Edwin A. Abbott (1838–1926)

This is a fascinating little book. Written in the latish 19th century, it is a despatch from a very simple two-dimensional world by one of its inhabitants, the supposed author: A Square. The first part of the book simply describes the society of Flatland for the benefit of we three-dimensional creatures, its intended audience. The second describes how the square came to learn of our three-dimensional world, as well as other zero- and one-dimensional worlds, and his efforts to educate his fellow bi-dimensional fellows about the higher dimensions.

Both sections are very different (the first has little plot, and more of the maths; the second is much more philosophical), but both are packed with allusions and layers of meaning. For example, the society shows antediluvian, barely qualified, attitudes to women and class - this is a little off-putting initially, until it becomes clear that this is social satire, of a Swiftian level. In describing his attempts to educate people about the higher-dimensions, Abbott is explicitly imploring the reader to be open-minded about radical abstract ideas, by way of making us consider that there are higher-dimensions of which we are not aware. And ultimately the story contains elements of traditional tragedy, of transformation - apotheosis even - and of attaining knowledge from a state of ignorance and of the resultant fall from grace.

On top of that, the book is crammed with references to Shakespeare and the classics. (And through all that it is written in beguilingly simple language (although in a slightly archaic style - even for the 19th century - to give it a timeless quality).

It is a deceptively simple, towering achievement.

This edition in particular is to be recommended. I found the notes on the maths, and Abbott's literary references very useful (although the ones explaining some of the language far less so). And almost more fascinating than Abbott's fable of abstract thought is the man that emerges in the other material in the book.

From the main text you discern a clever, thorough, drily witty and whimsical man; and the basic notes clearly illustrate through their detailing of classical and literary allusions, a highly - and widely - learned man; but that barely scratches the many surfaces of Abbott. Fortunately there is considerable back material in the appendices to fill in some of the detail. His accomplishments include

Legendary headmaster (Prime Minister Asquith attended the City of London School while Abbott was in charge)
An award-winning Cambridge scholar (top in his year in Classics)
A renowned preacher
A bible scholar and leading progressive thinker on the non-miraculous Jesus (reminiscent of Thomas Jefferson's 'The Life and Morals of Jesus of Nazare')
Shakespearean scholar
A biographer and critic of Cardinal Newman
Educational reformer (an early proponent of formal teacher training; promoting teaching for lower classes)
Active Proponent of women's education and suffrage
Admiree (reciprocated) of George Eliot
Author of numerous books and essays, on a range of topics encompassing most of the above

And, of course, a writer of whimsical mathematical fiction, which - along with beautifully communicated (and occasionally entertainingly illustrated) higher mathematical concepts - incorporates existentialism, social criticism, and a plea for scientific rigour and open-mindedness.

I have a new hero.
… (més)