Flatland: A Romance of Many Dimensions
A satirical novel by Edwin A. Abbott,1
first published in 1884, that portrays a two-dimensional
world, like the surface of a map, over which its inhabitants move. Flatlanders
have no concept of up and down, and appear to each other as mere points
or lines. From our three-dimensional perspective we can look down on Flatland
and see that its people are "really" a variety of shapes, including straight
lines (females), narrow isosceles triangles (soldiers and workmen), equilateral
triangles (lower middle-class men), squares and pentagons (professional
men, including the pseudonymous author of the tale, A. Square), hexagons
and other regular polygons with still more sides (the nobility), and circles
(priests). Abbott uses these geometrical distinctions, especially the appearance
of Flatland females and the working class, as a commentary on the discrimination
against women, the rigid class stratification, and the lack of tolerance
for "irregularity" that was prevalent in Victorian Britain. In a dream,
A. Square visits the one-dimensional world of Lineland where he tries, unsuccessfully,
to persuade the king that there is such a thing as a second dimension. In
turn, the narrator is told of three-dimensional space by a sphere
who moves slowly through the plane of Flatland, growing and shrinking as
his cross-section changes in size. (If a hypersphere
were to move through our three-dimensional world, we would see a sphere
appear, grow to a maximum size, and then shrink again before disappearing.)
Abbott is aware that he cheats a little in his description of what the inhabitants
of Flatland actually see. In his preface to the second edition, he gives
a lengthy but not-too-convincing reply to the objection, raised by some
readers, that a Flatlander, "seeing a Line, sees something that must be
thick to the eye as well as long to the eye (otherwise it
would not be visible...)." The curious and often-neglected fact is that
we are just as unable to imagine what it would truly be like to see in two
dimensions as we are to conceive of four
dimensions!
Reference
- Abbott. Edwin A. Flatland: A Romance of Many Dimensions.
London: Seely and Co., 1884. Reprinted Mineola, NY: Dover Publications,
1992.
Related categories
• SPACE
AND TIME
• GEOMETRY
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