Flatterland: Like Flatland, Only More So by Ian Stewart
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Book Reviews of Flatterland: Like Flatland, Only More So
Book Review: Thought-provoking book!
Summary: 5 Stars
I actually borrowed this book from the local library because I loved the "prequel" so well and thought this looked interesting. I was not at all disappointed. "Flatterland" is truly like Flatland, only more so. Stewart takes the reader on a journey through different mathematical "places" and in doing so explains a wide variety of theories and aspects of mathematics in an easy-to-understand style that even a novice can appreciate. Even months after I read it, parts came back to me and helped me see things in a different light. I bought this book for my own library because it is one that I love to go back to time and again; each time, I learn something new. I think you will, too. Enjoy!Book Review: Great sequel to Flatland and intro to higher mathematical concepts
Summary: 4 Stars
While the author of Flatterland does not have the same objectives in mind as Abbott had in the original, I think this is a great book and excellent introduction into higher mathematical concepts. Stewart maintains the same premise and style as the original while adding a modern twist; namely, the VUE finder that helps Victoria Line better understand mathematical spaces and concepts.
As a math major and future math teacher, I think this book is a great introduction to some of the more abstract and interesting concepts in mathematics. I could see how someone with a minimal math background would not understand every math concept introduced in Flatterland; however, it is still useful to get a taste of the challenging concepts. I plan on trying to incorporate this book into my geometry classroom once I begin teaching and would recommend this book to anyone who is interested in getting a taste of dimensions without trudging through a textbook.
Book Review: Oh, QuaternIan! Those Awful Puns!
Summary: 3 Stars
A little more than a century ago, an English minister named Edwin Abbott Abbott penned a remarkable story called FLATLAND. In it, Abbott laid out his case for the seemingly incomprehensible notion (certainly to his fellow citizens of Victorian England) that the universe might contain spatial dimensions beyond the three we recognize. Abbott built his argument through a form of inductive reasoning, much like a mathematical proof by induction, in which he took his readers on a journey through four dimensions, from Pointland (zero dimensions) and Lineland (one) to Flatland (two), and finally Spaceland (three). Each of these "worlds" could be easily imagined by his readers, and movements from one to another required only moving in an obviously "perpendicular" direction into the next plane. This approach allowed Abbott to pose the rhetorical questions, "Why stop at three dimensions? Why not imagine moving `perpendicularly' into the fourth dimension?" Of course, Riemann, Poincare, Dirichlet, and other mathematicians and physicists had already long been at work on multidimensional and non-Euclidean spaces, and it would only be a few more years after FLATLAND's publication that Einstein would put their ideas to revolutionary use.
In the present day, mathematician and writer Ian Stewart set out to build on FLATLAND and introduce modern readers to the many new worlds of multidimensional mathematics that have evolved since Abbott's time. Dangerously for a writer of any talent, Stewart opted to mimic the structure and style of a literary classic and, to paraphrase Lloyd Bentsen's memorable Vice Presidential debate putdown of Dan Quayle, "Mr. Stewart, you are no Edwin Abbott Abbott."
Mr. Stewart builds his exposition around Victoria Line (no apologies offered to the London Underground authorities), a two-dimensional lineal (ouch) descendant of A. Square, the tragic hero of FLATLAND. Vikki is an inquisitive, modern sort of line (in Flatland, all women are straight lines) who discovers her great-great-grandfather's old manuscript describing his adventures visiting other dimensions a century earlier with his Sphere tour guide. This time around, Vikki is accompanied by Space Hopper, a creature capable of passing through any dimension or space in the known Mathiverse. Vikki and Space Hopper progress from four dimensional space to mathematically multidimensional space (linear programming and optimization), sphere packing and self-correcting codes, fractional dimensional space (fractal geometry), topological (curved) space, finite geometry (graph theory), and non-Euclidean (hyperbolic geometry) space, stopping at each for an exposition by Space Hopper on the mathematical origins and significance of each. These discussions are descriptive in nature, designed as introductions to each topic while avoiding any mathematics whatsoever. Once this array of mathematical spaces has been exhausted, Space Hopper takes Vicky on a tour of quantum and relativistic physics, followed by a jump to the cosmological level to consider Minkowski spacetime, light cones, time travel, Schwarzschild radii, black holes, p-branes, superstring theory, the Big Bang, and the shape of the universe. If all of this seems like too much to cram into a 294-page fairy tale, it is.
Mr. Stewart's goal is a worthy one, and he does indeed manage to convey at least some sense of the mathematics and physics he seeks to explain. However, where Edwin Abbott wrote for an audience he knew had little formal mathematical background, Mr. Stewart seems far less sure of his audience. His discussion of mathematical worlds in the first half of the book are likely to leave a novice confused about where these ideas come from (what exactly is a hyperbolic plane, and how exactly do you generate a fractal fern?) and a knowledgeable reader bored and bemused. In the latter half of the book, Mr. Stewart seems to have abandoned his novice readers, writing at confusing length about Penrose maps, quantum spin, quantum infinities, mathematically feasible time machines, and "some kind of p-braned topological hypersurface in a higher-dimensional space."
As if not writing to a clearly-defined audience wasn't problematic enough, Mr. Stewart compounds the deficiency by insisting on the use of endlessly cloying puns throughout. Readers are forced to tolerate such "gems" as "the catenary was out of the bag," "there will be convex hull to pay," "I'm certain as Squares fit [bears s--t] in the Woods," "they'd just get you segment [pregnant] and dump you," "a used cardiod dealer," "Queens i Way," a bag marked "Doughnut Disturb," a cow named Moobius, projective lions, edgehogs, and squarrels, the Space Girls (Curvy, Bendy, Pushy, and Squarey), "crisp moose [Christmas] cards," and too painfully many others. Late in the book, Mr. Stewart adds a chapter about time travel through wormholes that inexplicably and ungraciously represents Stephen Hawking as the "Hawk King," a greedy and imperious wretch whose Domain is "right next to the Public Domain." They are forced to bribe their way into an audience with "His Majesty," who sits at the far end of a vast audience room on a splendid throne (an unfortunate choice, given the general tone and Mr. Hawking's actual physical condition). The Hawk King closes their meeting with a disdainful, "You are dismissed." No other human in the book is referenced in such misplaced and disparaging terms, and the entire scene comes across as mean-spirited and petty sniping.
One of Edwin Abbott's remarkable accomplishments in FLATLAND was to combine his mathematical/philosophical ponderings of multidimensional space with a biting satire of Victorian society worthy of Jonathan Swift. As if in faint recognition of Abbott's social commentary, Stewart occasionally tosses in a less-than-heartfelt comment about Vicky's incipient feminism, even going so far as to suggest that Flatland's straight line females (considered the lowest level of Flatland society because they have only one side) are in fact pentagons in an unseen, other-dimensional "shadow world." These silly efforts at social relevance only serve to amplify the shortcomings of FLATTERLAND relative to its renowned progenitor.
Ian Stewart's FLATTERLAND does offer some introductory explication of multidimensional and non-Euclidean mathematics and physics in a format suited to entertain teenagers. However, I believe it will leave them at least as confused as informed, as well as groaning over the incessant bad punning. In the end, this book is neither a worthy successor to FLATLAND nor an effective introduction to its mathematics and physics content. Better to read Abbott's original FLATLAND followed by Michiko Kaku's HYPERSPACE and/or Brian Greene's THE ELEGANT UNIVERSE.
Book Review: Good teaching tool
Summary: 3 Stars
I've used Flatland and Sphereland in my High School Pre-Calculus class. They're both entertaining books, but also ones that are a bit elementary for the class. I would say they are written for entertainment first, enlightenment second. Flatterland is NOT the same type of book. I have never been an Ian Stewart fan, but I do like this book. While the first two books are easy enough for a 7th grade student to understand, the topics in this book will require most high school students to be walked through the material. It's not an easy read. I will use this book with some of my students in the future, but only those that enjoy a challenge. It's true that the book tries to cover too much, but I think you should view it as a survey of modern mathematics. In my opinion, this is some of the best writing I've seen from Stewart, but definitely not up to the literary level set by Flatland and Sphereland.Book Review: Disappointed - it left me flat
Summary: 2 Stars
I enjoyed Flatland and Sphereland, so I received this book as a gift. It will be for sale, in mint condition, momentarily. The second half of the book will remain unseen by me, because I simply could not bring myself to continue.Flatland was interesting and entertaining both mathematically and for its social satire. Sphereland was also interesting and entertaining. But Flatterland tries too hard. In the inroduction the author says he had the idea for explaining multiple dimensions using a similar approach to the earlier books, and then developed those ideas into this book. Sounds like a good idea, but the book lacks the wit to keep it interesting. And in some places lacks adequate explanations of concepts. I can imagine that somoene already familar with the concepts and enamored of the topic might think the author did a clever job of explaining someting that they have had difficulty explaining themselves. But, for someone who doesn't work in the field and hasn't had the challenges of explaining the concepts this book is nether fascinating nor interesting and only sometimes achieves the goal of explaining. It is mostly boring, although the introduction is interesting and explains a possible satirical reference to the origin of A. Square's name that would have probably eluded anyone not from London.
On page 32 there is the assertion that a cube of side 1.06 can fit through a cube of side 1. There is an illustration to demonstrate that. The illustration is not clear and I believe it has errors in it. Unfortunately there is no information to find other sources that explain this obscure factoid. On page 72, in the chapter explaining fractals he makes the assertion that if you take one segment of a snowflake and fit together four copies you will have an area three times the size. This turns out to be an important assertion for his example, but it sure ins't obvious and there is no explanation of why that assertion might be true.
But, by now these comments are probably as boring and of diminishing interest as the book itself. You and I both have better ways to spend our time.