Flatland: A Romance Of Many Dimensions, by A Square (Edwin A. Abbott)
This book is a classic work dealing with mathematics and the imagination of strange worlds, and one I have pondered about often , and in reading it, the book absolutely lives up to the hype, as it explores the thinking of a decent sort of person whose traumatic experience in various other dimensions had led him to become a dangerous figure to his own society. Where this book particularly excels is in reminding us that we too are beings of a sort that are not unlike Flatlanders, and for us to have experience of further dimensions and matters beyond our experience would lead us to be disrespected and dangerously isolated from our neighbors and in danger of being viewed as a lunatic or worse. If this is not a pleasant reminder it is nevertheless the sort of reminder of our own humanity and fallibility that we need to have from time to time to keep us humble. And what could be more humble than an account of a flat world told from the perspective of an imprisoned square who had been present in numerous other worlds and then found himself unable to communicate the truth of his experiences to others.
This book is a bit more than 100 pages long. It begins with an introduction and foreword that set up the book and humbly express gratitude for praise. After that the book is divided into two parts. In the first part of the book the narrator, a square, discusses the world of Flatland. This is done through a discussion of the nature of the world, of its climate and houses, inhabitants, women in particular, methods of recognizing one another, including recognition by sight, dealing with irregular figures, the importance of painting, and some laws as well as some discussion of the priests. Through this part of the book the reader is likely to find the book entertaining but a bit odd. It is in the second part of the book where matters get more poignant and emotionally resonant. The narrator expresses his vision of Lineland and how he tried to explain to the monarch of that realm the nature of Flatland. He then has to deal with a visitor from Spaceland who shows him the mystery of the third dimension after having vainly tried to explain what it was like to the square. After that the narrator expresses the insights he gained from traveling into the third dimension and seeing his world from the outside, and then how this led to his own imprisonment by his people when he was thought to be a crackpot.
Can you feel sad about the fate of a geometric shape? In general, squares are not fondly viewed even by most people who care about geography. And while as I have never visited Flatland I do not know if squares are viewed with more respect by those who live there, I can say that this book was well-written enough that it poignantly presents a geometrical figure of some quirks as its protagonist. And the fact that this square finds himself a traveler in many dimensions allows us to reflect upon what our lives and our world would be like if viewed from the outside. The author’s not very subtle point is that the traditions and habits and viewpoint of our own society, however much we may be proud of it, may look just as silly to someone else as Flatland’s world looks to the reader, or that Lineland’s views look to the narrator. And, perhaps even more to the point, our own lonely and isolated existence in the contemporary world makes the sad fate of Pointland something that we can easily relate to as well. How many books infuse the subjects of geometry with real emotional depth?
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