Flatterland: Like Flatland, Only More So [Paperback]

Ian Stewart (Author)

Book Description

Publication Date: April 16, 2002

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.

Editorial Reviews

Amazon.com Review

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 --This text refers to the Hardcover edition.

From Publishers Weekly

Higher mathematics and low comedy intersect acutely in this fuzzy follow-up to Edwin Abbott's 1884 classic, Flatland. Where Abbott's compact fable about a two-dimensional world discomposed by the discovery of a third dimension was a jeu d'esprit that slyly satirized rigid Victorian society, Stewart's sequel is an episodic ramble through the "flatterland" of modern mathematical theory that begins when teenaged Flatlander Vikki Line, great-great-granddaughter of Abbott's narrator, uses her ancestor's "hysterical document" as a passport to the Mathiverse. Accompanied by a Space Hopper guide, she tours landmarks of the post-Einsteinian universe that include fractal geometry, black holes, cosmic strings and quantum theory. Stewart (The Science of Discworld) keeps the tone light with incessant puns (a one-sided cow named "Moobius") and plays on names ("the Hawk King," who presides over a wormhole-ridden realm in the space-time continuum). The many line drawings that illustrate the text are both amusing and instructive. But the terrain Stewart sets out to explore is vast and abstract, and not all of the subjects he covers find a proper social analogue or cultural referent. The result is that lessons Vikki learns on some of the more abstruse principles still have a textbook stuffiness that even the author's Carrollian wit can't leaven. Though perplexing in spots, the tale is ever enchanting, and its user-friendly blend of fiction and nonfiction proves that the comic and cosmic need not be mutually exclusive. (May 1)Forecast: With advertising in Scientific American and the New Yorker and a 50,000-copy first printing, this should be a hit with the literate elite who also appreciate math and science.

Copyright 2001 Cahners Business Information, Inc.

--This text refers to the Hardcover edition.

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Product Details

• Paperback: 320 pages
• Publisher: Basic Books (April 16, 2002)
• Language: English
• ISBN-10: 073820675X
• ISBN-13: 978-0738206752
• Product Dimensions: 8.2 x 5.5 x 0.8 inches
• Shipping Weight: 10.6 ounces (View shipping rates and policies)
• Average Customer Review: 3.1 out of 5 stars  See all reviews (37 customer reviews)
• Amazon Best Sellers Rank: #346,666 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

31 of 31 people found the following review helpful:

5.0 out of 5 stars No Words to Describe It!, January 12, 2004

By A Customer

This review is from: Flatterland: Like Flatland, Only More So (Paperback)

As a high school student, I was tortured into reading this book for Math Analysis. Having previously read Flatland, I was not keen on the idea of reading the sequel. My grade-conscious self got the better of me and I started to read the book. From the first chapter I was enthralled! Ian Stewart knew how to write and keep my attention. My parents had to threaten me so I would put it down so I could eat. (Imagine: a high schooler entranced in a MATH book!) I so totally recommend this book because I would have NEVER understood Mandelblot (er... Mandelbrot) nor would I have read on to discover a plethora of new dimensions (one and a quarter). I would recommend any person, avid mathematician or high schooler, to read this. It was easily understood and Ian Stewart is a fantastic writer! Too bad they didn't have ten stars!

29 of 29 people found the following review helpful:

3.0 out of 5 stars Good teaching tool, June 21, 2004

By A Customer

This review is from: Flatterland: Like Flatland, Only More So (Paperback)

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.

39 of 45 people found the following review helpful:

3.0 out of 5 stars Oh, QuaternIan! Those Awful Puns!, July 31, 2006

By 

Steve Koss (New York, NY United States) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: Flatterland: Like Flatland, Only More So (Paperback)

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.