Everything and More: A compact history of ∞
by David Foster Wallace (2003)
Short and Unnecessary Foreword
Before I describe the book I should like to set the scene, as it were, by describing how it was recommended to me in glowing terms by my new friend, viz. Xtian, whom I hold in high regard w.r.t. both intellectual pursuits and such matters of taste as one's reading material. Such an introduction lead me to have high expectations of E&M, and I shall now relate the extent to which these were fulfilled. But first, for your convenience, a glossary of abbreviations:
- E&M - Everything and More
- DSP - Digital signal processing
- NZ - New Zealand
- YMMV - Your mileage may vary
 Who hails from NZ, which is known, amongst other things, for its geographical isolation, being some 2,000km from its nearest neighbour, SE Australia.
 See (a) below.
§1a. It is probably appropriate, when writing about a book such as this, to describe my own mathematical background, which is that I have a ten-year-old B.Sc in Physics and Electronics, following which I spent a couple of years using stuff like Fourier and digital domain transformations fairly heavily, working in R&D on the software analysis of radar echoes from "non-co-operative targets". Since then, however, my math usage dropped off pretty much to zero, leading to the present day in which I find myself so completely rusty that, while I'm happy and comfortable arm-waving around the concepts , I'd have substantial revision to do in order to be able to coax out any kind of actually useful derivations .
 For example, I once abandoned an otherwise delightful pub crawl halfway through, when I received a last-minute invite to attend a math lecture by Prof. "chaos theory" Mandelbrot across town instead.
 Beyond the basics, that is. Obviously I could still limp through some fundamentals.
§2a. So, the first thing to relate is that Mr. Wallace's descriptions of the nature of, and relationships between, all the transfinites** brought me genuinely thrilling moments of heart-racing excitement and revelatory wonder - not once, but several times. The subject matter is indeed a captivating one, and made all the more so for me because it covers topics which I have not previously studied, namely the central one of infinity itself, but also peripheral ones such as the difficulties the Ancient Greeks had in wresting with abstraction, as hinted at by their lack of a verb meaning 'to exist'. This, of course, caused them no end of problems mathematically, which is arguably nothing but abstractions, and they therefore had problems not just with infinity, but also with significantly more mundane concepts such as zero  and irrationals .
 which they didn't have and apparently never missed
** due to Cantor, et al,
 which, if I were Bill Bryson, I would describe as "all the fiddly fractions  that exist in the gaps between the familiar, round-number fractions*** such as 3/4, 1/8 and 34/978."
 The A.Greeks refused to believe irrationals  existed, and when they eventually realised that even some of the most basic measurements from geometry(a) could not ever be expressed as the ratio of two whole numbers, it shook their mathematical confidence in ways from which they arguably never really recovered.
(a) (such as the diagonal of a unit square)
*** viz. the rationals.
§2b. However, there is one other factor about the book which (B) I should probably mention, and that is that I have never, in all my life, read a document of any description which was as poorly organised, as haphazardly ordered, and ridiculously and unnecessarily over-footnoted, as inconsistently titled and annotated and bracketed by section headings and end-of-section headings, as pointlessly cross-referenced, and as littered with notes to the effect that his editor suggested he should make the following changes. It is in the exact state that I would expect to find it if I had found a first draft abandoned on a park bench, heavily marked with red biro as the result of several furious exchanges with an increasingly antagonistic publisher. And reading an entire paperback of this idiocy almost drove me BATSHIT SCREAMING INSANE.
End of the negatives
(B) in the interests of fairness
§3. So there you have it. YMMV. I'm am glad I read it, but god I found it hard work - not because the math was hard to follow, just simply because the shambolic prose annoyed the living snot out of me. If you have a potential interest in the subject matter, and the style of this review doesn't make your hackles stand on end, then this book is for you (c).
Rating: ∞ x 0. Er... 6?