# Everything and More: A compact history of ∞

*by David Foster Wallace.* 2003.
On Amazon.co.uk

**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*[1]*, 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.*[2]*
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

*[1]* Who hails from NZ, which is known, amongst other things, for its
geographical isolation, being some 2,000km from its nearest neighbour,
SE Australia.

*[2]* 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 *[3]*, I’d have
*substantial* revision to do in order to be able to coax out any kind of
actually useful derivations *[4]*.

*[3]* 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.

*[4]* 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 *[5]* and irrationals *[6]*.

*[5]* which they didn’t have and apparently never missed

** due to Cantor, et al,

*[6]* which, if I were Bill Bryson, I would describe as “all the
fiddly fractions *[7]* that exist in the gaps between the familiar,
round-number fractions*** such as 3/4, 1/8 and 34/978.”

*[7]* The A.Greeks refused to believe irrationals *[6]* 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*.

The negatives

§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)*.

*(c)* probably

Rating: ∞ x 0. Er… 6?