Everything and More: A Compact History of Infinity by David Foster Wallace
(W. W. Norton & Co., 2003)
Robyn Jodlowski
There are certain expectations one has before beginning a text by David Foster Wallace. One: the reading will be pleasurable but by no means leisurely. Two: you will learn about subjects both tangential and unrelated to the supposed topic at hand. And three: there will be lots of footnotes, abbreviations and surprisingly hip professor slang. All these hold true and then some in Everything and More.
This particular text was written for the “Great Discoveries Series” which, according to their website, “pairs today’s top writers with crucial scientific breakthroughs in ways that are both surprising and illuminating.” As Wallace explains (indeed, almost apologizes for) in his “Small But Necessary Foreword”:
“[The book’s] subject is a set of mathematical achievements that are extremely abstract and technical, but also extremely profound and interesting, and beautiful. The aim is to discuss these achievements in such a way that they’re vivid and comprehensible to readers who do not have pro-grade technical backgrounds and expertise. To make math beautiful—or at least to get the reader to see how someone might find it so.”
You know you’re getting into some heavy stuff if DFW not only gives a disclaimer, but begins his book with a dedication to his parents in Greek.
The foreword, complete with abbreviation glossary (one of several), then moves into the problem of infinity and the history of mathematics on both the meta and micro levels. Georg F. L. P. Cantor, we learn, is the cat behind the book, the guy who “solved” infinity in a sense. Infinity, seemingly either straightforward or baffling, is both and neither.
In the next section (divisions are marked with the mathematically-appropriate § symbol throughout the text), he backs up to think about just how abstract math and numbers truly are. Somehow Wallace uses quotes from math historians, O.E.D definitions of “abstract,” and common stumbling blocks for grade schoolers learning numbers to illuminate the distinction between saying there are five oranges on the table versus the concept of the number five: math suddenly seems much harder, but in a whole new way. Even the innocent number line gets a good philosophizing while symbols and representation reemerge throughout as important concepts of infinity, the term being represented by Wallace with the lemniscate symbol rather than linguistically to remind us of the utter abstraction with which we’re dealing.
The tale really begins with logical traps like Galileo’s and Zeno’s paradoxes, the latter of which goes something like this: in order to cross the street, you must cross every single point between one side (A) and the other (B). Because there are an infinite amount of points between A and B, it should be impossible to traverse that distance of infinity, therefore we shouldn’t be able to cross the street.
Obviously we’ve all crossed the road before, so something is instantly fishy. Stuck on this and similar mind traps, early mathematicians ignored or brushed aside infinity and greats like Plato and Aristotle developed incorrect theories that misled the math world for centuries. It wasn’t until the 1600s that mathematicians, by divorcing themselves from geometrical referents like the number line, were finally able to begin developing a rigorous definition for what had become the “problem” of infinity.
The book proceeds in much the same way as it begins: history of math, trimmed and in context; tight, clear reminders of common mathematical concepts and rules; no-nonsense explanations to bring you to his next arithmetical point.
What Wallace ends up achieving is a beautiful book, but not one that’s available to just any audience as the series wants him to do. By no means a technocrat or math genius (I took AP Calculus in high school and even retained a bit of that derivative and integral business), there were still parts of the text, full of symbols and variables, that I couldn’t quite wrap my head around, even with rereads of Wallace’s patient prose. At the very least, readers would benefit from a calculus class, a philosophy course, and probably another book or two of Wallace’s under their belt before they attempt Everything and More.
There are also sections with an overload of abbreviations and incomplete sentences that give it a not-quite-finished draft feel, though given the glut of research and rewriting the work must have taken, I can’t fault Wallace and the editors for not smoothing those out.
That being said, math types have found calculable problems with the text—problems I am too dense to understand but did the equivalent of a vacant head nod as I read about them online. Wallace seemed to anticipate this, as his acknowledgment ends with, “It goes without saying that the author is solely responsible for any errors or imprecisions in this booklet.”
I won’t give away the ending, mostly because I can’t, but let’s just say that the levels of abstraction increase quite a ways above the problem of five oranges and reach a universe of symbols I’ve never seen before, in arithmetic or otherwise. Rules are broken, infinities are found, and I’m back to feeling like a grade schooler.
All abstraction and mind-boggling philosophy-math aside, I’d say the book is worth a try—at least the first hundred pages if you’re weak at math but strong at patience. It’s interesting to see DFW in a realm he was interested in (his senior thesis was on modal logic), but not well-known for, and after reading, I felt like I had sat in on one of his lectures. The voice here is teacherly, kind, and witty. More than ever, I saw his dexterity, his mastery of language and thought, as he twisted around purely conceptual subjects and bowed under the weight of his characteristic sensitivity to ensure understanding, or at least interest. It’s wild to see spots where even a master like him couldn’t quite bend the language his way.
Like most of his work, and infinity itself, Everything and More is about one thing and everything, base and beautiful, floating somewhere in the realm of ideas.
Robyn Jodlowski is a nonfiction MFA candidate at the University of Pittsburgh and the book review editor at Hot Metal Bridge. To read more of her work visit http://www.politicsunlocked.com/