Flatterland

Ian Stewart's one-century-on sequel to Edwin Abbott's Flatland is far longer and in many ways more wide-ranging than its Victorian original. Almost taking hypergeometry for granted, it also treats qualitative dimensionality, fractals, topology, projective geometry, and an assortment of geometric issues implicated in theoretical physics: relativistic cosmology, quantum physics, and M-theory. These last topics may have aged a bit, but my own physics understanding is still back around the 2001 date of this book, so nothing put me off there, and the mathematical issues haven't changed at any rate.

Protagonist Vikki Line's psychopomp is the Space Hopper, inspired by a UK-model hippity-hop bouncing toy, and he equips her with a "Virtual show more Unreality Engine" that allows her (if not always the reader) to visualize and operate in all of the exotic geometries treated in the story. There is a rather comical Faust and Mephistopheles air to the relationship here.

Flatterland is full of nods to Lewis Carroll, with Vikki clearly taking the role of Alice in a "mathiversal" wonderland. This homage reaches its peak in Chapter 6 "The Topologist's Tea Party." The book is thick with puns and dadjokery. I am glad that I was already sufficiently well-read mathematically to perceive the conventional names of the topics and concepts sometimes screened behind layers of wordplay. Humans are "Planiturthians," whose proper names are given without breaks, like Ianstewart.

Stewart recognizes and praises the social satire in Abbott's original Flatland, but his own version of it is a feminism that was hardly daring at the turn of the millennium. As the book progressed into more diverse mathematical topics, I thought he had even left the social commentary behind, but he did return to it in a mildly satisfying manner at the end. The text makes it clear that "Flatterland" doesn't have anything to do with flattery; or does it? show less

Whimsical, pun-laden (e.g. Moobius the one-sided cow) tale touching on extradimensionality, fractals, topology, non-Euclidean geometry, quantum physics, relativity, time travel, cosmology, string theory. A delight.

The main issue I have with this book is that, in relation to the concepts presented, I found it 'too much, too soon'. While the themes themselves were extremely interesting, half of it flew over my head - there were just too many concepts, too many 'spaces', and too many theories to take in at once if you don't have some background knowledge on these topics already.

As far as the story telling goes, the main character is A. Square's granddaughter, which will continue his journey many years later. The story was really just a setting for presenting the topics at hand though, and for me it is one of the weakest points in the book. Story-wise, I found it pretty poor - it's really just Victoria Line and her guide travelling through the show more several universes/topologies. They do get stuck in a black hole near the end, but apart from that it was pretty uneventful overall.

In hindsight, I think I would have liked (and understood) this book a lot better if it was only just a 'story book', or a science book. The way it's done, while remarkable for the attempt, leaves the presentation of both 'parts' sub par. show less

About 220 pages in, the math got too complicated for me to keep following, but I think I still got some of it. A very interesting story!

I heard about this book from a friend who is a freelance proof reader. She'd read it and admitted that most of it had gone straight over her head. However she did recommend it highly.I picked up a copy at the same time as [book:Flatland] and read the two books one after the other.Whereas the first book was about a flat being being shown life in three dimensions, Flatterland shows the adventures of a person being taken into a world of many non-euclidian dimensions. The space it talks about is often well understood by mathematicians, but because they bear no resemblance to normal space they are completely mysterious to the uninitiated. And they have strange properties! A flat plane where parallel lines converge (despite the definition of show more a pair of parallel lines is that they don't do that!) and a myriad of other oddities.In reality the stories told in this book are not as striking as those of Flatland. This is at least in part because as people in a three dimensional universe we understand almost instinctively the nature of that reality. That means we understand the original story more strongly than those strange worlds that this book talks of. But it is still a magnificent book, and the ideal thought provoker for those interested in geometry and maths. show less

Flatterland is an extension of Flatland only on subjects of mathematics (from the elementary to the Hawk King). It fails to expand in the areas of politics, spirituality, and equality - only hinting at them as though they were afterthoughts - that made Flatland such a well-rounded read. Flatterland is nonetheless entertaining and informative, and is recommended.

This and Flatland are books even the mathematically-challenged should read to help them understand not just math, but their prespective of life.