Flatland: A Romance of Many Dimensions

Flatland is a fictional account of “A Square” who is the brother of “B Square” and their interactions with those powerful personages of the two dimensional world in which they live. There is also a problem with Colorization, or Chromatism, in Flatland and some of the citizens refuse to have their “irregular” children fixed, which has resulted in an oddly shaped and colorful member elected to the Legislative body of Flatland. (Most of the ruling elite are “Circles”… each generation gains a side. Women are straight lines and have to screech when approaching men and wiggle themselves to alert men to the danger (so as to not stab them). Lowest ranked males are triangles, with Squares being the basic educated class of Flatland.

Pentagons, then hexagons… until so many sides blend to become “circular” and enable the males to advance to higher academic and political positions. There is a correctional facility to “fix” oddly shaped children.

(Women never gain additional sides, but in the book it is pointed out that enough women gathered together can create a more perfect circle than any multi-sided male. It is rather cleverly written… the film does a fair job, though it is more humorous than the book, as I remember.)

A Square is “chosen” by Messiah, Incorporated to be the Apostle given the opportunity to grasp the 3rd dimension when visited by a Sphere. This happens every thousand years and the event is so traumatic to the powerful people of Flatland they create a war just to prevent the visit from having impact. When “A Square” is to be destroyed for his heresy, the Sphere pulls him OUT of Flatland and takes him into the 3rd dimension.

The viewpoint in the book is assisted with a number of creative drawings (the book was written and published in 1884) and the little film from 2007 provides some very good viewpoint support, I believe. I would suggest looking through the chapter/section headings in the PDF link, which will jump you to each highlighted section easily.

There is also a summary at the top.

It is quite an interesting book for children who who interest in math, geometry and the possibility of alternative viewpoints.

I didn’t realize Flatland was unfamiliar… I grew up with it and thought only the movie was “new.”

Each section is just a couple of pages, usually with drawings… I’ve made some photo images below for quick reference.

The first part of the Intro…

FLATLAND: A Romance of Many Dimensions – E. Abbott

1. Of the Nature of Flatland

I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space. Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows – only hard and with luminous edges – and you will then have a pretty correct notion of my country and countrymen.

Alas, a few years ago, I should have said my universe”; but now my mind has been opened to higher views of things. In such a country, you will perceive at once that it is impossible that there should be anything of what you call a solid” kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles, Squares, and other figures, moving about as I have described them.

On the contrary, we could see nothing of the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to us, except Straight Lines; and the necessity of this I will speedily demonstrate. Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle. But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view; and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.

Take for example an equilateral Triangle – who represents with us a Tradesman of the respectable class. Fig. 1 represents the Tradesman as you would see him while you were bending over him from above; figs. 2 and 3 represent the Tradesman, as you would see him if your eye were close to the level, or all but on the level of the table; and if your eye were quite on the level of the table (and that is how we see him in Flatland) you would see nothing but a straight line.