Flatland: A Romance of Many Dimensions

Sep 17, 2013 by


Flatland: A Romance of Many Dimensions by A. Square was originally published in 1884 and is a book that appears to be way ahead of its time.  It is a very well known classic of mathematical and scientific fiction that describes the travels of someone by the name of A. Square and his experiences in Spaceland (which is three dimensional), Lineland (which is one dimensional) and Pointland  (which has no dimensions).  A. Square ponders traveling to a land of four dimensions, a crazy wild idea which causes him to be banished from Spaceland.  If you are looking for something old yet thought provoking, this is the book for you.
Here are a few paragraphs from the intro to give you a feel for it:
“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 Flatland citizen) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line. The same thing would happen if you were to treat in the same way a Triangle, or Square, or any other figure cut out of pasteboard. As soon as you look at it with your eye on the edge of the table, you will find that it ceases to appear to you a figure, and that it becomes in appearance a straight line.
Take for example an equilateral Triangle who represents with us a Tradesman of the respectable class. Fig. I represents the Tradesman as you would see him while you were bending over him from above ; (2) 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 (3) 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. When I was in Spaceland I heard that your sailors have very similar experiences while they traverse your seas and discern some distant island or coast lying on the horizon.

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