A few weeks ago, BBC News published Why physics suggests other dimensions exist. Although the mathematics of physics strongly suggests that higher dimensions do exist, I have found it difficult to wrap my head around them. That got me to thinking about a book, Flatland: A Romance of Many Dimensions, by Edwin A. Abbot, published in 1884. It was time for me to read it again. (Image from BBC Reel.)
The narrator of the book (Mr. A. Square) lives in a two-dimensional space, Flatland. As its name suggests, the beings living in the land cannot comprehend three dimensions. Much of the book is devoted to describing the land—the shapes of the people (the narrator refers to men, women, children), the strata of society, the conventions, shapes of houses, and so on. It is a very classist society, with strict rules for how one may or may not climb the social ladder.
Edwin Abbot’s description of women is so off-putting that the first time I tried to read this book, I ended up putting it down. After he was labeled a misogynist, he explained in a later edition that his intention was to satire Victorian society. If you decide to read the book, just press on as all the good stuff about dimensions come after his descriptions of women's role in society.
Every millennium, a being from the third dimension appears to a Flatlander to evangelize about the third dimension. Our narrator is graced with the visit. However, the priests and dignitaries of Flatland know of these so-called visitations and will kill or imprison anyone claiming to have been visited. Those in charge deny any other dimension exists.
At first, our narrator does not believe the 3-D guy and his description of 3-D world, so the visitor has no choice but to whisk Mr. Flatlander into the third dimension. He is astounded. Later on , our 2-D guy visits 1-D land and tries to evangelize the second dimension to one of their kings. No luck. The King (who is simply a point), cannot comprehend.
Eventually our 2-D guy reasons that if there are 1-D, 2-D, and 3-D lands, that there must exist higher dimension spaces, even though they are difficult to imagine. Mr. 3D thinks this is all hogwash, even as Mr. Flatlander explains how if a square gives rise to a cube, then a cube should give rise to a hypercube, and so on. Still, Mr. 3-D won’t agree.
These arguments for other dimensions, written in the 1880’s, are brilliant. For anyone wanting to understand other dimensions, I recommend reading Flatland and then watching the BBC piece.