May 1, 2005 -- -- At first glance (and maybe the second one too), narrative and mathematics don't seem to be natural companions, but recent years have made the juxtaposition much more common.
There have, for example, been many biographies about mathematicians ranging from Sylvia Nasar's "A Beautiful Mind" about John Nash to Rebecca Goldstein's just released "Incompleteness: The Proof and Paradox of Kurt Godel."
There have been many narrative accounts of mathematical ideas and theorems as well, ranging from Simon Singh's Fermat's "Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem" to a spate of tomes on the Riemann Hypothesis by Karl Sabbagh, John Derbyshire, Marcus Du Sautoy and others.
There have also been dramatic renditions of mathematical ideas or mathematicians in works such as David Auburn's "Proof," Tom Stoppard's "Arcadia," John Barrow's "Infinities" and Apostolos Doxiadis' "Uncle Petros and the Goldbach Conjecture."
There's even a new television murder mystery show, "Numb3rs," featuring a crime-solving mathematician. (This latter reminds me of a joke that generally appeals only to mathematicians: How do you spell Henry? Answer. Hen3ry. The 3 is silent.) And these just scratch the surface. Countless -- well, not really, you can count them -- narrative renderings of things mathematical have poured forth in recent years.
Arguably even books such as "The Da Vinci Code," which are about neither mathematics nor mathematicians, derive some of their appeal from mathematical elements within them. So, I think, does much humor but that's another story.
From the Narrative of Math to the Math of Narrative
With all this ferment it's perhaps not surprising that the phenomenon has attracted academic interest. Scheduled for July 12-15 in Mykonos, Greece, an international conference on Mathematics and Narrative will explore the interplay between these two seemingly disparate ways of viewing the world. There will be mathematicians (among them, myself), computer scientists, writers and none-of-the-aboves who will examine the math-narrative nexus from many different perspectives.
In addition to looking at the narrative of mathematics, some contributors will discuss the mathematics of narrative, utilizing mathematical ideas to study narrative techniques. Hypertext, recursion theory, combinatorics and other mathematical notions can no doubt shed light on these techniques.
The underlying logic of narrative and mathematics is different in many ways and this will also be explored. In mathematics, for example, equals can always be substituted for equals without changing the truth-value of statements. That is, whether we use 3 or the square root of 9 in mathematical contexts doesn't affect the truth of our theorem or the validity of our calculation. Not so in narrative contexts.
Lois Lane knows that Superman can fly, but she doesn't know that Clark Kent can fly even though Superman equals Clark Kent. The substitution of one for the other can't be made. Similarly, former President Reagan may have believed, as the apocryphal story has it, that Copenhagen is in Norway, but even though Copenhagen equals the capital of Denmark, it can't be concluded by substitution that Reagan believed that the capital of Denmark is in Norway.
Math and Meta4
The symbiotic way in which mathematical metaphors elucidate everyday speech and, conversely, the way in which mathematical notions derive from everyday stories and activities is of interest as well. Notions of probability and statistics, for example, did not suddenly appear in the full dress regalia we encounter in mathematics classes.
There were glimmerings of these concepts in stories dating from antiquity, when bones and rocks were already in use as dice. References to likelihood appear in classical literature, and the importance of chance in everyday life must have been understood by at least a few. It's not hard to imagine thoughts of probability flitting through our ancestors' minds. "If I'm lucky, I'll get back before they finish eating the beast."
Consider too the statistical notions of central tendency -- average, median, mode, etcetera. They most certainly grew out of workaday words like "usual," "customary," "typical," "same," "middling," "most," "standard," "expected," "normal," "ordinary," "medium," "conventional," "commonplace," "so-so," and so on.
It is hard to imagine prehistoric humans, even those lacking the vocabulary above, not possessing some sort of rudimentary idea of the typical. Any situations or entities -- storms, animals, rocks -- that recurred again and again would lead naturally to the notion of a typical or average recurrence. Similar derivations for statistical variation, probability itself, correlation, and other notions also grew naturally out of the everyday stories in which they were imbedded, and the process continues with newer terms and ideas.
Many other topics might be mentioned (and will be at the conference), but suffice it to say that an increasing appetite for abstraction as well as other aspects of contemporary culture will insure that the confluence of mathematics and narrative will intensify.
I'll end with this plaint from Lewis Carroll, who unfortunately will not be in attendance:
Yet what mean all such gaieties to me
Whose life is full of indices and surds
X^2 + 7X +53 = 11/3
-- Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books, including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNEWS.com appears the first weekend of every month.