Flatland: a romance of many dimensions

My last book post was all about voice, books written to be read out loud to a child or a clan.  But don’t think for a minute that I meant that books that defy vocalisation are no good.

I love Flatland, but with a fiercely cerebral love.  Rather like the higher and lower dimensions it describes, it occupies a separate, otherworldly space that seems to have nothing to do with anything that can be touched, tasted or seen.  The characters of Flatland, and even the supporting cast from Pointland, Lineland, and Spaceland, are monochrome, regular, and in some cases even flat.  The narrator, the aptly named A. Square, speaks in interminably long Victorian prose consisting of clause after clause, chain-linked, prolonged and supported by commas, semicolons, dashes, conjunctions and parentheses.  Try reading that stuff aloud and you’ll run out of breath.  Your mind will wander, distracted, your eyes race will ahead to catch just one glimpse of that elusive but much desired terminal point, the full stop.

But that’s the charm of Flatland, because it is all about breaking beyond our boundaries in spite of our environment and ourselves.  The first half of this book is dedicated to the description of a regimented, hierarchical world of geometric beings with Circles and multisided polygons the nobility, pentagons and squares the professionals (doctors and lawyers and such), equilateral triangles the solid middle class, and isosceles triangles of ever-narrowing angles the despised lower class.  Women, who are straight lines with no angle at all, occupy the lowest rank.  It is a description that is pure and unashamed satire of the Victorian society and mores.

And yet it has a sadly familiar echo.  Read A. Square’s opinion on those who do not conform to society’s norms, and insert the disadvantaged group of your choice:

Doubtless, the life of an Irregular is hard; but the interests of the Greater Number require that it should be hard.  If a man with a triangular front and a polygonal back were allowed to exist and to propagate a still more Irregular posterity, what would become of the arts of life?  Are the houses and doors and churches in Flatland to be altered in order to accommodate such monsters? Are our ticket-collectors to be required to measure every man’s perimeter before they allow him to enter a theatre, or to take his place in a lecture room?  Is an Irregular to be exempted from the militia?  And if not, how is he to be prevented from carrying desolation into the ranks of his comrades?  Again, what irresistible temptations to fraudulent impostures must needs beset such a creature!  How easy for him to enter a shop with his polygonal front foremost, and to order goods to any extent from a confiding tradesman!  Let the advocates of a falsely called Philanthropy plead as they may for the abrogation of the Irregular Penal Laws, I for my part have never known an Irregular who was not also what Nature evidently intended him to be – a hypocrite, a misanthropist, and, up to the limits of his power, a perpetrator of all manner of mischief.

This is science fiction (or should we say maths fiction) at its best.  It takes the familiar and reframes it just enough for us to see it objectively, yet still recognise its relatedness to our own condition.

The second part of the book consists of a visitation and two visions.  First the Square dreams of Lineland and sees how limited its inhabitants are.  Then he is visited by a Sphere whose stated purpose is to reveal to him the Gospel of Three Dimensions in all benevolence and altruism, but who really seems get a kick out of patronising the poor Square and showing off his greater powers of motion and perception.  A. Square is not merely overwhelmed, he is so enthusiastic about this new way of thinking that he begins feverishly postulating even higher dimensions than three, and so, by extension, more perfect and more highly-ranking shapes than Spheres.  This prospect seems to anger the Sphere, causing him to boot his presumptuous disciple back to Flatland.  Undaunted, A. Square later has a dream of Pointland, whose sole inhabitant is a quite literally self-centred, self-absorbed being who fancies itself a god.

Finally, the Square sets himself the task of trying to explain what he has learned to his family and friends, only to discover that people are not comfortable with any form of truth that overturns their established world views.  The consequences are predictable.

Flatland was written in 1884 by an English clergyman schoolmaster who specialised in literature, theology and the classics, but also dabbled in mathematics.  It’s all there – theology, mathematics, social commentary, philosophy –  in less than 100 pages of Swiftian parody.  If that isn’t a bargain, I don’t know what is.