Edwin Abbott’s 1884 book Flatland: A Romance of Many Dimensions is one of my favourite works of early British SF. Deeply strange, it was part of the general fascination with a speculated 4th dimension toward the end of the century. Talk of a 4th dimension was a more or less bowdlerized version of non-Euclidean geometry and Abbott’s work had a profound influence on H.G. Wells and his creation of The Time Machine, perhaps the definitive scientific romance text. So, while Wells and his work enjoy the limelight, Abbott and his text have not received the same degree of attention. Fortunately, the good people at The Public Domain Review are rectifying that and have published a short piece on Abbott titled “Aspiring to a Higher Plane.”
From the site: “On the surface — and the setting, the imaginary world of Flatland, is a surface, an infinite Euclidean plane — the book is a straightforward narrative about geometrically shaped beings that live in a two-dimensional world. A. Square, an ordinary sort of chap, undergoes a mystical experience: a visitation by the mysterious Sphere from the Third Dimension, who carries him to new worlds and new geometries. Inspired by evangelical zeal, he strives to convince his fellow citizens that the world is not limited to the two dimensions accessible to their senses, falls foul of the religious authorities, and ends up in jail.
The story has a timeless appeal, and has never been out of print since its first publication. It has spawned several sequels and has been the subject of at least one radio programme and two animated films. Not only is the book about hidden dimensions: it has its own hidden dimensions. Its secret mathematical agenda is not the notion of two dimensions, but that of four. Its social agenda pokes fun at the rigid stratification of Victorian society, especially the low status of women, even the wives and daughters of the wealthy.”
Here is another link that will take you to a video of Carl Sagan explaining the text in his inimitable way. Now that was a man with some serious elocution: http://www.theverge.com/2012/4/16/2952330/flatland-redux-watch-carl-sagan-explain-the-science-of-fez