Everything and More: A Compact History of Infinity
By David Foster Wallace, Atlas Books, 2003

Philosopher and musical poet David St. Hubbins put into words the dilemma of infinity perhaps more clearly and concisely than any great thinker to come before him or after when he said, “What does the end feel like? It’s like trying to extrapolate the end of the Universe. If the Universe is, indeed, infinite, then what does that mean? How far is all the way, and if it stops, then what’s stoppin’ it, and then what’s behind what’s stoppin’ it, so what’s the end?” Given such a simple explanation of such a mind-boggling concept, it doesn’t seem likely that anyone could do any better, but David Foster Wallace attempts to do just that in Everything and More: A Compact History of Infinity, part of the Great Discovery series from Atlas Books which tries to present great moments in science in a mainstream, enjoyable manner. One has to wonder if Wallace, the author of the intentionally obscure and bloated novel Infinite Jest, is the right person to look to for an accessible explanation of the most difficult of mathematical concepts. His stylistic affectation, his need to make his prose difficult just because he can, seems to run counter to the desire for clarity. But his most popular book did have the word “infinite” in the title, so here we are.

Most of the early part of the book is devoted to explaining why infinity is a concept that does not have a place in the real, practical world. Wallace uses the example of Zeno’s Dichotomy, a problem set up by a Greek philosopher who argued that, thanks to infinity, motion is impossible. The problem goes like this: Say you set out to cross the street. In order to cross the street, you first have to go halfway across. But to go halfway, you first have to go halfway to the halfway point. But to get to that point, you first have to go halfway to the halfway point to the halfway point. And so on, to infinity. As you can see, in a finite amount of time, you’ll never be able to cross the street because you’ll always be less than halfway there.

Or look at it this way: Almost everyone is familiar with the concept of the repeating decimal, such when you divide 1 by 3 and get .3333333333... Now imagine that x equals the repeating decimal .9999999... Then 10x would equal 9.9999999... Now subtract x (which is .9999999...) from 10x. You’ll get 9x=9.0. Which means that x equals 1.0, when it was supposed to equal .9999999...

This just goes to show that the rules governing mathematical infinity don’t apply in the concrete world. We can all say with sufficient certainty that we can cross the street in a matter of seconds, and if we divide a pie into three equal pieces, we don’t, unfortunately, end up with .3333333... of a pie that, no matter how many bites we take, lasts forever. For most of us who don’t have a deep interest in purely theoretical math, that’s enough. We can simply conclude that infinity is a mathematical aberration, caused by either a glitch in our concept of numbers or an incomplete understanding of how the universe works, and then we can get on with our street-crossing and pie-cutting without losing a minute of sleep. But Wallace is just getting started.

The book pretty quickly finds itself waist-deep in fairly advanced math, and despite the publisher’s hope that the subject matter will appeal to lay people and non-specialists, those without a burning interest in functions and arrays are going to lose interest in short order. It’s difficult to blame Wallace for being comprehensive, but his goal of making the material “comprehensible to readers who do not have pro-grade technical backgrounds and expertise” isn’t really achieved. While you don’t have to be a mathematician to understand this stuff, you’re going to be lost if you only got a C in eighth-grade algebra.

The real question is this: Does David Foster Wallace makes this extremely complicated and intellectually elusive subject matter accessible to a non-specialist audience? The answer, for the most part, is yes. His language is clear and concise, and his use of examples is careful and well-placed. As readers of his previous work might suspect, his weakness lies in an infatuation with stylistic tics and flourishes that are esoteric and unnecessary and which sometimes threaten to get in the way of readability. For example, he repeatedly uses the abbreviation “W/r/t” to avoid writing “With respect to” over and over again, while a disciplined writer might consider using a different phrase now and then. Similarly, he uses “& c.” instead of the more common “etc.,” presumably to show that he’s clever enough to know they mean the same thing. The first two pages of the book are used to explain another abbreviation created by Wallace, IYI, which stands for “If You’re Interested.” IYI is used to identify footnotes and paragraphs that contain information that is not essential to an understanding of the main text. One could argue that all footnotes, by definition, fall into that category, and it is not necessary to saddle us with a new notation. Then again, Wallace is the guy who insists on using the symbol Ź instead of the word “paragraph.”

The Great Discoveries series is a noble idea. Much of science is unfairly pigeonholed as obscure and ignored by the mainstream, and much of it could be easily understood by most of us if it were explained in a down-to-earth manner. However, anyone with only a passing interest in the mathematical bases of infinity should not get too excited in anticipation of Everything and More. Wallace’s book is anything but a Science for Dummies sort of book; if you want that, read Bill Bryson’s A Short History of Nearly Everything. Or just watch This is Spinal Tap again.

Copyright 2004 Ad Media Inc.