Upstate Case Study

Flatland Book Review

The main character in Edwin Abbott Abbott’s satirical novella, “Flatland: A Romance of Many Dimensions ” is a two-dimensional creature, A Square, who visits one-dimensional Lineland and three-dimensional Spaceland. A Square tries to convince the king of Lineland of the existence of dimensions beyond the one he knows. A Square is helpless in imagining a three-dimensional world before he is pulled out of Flatland and experiences Spaceland. Although A Square is trying to explain to others of higher dimensional worlds, he himself has trouble understanding them.

After reading Flatland, I am convinced that higher dimensional worlds do exist; the intersection between four-dimensional world and our Spaceland is time.

Despite Abbotts’ description of flatland, more importantly, he raises the topic of higher dimensions. In Part 2(Other Worlds), A Square dreams of Lineland, a place that only has a straight line populated by points and line segments. As the King could only see A Square when there is an intersection between Lineland and A Square, he doesn’t believe the existence of higher dimensions beyond one dimension. The next day A Square is visited by a mysterious being. As Thomas Banchoff describes: “he witnesses this creature manifesting in Flatland as a circle that gradually widens until it reaches its fullest extent, thereafter diminishing” (Banchoff 221). This being is A Sphere, which “ impinges on Flatland” (Banchoff 222). A Sphere tries to convince A Square of the existence of the third dimension. Ultimately, A Sphere pulls A Square out of Flatland and allows him to experience Spaceland. A Square begins to recognize that the line world is a one-dimensional slice of Flatland and that Flatland is a two-dimensional slice of three-dimensional space. By analogy he comes to the conclusion that three-dimensional space is a slice of four-dimensional space and so on (Banchoff 242).

A Square is not able to visualize a three-dimensional space,...