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.simonsrock.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.cuttheknot.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: SpringerVerlag, 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:
SpringerVerlag, 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
``NoSide 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:
SpringerVerlag, 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: SpringerVerlag, 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 wellrounded 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 selfreferential 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: SpringerVerlag,
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, nonEuclidean 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 NonPeriodic 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: SpringerVerlag, 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 parttime private investigator, who also
happens to be a mathematician, investigates the murder of a wellknown 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 nottoobiased 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,
truthtelling 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.)
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