics Education. http://forum.swarthmore.edu/mathed/. (Hundreds of links to articles on math education.)

[29]

The Mathematical Association of America. Popular and Expository. http://www.maa.org/pubs/books/popexpo.html. (Reviews of popular and expository mathematical literature.)

[30]

Meyerson, Mark D. Pythagorean Theorem Proof. http://www.nadn.navy.mil/MathDept/mdm/pyth.html. (An animated proof of the Pythagorean Theorem.)

[31]

Mosteller, Frederick. Fifty Challenging Problems in Probability. New York, NY: Dover, 1987. (A book of brainteasers with good explanations. It's definitely one of the best books of math puzzles that I have read. Problems include assorted gambling odds, the prisoner's dilemma, coin tosses, the Monty Hall problem, the three cornered duel, lengths of random chords, birthday problems, random walks, Buffon's needle, and Molina's urns.)

[32]

Pappas, Theoni. The Joy of Mathematics: Discovering Mathematics All Around You. San Carlos, CA: Wide World Publishing/Tetra, 1989. (Great book. Theoni Pappas provides brief introductions to over 200 topics in mathematics. Among these are properties of cycloids, Fibonacci numbers, the Moebius strip, non-Euclidean geometry, the Königsberg bridge problem, the four color theorem, conic sections, and soap bubbles.)

[33]

Pappas, Theoni. The Magic of Mathematics: Discovering the Spell of Mathematics. San Carlos, CA: Wide World Publishing/Tetra, 1994. (Sections include ``The Mouse's Tale'', ``A Mathematical Visit'', ``Art, the 4th Dimension, and Non-Periodic Tiling'', ``Cantor and the Infinite Cardinal Numbers'', ``Fractalizing the Surface of the Earth'', ``Mathematics Rides the Crest of the Wave'', and ``Mathematics and Sound''.)

[34]

Pappas, Theoni. More Joy of Mathematics: Exploring Mathematics All Around You. San Carlos, CA: Wide World Publishing/Tetra, 1991. (The sequel to Joy of Mathematics. Topics include hexaflexagons, polygonal numbers, origami, paradoxes, the 17 symmetric groups in the Alhambra, and the golden ratio.)

[35]

Peterson, Ivars. Islands of Truth: A Mathematical Mystery Cruise. New York, NY: W. H. Freeman and Company, 1990. (More explorations in mathematics. Peterson discusses topology, sphere packing, fractals, match problems, polynominoes, partitions, 1729, and many other topics in mathematics.)

[36]

Peterson, Ivars. The Jungle of Randomness: A Mathematical Safari. New York, NY: John Wiley & Sons, 1998. (Ten mathematical excursions. One of them is on fireflies and oscillators; another is about probability matrices of games such as Monopoly and Chutes & Ladders; a third is about Ramsey numbers. Also of interest are random walks and birthday problems.)

[37]

Ramsay, Arlan and Robert D. Richtmyer. Introduction to Hyperbolic Geometry. New York, NY: Springer-Verlag, 1995. (An undergraduate hyperbolic geometry textbook.)

[38]

Rosenthal, Erik. The Calculus of Murder. New York, NY: St. Martin's Press, 1986. (A detective story in which a part-time private investigator, who also happens to be a mathematician, investigates the murder of a well-known San Francisco businessman. The mathematics is interesting but sparse; the story can also easily be enjoyed without reading the math.)

[39]

Rothstein, Edward. Emblems of Mind: The Inner Life of Music and Mathematics. New York, NY: Random House, 1995. (Rothstein discusses some correlations between math and music. He gives some good examples of proofs and discusses ratios and proportions.)

[40]

Rucker, Rudy, Ed. Mathenauts: Tales of Mathematical Wonder. New York, NY: Arbor House, 1987. (An anthology of short stories similar to Clifton Fadiman's collections. I agree with many of the statements he makes in his introduction. Greg Bear's ``Tangents'' is about a small boy who has a gift for understanding the fourth dimension. Rucker's own ``A New Golden Age'' is about the consequences of popularizing pure mathematics; his ``Message Found in a Copy of Flatland'' locates Abbott's Flatland in the basement of a Pakistani restaurant. ``The Maxwell Equations'' by Anatoly Dnieprov is a story of a mathematician who outsmarts a Nazi war criminal who is forcing mathematicians to be computers by manipulating their brain frequencies. George Zebrowski's ``Gödel's Dream'' is about a computer program that must run forever. ``Cubeworld'' by Henry H. Gross discusses the implications of turning the Earth into a cube.)

[41]

Stewart, Ian. The Magical Maze: Seeing the World Through Mathematical Eyes. New York, NY: John Wiley & Sons, 1998. (An excellent recreational math book that includes sections on Pythagoras, Fibonacci numbers and the golden ratio, the Monty Hall problem, wallpaper patterns, and Gödel's theorem.)

[42]

Stewart, Ian. Nature's Numbers. New York, NY: HarperCollins, 1995. (An extremely readable book about mathematics in nature. Stewart addresses the question ``What is mathematics?'' I found the section on the golden ratio to be particularly interesting.)

[43]

Stoffel, Stephanie Lovett. Lewis Carroll in Wonderland: The Life and Times of Alice and Her Creator. New York, NY: Harry N. Abrams, 1997. (A not-too-biased biography of Carroll with nice illustrations.)

[44]

Sved, Marta. Journey into Geometries. Washington, D.C.: The Mathematical Association of America, 1991. (This story of Alice's journey into hyperbolic geometry is intended for those with a high school mathematics background and attempts both to teach and to show that geometry is fun. Each chapter contains problems and exercises for which solutions are provided. When I ran across it in February, I found it interesting to compare Sved's approach with my own.)

[45]

Wakeling, Edward, Ed. Lewis Carroll's Games and Puzzles. New York, NY: Dover, 1992. (42 of Lewis Carroll's puzzles with solutions, including cake problems, truth-telling problems, urn problems, and properties of square numbers.)

[46]

Wakeling, Edward, Ed. Rediscovered Lewis Carroll Puzzles. New York, NY: Dover, 1995. (42 more puzzles with solutions.)