Everything and More is a non-fiction novel about the history and understanding of infinity in mathematics. It is written by renowned post-modern novelist David Foster Wallace, the author of two novels I've previously read: Infinite Jest and The Pale King. Everything and More was part of a series of novels about science and mathematics, commissioned by the publisher, W.W Norton, called "Great Discoveries" - the intention of which was to allow contemporary fiction writers to take on such subjects. I have not read any of the other books in the series, but if Everything and More was any indication, they probably should have left the technical writing to the experts. 

David Foster Wallace is well known for his literary style and distinctly post-modern writing techniques; this includes the rampant use of acronyms and abbreviations, footnotes, and what I would call "flexible prose", i.e the use of unique words and phrases, non-conventional syntax and semantics, liberal re-purposing of punctuation and run-on sentences like this one. Basically his writing intends to make the reader put in some effort so as to not be spoon fed the important information. I can appreciate the merit of writing in this style - it pushes the boundaries of writing and also engages and challenges the reader. However, it is unfortunate that Wallace decided that writing a non-fiction novel about an immensely complex and intricate subject was no reason to change this style.

Everything and More book cover

The goal of a book like this should be to confer a greater understanding of the subject matter, and hopefully illuminate the significance and value of the subject  to the reader. By not sacrificing his artistic integrity for the sake of clarity, I feel that DFW has lost on both fronts in this case. I would have probably gained more from reading a more conventional text on infinity in math, of which there seems to be a multitude.  That's not to say I regret reading Everything and More, in fact I thought I learned quite a bit about the history of infinity as a concept, and it was taught through the words of one of my favourite writers. Although I wouldn't advocate for DFW to write any math textbooks, his writing is nonetheless very colourful and expressive. 

I feel like I may be in a better position than most to have enjoyed this book, seeing that I was exposed to some pretty advanced math during my undergraduate studies, therefore a lot of the concepts and arguments Wallace talked about were familiar to me. For someone with little math background, I can imagine it would be somewhat of a nightmare trying to comprehend the math while having to deal with parsing Wallace's writing as well. Which leads to my other advantage in that I've read a bit of DFW before, which if expressed as a Venn diagram in conjunction with my semi-advanced math background I would guess the overlap would be quite narrow. Therefore, as much as I didn't very much enjoy the book, I am confident most readers would enjoy it much less.

I don't have too much else to say about Everything and More. Despite learning about some of these mathematical concepts in school I am by no means in any position to critique the veracity of Wallace's proofs and explanations. However, from reading a couple reviews[LINKS] of the novel by people who are in such a position, it sounds like there are quite a few mathematical inaccuracies; both reviewers were also in agreement that the writing comes off as unnecessarily confusing - both were quite negative overall.

One of my favourite parts of the book was the introduction actually, written by science-fiction writer Neal Stephenson. It was a light-hearted and intriguing explanation of Wallace's character and how it was influenced by the nature of his upbringing. Stephenson describes the cultural identity of a MACT - a Midwestern American College Town, which is where both he and Wallace grew up:

The premise of this introduction, which will be nailed to the mast very shortly, is that in Everything and More David Foster Wallace is speaking in a language and employing a style of inquiry that might strike people who have not breathed the air of Ames, Bloomington-Normal, and Champaign-Urbana as unusual enough to demand some sort of an explanation. And that, lacking such background, many of DFW’s critics fall into a common pattern of error, which consists of attempting to explain his style and approach by imputing certain stances or motives to him, then becoming nonplussed, huffy, or downright offended by same. It’s a mistake that befuddles MACT natives who see this book as simply what it is: one of the other smart kids trying to explain some cool stuff.

— Neal Stephenson, "Everything and More" pg. 14

The first half of the introduction is essentially a look into the characteristics and peculiarities of a MACT, and how this is evident in both Wallace's persona and his writing. The second half is an analysis of the category that a book like Everything and More would belong to; unique in that it's a heavily technical non-fiction book, written with a causal slang-laden style by a fiction novelist with no technical background. Stephenson writes,

To begin with, DFW was arguably a science fiction writer (Infinite Jest), although he probably would not have classified himself as such. Of course Everything and More is not SF, or even F, at all, pace some of its detractors, but the mere fact of DFW’s having been an SF kind of guy muddies the taxonomic waters before we have even gotten started. Novelists—who almost by definition hold motley and informal credentials, when they are credentialed at all—make for an uneasy fit with the academic world, where credentials are everything. And writers who produce books on technical subjects aimed at non-technical readers are doomed to get cranky reviews from both sides: anything short of a fully peer-reviewed monograph is simply wrong and subject to censure from people whose job it is to get it right, and any material that requires unusual effort to read undercuts the work’s claim to be accessible to a general audience. So in writing a book such as Everything and More, DFW reminds us of the soldier who earns a medal by calling in an artillery strike on his own position, with the possible elaboration that in this case he’s out in the middle of no-man’s land calling in strikes from both directions.

— Stephenson, pg. 24

As for the actual text, Wallace does a fair job of exploring the history and progress of infinity as a concept throughout time. I learned a lot about the problems that philosophers and mathematicians alike have grappled with in the past as the definition of infinity has changed and been refined. Heavyweights like Aristotle, Pythagoras, Kant, and others have all had their hand at trying to rationalize and rigorously define infinity, but most ended up either shoehorning it into the existing axiomatic systems of math, or just hiding it's existence using words. For example, summarizing Aristotle's viewpoints from his Metaphysics, Wallace writes:

The distinction is between actuality and potentiality as predicable qualities; and Aristotle’s general argument is that ∞ is a special type of thing that exists potentially but not actually, and that the word ‘infinite’ needs to be predicated of things accordingly, as the Dichotomy’s confusion demonstrates. Specifically, Aristotle claims that no spatial extension (e.g. the intercurb interval AB) is ‘actually infinite,’ but that all such extensions are ‘potentially infinite’ in the sense of being infinitely divisible.

— David Foster Wallace, "Everything and More" pg. 167

It's only as this historical tour of infinity reaches the 19th and 20th centuries that Wallace's explanatory coherence begins to wane. Perhaps it's because the arguments of Cantor and Weierstrauss and Dedekind were too complex and technical for Wallace to explain them concisely. Or maybe they are too advanced for me. Either way, I found the last few sections rather tedious to get through, which is unfortunate as the ideas Wallace introduced were described as being solutions to the centuries-old intractable problems that had plagued infinity. Cantor's Set Theory finally provided a rigourous proof of the infinitely dense, continuous nature of the number line, which had been an underlying assumption of calculus but had never been officially proven until then. It was especially important for justifying the use of differentials, i.e the little "dx" you see sprinkled throughout calculus problems, which has some strange arithmetical properties like dx*y/dx = y and y + dx = y

Cantor proved, by deduction from first principles, that the set of "real" numbers (rational + irrational) comprise a type of infinity which is greater than the infinity of the "natural" numbers (only rational numbers). This proof put the assumptions about continuity and motion, as formulated in calculus, on solid footing for the first time. In my mind I think of it as the irrational numbers providing the "glue" which bridges the rational numbers, as there are an infinity of irrational numbers in between any two rational numbers. That is pretty mind blowing if you think about it. Irrational numbers are essentially unending sequences of numerical specificity (3.14159...), so I imagine this property, which prevents them from ever being precisely "located" at a zero-dimensional point is what allows them to connect their rational neighbours. Of course this explanation is entirely unsubstantiated, but I think it is decently intuitive, and provides somewhat of an answer for why the existence of irrational numbers is so necessary.

All in all, Everything and More wasn't awful. I suspect it'll probably end up being my least favorite book DFW ever wrote, but that's okay because now I know. I'm still going to read the rest of his stuff. The subject matter and tone was similar to that of Godel, Escher, Bach by Douglas Hofstadter, which is one of my favourite books of all time, so it was definitely nice to delve into these ideas again. Unfortunately Wallace did not deliver the same level of insight and depth that Hofstadter managed to. Oh well. I'll end my review of Everything and More with its own final words:

If you’re interested, Gödel’s own personal view was that the Continuum Hypothesis is false, that there are actually a whole ∞ of Zeno-type ∞s nested between  and c, and that sooner or later a principle would be found that proved this. As of now no such principle’s ever been found. Gödel and Cantor both died in confinement bequeathing a world with no finite circumference. One that spins, now, in a new kind of all-formal Void. Mathematics continues to get out of bed.

— Wallace, pg. 797