[Invited Editorial] 

MythematiCS: (1)

In Praise of Storytelling in the Teaching of  
Computer Science and Math 
 
 

Computer Science Division  
Electrical Engineering and Computer Sciences Department  
University of California at Berkeley  
Berkeley, California 94720 USA  
christos@cs.berkeley.edu

www.cs.berkeley.edu/~christos

“There is no idea worth explaining that  
cannot be explained by a good story”          

Narrative as Epistemic and Didactic Modality

I start by arguing (based on a recent and rather superficial brush with the very extensive and exploding literature on the subject) that narrative is a fundamental epistemic modality.  Narrative Psychology is a well-developed viewpoint within psychology interested in the ways in which humans understand their world and their experience by constructing stories and assimilating stories by others (see, for example, web.lemoyne.edu/~hevern/narpsych .html).  Narrative psychologists recognize two fundamental modes of thinking:  Paradigmatic thinking (logico-deductive and classificatory discourse) and narrative thinking (i.e., storied discourse).  Neurological findings seem to support this separation, in that narrative memory (sometimes called episodic memory) appears to be concentrated in the hippocampus, as opposed to the cortex.

      Related to this last point is the observation that storytelling happens to be alive and well, and broadly practiced, precisely in those places and cultures that are in dire need of CS and math education —the Third World and the ghettos of poverty and illiteracy.  In addition, women appear both to excel and to be interested in storytelling.

      Finally, and independently of all these needs and opportunities, storytelling is useful in teaching CS simply because it is different; as we all know, variety and multimodality are very desirable in the practice of education.  Fifty minutes are too many minutes; seventy-five minutes are an eternity.  Nothing can break the monotony of one-way information transfer as effectively, amusingly, and productively as a good story. 

The Three Modes

I can see three principal ways of using storytelling in the teaching of a technical subject: Providing historical/biographical context to a subject; illustrating a concept by a story; and embedding educational material into a story. 

Placing an idea in its historical context 
 
 
 

What a waste, to introduce Galois theory and finite fields without stopping to remember Evariste’s tumultuous short life and sad end.  Alternatively, to define the Turing machine without mentioning that it was the final nail in the coffin of Hilbert’s scientific optimism –as well as in the cradle of the modern computer.  (And, that Turing went on to become a World War II code-breaker hero, as well as the victim of ungrateful Britain’s criminal bigotry.)  And how inexcusable to plunge into a programming course without first sharing with students Al Khwarizmi’s discovery of arithmetic algorithms, or Ada Byron’s notes on how to calculate the Bernoulli numbers “without human head and hand.” (4)

      But beyond biography, our science teems with fascinating tales about artifacts.  The story of OS360 (recall Brooks’ The Mythical Man Month), of computer design (remember the tale of the ENIAC, as well as Kidder’s The Soul of a New Machine) and of programming languages.  The thriller of cryptography and the epic of the internet, even the saga of the Unix command grep (which I was lucky enough to hear many years ago from the mouth of Ken Thompson) —not to mention the touching story of open source (see for example Steve Weber’s The Success of Open Source, Harvard University Press 2003).  Incidentally, I often find that my more competitive-minded students cannot resist stories of intellectual rivalry, credit and authorship dispute, and scooping. 

Narrative illustration

Many ways exist to introduce and illustrate exponential growth, besides the dry mathematical expression with n up high or the graph that pierces the page’s upper right margin.  Perhaps in terms of the physical world, via chain reactions and the initial growth of bacteria and embryos; or by recalling the Malthusian argument about the growth of populations and resources; or by discussing Moore’s Law and the way it has been driving the world.  Or, even better, by recounting the tale of the wise man who asked the grateful caliph to simply place for him one grain of rice at the first square of the chessboard, two at the second, four at the third, and so forth.  (But for me, nothing surpasses the nightmarish description of the inn at Procopia in Italo Calvino’s Invisible Cities.)   
 

      When I introduce depth-first search I start by recounting the myth of Theseus and Ariadne.  To search a maze effectively you need a ball of string and a chalk—or their cyber-equivalents of a stack/recursion and an array of bits.  (Blaming the subsequent tragic break-up of the couple on the omission of the chalk part by the Cretan princess is optional.)  On a more contemporary plane, it is often helpful to students to see Dijkstra’s algorithm as a discrete-event simulation of wave propagation on a physical model of the graph. 
 

      Not surprisingly, theater provides the most dramatic opportunities for narrative illustration.  In Michael Frayn’s play Copenhagen, Heisenberg’s uncertainty principle is at work during the great physicist’s famous (and famously mysterious) visit to Niels Bohr during the War.  Moreover, in Apostolos Doxiadis’s exquisite new play Incompleteness: A Play and a Theorem, (see http://www. apostolosdoxiadis.com/page/), a nutritionist’s valiant efforts to prove to an old and paranoid Kurt Gödel that he is not being poisoned are frustrated by the tragedy of incompleteness.  (Indeed, Gödel did starve himself to death during a crisis of paranoia in 1979.)

      By the way, much conventional educational practice can be seen as “low-intensity” narrative illustration.  Word problems such as, for example recounting that “Sally bought candy at six cents a piece…” is decidedly more inspiring than just writing “48 : 6 = ?”  Moreover, in our field, graphic terminology can be seen as implicit storytelling such as the traveling salesman problem, two-phase locking, bubblesort, and the coupon collector problem.  They each tell us a story of some kind.  (And let us not forget the all-time favorite taxicab rip-off problem, the problem of finding the longest non-repeating path in a graph.)  

Embedded Lessons 
 

However, the most radical use of storytelling in teaching is by embedding the lecture in a story, especially one that prompts the pupil to relate the subject with the learning experience and the rest of her life.  The trick goes at least as far back as Hesiod’s Works and Days, but recently we have seen a few examples in the realm of mathematics and computer science.  In Denis Guedj’s The Parrot’s Theorem (St. Martin Press, 2001), a bizarre coterie (including an old Paris book-seller, a deaf kid, and a parrot, among others) puzzles over the mystery of a murder that happened far away, and along the way is treated to a beautiful exposition of mathematics and its history.   
 
 
 

      On the other hand, Apostolos Doxiadis’s Uncle Petros and the Goldbach Conjecture (Blumbury 2001) tells the tale of the world’s most likeable mathematician (and the black sheep in the conservative family of the narrating nephew) who, against all prudent advice, spent his life obsessed with the world’s toughest mathematical puzzle.  And let us not forget a beautiful early example of the genre, Don Knuth’s book Surreal Numbers (Addison-Wesley, 1974), in which two students, male and female, discover in a remote beach the beauty and inevitability of mathematics (among many other things). (5)   
 

      Finally, in my own forthcoming book Turing: a Novel about Computation, lessons on various aspects of computer science (and not just) are embedded in a contemporary love story.  Alexandros, a melancholic archeologist, is abandoned by Ethel, a dot-com queen (and namesake of Alan Turing’s mother, by the way), after a short idyll under the Mediterranean sun.  As he seeks her on the internet, Alexandros finds instead Turing, a computer program eager to tell him about the history of ideas, about computers and CS, about life and love, in sessions that are interleaved (and intertwined) with the progress of the story.  

Storytelling vs. Programming

      Incidentally, writing a lecture-embedding story is a constant struggle against a novelistic bug which Umberto Ecco calls salgarism, after the Italian author Emilio Salgari (1862-1911).  Salgarism’s telltale symptoms are incongruity and discontinuity between story and embedded information, as in the following made-up fragment: 

…Suddenly, looking back, the two lovers realized that they were being pursued by a fierce crocodile.

Crocodiles are large carnivorous reptiles living in Africa and parts of America and Australia… 
 

In Conclusion… 

Enriching our lectures, teaching methods, and curriculum with elements of fiction and storytelling, at a variety of levels and modes, can help bring the beauty, power, and coolness of our message with more clarity, and less pain, to a wider and more diverse audience. 

And what a great story that would be. 

Endnotes

(1) From the Greek word mythos, a story that serves to unfold a world view or explain a practice, belief, or natural phenomenon.  Greek scholars would argue that a more correct form is mytheumatics.  This paper is based on the talk that I gave at the 2003 ITICSE conference on July 2, 2003 in Thessaloniki, Greece; that presentation is available at www.cs.berkeley.edu/~christos

(2) Or this is a corollary?  Affinity with the self may well be the definition of what we mean by “interest.”

(3) The situation with Mathematics is, of course, much-much worse. For a treatise, very similar in spirit with the present one, focused on Mathematics, written by the author of Uncle Petros and the Goldbach Conjecture, see Apostolos Doxiadis, “Embedding mathematics in the soul: narrative as a force in mathematics education” opening address ar the Mediterranean Conference of Mathematics Education, January 3rd, 2003, Athens, Greece; www.apostolosdoxiadis.com/files/essays/embeddingmath.pdf

(4) Google “logicomix” for information on a current project by Apostolos Doxiadis and myself, which was a big part of my ITICSE talk.  It is the story of  how 20th century logicians exposed the incomplete nature of mathematical truth, and in the process brought us closer to the computer — pausing to puzzle on how come so many of those great men died insane.

(5) For a more complete list of  mathematical fiction see the website http://math.cofc.edu/faculty/kasman/MATHFICT/mf-all-ttl.html 
 
 

Editor’s Note

Christos and I met at ITiCSE 2003 in Thessaloniki and I was delighted when he accepted my invitation to write an Invited Editorial for inroads.  As many of you know, I have promoted history in computing for many years, so this Invited Editorial is especially gratifying for me.  Christos’ new book, Turing: a Novel about Computation, MIT Press, October 2003, should prove to be an exciting journey of historical interludes surrounding the computing genius for the 20th century.  I hope you get the opportunity to enjoy it.

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