Flatland: A Romance of Many Dimensions by Edwin A. Abbott

Very important read for this day and age.

Love this classic. A new perspective and can open you up to seeing things differently and in more interesting ways.

Really cool explanation of why people living in a 3D world might be entirely unaware of a 4th spatial dimension. Flatland is a 2D world. Its characters trip across Lineland, a 1D world and try to tell the residents about left and right, but they know only forward and backward. Then a 3D sphere intersects the plane of Flatland and tries to tell the Flatland residents about up and down, but they know only forward, backward, left, right. Gets you thinking about how, if there truly were a 4th spatial dimension, we in our 3D world would be entirely unable to look in the right direction to even notice it. Warning: The interesting mathematical parts are embedded in the most extreme misogynistic, "woman-are-stupid-men- are-much-smarter" commentary I've ever seen. The book was written in 1884, but still... Don't read it if you're not prepared to actively ignore all that crap. --Fred

This is a very special book, but it is certainly not for everyone. This is for the fan of philosophy and science. It approaches the topic of dimensions in clever and thoughtful way. While simple on the face of it, it took highly intelligent mind to create this little timeless gem. I first read it probably 25 years ago, and was prompted to re-read it after reading "The God Equation," a book about string theory. "The God Equation's" discussion of multiple dimensions made me think back to this wonderful book written so long ago.

i like this book

A review of Edwin A. Abbott’s “Flatland: A Romance of Many Dimensions” “Flatland” is first and foremost a geometry maths book. I first read this book as a pre-teen kid, having read the colourfully illustrated “The Number Devil” maths book shortly before. With “Flatland,” rudimentary concepts about space and its dimensions still stick with me today. I vividly remember the short commentary on shadows. Shadows remove one dimension such that the shadow of a 1D line is a 0D point, the shadow of a 2D shape is a 1D line, the shadow of a 3D solid is a 2D shape, and thus it follows that the shadow of a 4D something is a 3D solid! Another thing that I markedly remember was its blatant sexism -- women exist as one lesser dimension, i.e. as a 1D line in the world of 2D shapes. Ten years later I decide to return to this story to see if I have any new thoughts. First, this book is just as sexist as I remembered it. Actually, it is probably more sexist since I now understand the derogatory implications better. As for the maths part, I didn’t really receive any new insights from it, but I think that’s a good thing. This only shows how thought-provoking and paradigm-shifting this book is on its first read. The ideas of this book are two-fold. The first part does some worldbuilding with Flatland, while the second part does the mathematical exploration with dimensions. The book is written clearly in layman terms, with helpful analogies and clean illustrations along the way. For the first part, I enjoyed the set-up of Flatland and especially how they see and navigate. Since all the inhabitants of Flatland live on a plane, they can only see other shapes represented as a line. This concept makes a lot of sense, but it isn’t something that we would think of intuitively. In addition to that, there is also some fun worldbuilding with the architecture and art of flatland, their social hierarchy, their laws, and their women. To the modern reader, the discussion of the latter is probably very jarring. This book is very clearly sexist in a harsh, matter-of-fact way. Some people might say that this book, and therefore its treatment of women, is merely a critique of Victorian society, but I think that’s not an honest assessment. For example, in later parts of the book where women are no longer being discussed, Abbott makes offhand comments like “this concept is so simple that even a woman can understand it.” The only thing I can say about this is that it’s important that we understand this book as a product of its time and move on. The second part is the most interesting part. The 0D, 1D, 2D, 3D, and 4D dimensions are discussed here. The main character (a square) has a dream about Lineland, where everyone is just a line. But since they live on a singular line, they can only see each other as points without length. Only the square, of higher dimension, is able to see them as lines. Later, a sphere would visit the square and he likewise comments that he is able to see the square as a shape instead of as just a line. My favourite interaction is the discussion on the “insides” of a dimensional object. Here, the square asks the sphere “how is it that we can now see the flatland citizen’s insides,” to which he means the plane of the 2D shape. The sphere responds that it is because they are of a higher dimension and can look down on to see the shape. Then, the square responds that a 4D being would likewise be able to see the insides of the sphere. How interesting! All of the concepts of dimensions here are laid out in purely factual terms, which provoke the imagination. What kind of 4D object could possibly see the insides of a 3D solid? And what would the insides even look like?

I've bought this book 4 times now because I keep giving away my copy. It's a short book, but pretty dense content. I've had 2 kids use this for book reports in middle school, and they both liked how it wasn't a typical fiction. Trying to understand a 3D world from the perspective of a flat world being is a great setup for the reader to try to imagine the 4th dimension. It triggered some fun discussions with my kids!

I like it. It's hard to give a book less than 5 stars since art is subjective. This book has language that is indicative of the year when it was written, but it's still easy to follow. Just be aware that it isn't a "read while not paying attention" kind of book.