Dystopia 02
The Mathematical Romance – “Flatland” [Related Post]
(sponsored by Amazon)
The BEST and ONLY mathematical romance ever. But also a comical and poignantly cynical critique of Victorian society. “Flatland: A Romance of Many Dimensions” (1884) by Edwin Abbott also challenges our narrow fixed ideas and prejudices through various dimensions.
“Flatland” explores higher-dimensional geometry through a 2D narrator, a Square, who was born in the 2D World, Flatland, and discovers the 1D World, Lineland, and the 3D World, Spaceland.
“Flatland” uses geometric shapes to explain dimensional slicing, perspective, and the concept of 4th and higher dimensions, at the same time, satirizing Victorian social hierarchy.
Read the full article on LAB Science Fiction!
“I (Square): I must indeed confess that I do not in the least understand your Lordship. When we in Flatland see a Line, we see length and brightness. If the brightness disappears, the Line is extinguished, and, as you say, ceases to occupy Space. But am I to suppose that your Lordship gives the brightness the title of a Dimension, and that what we call “bright” you call “high”?
Stranger (Sphere): No, indeed. By “height” I mean a Dimension like your length: only, with you, “height” is not so easily perceptible, being extremely small.” (§16. How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland, Flatland)
Dimensionality
“Sphere: Now stretch your imagination a little, and conceive a Square in Flatland, moving parallel to itself upward.
I (Square): What? Northward?
Sphere: No, not Northward; upward; out of Flatland altogether. If it moved Northward, the Southern points in the Square would have to move through the positions previously occupied by the Northern points. But that is not my meaning.” (§16. How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland, Flatland)
Geometric Social Hierarchy of Flatland
1: Women – Straight Lines
“The dangers to which we are exposed from our Women must now be manifest to the meanest capacity of Spaceland. If even the angle of a respectable Triangle in the middle class is not without its dangers; if to run against a Working Man involves a gash; if collision with an Officer of the military class necessitates a serious wound; if a mere touch from the vertex of a Private Soldier brings with it danger of death;—what can it be to run against a woman, except absolute and immediate destruction? And when a Woman is invisible, or visible only as a dim sub-lustrous point, how difficult must it be, even for the most cautious, always to avoid collision!” (§4. Concerning the Women, Flatland)
2: Soldiers and Workmen – Isosceles Triangles
“Our Soldiers and Lowest Class of Workmen are Triangles with two equal sides, each about eleven inches long, and a base or third side so short (often not exceeding half an inch) that they form at their vertices a very sharp and formidable angle. Indeed when their bases are of the most degraded type (not more than the eighth part of an inch in size), they can hardly be distinguished from Straight lines or Women; so extremely pointed are their vertices. With us, as with you, these Triangles are distinguished from others by being called Isosceles…” (§3. Concerning the Inhabitants of Flatland, Flatland)
3: Middle Class and Professionals – Equilateral Triangles, Squares, Pentagons
4: Nobility – Hexagons to Many-Sided Polygons
“Next above these come the Nobility, of whom there are several degrees, beginning at Six-Sided Figures, or Hexagons, and from thence rising in the number of their sides till they receive the honourable title of Polygonal, or many-Sided. Finally when the number of the sides becomes so numerous, and the sides themselves so small, that the figure cannot be distinguished from a circle, he is included in the Circular or Priestly order; and this is the highest class of all.” (§3. Concerning the Inhabitants of Flatland, Flatland)
5: Priests / The Ruling Class – Circles
“It is a Law of Nature with us that a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility. Thus the son of a Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on.” (§3. Concerning the Inhabitants of Flatland, Flatland)
Social Evolution of Flatland
Eugenics in Flatland – Irregularity
 |
| Eugenics Society exhibit in 1930s |
“The art of healing also has achieved some of its most glorious triumphs in the compressions, extensions, trepannings, colligations, and other surgical or dietetic operations by which Irregularity has been partly or wholly cured.” (§7. Concerning Irregular Figures, Flatland)
Read the full article on LAB Science Fiction!
Further reading (sponsored by Amazon):
● Rudolf Rucker (2012). Geometry, Relativity and the Fourth Dimension (Dover Books on Mathematics). 159 pages. Dover Publications.
(sponsored by Amazon)
“Geometry, Relativity and the Fourth Dimension” is a highly readable, popular exposition of the 4th dimension and the structure of the Universe! In “Geometry, Relativity and the Fourth Dimension,” a remarkable pictorial discussion of the curved space-time we call home, it achieves even greater impact through the use of 141 excellent illustrations!
Finding a perfect analogy in the situation of the geometrical characters in “Flatland,” Professor Rudolf Rucker continues the adventures of the 2-dimensional world visited by a 3-dimensional being to explain our 3-dimensional world in terms of the 4th dimension in “Geometry, Relativity and the Fourth Dimension”!
Table of Contents
Preface
1: The Fourth Dimension
2: Non-Euclidean Geometry
3: Curved Space
4: Time as a Higher Dimension
5: Special Relativity
6: Time Travel
7: The Shape of Space-Time
8: Conclusion
Annotated Bibliography
