Written by Matt Cardwell, WUNDERKAMMER

Tuesday, 10 November 2009 08:56

When initially approached to write a review of the US edition of Apostolos Doxiadis and Christos Papadimitriou’s graphic novel, Logicomix: An Epic Search for Truth, I felt admittedly out of my league. My experience in the graphic novel genre, to this point, has included little more than recreational enjoyment of a sampling of the oeuvres of Alan Moore, Frank Miller, and Neil Gaiman—certainly, nothing to warrant critical insight. Further, I knew that I would really love this book—again, a barrier to critical insight.

To address this second concern and simultaneously qualify the grossness of my bias, two things are important to note: (1) I am well on my way to holding a PhD in mathematics; (2) Logicomix chronicles the biography of Bertrand Russell and several other mathematicians in the early 1900s. It is very literally a comic book populated by my superheroes. I had initial delusions that the authors penned such a book for me and three other people, maybe. A day after purchasing the novel, I learned that a friend had also purchased a copy in the previous week. Not surprisingly, he is also employed by my university’s math department. More importantly, I had found one other reader: another mathematician.

As expected, the actual reading of Logicomix brought great enjoyment. I was surprised, however, to find that it was a rather complex work. The story plays out in three different settings. In the first, the authors and illustrators have placed themselves in the book in their studio in Greece. (The book was first published there in October 2008.) They do this in a rather metacognitive, “Let’s investigate why anyone would endeavor to write a graphic novel whose main characters are logicians and mathematicians” sort of way. To me, the question is obvious. These men were awesome. For most everyone else, this plot device allows Logicomix to work on a level that does not require an advanced degree in mathematics. Consider two other sets of individuals: those interested in the graphic novel medium and those wishing to learn a bit more about mathematics. And if we’re to be rigorous, these sets are not mutually exclusive, that is, their intersection is non-empty.

Now I talk like this on a daily basis [push glasses up nose with index finger now], so I wouldn’t mind a graphic novel that requires a few years of graduate work. Perhaps I could embark on this task someday [push up glasses again… audible groan, mouth breathing]. For this reason, it was the second and third settings that drew far more interest for me. While the authors discuss the meaning of their novel, the larger work concerns the life of the mathematician cum logician Bertrand Russell. Setting #2: Russell lectures to a 1940s American audience upon the role that reason and logic should play in the decision for entry into the European fight against the Nazis. To accomplish such a weighty task, he entreats his audience to answer the question, “What is logic?” His mode of inquiry into this question is by way of an investigation of his own past. Herein lies the third setting: Russell’s life.

I’ll speak briefly to the second audience now: the graphic novel bibliophiles. As I mentioned before, I can’t feign too great an expertise in this area—thus, the brevity. What is unmistakable, however, is this: the authors use their medium to great advantage. They deftly weave together their three-pronged attack on logic and Russell’s life, cleverly mirroring panels between the historical segments and the bulletin boards in their own cartooned offices in Greece. Altogether, I am convinced that their concept could not function as successfully in a less visual format. Beyond this trait, any additional critique would be largely worthless (e.g. the drawing was nicely done, and I liked the pictures).

It’s now to the third reader that I move: the one interested to learn a bit more about mathematics. This person really excites me because I rarely find them outside of Reader #1, and this is a sad thing. However, I will attempt to argue that Logicomix could be even more instrumental than Winnie from the Wonder Years in reversing this trend, that is, the trend where my wife groans whenever I begin talking about what I do. She has yet to read Logicomix. But when she or anyone else of this same mindset does, I hope that the effect of reading is revelatory. I hope that in reading, there can be a better appreciation of what mathematicians do, or more crucially why. To truly understand what this appreciation would mean to me, though, some background is necessary.

Six months ago I had occasion to confront a problem in how I view my academic pursuit. At issue was how I had always defended my course of study. At the heart of my argument—although not always cited explicitly—was the physicist and mathematician Eugene Wigner’s 1960 article titled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” To summarize the theme of Wigner’s paper, consider this somewhat more contemporary example:

Around 1920, the mathematician Johann Radon developed a purely mathematical object: the Radon transform. Fifty years later it became the chief computational tool used in CT scans.

Like Wigner, such artifacts have always surprised me. And I have often asked myself the same question: how is it that purely abstract concepts come to have such practical uses?

Until now, though, I have tended to use such examples as a poorly constructed defense for my current work. Altogether, my apology for my studies has been one of “See, Wigner says that I don’t need to have any concern for the practicality of my work. Someone will find something useful for it within 50 years.” While such an argument quickly placates those who wonder why my efforts are fruitful, I have recently come to an important conclusion. Such a view is disingenuous to the discipline of mathematics and arises from a poorly conceived notion of what mathematics is.

Certainly, I would have trouble myself concisely defining what I do. Some mathematicians joke that their profession involves doing mathematics, and mathematics is what mathematicians do. In a less circular way, I might borrow a phrase from Justice Potter’s opinion on obscenity: namely, “I’ll know mathematics when I see it.” But even without a short and precise definition—something which mathematicians are usually wont to have—I am becoming more convinced that mathematics is not what Wigner describes. He writes, “Mathematics is the science of skillful operations with concepts and rules invented just for this purpose.” Still circular in its description, Wigner’s view equates mathematics to a game of chess that includes only the rules for manipulating the pieces, bereft of any object of winning, or any object whatsoever.

At precision’s cost, I would describe my current studies in complex analysis as calculus with imaginary numbers, but I see my work apart from Wigner’s classification. On the outside, it may appear to be pushing symbols around on paper, but I see beauty and surprise daily in my reading and deduction. And while I cannot rigorously define what I do, such a definition is not important compared to the motivation behind such work. Such a distinction may seem a less blithe way of stating that “if you love what you do you’ll never work a day in your life.” Regardless, my recent reflection on such things has positively shifted my focus.

For Logicomix’ third set of readers, I hope that this less apologetic view of math emerges. The illustrations capture the struggle and excitement that I experience each day, and this is truly why I enjoyed this book. It elicits pictorially what I generally fail to do verbally. Further, this novel makes accessible the controversy that surrounded mathematics in the early 1900s, a time when uncertainty over the source of mathematical truth gripped the discipline. This important historical episode surely lies outside a general education curriculum but is essential to understanding the deep, philosophical foundations of mathematics. Perhaps it is on this level that the non-mathematician can enter my lovely corner of academia, for it is a point of entry that does not require arithmetic or algebra or long-forgotten calculus.

Logicomix exposes a usually hidden part of the discipline, one that I often neglect to consider: there is uncertainty in mathematics. Although the authors treat the subject somewhat hyperbolically–the medium is rather conducive to such drama–they do so with great care and appreciation for that which I love. I simply hope that their pursuit is successful, that they reach other readers, and that those readers would find joy and a new measure of understanding in this work as well.

Matt Cardwell is a graduate student at Northern Illinois University and lives with his wife in Geneva, IL.

Read the article on the Wunderkammer website.