Guest Blog--Flatland

A very thoughtful piece from my colleague, Associate Dean and Professor of Mathematics, Michael Lachance:


In Edwin A. Abbott’s 1884 80-page Victorian allegory and geometric treatise, Flatland: A Romance of many dimensions, he envisioned a two-dimensional universe in which there was no up or down, only north, south, east, and west. In this planar world women were represented as line segments: visible only from the side, invisible if approaching you, and hence dangerous. Only slightly superior to women were soldiers, skinny isosceles triangles. Men were regular convex polygons. Each union between man and woman would yield a son, with one more side than his father. Long-lived families would have so many sides as to become indistinguishable from circles, the priestly class. Offspring that were not regular, that did not have sides of equal lengths, were destroyed.

Enter into this scenario a sphere hovering above the planar universe. The sphere reaches out to a Mr. A. Square, and eventually persuades him of the possibility, indeed the reality, of a third dimension. With the sphere’s help Mr. Square is able to escape from the plane and to see his universe for what it is. When Mr. Square asks the sphere if there is a fourth dimension, the sphere replies that that is absurd! Puzzled by this, but excited to share his newfound insights with his countrymen, he returns to the plane and is promptly imprisoned for heresy by the priests, put under the guard of lowly soldiers.

So how does one become aware of a booklet like this? And what does one do with a story like this? What’s the point? There are a number of things brought up in this summary alone that one can seize upon: the obvious insult to women, the cruelty directed at irregular children, and the arrogance of the priests. There is also the notion of a flat universe, ignorance of directions or dimensions beyond what is evident, and the certainty that nothing exists beyond your experience.

Most folks become aware of books like this, and discuss ideas like these, in universities, and more specifically in colleges of liberal arts. Universities offer a dimension, a direction, that enables us to escape our otherwise flat land.