The advance buzz on David Foster Wallace's new book was that it would be a biography of the 19th-century mathematician Georg Cantor. But instead of biography or even history, Everything and More chronicles the conceptual development of infinity from the Greeks to modern times, singling out Cantor's contributions as the heady theoretical pinnacle.
If you're of the more literary type who liked Wallace's previous novels and short stories, a flip through his new book reveals pages of numerical diagrams that look distressingly like excerpts from a math textbook, with all kinds of strange symbols and Greek and Hebrew letters. But this was the argot Cantor used to explore the different natures of infinity, proving that some types of numbers are more infinite than others. For instance, the integers such as 1, 2, 3, 4, 5 are not in the same category of infinity as irrational numbers, such as pi and the square root of 5. In Section 7, the book's dramatic high point of Cantorian set theory, Wallace sums up mind-bending passages of mathematical proofs: "In real set theory, we're dealing with abstract aggregates of abstract entities so numerous they cannot ever be counted or completed or comprehended — and yet we are proving, deductively and thus definitively, truths about the makeup and relations of such things." It all seems, as Wallace himself might say, skull-clutchingly difficult.
And this from an author whose most talked-about novel, Infinite Jest, weighed in at a pause-worthy 1,079 pages when it arrived in 1996. That doorstop was relatively easy reading compared with the pure abstractness Wallace squeezes into the mere 300 pages of Everything and More. Mathematicians, though, might find Wallace's new book too light, while literary critics will find it too abstruse. It's definitely only for readers willing to buckle down and commit a significant bit of brain power to abstract logic.
Nevertheless, the book is incredibly friendly and warm. Wallace uses his famous footnotes to cajole the reader along, offering bits of support like, "If the following couple of [paragraphs] seem brutal, please don't lose heart. The brutal part will be over quickly." There are also tantalizing hints that Cantor's theories could have an awful lot to do with some of the themes Wallace explores in his novels. Abstractness of thought is one of the hallmarks of human interiority, and in Infinite Jest the characters used drugs and alcohol to stave off the emptiness. Perhaps arcane mathematical theory feeds a similar hole in our souls.