Flatterland: Like Flatland, Only More So

Author - Ian Stewart ... [Goo?] [Posters]

This Paperback Book item from Basic Books was reviewed on 6-Nov-2008.

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1) Paperback Book Flatterland: Like Flatland, Only More So by Basic Books. 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!¤

2) Paperback Book Flatterland: Like Flatland, Only More So by Basic Books. The first person narrative was refreshing to read at the beginning, and the adventure-like storyline was a welcome deviation from other popular math books, at least that was what I thought at the beginning... Apparently the author is better at mathematics than writing, and his ideas of following the writing style of "Flatland" quickly gets old. The book is filled with supposedly "amusing" dialogues between the main characters of the story very intrusive. These dialogues add little value towards the goal of the book, namely explaining the mathematical ideas to non-mathematicians. Sometimes I even found them distracting. After the first 2 chapters, I found myself often skipping over pages of the book (filled with dull dialogues that only the author might find interesting) and jumping over to the conclusion directly. May be because so many pages are wasted by the "story" and "dialogues" instead of discussing interesting mathematics, the mathematical ideas in the book often lack in-depth explanations and are not fully developed. But given the broad agenda the author set out for himself, this seem to be rather inevitable.

I would not recommend this book to others.¤

3) Paperback Book Flatterland: Like Flatland, Only More So by Basic Books. 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.¤

4) Paperback Book Flatterland: Like Flatland, Only More So by Basic Books. The author describes his main character as "a thoroughly modern young woman in a society rather like Britain and the US in the early sixties."
His interpretation of how such a person thinks and talks is so distracting. It is like reading Nancy Drew mixed with Donna Reed dialogue. The main character writes in her diary with sentences like "Oh, Diary Dearest" and follows with other nauseating dialogue with her parents. It made me want to throw the book across the room. I seriously considered not reading it after the first few pages.

In her diary entries, she is merging terms together that are new to her. For instance "Planiturth" for "planet Earth." When one is describing complex mathematic concepts, there is no need to add mumbo jumbo like that. The concepts are alfready difficult to grasp, without having to sort what she is referring to. I don´t see the value of doing this.

The mathematics writing is adequate for the most part. The concepts were easy for me to understand. And these are rather complex concepts. I studied no further than calulus in school, so not a good deal of foreknowledge is needed. Although a lot of patience is needed. He makes several contradictory statments. "The red ball got bigger and bigger until she could only see a small part of it." If it is getting bigger, why is she seeing less of it? All things considered he would have been better off just writing a math book, rather than trying to make it into a crappy, cutesy story. He had a lot of hubris to think he could stay on par with the original classic.¤

5) Paperback Book Flatterland: Like Flatland, Only More So by Basic Books. 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.

¤

6) Paperback Book Flatterland: Like Flatland, Only More So by Basic Books. The brilliant "sequel" to one of the all-time classics of popular mathematics.

First there was Edwin A. Abbott´s remarkable Flatland, published in 1884, and one of the all-time classics of popular mathematics. Now, from mathematician and accomplished science writer Ian Stewart, comes what Nature calls "a superb sequel." Through larger-than-life characters and an inspired story line, Flatterland explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications. The journey begins when our heroine, Victoria Line, comes upon her great-great-grandfather A. Square´s diary, hidden in the attic. The writings help her to contact the Space Hopper, who tempts her away from her home and family in Flatland and becomes her guide and mentor through ten dimensions. In the tradition of Alice in Wonderland and The Phantom Toll Booth, this magnificent investigation into the nature of reality is destined to become a modern classic.¤

7) Paperback Book Flatterland: Like Flatland, Only More So by Basic Books. In 1884, an amiably eccentric clergyman and literary scholar named Edwin Abbott Abbott published an odd philosophical novel called Flatland, in which he explored such things as four-dimensional mathematics and gently satirized some of the orthodoxies of his time. The book went on to be a bestseller in Victorian England, and it has remained in print ever since.

With Flatterland, Ian Stewart, an amiable professor of mathematics at the University of Warwick, updates the science of Flatland, adding literally countless dimensions to Abbott´s scheme of things ("Your world has not just four dimensions," one of his characters proclaims, "but five, fifty, a million, or even an infinity of them! And none of them need be time. Space of a hundred and one dimensions is just as real as a space of three dimensions"). Along his fictional path, Stewart touches on Feynman diagrams, superstring theory, time travel, quantum mechanics, and black holes, among many other topics. And, in Abbott´s spirit, Stewart pokes fun at our own assumptions, including our quest for a Theory of Everything.

You can´t help but be charmed by a book with characters named Superpaws, the Hawk King, the Projective Lion, and the Space Hopper and dotted with doggerel such as "You ain´t nothin´ but a hadron / nucleifyin´ all the time" and "I can´t get no / more momentum." And, best of all, you can learn a thing or two about modern mathematics while being roundly entertained. That´s no small accomplishment, and one for which Stewart deserves applause. --Gregory McNamee¤

Page Updated: Robert N. Goolsby, 4-Dec-2008, 073820675X9780738206752, 330-020-3X0-5X0-710-28B-FMB-8

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