Flatland · Chapter
How the Stranger Vainly Endeavoured to Reveal to Me in Words the Mysteries of Spaceland explained
The Stranger (Sphere) attempts to explain the concept of a third dimension to the Square through words and analogy, but the Square fails to comprehend and ultimately attacks the Stranger in frustration.
What happens
The Stranger (Sphere) attempts to explain the concept of a third dimension to the Square through words and analogy, but the Square fails to comprehend and ultimately attacks the Stranger in frustration.
Themes in this chapter
Perception and Reality
The Square cannot perceive the third dimension directly, leading him to doubt the Sphere's reality and accuse him of being a juggler or magician.
The Limits of Imagination
The Square's mind is constrained by two-dimensional experience, making it impossible for him to grasp the concept of 'upward' or a third dimension.
Mathematics and Analogy
The Sphere uses mathematical progression (1, 2, 4, 8) and analogy from points to lines to squares to cubes to explain the third dimension.
Characters to notice
- The Narrator (A Square)
The Square struggles to understand the Sphere's explanations and becomes increasingly frustrated, eventually attacking the Stranger.
- The Sphere
The Sphere tries to teach the Square about Spaceland using analogy and demonstration, but is met with disbelief and hostility.
- The Stranger
The Stranger reveals himself as a Sphere and attempts to convince the Square of the third dimension through words and examples.
Key passages
“For even a Sphere—which is my proper name in my own country—if he manifest himself at all to an inhabitant of Flatland—must needs manifest himself as a Circle.”
A Sphere from Spaceland, when appearing in Flatland, can only be seen as a Circle because Flatland lacks the dimensions to show its full form.
The Sphere explains why he appears as a Circle to the Square.
“Now conceive the Northward straight Line moving parallel to itself, East and West, so that every point in it leaves behind it the wake of a straight Line. What name will you give to the Figure thereby formed?”
Imagine a line moving sideways; the shape it traces is a square.
The Sphere uses analogy to describe how a line generates a square.
“Monster, I shrieked, be thou juggler, enchanter, dream, or devil, no more will I endure thy mockeries. Either thou or I must perish.”
The Square, enraged and unable to understand, attacks the Sphere, calling him a monster and demanding an end to the torment.
The Square's frustration boils over into violence.